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FactorsHelper.singleton (n : ℕ) {a : ℕ} (h₁ : Nat.blt a n) (h₂ : IsNat (minFac n) n) : FactorsHelper n a [n] := FactorsHelper.nil.cons _ ⟨mul_one _⟩ h₁ h₂
theorem
Tactic
[ "Mathlib.Data.Nat.Factors", "Mathlib.Tactic.NormNum.Prime" ]
Mathlib/Tactic/Simproc/Factors.lean
FactorsHelper.singleton
null
FactorsHelper.cons_self {n m : ℕ} (a : ℕ) {l : List ℕ} (h : IsNat (a * m) n) (H : FactorsHelper m a l) : FactorsHelper n a (a :: l) := fun pa => H.cons_of_le _ h le_rfl (Nat.prime_def_minFac.1 pa).2 pa
theorem
Tactic
[ "Mathlib.Data.Nat.Factors", "Mathlib.Tactic.NormNum.Prime" ]
Mathlib/Tactic/Simproc/Factors.lean
FactorsHelper.cons_self
null
FactorsHelper.singleton_self (a : ℕ) : FactorsHelper a a [a] := FactorsHelper.nil.cons_self _ ⟨mul_one _⟩
theorem
Tactic
[ "Mathlib.Data.Nat.Factors", "Mathlib.Tactic.NormNum.Prime" ]
Mathlib/Tactic/Simproc/Factors.lean
FactorsHelper.singleton_self
null
FactorsHelper.primeFactorsList_eq {n : ℕ} {l : List ℕ} (H : FactorsHelper n 2 l) : Nat.primeFactorsList n = l := let ⟨h₁, h₂, h₃⟩ := H Nat.prime_two have := List.isChain_iff_pairwise.1 (@List.IsChain.tail _ _ (_ :: _) h₁) (List.eq_of_perm_of_sorted (Nat.primeFactorsList_unique h₃ h₂) this (Nat.primeFactorsList_sorted _)).symm open Lean Elab Tactic Qq
theorem
Tactic
[ "Mathlib.Data.Nat.Factors", "Mathlib.Tactic.NormNum.Prime" ]
Mathlib/Tactic/Simproc/Factors.lean
FactorsHelper.primeFactorsList_eq
null
private partial evalPrimeFactorsListAux {en enl : Q(ℕ)} {ea eal : Q(ℕ)} (ehn : Q(IsNat $en $enl)) (eha : Q(IsNat $ea $eal)) : MetaM ((l : Q(List ℕ)) × Q(FactorsHelper $en $ea $l)) := do /- In this function we will use the convention that all `e` prefixed variables (proofs or otherwise) contain `Expr`s. The variables starting with `h` are proofs about the _meta_ code; these will not actually be used in the construction of the proof, and are simply used to help the reader reason about why the proof construction is correct. -/ let n := enl.natLit! let ⟨hn0⟩ ← if h : 0 < n then pure <| PLift.up h else throwError m!"{enl} must be positive" let a := eal.natLit! let b := n.minFac let ⟨hab⟩ ← if h : a ≤ b then pure <| PLift.up h else throwError m!"{q($eal < $(enl).minFac)} does not hold" if h_bn : b < n then let m := n / b have em : Q(ℕ) := mkRawNatLit m have ehm : Q(IsNat (OfNat.ofNat $em) $em) := q(⟨rfl⟩) if h_ba_eq : b = a then have eh : Q($eal * $em = $en) := have : a * m = n := by simp [m, b, ← h_ba_eq, Nat.mul_div_cancel' (minFac_dvd _)] (q(Eq.refl $en) : Expr) let ehp₁ := q(isNat_mul rfl $eha $ehm $eh) let ⟨el, ehp₂⟩ ← evalPrimeFactorsListAux ehm eha pure ⟨q($ea :: $el), q(($ehp₂).cons_self _ $ehp₁)⟩ else have eb : Q(ℕ) := mkRawNatLit b have ehb : Q(IsNat (OfNat.ofNat $eb) $eb) := q(⟨rfl⟩) have ehbm : Q($eb * $em = $en) := have : b * m = n := Nat.mul_div_cancel' (minFac_dvd _) (q(Eq.refl $en) : Expr) have ehp₁ := q(isNat_mul rfl $ehb $ehm $ehbm) have ehp₂ : Q(Nat.blt $ea $eb = true) := have : a < b := lt_of_le_of_ne' hab h_ba_eq (q(Eq.refl (true)) : Expr) let .isNat _ lit ehp₃ ← evalMinFac.core q($eb) q(inferInstance) q($eb) ehb b | failure assertInstancesCommute have : $lit =Q $eb := ⟨⟩ let ⟨l, p₄⟩ ← evalPrimeFactorsListAux ehm ehb pure ⟨q($eb :: $l), q(($p₄).cons _ $ehp₁ $ehp₂ $ehp₃ )⟩ else have hbn_eq : b = n := (minFac_le hn0).eq_or_lt.resolve_right h_bn if hba : b = a then have eh : Q($en = $ea) := have : n = a := hbn_eq.symm.trans hba (q(Eq.refl $en) : Expr) pure ⟨q([$ea]), q($eh ▸ FactorsHelper.singleton_self $ea)⟩ else do let eh_a_lt_n : Q(Nat.blt $ea $en = true) := ...
def
Tactic
[ "Mathlib.Data.Nat.Factors", "Mathlib.Tactic.NormNum.Prime" ]
Mathlib/Tactic/Simproc/Factors.lean
evalPrimeFactorsListAux
Given `n` and `a` (in expressions `en` and `ea`) corresponding to literal numerals (in `enl` and `eal`), returns `(l, ⊢ factorsHelper n a l)`.
evalPrimeFactorsList {en enl : Q(ℕ)} (hn : Q(IsNat $en $enl)) : MetaM ((l : Q(List ℕ)) × Q(Nat.primeFactorsList $en = $l)) := do match enl.natLit! with | 0 => have _ : $enl =Q nat_lit 0 := ⟨⟩ have hen : Q($en = 0) := q($(hn).out) return ⟨_, q($hen ▸ Nat.primeFactorsList_zero)⟩ | 1 => let _ : $enl =Q nat_lit 1 := ⟨⟩ have hen : Q($en = 1) := q($(hn).out) return ⟨_, q($hen ▸ Nat.primeFactorsList_one)⟩ | _ => do have h2 : Q(IsNat 2 (nat_lit 2)) := q(⟨Eq.refl (nat_lit 2)⟩) let ⟨l, p⟩ ← evalPrimeFactorsListAux hn h2 return ⟨l, q(($p).primeFactorsList_eq)⟩
def
Tactic
[ "Mathlib.Data.Nat.Factors", "Mathlib.Tactic.NormNum.Prime" ]
Mathlib/Tactic/Simproc/Factors.lean
evalPrimeFactorsList
Given a natural number `n`, returns `(l, ⊢ Nat.primeFactorsList n = l)`.
private NameStruct where /-- The namespace that the final name will reside in. -/ parent : Name /-- A list of pieces to be joined by `toName`. -/ components : List String
structure
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
NameStruct
An internal representation of a name to be used for a generated lemma.
private NameStruct.toName (n : NameStruct) : Name := Name.mkStr n.parent <| match n.components with | [] => "" | [x] => s!"{x}_def" | e => "_".intercalate e
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
NameStruct.toName
Join the components with `_`, or append `_def` if there is only one component.
private NameStruct.update (nm : NameStruct) (s : String) (isPrefix : Bool := false) : NameStruct := { nm with components := if isPrefix then s :: nm.components else nm.components ++ [s] }
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
NameStruct.update
`update nm s isPrefix` adds `s` to the last component of `nm`, either as prefix or as suffix (specified by `isPrefix`). Used by `simps_add_projections`.
mkSimpContextResult (cfg : Meta.Simp.Config := {}) (simpOnly := false) (kind := SimpKind.simp) (dischargeWrapper := DischargeWrapper.default) (hasStar := false) : MetaM MkSimpContextResult := do match dischargeWrapper with | .default => pure () | _ => if kind == SimpKind.simpAll then throwError "'simp_all' tactic does not support 'discharger' option" if kind == SimpKind.dsimp then throwError "'dsimp' tactic does not support 'discharger' option" let simpTheorems ← if simpOnly then simpOnlyBuiltins.foldlM (·.addConst ·) ({} : SimpTheorems) else getSimpTheorems let simprocs := #[← if simpOnly then pure {} else Simp.getSimprocs] let congrTheorems ← getSimpCongrTheorems let ctx : Simp.Context ← Simp.mkContext cfg (simpTheorems := #[simpTheorems]) (congrTheorems := congrTheorems) if !hasStar then return { ctx, simprocs, dischargeWrapper } else let mut simpTheorems := ctx.simpTheorems let hs ← getPropHyps for h in hs do unless simpTheorems.isErased (.fvar h) do simpTheorems ← simpTheorems.addTheorem (.fvar h) (← h.getDecl).toExpr let ctx := ctx.setSimpTheorems simpTheorems return { ctx, simprocs, dischargeWrapper }
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
mkSimpContextResult
Make `MkSimpContextResult` giving data instead of Syntax. Doesn't support arguments. Intended to be very similar to `Lean.Elab.Tactic.mkSimpContext` Todo: support arguments.
mkSimpContext (cfg : Meta.Simp.Config := {}) (simpOnly := false) (kind := SimpKind.simp) (dischargeWrapper := DischargeWrapper.default) (hasStar := false) : MetaM Simp.Context := do let data ← mkSimpContextResult cfg simpOnly kind dischargeWrapper hasStar return data.ctx
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
mkSimpContext
Make `Simp.Context` giving data instead of Syntax. Doesn't support arguments. Intended to be very similar to `Lean.Elab.Tactic.mkSimpContext` Todo: support arguments.
ProjectionData where /-- The name used in the generated `simp` lemmas -/ name : Name /-- An Expression used by simps for the projection. It must be definitionally equal to an original projection (or a composition of multiple projections). These Expressions can contain the universe parameters specified in the first argument of `structureExt`. -/ expr : Expr /-- A list of natural numbers, which is the projection number(s) that have to be applied to the Expression. For example the list `[0, 1]` corresponds to applying the first projection of the structure, and then the second projection of the resulting structure (this assumes that the target of the first projection is a structure with at least two projections). The composition of these projections is required to be definitionally equal to the provided Expression. -/ projNrs : List Nat /-- A Boolean specifying whether `simp` lemmas are generated for this projection by default. -/ isDefault : Bool /-- A Boolean specifying whether this projection is written as prefix. -/ isPrefix : Bool deriving Inhabited
structure
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
ProjectionData
An `(attr := ...)` option for `simps`. -/ syntax simpsOptAttrOption := atomic(" (" &"attr" " := " Parser.Term.attrInstance,* ")")? /-- Arguments to `@[simps]` attribute. Currently, a potential `(attr := ...)` argument has to come before other configuration options. -/ syntax simpsArgsRest := simpsOptAttrOption Tactic.optConfig (ppSpace ident)* /-- The `@[simps]` attribute automatically derives lemmas specifying the projections of this declaration. Example: ```lean @[simps] def foo : ℕ × ℤ := (1, 2) ``` derives two `simp` lemmas: ```lean @[simp] lemma foo_fst : foo.fst = 1 @[simp] lemma foo_snd : foo.snd = 2 ``` * It does not derive `simp` lemmas for the prop-valued projections. * It will automatically reduce newly created beta-redexes, but will not unfold any definitions. * If the structure has a coercion to either sorts or functions, and this is defined to be one of the projections, then this coercion will be used instead of the projection. * If the structure is a class that has an instance to a notation class, like `Neg` or `Mul`, then this notation is used instead of the corresponding projection. * You can specify custom projections, by giving a declaration with name `{StructureName}.Simps.{projectionName}`. See Note [custom simps projection]. Example: ```lean def Equiv.Simps.invFun (e : α ≃ β) : β → α := e.symm @[simps] def Equiv.trans (e₁ : α ≃ β) (e₂ : β ≃ γ) : α ≃ γ := ⟨e₂ ∘ e₁, e₁.symm ∘ e₂.symm⟩ ``` generates ``` @[simp] lemma Equiv.trans_toFun : ∀ {α β γ} (e₁ e₂) (a : α), ⇑(e₁.trans e₂) a = (⇑e₂ ∘ ⇑e₁) a @[simp] lemma Equiv.trans_invFun : ∀ {α β γ} (e₁ e₂) (a : γ), ⇑((e₁.trans e₂).symm) a = (⇑(e₁.symm) ∘ ⇑(e₂.symm)) a ``` * You can specify custom projection names, by specifying the new projection names using `initialize_simps_projections`. Example: `initialize_simps_projections Equiv (toFun → apply, invFun → symm_apply)`. See `initialize_simps_projections` for more information. * If one of the fields itself is a structure, this command will recursively create `simp` lemmas for all fields in that structure. * Exception: by default it will not recursively create `simp` lemmas for fields in the structures `Prod`, `PProd`, and `Opposite`. You can give explicit projection names or change the value of `Simps.Config.notRecursive` to override this behavior. Example: ```lean structure MyProd (α β : Type*) := (fst : α) (snd : β) @[simps] def foo : Prod ℕ ℕ × MyProd ℕ ℕ := ⟨⟨1, 2⟩, 3, 4⟩ ``` generates ```lean @[simp] lemma foo_fst : foo.fst = (1, 2) @[simp] lemma foo_snd_fst : foo.snd.fst = 3 @[simp] lemma foo_snd_snd : foo.snd.snd = 4 ``` * You can use `@[simps proj1 proj2 ...]` to only generate the projection lemmas for the specified projections. * Recursive projection names can be specified using `proj1_proj2_proj3`. This will create a lemma of the form `foo.proj1.proj2.proj3 = ...`. Example: ```lean structure MyProd (α β : Type*) := (fst : α) (snd : β) @[simps fst fst_fst snd] def foo : Prod ℕ ℕ × MyProd ℕ ℕ := ⟨⟨1, 2⟩, 3, 4⟩ ``` generates ```lean @[simp] lemma foo_fst : foo.fst = (1, 2) @[simp] lemma foo_fst_fst : foo.fst.fst = 1 @[simp] lemma foo_snd : foo.snd = {fst := 3, snd := 4} ``` * If one of the values is an eta-expanded structure, we will eta-reduce this structure. Example: ```lean structure EquivPlusData (α β) extends α ≃ β where data : Bool @[simps] def EquivPlusData.rfl {α} : EquivPlusData α α := { Equiv.refl α with data := true } ``` generates the following: ```lean @[simp] lemma bar_toEquiv : ∀ {α : Sort*}, bar.toEquiv = Equiv.refl α @[simp] lemma bar_data : ∀ {α : Sort*}, bar.data = true ``` This is true, even though Lean inserts an eta-expanded version of `Equiv.refl α` in the definition of `bar`. * You can add additional attributes to all lemmas generated by `simps` using e.g. `@[simps (attr := grind =)]`. * For configuration options, see the doc string of `Simps.Config`. * The precise syntax is `simps (attr := a) config ident*`, where `a` is a list of attributes, `config` declares configuration options and `ident*` is a list of desired projection names. * Configuration options can be given using `(config := e)` where `e : Simps.Config`, or by specifying options directly, like `-fullyApplied` or `(notRecursive := [])`. * `@[simps]` reduces let-expressions where necessary. * When option `trace.simps.verbose` is true, `simps` will print the projections it finds and the lemmas it generates. The same can be achieved by using `@[simps?]`. * Use `@[to_additive (attr := simps)]` to apply both `to_additive` and `simps` to a definition This will also generate the additive versions of all `simp` lemmas. -/ /- If one of the fields is a partially applied constructor, we will eta-expand it (this likely never happens, so is not included in the official doc). -/ syntax (name := simps) "simps" "!"? "?"? simpsArgsRest : attr @[inherit_doc simps] macro "simps?" rest:simpsArgsRest : attr => `(attr| simps ? $rest) @[inherit_doc simps] macro "simps!" rest:simpsArgsRest : attr => `(attr| simps ! $rest) @[inherit_doc simps] macro "simps!?" rest:simpsArgsRest : attr => `(attr| simps ! ? $rest) @[inherit_doc simps] macro "simps?!" rest:simpsArgsRest : attr => `(attr| simps ! ? $rest) end Attr /-- Linter to check that `simps!` is used when needed -/ register_option linter.simpsNoConstructor : Bool := { defValue := true descr := "Linter to check that `simps!` is used" } /-- Linter to check that no unused custom declarations are declared for simps. -/ register_option linter.simpsUnusedCustomDeclarations : Bool := { defValue := true descr := "Linter to check that no unused custom declarations are declared for simps" } namespace Command /-- Syntax for renaming a projection in `initialize_simps_projections`. -/ syntax simpsRule.rename := ident " → " ident /-- Syntax for making a projection non-default in `initialize_simps_projections`. -/ syntax simpsRule.erase := "-" ident /-- Syntax for making a projection default in `initialize_simps_projections`. -/ syntax simpsRule.add := "+" ident /-- Syntax for making a projection prefix. -/ syntax simpsRule.prefix := &"as_prefix " ident /-- Syntax for a single rule in `initialize_simps_projections`. -/ syntax simpsRule := simpsRule.prefix <|> simpsRule.rename <|> simpsRule.erase <|> simpsRule.add /-- Syntax for `initialize_simps_projections`. -/ syntax simpsProj := ppSpace ident (" (" simpsRule,+ ")")? /-- This command allows customisation of the lemmas generated by `simps`. By default, tagging a definition of an element `myObj` of a structure `MyStruct` with `@[simps]` generates one `@[simp]` lemma `myObj_myProj` for each projection `myProj` of `MyStruct`. There are a few exceptions to this general rule: * For algebraic structures, we will automatically use the notation (like `Mul`) for the projections if such an instance is available. * By default, the projections to parent structures are not default projections, but all the data-carrying fields are (including those in parent structures). This default behavior is customisable as such: * You can disable a projection by default by running `initialize_simps_projections MulEquiv (-invFun)` This will ensure that no simp lemmas are generated for this projection, unless this projection is explicitly specified by the user (as in `@[simps invFun] def myEquiv : MulEquiv _ _ := _`). * Conversely, you can enable a projection by default by running `initialize_simps_projections MulEquiv (+toEquiv)`. * You can specify custom names by writing e.g. `initialize_simps_projections MulEquiv (toFun → apply, invFun → symm_apply)`. * If you want the projection name added as a prefix in the generated lemma name, you can use `as_prefix fieldName`: `initialize_simps_projections MulEquiv (toFun → coe, as_prefix coe)` Note that this does not influence the parsing of projection names: if you have a declaration `foo` and you want to apply the projections `snd`, `coe` (which is a prefix) and `fst`, in that order you can run `@[simps snd_coe_fst] def foo ...` and this will generate a lemma with the name `coe_foo_snd_fst`. Here are a few extra pieces of information: * Run `initialize_simps_projections?` (or `set_option trace.simps.verbose true`) to see the generated projections. * Running `initialize_simps_projections MyStruct` without arguments is not necessary, it has the same effect if you just add `@[simps]` to a declaration. * It is recommended to call `@[simps]` or `initialize_simps_projections` in the same file as the structure declaration. Otherwise, the projections could be generated multiple times in different files. Some common uses: * If you define a new homomorphism-like structure (like `MulHom`) you can just run `initialize_simps_projections` after defining the `DFunLike` instance (or instance that implies a `DFunLike` instance). ``` instance {mM : Mul M} {mN : Mul N} : FunLike (MulHom M N) M N := ... initialize_simps_projections MulHom (toFun → apply) ``` This will generate `foo_apply` lemmas for each declaration `foo`. * If you prefer `coe_foo` lemmas that state equalities between functions, use `initialize_simps_projections MulHom (toFun → coe, as_prefix coe)` In this case you have to use `@[simps -fullyApplied]` whenever you call `@[simps]`. * You can also initialize to use both, in which case you have to choose which one to use by default, by using either of the following ``` initialize_simps_projections MulHom (toFun → apply, toFun → coe, as_prefix coe, -coe) initialize_simps_projections MulHom (toFun → apply, toFun → coe, as_prefix coe, -apply) ``` In the first case, you can get both lemmas using `@[simps, simps -fullyApplied coe]` and in the second case you can get both lemmas using `@[simps -fullyApplied, simps apply]`. * If you declare a new homomorphism-like structure (like `RelEmbedding`), then `initialize_simps_projections` will automatically find any `DFunLike` coercions that will be used as the default projection for the `toFun` field. ``` initialize_simps_projections relEmbedding (toFun → apply) ``` * If you have an isomorphism-like structure (like `Equiv`) you often want to define a custom projection for the inverse: ``` def Equiv.Simps.symm_apply (e : α ≃ β) : β → α := e.symm initialize_simps_projections Equiv (toFun → apply, invFun → symm_apply) ``` -/ syntax (name := initialize_simps_projections) "initialize_simps_projections" "?"? simpsProj : command @[inherit_doc «initialize_simps_projections»] macro "initialize_simps_projections?" rest:simpsProj : command => `(initialize_simps_projections ? $rest) end Command end Lean.Parser initialize registerTraceClass `simps.verbose initialize registerTraceClass `simps.debug namespace Simps /-- Projection data for a single projection of a structure
ParsedProjectionData where /-- name for this projection used in the structure definition -/ strName : Name /-- syntax that might have provided `strName` -/ strStx : Syntax := .missing /-- name for this projection used in the generated `simp` lemmas -/ newName : Name /-- syntax that provided `newName` -/ newStx : Syntax := .missing /-- will simp lemmas be generated for with (without specifically naming this?) -/ isDefault : Bool := true /-- is the projection name a prefix? -/ isPrefix : Bool := false /-- projection expression -/ expr? : Option Expr := none /-- the list of projection numbers this expression corresponds to -/ projNrs : Array Nat := #[] /-- is this a projection that is changed by the user? -/ isCustom : Bool := false
structure
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
ParsedProjectionData
The `Simps.structureExt` environment extension specifies the preferred projections of the given structure, used by the `@[simps]` attribute. - You can generate this with the command `initialize_simps_projections`. - If not generated, the `@[simps]` attribute will generate this automatically. - To change the default value, see Note [custom simps projection]. - The first argument is the list of names of the universe variables used in the structure - The second argument is an array that consists of the projection data for each projection. -/ initialize structureExt : NameMapExtension (List Name × Array ProjectionData) ← registerNameMapExtension (List Name × Array ProjectionData) /-- Projection data used internally in `getRawProjections`.
ParsedProjectionData.toProjectionData (p : ParsedProjectionData) : ProjectionData := { p with name := p.newName, expr := p.expr?.getD default, projNrs := p.projNrs.toList }
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
ParsedProjectionData.toProjectionData
Turn `ParsedProjectionData` into `ProjectionData`.
ProjectionRule where /-- A renaming rule `before→after` or Each name comes with the syntax used to write the rule, which is used to declare hover information. -/ | rename (oldName : Name) (oldStx : Syntax) (newName : Name) (newStx : Syntax) : ProjectionRule /-- An adding rule `+fieldName` -/ | add : Name → Syntax → ProjectionRule /-- A hiding rule `-fieldName` -/ | erase : Name → Syntax → ProjectionRule /-- A prefix rule `prefix fieldName` -/ | prefix : Name → Syntax → ProjectionRule
inductive
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
ProjectionRule
The type of rules that specify how metadata for projections in changes. See `initialize_simps_projections`.
projectionsInfo (l : List ProjectionData) (pref : String) (str : Name) : MessageData := let ⟨defaults, nondefaults⟩ := l.partition (·.isDefault) let toPrint : List MessageData := defaults.map fun s ↦ let prefixStr := if s.isPrefix then "(prefix) " else "" m!"Projection {prefixStr}{s.name}: {s.expr}" let print2 : MessageData := String.join <| (nondefaults.map fun nm : ProjectionData ↦ toString nm.1).intersperse ", " let toPrint := toPrint ++ if nondefaults.isEmpty then [] else [("No lemmas are generated for the projections: " : MessageData) ++ print2 ++ "."] let toPrint := MessageData.joinSep toPrint ("\n" : MessageData) m!"{pref} {str}:\n{toPrint}"
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
projectionsInfo
Returns the projection information of a structure.
findProjectionIndices (strName projName : Name) : MetaM (List Nat) := do let env ← getEnv let some baseStr := findField? env strName projName | throwError "{strName} has no field {projName} in parent structure" let some fullProjName := getProjFnForField? env baseStr projName | throwError "no such field {projName}" let some pathToField := getPathToBaseStructure? env baseStr strName | throwError "no such field {projName}" let allProjs := pathToField ++ [fullProjName] return allProjs.map (env.getProjectionFnInfo? · |>.get!.i)
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
findProjectionIndices
Find the indices of the projections that need to be applied to elaborate `$e.$projName`. Example: If `e : α ≃+ β` and ``projName = `invFun`` then this returns `[0, 1]`, because the first projection of `MulEquiv` is `toEquiv` and the second projection of `Equiv` is `invFun`.
private dropPrefixIfNotNumber? (s : String) (pre : String) : Option Substring := do let ret ← s.dropPrefix? pre let flag := ret.toString.data.head?.elim false Char.isDigit if flag then none else some ret
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
dropPrefixIfNotNumber
A variant of `Substring.dropPrefix?` that does not consider `toFoo` to be a prefix to `toFoo_1`. This is checked by inspecting whether the first character of the remaining part is a digit. We use this variant because the latter is often a different field with an auto-generated name.
private isPrefixOfAndNotNumber (s p : String) : Bool := (dropPrefixIfNotNumber? p s).isSome
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
isPrefixOfAndNotNumber
A variant of `String.isPrefixOf` that does not consider `toFoo` to be a prefix to `toFoo_1`.
private splitOnNotNumber (s delim : String) : List String := (process (s.splitOn delim).reverse "").reverse where process (arr : List String) (tail : String) := match arr with | [] => [] | (x :: xs) => let flag := x.data.head?.elim false Char.isDigit if flag then process xs (tail ++ delim ++ x) else List.cons (x ++ tail) (process xs "")
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
splitOnNotNumber
A variant of `String.splitOn` that does not split `toFoo_1` into `toFoo` and `1`.
partial getCompositeOfProjectionsAux (proj : String) (e : Expr) (pos : Array Nat) (args : Array Expr) : MetaM (Expr × Array Nat) := do let env ← getEnv let .const structName _ := (← whnf (← inferType e)).getAppFn | throwError "{e} doesn't have a structure as type" let projs := getStructureFieldsFlattened env structName let projInfo := projs.toList.map fun p ↦ do ((← dropPrefixIfNotNumber? proj (p.lastComponentAsString ++ "_")).toString, p) let some (projRest, projName) := projInfo.reduceOption.getLast? | throwError "Failed to find constructor {proj.dropRight 1} in structure {structName}." let newE ← mkProjection e projName let newPos := pos ++ (← findProjectionIndices structName projName) if projRest.isEmpty then let newE ← mkLambdaFVars args newE return (newE, newPos) let type ← inferType newE forallTelescopeReducing type fun typeArgs _tgt ↦ do getCompositeOfProjectionsAux projRest (mkAppN newE typeArgs) newPos (args ++ typeArgs)
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
getCompositeOfProjectionsAux
Auxiliary function of `getCompositeOfProjections`.
getCompositeOfProjections (structName : Name) (proj : String) : MetaM (Expr × Array Nat) := do let strExpr ← mkConstWithLevelParams structName let type ← inferType strExpr forallTelescopeReducing type fun typeArgs _ ↦ withLocalDeclD `x (mkAppN strExpr typeArgs) fun e ↦ getCompositeOfProjectionsAux (proj ++ "_") e #[] <| typeArgs.push e
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
getCompositeOfProjections
Suppose we are given a structure `str` and a projection `proj`, that could be multiple nested projections (separated by `_`), where each projection could be a projection of a parent structure. This function returns an expression that is the composition of these projections and a list of natural numbers, that are the projection numbers of the applied projections. Note that this function is similar to elaborating dot notation, but it can do a little more. Example: if we do ``` structure gradedFun (A : ℕ → Type*) where toFun := ∀ i j, A i →+ A j →+ A (i + j) initialize_simps_projections (toFun_toFun_toFun → myMul) ``` we will be able to generate the "projection" `fun {A} (f : gradedFun A) (x : A i) (y : A j) ↦ ↑(↑(f.toFun i j) x) y`, which projection notation cannot do.
mkParsedProjectionData (structName : Name) : CoreM (Array ParsedProjectionData) := do let env ← getEnv let projs := getStructureFields env structName if projs.size == 0 then throwError "Declaration {structName} is not a structure." let projData := projs.map fun fieldName ↦ { strName := fieldName, newName := fieldName, isDefault := isSubobjectField? env structName fieldName |>.isNone } let parentProjs := getStructureFieldsFlattened env structName false let parentProjs := parentProjs.filter (!projs.contains ·) let parentProjData := parentProjs.map fun nm ↦ {strName := nm, newName := nm} return projData ++ parentProjData
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
mkParsedProjectionData
Get the default `ParsedProjectionData` for structure `str`. It first returns the direct fields of the structure in the right order, and then all (non-subobject fields) of all parent structures. The subobject fields are precisely the non-default fields.
applyProjectionRules (projs : Array ParsedProjectionData) (rules : Array ProjectionRule) : CoreM (Array ParsedProjectionData) := do let projs : Array ParsedProjectionData := rules.foldl (init := projs) fun projs rule ↦ match rule with | .rename strName strStx newName newStx => if (projs.map (·.newName)).contains strName then projs.map fun proj ↦ if proj.newName == strName then { proj with newName, newStx, strStx := if proj.strStx.isMissing then strStx else proj.strStx } else proj else projs.push {strName, strStx, newName, newStx} | .erase nm stx => if (projs.map (·.newName)).contains nm then projs.map fun proj ↦ if proj.newName = nm then { proj with isDefault := false, strStx := if proj.strStx.isMissing then stx else proj.strStx } else proj else projs.push {strName := nm, newName := nm, strStx := stx, newStx := stx, isDefault := false} | .add nm stx => if (projs.map (·.newName)).contains nm then projs.map fun proj ↦ if proj.newName = nm then { proj with isDefault := true, strStx := if proj.strStx.isMissing then stx else proj.strStx } else proj else projs.push {strName := nm, newName := nm, strStx := stx, newStx := stx} | .prefix nm stx => if (projs.map (·.newName)).contains nm then projs.map fun proj ↦ if proj.newName = nm then { proj with isPrefix := true, strStx := if proj.strStx.isMissing then stx else proj.strStx } else proj else projs.push {strName := nm, newName := nm, strStx := stx, newStx := stx, isPrefix := true} trace[simps.debug] "Projection info after applying the rules: {projs}." unless (projs.map (·.newName)).toList.Nodup do throwError "\ Invalid projection names. Two projections have the same name.\n\ This is likely because a custom composition of projections was given the same name as an \ existing projection. Solution: rename the existing projection (before naming the \ custom projection)." pure projs
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
applyProjectionRules
Execute the projection renamings (and turning off projections) as specified by `rules`.
findProjection (str : Name) (proj : ParsedProjectionData) (rawUnivs : List Level) : CoreM ParsedProjectionData := do let env ← getEnv let (rawExpr, nrs) ← MetaM.run' <| getCompositeOfProjections str proj.strName.lastComponentAsString if !proj.strStx.isMissing then _ ← MetaM.run' <| TermElabM.run' <| addTermInfo proj.strStx rawExpr trace[simps.debug] "Projection {proj.newName} has default projection {rawExpr} and uses projection indices {nrs}" let customName := str ++ `Simps ++ proj.newName match env.find? customName with | some d@(.defnInfo _) => let customProj := d.instantiateValueLevelParams! rawUnivs trace[simps.verbose] "found custom projection for {proj.newName}:{indentExpr customProj}" match (← MetaM.run' <| isDefEq customProj rawExpr) with | true => _ ← MetaM.run' <| TermElabM.run' <| addTermInfo proj.newStx <| ← mkConstWithLevelParams customName pure { proj with expr? := some customProj, projNrs := nrs, isCustom := true } | false => let customProjType ← MetaM.run' (inferType customProj) let rawExprType ← MetaM.run' (inferType rawExpr) if (← MetaM.run' (isDefEq customProjType rawExprType)) then throwError "Invalid custom projection:{indentExpr customProj}\n\ Expression is not definitionally equal to {indentExpr rawExpr}" else throwError "Invalid custom projection:{indentExpr customProj}\n\ Expression has different type than {str ++ proj.strName}. Given type:\ {indentExpr customProjType}\nExpected type:{indentExpr rawExprType}\n\ Note: make sure order of implicit arguments is exactly the same." | _ => _ ← MetaM.run' <| TermElabM.run' <| addTermInfo proj.newStx rawExpr pure {proj with expr? := some rawExpr, projNrs := nrs}
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
findProjection
Auxiliary function for `getRawProjections`. Generates the default projection, and looks for a custom projection declared by the user, and replaces the default projection with the custom one, if it can find it.
checkForUnusedCustomProjs (stx : Syntax) (str : Name) (projs : Array ParsedProjectionData) : CoreM Unit := do let nrCustomProjections := projs.toList.countP (·.isCustom) let env ← getEnv let customDeclarations := env.constants.map₂.foldl (init := #[]) fun xs nm _ => if (str ++ `Simps).isPrefixOf nm && !nm.isInternalDetail && !isReservedName env nm then xs.push nm else xs if nrCustomProjections < customDeclarations.size then Linter.logLintIf linter.simpsUnusedCustomDeclarations stx m!"\ Not all of the custom declarations {customDeclarations} are used. Double check the \ spelling, and use `?` to get more information."
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
checkForUnusedCustomProjs
Checks if there are declarations in the current file in the namespace `{str}.Simps` that are not used.
findAutomaticProjectionsAux (str : Name) (proj : ParsedProjectionData) (args : Array Expr) : TermElabM <| Option (Expr × Name) := do if let some ⟨className, isNotation, findArgs⟩ := notationClassAttr.find? (← getEnv) proj.strName then let findArgs ← unsafe evalConst findArgType findArgs let classArgs ← try findArgs str className args catch ex => trace[simps.debug] "Projection {proj.strName} is likely unrelated to the projection of \ {className}:\n{ex.toMessageData}" return none let classArgs ← classArgs.mapM fun e => match e with | none => mkFreshExprMVar none | some e => pure e let classArgs := classArgs.map Arg.expr let projName := (getStructureFields (← getEnv) className)[0]! let projName := className ++ projName let eStr := mkAppN (← mkConstWithLevelParams str) args let eInstType ← try withoutErrToSorry (elabAppArgs (← Term.mkConst className) #[] classArgs none true false) catch ex => trace[simps.debug] "Projection doesn't have the right type for the automatic projection:\n\ {ex.toMessageData}" return none return ← withLocalDeclD `self eStr fun instStr ↦ do trace[simps.debug] "found projection {proj.strName}. Trying to synthesize {eInstType}." let eInst ← try synthInstance eInstType catch ex => trace[simps.debug] "Didn't find instance:\n{ex.toMessageData}" return none let projExpr ← elabAppArgs (← Term.mkConst projName) #[] (classArgs.push <| .expr eInst) none true false let projExpr ← mkLambdaFVars (if isNotation then args.push instStr else args) projExpr let projExpr ← instantiateMVars projExpr return (projExpr, projName) return none
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
findAutomaticProjectionsAux
If a structure has a field that corresponds to a coercion to functions or sets, or corresponds to notation, find the custom projection that uses this coercion or notation. Returns the custom projection and the name of the projection used. We catch most errors this function causes, so that we don't fail if an unrelated projection has an applicable name. (e.g. `Iso.inv`) Implementation note: getting rid of TermElabM is tricky, since `Expr.mkAppOptM` doesn't allow to keep metavariables around, which are necessary for `OutParam`.
findAutomaticProjections (str : Name) (projs : Array ParsedProjectionData) : CoreM (Array ParsedProjectionData) := do let strDecl ← getConstInfo str trace[simps.debug] "debug: {projs}" MetaM.run' <| TermElabM.run' (s := {levelNames := strDecl.levelParams}) <| forallTelescope strDecl.type fun args _ ↦ do let projs ← projs.mapM fun proj => do if let some (projExpr, projName) := ← findAutomaticProjectionsAux str proj args then unless ← isDefEq projExpr proj.expr?.get! do throwError "The projection {proj.newName} is not definitionally equal to an application \ of {projName}:{indentExpr proj.expr?.get!}\nvs{indentExpr projExpr}" if proj.isCustom then trace[simps.verbose] "Warning: Projection {proj.newName} is given manually by the user, \ but it can be generated automatically." return proj trace[simps.verbose] "Using {indentExpr projExpr}\nfor projection {proj.newName}." return { proj with expr? := some projExpr } return proj return projs
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
findAutomaticProjections
Auxiliary function for `getRawProjections`. Find custom projections, automatically found by simps. These come from `DFunLike` and `SetLike` instances.
getRawProjections (stx : Syntax) (str : Name) (traceIfExists : Bool := false) (rules : Array ProjectionRule := #[]) (trc := false) : CoreM (List Name × Array ProjectionData) := do withOptions (· |>.updateBool `trace.simps.verbose (trc || ·)) <| do let env ← getEnv if let some data := (structureExt.getState env).find? str then withOptions (· |>.updateBool `trace.simps.verbose (traceIfExists || ·)) <| do trace[simps.verbose] projectionsInfo data.2.toList "The projections for this structure have already been \ initialized by a previous invocation of `initialize_simps_projections` or `@[simps]`.\n\ Generated projections for" str return data trace[simps.verbose] "generating projection information for structure {str}." trace[simps.debug] "Applying the rules {rules}." let strDecl ← getConstInfo str let rawLevels := strDecl.levelParams let rawUnivs := rawLevels.map Level.param let projs ← mkParsedProjectionData str let projs ← applyProjectionRules projs rules let projs ← projs.mapM fun proj ↦ findProjection str proj rawUnivs checkForUnusedCustomProjs stx str projs let projs ← findAutomaticProjections str projs let projs := projs.map (·.toProjectionData) let projs ← projs.mapM fun proj ↦ do match (← MetaM.run' <| isProof proj.expr) with | true => pure { proj with isDefault := false } | false => pure proj trace[simps.verbose] projectionsInfo projs.toList "generated projections for" str structureExt.add str (rawLevels, projs) trace[simps.debug] "Generated raw projection data:{indentD <| toMessageData (rawLevels, projs)}" pure (rawLevels, projs) library_note "custom simps projection" /-- You can specify custom projections for the `@[simps]` attribute. To do this for the projection `MyStructure.originalProjection` by adding a declaration `MyStructure.Simps.myProjection` that is definitionally equal to `MyStructure.originalProjection` but has the projection in the desired (simp-normal) form. Then you can call ``` initialize_simps_projections (originalProjection → myProjection, ...) ``` to register this projection. See `elabInitializeSimpsProjections` for more information. You can also specify custom projections that are definitionally equal to a composite of multiple projections. This is often desirable when extending structures (without `oldStructureCmd`). `CoeFun` and notation class (like `Mul`) instances will be automatically used, if they are definitionally equal to a projection of the structure (but not when they are equal to the composite of multiple projections). -/
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
getRawProjections
Get the projections used by `simps` associated to a given structure `str`. The returned information is also stored in the environment extension `Simps.structureExt`, which is given to `str`. If `str` already has this attribute, the information is read from this extension instead. See the documentation for this extension for the data this tactic returns. The returned universe levels are the universe levels of the structure. For the projections there are three cases * If the declaration `{StructureName}.Simps.{projectionName}` has been declared, then the value of this declaration is used (after checking that it is definitionally equal to the actual projection. If you rename the projection name, the declaration should have the *new* projection name. * You can also declare a custom projection that is a composite of multiple projections. * Otherwise, for every class with the `notation_class` attribute, and the structure has an instance of that notation class, then the projection of that notation class is used for the projection that is definitionally equal to it (if there is such a projection). This means in practice that coercions to function types and sorts will be used instead of a projection, if this coercion is definitionally equal to a projection. Furthermore, for notation classes like `Mul` and `Zero` those projections are used instead of the corresponding projection. Projections for coercions and notation classes are not automatically generated if they are composites of multiple projections (for example when you use `extend` without the `oldStructureCmd` (does this exist?)). * Otherwise, the projection of the structure is chosen. For example: ``getRawProjections env `Prod`` gives the default projections. ``` ([u, v], [(`fst, `(Prod.fst.{u v}), [0], true, false), (`snd, `(@Prod.snd.{u v}), [1], true, false)]) ``` Optionally, this command accepts three optional arguments: * If `traceIfExists` the command will always generate a trace message when the structure already has an entry in `structureExt`. * The `rules` argument specifies whether projections should be added, renamed, used as prefix, and not used by default. * if `trc` is true, this tactic will trace information just as if `set_option trace.simps.verbose true` was set.
elabSimpsRule : Syntax → CommandElabM ProjectionRule | `(simpsRule| $id1 → $id2) => return .rename id1.getId id1.raw id2.getId id2.raw | `(simpsRule| - $id) => return .erase id.getId id.raw | `(simpsRule| + $id) => return .add id.getId id.raw | `(simpsRule| as_prefix $id) => return .prefix id.getId id.raw | _ => Elab.throwUnsupportedSyntax
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
elabSimpsRule
Parse a rule for `initialize_simps_projections`. It is `<name>→<name>`, `-<name>`, `+<name>` or `as_prefix <name>`.
@[command_elab «initialize_simps_projections»] elabInitializeSimpsProjections : CommandElab | stx@`(initialize_simps_projections $[?%$trc]? $id $[($stxs,*)]?) => do let stxs := stxs.getD <| .mk #[] let rules ← stxs.getElems.raw.mapM elabSimpsRule let nm ← resolveGlobalConstNoOverload id _ ← liftTermElabM <| addTermInfo id.raw <| ← mkConstWithLevelParams nm _ ← liftCoreM <| getRawProjections stx nm true rules trc.isSome | _ => throwUnsupportedSyntax
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
elabInitializeSimpsProjections
Function elaborating `initialize_simps_projections`.
Config where /-- Make generated lemmas simp lemmas -/ isSimp := true /-- Other attributes to apply to generated lemmas. -/ attrs : Array Syntax := #[] /-- simplify the right-hand side of generated simp-lemmas using `dsimp, simp`. -/ simpRhs := false /-- TransparencyMode used to reduce the type in order to detect whether it is a structure. -/ typeMd := TransparencyMode.instances /-- TransparencyMode used to reduce the right-hand side in order to detect whether it is a constructor. Note: was `none` in Lean 3 -/ rhsMd := TransparencyMode.reducible /-- Generated lemmas that are fully applied, i.e. generates equalities between applied functions. Set this to `false` to generate equalities between functions. -/ fullyApplied := true /-- List of types in which we are not recursing to generate simplification lemmas. E.g. if we write `@[simps] def e : α × β ≃ β × α := ...` we will generate `e_apply` and not `e_apply_fst`. -/ notRecursive := [`Prod, `PProd, `Opposite, `PreOpposite] /-- Output debug messages. Not used much, use `set_option simps.debug true` instead. -/ debug := false /-- The stem to use for the projection names. If `none`, the default, use the suffix of the current declaration name, or the empty string if the declaration is an instance and the instance is named according to the `inst` convention. -/ nameStem : Option String := none deriving Inhabited
structure
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
Config
Configuration options for `@[simps]`
@[deprecated "use `-fullyApplied` instead" (since := "2025-03-10")] Config.asFn : Simps.Config where fullyApplied := false
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
Config.asFn
Function elaborating `Config` -/ declare_command_config_elab elabSimpsConfig Config /-- A common configuration for `@[simps]`: generate equalities between functions instead equalities between fully applied Expressions. Replaced by `@[simps -fullyApplied]`.
@[deprecated "use `-isSimp` instead" (since := "2025-03-10")] Config.lemmasOnly : Config where isSimp := false
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
Config.lemmasOnly
A common configuration for `@[simps]`: don't tag the generated lemmas with `@[simp]`. Replaced by `@[simps -isSimp]`.
partial _root_.Lean.Expr.instantiateLambdasOrApps (es : Array Expr) (e : Expr) : Expr := e.betaRev es.reverse true -- check if this is what I want
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
_root_.Lean.Expr.instantiateLambdasOrApps
`instantiateLambdasOrApps es e` instantiates lambdas in `e` by expressions from `es`. If the length of `es` is larger than the number of lambdas in `e`, then the term is applied to the remaining terms. Also reduces head let-expressions in `e`, including those after instantiating all lambdas. This is very similar to `expr.substs`, but this also reduces head let-expressions.
getProjectionExprs (stx : Syntax) (tgt : Expr) (rhs : Expr) (cfg : Config) : MetaM <| Array <| Expr × ProjectionData := do let params := tgt.getAppArgs if cfg.debug && !(← (params.zip rhs.getAppArgs).allM fun ⟨a, b⟩ ↦ isDefEq a b) then throwError "unreachable code: parameters are not definitionally equal" let str := tgt.getAppFn.constName?.getD default let rhsArgs := rhs.getAppArgs.toList.drop params.size let (rawUnivs, projDeclata) ← getRawProjections stx str projDeclata.mapM fun proj ↦ do let expr := proj.expr.instantiateLevelParams rawUnivs tgt.getAppFn.constLevels! let proj := if ← isProof expr then { proj with isDefault := false } else proj return (rhsArgs.getD (fallback := default) proj.projNrs.head!, { proj with expr := expr.instantiateLambdasOrApps params projNrs := proj.projNrs.tail }) variable (ref : Syntax) (univs : List Name)
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
getProjectionExprs
Get the projections of a structure used by `@[simps]` applied to the appropriate arguments. Returns a list of tuples ``` (corresponding right-hand-side, given projection name, projection Expression, future projection numbers, used by default, is prefix) ``` (where all fields except the first are packed in a `ProjectionData` structure) one for each projection. The given projection name is the name for the projection used by the user used to generate (and parse) projection names. For example, in the structure Example 1: ``getProjectionExprs env `(α × β) `(⟨x, y⟩)`` will give the output ``` [(`(x), `fst, `(@Prod.fst.{u v} α β), [], true, false), (`(y), `snd, `(@Prod.snd.{u v} α β), [], true, false)] ``` Example 2: ``getProjectionExprs env `(α ≃ α) `(⟨id, id, fun _ ↦ rfl, fun _ ↦ rfl⟩)`` will give the output ``` [(`(id), `apply, (Equiv.toFun), [], true, false), (`(id), `symm_apply, (fun e ↦ e.symm.toFun), [], true, false), ..., ...] ```
addProjection (declName : Name) (type lhs rhs : Expr) (args : Array Expr) (cfg : Config) : MetaM Unit := do trace[simps.debug] "Planning to add the equality{indentD m!"{lhs} = ({rhs} : {type})"}" let env ← getEnv let lvl ← getLevel type let mut (rhs, prf) := (rhs, mkAppN (mkConst `Eq.refl [lvl]) #[type, lhs]) if cfg.simpRhs then let ctx ← mkSimpContext let (rhs2, _) ← dsimp rhs ctx if rhs != rhs2 then trace[simps.debug] "`dsimp` simplified rhs to{indentExpr rhs2}" else trace[simps.debug] "`dsimp` failed to simplify rhs" let (result, _) ← simp rhs2 ctx if rhs2 != result.expr then trace[simps.debug] "`simp` simplified rhs to{indentExpr result.expr}" else trace[simps.debug] "`simp` failed to simplify rhs" rhs := result.expr prf := result.proof?.getD prf let eqAp := mkApp3 (mkConst `Eq [lvl]) type lhs rhs let declType ← mkForallFVars args eqAp let declValue ← mkLambdaFVars args prf if (env.find? declName).isSome then -- diverging behavior from Lean 3 throwError "simps tried to add lemma{indentD m!"{.ofConstName declName} : {declType}"}\n\ to the environment, but it already exists." trace[simps.verbose] "adding projection {declName}:{indentExpr declType}" prependError "Failed to add projection lemma {declName}:" do addDecl <| .thmDecl { name := declName levelParams := univs type := declType value := declValue } inferDefEqAttr declName addDeclarationRangesFromSyntax declName (← getRef) ref TermElabM.run' do _ ← addTermInfo (isBinder := true) ref <| ← mkConstWithLevelParams declName if cfg.isSimp then addSimpTheorem simpExtension declName true false .global <| eval_prio default let attrs ← elabAttrs cfg.attrs Elab.Term.applyAttributes declName attrs
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
addProjection
Add a lemma with `nm` stating that `lhs = rhs`. `type` is the type of both `lhs` and `rhs`, `args` is the list of local constants occurring, and `univs` is the list of universe variables.
partial headStructureEtaReduce (e : Expr) : MetaM Expr := do let env ← getEnv let (ctor, args) := e.getAppFnArgs let some (.ctorInfo { induct := struct, numParams, ..}) := env.find? ctor | pure e let some { fieldNames, .. } := getStructureInfo? env struct | pure e let (params, fields) := args.toList.splitAt numParams -- fix if `Array.take` / `Array.drop` exist trace[simps.debug] "rhs is constructor application with params{indentD params}\nand fields {indentD fields}" let field0 :: fieldsTail := fields | return e let fieldName0 :: fieldNamesTail := fieldNames.toList | return e let (fn0, fieldArgs0) := field0.getAppFnArgs unless fn0 == struct ++ fieldName0 do trace[simps.debug] "{fn0} ≠ {struct ++ fieldName0}" return e let (params', reduct :: _) := fieldArgs0.toList.splitAt numParams | unreachable! unless params' == params do trace[simps.debug] "{params'} ≠ {params}" return e trace[simps.debug] "Potential structure-eta-reduct:{indentExpr e}\nto{indentExpr reduct}" let allArgs := params.toArray.push reduct let isEta ← (fieldsTail.zip fieldNamesTail).allM fun (field, fieldName) ↦ if field.getAppFnArgs == (struct ++ fieldName, allArgs) then pure true else isProof field unless isEta do return e trace[simps.debug] "Structure-eta-reduce:{indentExpr e}\nto{indentExpr reduct}" headStructureEtaReduce reduct
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
headStructureEtaReduce
Perform head-structure-eta-reduction on expression `e`. That is, if `e` is of the form `⟨f.1, f.2, ..., f.n⟩` with `f` definitionally equal to `e`, then `headStructureEtaReduce e = headStructureEtaReduce f` and `headStructureEtaReduce e = e` otherwise.
partial addProjections (nm : NameStruct) (type lhs rhs : Expr) (args : Array Expr) (mustBeStr : Bool) (cfg : Config) (todo : List (String × Syntax)) (toApply : List Nat) : MetaM (Array Name) := do trace[simps.debug] "Type of the Expression before normalizing: {type}" withTransparency cfg.typeMd <| forallTelescopeReducing type fun typeArgs tgt ↦ withDefault do trace[simps.debug] "Type after removing pi's: {tgt}" let tgt ← whnfD tgt trace[simps.debug] "Type after reduction: {tgt}" let newArgs := args ++ typeArgs let lhsAp := lhs.instantiateLambdasOrApps typeArgs let rhsAp := rhs.instantiateLambdasOrApps typeArgs let str := tgt.getAppFn.constName trace[simps.debug] "todo: {todo}, toApply: {toApply}" let todoNext := todo.filter (·.1 ≠ "") let env ← getEnv let stx? := todo.find? (·.1 == "") |>.map (·.2) /- The syntax object associated to the projection we're making now (if any). Note that we use `ref[0]` so that with `simps (config := ...)` we associate it to the word `simps` instead of the application of the attribute to arguments. -/ let stxProj := stx?.getD ref[0] let strInfo? := getStructureInfo? env str /- Don't recursively continue if `str` is not a structure or if the structure is in `notRecursive`. -/ if strInfo?.isNone || (todo.isEmpty && str ∈ cfg.notRecursive && !mustBeStr && toApply.isEmpty) then if mustBeStr then throwError "Invalid `simps` attribute. Target {str} is not a structure" if !todoNext.isEmpty && str ∉ cfg.notRecursive then let firstTodo := todoNext.head!.1 throwError "Invalid simp lemma {nm.update firstTodo false |>.toName}.\nProjection \ {(splitOnNotNumber firstTodo "_")[1]!} doesn't exist, \ because target {str} is not a structure." if cfg.fullyApplied then addProjection stxProj univs nm.toName tgt lhsAp rhsAp newArgs cfg else addProjection stxProj univs nm.toName type lhs rhs args cfg return #[nm.toName] let some (.inductInfo { isRec := false, ctors := [ctor], .. }) := env.find? str | unreachable! trace[simps.debug] "{str} is a structure with constructor {ctor}." let rhsEta ← headStructureEtaReduce rhsAp let addThisProjection := stx?.isSome && toApply.isEmpty if addThisProjection then if cfg.fullyApplied then addProjection stxProj univs nm.toName tgt lhsAp rhsEta newArgs cfg else addProjection stxProj univs nm.toName type lhs rhs args cfg let rhsWhnf ← withTransparency cfg.rhsMd <| whnf rhsEta trace[simps.debug] "The right-hand-side {indentExpr rhsAp}\n reduces to {indentExpr rhsWhnf}" if !rhsWhnf.getAppFn.isConstOf ctor then if cfg.rhsMd == .reducible && (mustBeStr || !todoNext.isEmpty || !toApply.isEmpty) then trace[simps.debug] "Using relaxed reducibility." ...
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
addProjections
Derive lemmas specifying the projections of the declaration. `nm`: name of the lemma If `todo` is non-empty, it will generate exactly the names in `todo`. `toApply` is non-empty after a custom projection that is a composition of multiple projections was just used. In that case we need to apply these projections before we continue changing `lhs`. `simpLemmas`: names of the simp lemmas added so far.(simpLemmas : Array Name)
simpsTac (ref : Syntax) (nm : Name) (cfg : Config := {}) (todo : List (String × Syntax) := []) (trc := false) : AttrM (Array Name) := withOptions (· |>.updateBool `trace.simps.verbose (trc || ·)) <| do let env ← getEnv let some d := env.find? nm | throwError "Declaration {nm} doesn't exist." let lhs : Expr := mkConst d.name <| d.levelParams.map Level.param let todo := todo.eraseDups |>.map fun (proj, stx) ↦ (proj ++ "_", stx) let mut cfg := cfg let nm : NameStruct := { parent := nm.getPrefix components := if let some n := cfg.nameStem then if n == "" then [] else [n] else let s := nm.lastComponentAsString if (← isInstance nm) ∧ s.startsWith "inst" then [] else [s]} MetaM.run' <| addProjections ref d.levelParams nm d.type lhs (d.value?.getD default) #[] (mustBeStr := true) cfg todo []
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
simpsTac
`simpsTac` derives `simp` lemmas for all (nested) non-Prop projections of the declaration. If `todo` is non-empty, it will generate exactly the names in `todo`. If `shortNm` is true, the generated names will only use the last projection name. If `trc` is true, trace as if `trace.simps.verbose` is true.
simpsTacFromSyntax (nm : Name) (stx : Syntax) : AttrM (Array Name) := match stx with | `(attr| simps $[!%$bang]? $[?%$trc]? $attrs:simpsOptAttrOption $c:optConfig $[$ids]*) => do let extraAttrs := match attrs with | `(Attr.simpsOptAttrOption| (attr := $[$stxs],*)) => stxs | _ => #[] let cfg ← liftCommandElabM <| elabSimpsConfig c let cfg := if bang.isNone then cfg else { cfg with rhsMd := .default, simpRhs := true } let cfg := { cfg with attrs := cfg.attrs ++ extraAttrs } let ids := ids.map fun x => (x.getId.eraseMacroScopes.lastComponentAsString, x.raw) simpsTac stx nm cfg ids.toList trc.isSome | _ => throwUnsupportedSyntax
def
Tactic
[ "Lean.Elab.Tactic.Simp", "Lean.Elab.App", "Mathlib.Tactic.Simps.NotationClass", "Mathlib.Lean.Expr.Basic" ]
Mathlib/Tactic/Simps/Basic.lean
simpsTacFromSyntax
elaborate the syntax and run `simpsTac`.
findArgType : Type := Name → Name → Array Expr → MetaM (Array (Option Expr))
def
Tactic
[ "Mathlib.Init", "Lean.Elab.Exception", "Batteries.Lean.NameMapAttribute", "Batteries.Tactic.Lint" ]
Mathlib/Tactic/Simps/NotationClass.lean
findArgType
The `@[notation_class]` attribute specifies that this is a notation class, and this notation should be used instead of projections by `@[simps]`. * This is only important if the projection is written differently using notation, e.g. `+` uses `HAdd.hAdd`, not `Add.add` and `0` uses `OfNat.ofNat` not `Zero.zero`. We also add it to non-heterogeneous notation classes, like `Neg`, but it doesn't do much for any class that extends `Neg`. * `@[notation_class* <projName> Simps.findCoercionArgs]` is used to configure the `SetLike` and `DFunLike` coercions. * The first name argument is the projection name we use as the key to search for this class (default: name of first projection of the class). * The second argument is the name of a declaration that has type `findArgType` which is defined to be `Name → Name → Array Expr → MetaM (Array (Option Expr))`. This declaration specifies how to generate the arguments of the notation class from the arguments of classes that use the projection. -/ syntax (name := notation_class) "notation_class" "*"? (ppSpace ident)? (ppSpace ident)? : attr open Lean Meta Elab Term namespace Simps /-- The type of methods to find arguments for automatic projections for `simps`. We partly define this as a separate definition so that the unused arguments linter doesn't complain.
defaultfindArgs : findArgType := fun _ className args ↦ do let some classExpr := (← getEnv).find? className | throwError "no such class {className}" let arity := classExpr.type.getNumHeadForalls if arity == args.size then return args.map some else if h : args.size = 1 then return .replicate arity args[0] else throwError "initialize_simps_projections cannot automatically find arguments for class \ {className}"
def
Tactic
[ "Mathlib.Init", "Lean.Elab.Exception", "Batteries.Lean.NameMapAttribute", "Batteries.Tactic.Lint" ]
Mathlib/Tactic/Simps/NotationClass.lean
defaultfindArgs
Find arguments for a notation class
copyFirst : findArgType := fun _ _ args ↦ return (args.push <| args[0]?.getD default).map some
def
Tactic
[ "Mathlib.Init", "Lean.Elab.Exception", "Batteries.Lean.NameMapAttribute", "Batteries.Tactic.Lint" ]
Mathlib/Tactic/Simps/NotationClass.lean
copyFirst
Find arguments by duplicating the first argument. Used for `pow`.
copySecond : findArgType := fun _ _ args ↦ return (args.push <| args[1]?.getD default).map some
def
Tactic
[ "Mathlib.Init", "Lean.Elab.Exception", "Batteries.Lean.NameMapAttribute", "Batteries.Tactic.Lint" ]
Mathlib/Tactic/Simps/NotationClass.lean
copySecond
Find arguments by duplicating the first argument. Used for `smul`.
nsmulArgs : findArgType := fun _ _ args ↦ return #[Expr.const `Nat [], args[0]?.getD default] ++ args |>.map some
def
Tactic
[ "Mathlib.Init", "Lean.Elab.Exception", "Batteries.Lean.NameMapAttribute", "Batteries.Tactic.Lint" ]
Mathlib/Tactic/Simps/NotationClass.lean
nsmulArgs
Find arguments by prepending `ℕ` and duplicating the first argument. Used for `nsmul`.
zsmulArgs : findArgType := fun _ _ args ↦ return #[Expr.const `Int [], args[0]?.getD default] ++ args |>.map some
def
Tactic
[ "Mathlib.Init", "Lean.Elab.Exception", "Batteries.Lean.NameMapAttribute", "Batteries.Tactic.Lint" ]
Mathlib/Tactic/Simps/NotationClass.lean
zsmulArgs
Find arguments by prepending `ℤ` and duplicating the first argument. Used for `zsmul`.
findZeroArgs : findArgType := fun _ _ args ↦ return #[some <| args[0]?.getD default, some <| mkRawNatLit 0]
def
Tactic
[ "Mathlib.Init", "Lean.Elab.Exception", "Batteries.Lean.NameMapAttribute", "Batteries.Tactic.Lint" ]
Mathlib/Tactic/Simps/NotationClass.lean
findZeroArgs
Find arguments for the `Zero` class.
findOneArgs : findArgType := fun _ _ args ↦ return #[some <| args[0]?.getD default, some <| mkRawNatLit 1]
def
Tactic
[ "Mathlib.Init", "Lean.Elab.Exception", "Batteries.Lean.NameMapAttribute", "Batteries.Tactic.Lint" ]
Mathlib/Tactic/Simps/NotationClass.lean
findOneArgs
Find arguments for the `One` class.
findCoercionArgs : findArgType := fun str className args ↦ do let some classExpr := (← getEnv).find? className | throwError "no such class {className}" let arity := classExpr.type.getNumHeadForalls let eStr := mkAppN (← mkConstWithLevelParams str) args let classArgs := .replicate (arity - 1) none return #[some eStr] ++ classArgs
def
Tactic
[ "Mathlib.Init", "Lean.Elab.Exception", "Batteries.Lean.NameMapAttribute", "Batteries.Tactic.Lint" ]
Mathlib/Tactic/Simps/NotationClass.lean
findCoercionArgs
Find arguments of a coercion class (`DFunLike` or `SetLike`)
AutomaticProjectionData where /-- `className` is the name of the class we are looking for. -/ className : Name /-- `isNotation` is a Boolean that specifies whether this is notation (false for the coercions `DFunLike` and `SetLike`). If this is set to true, we add the current class as hypothesis during type-class synthesis. -/ isNotation := true /-- The method to find the arguments of the class. -/ findArgs : Name := `Simps.defaultfindArgs deriving Inhabited
structure
Tactic
[ "Mathlib.Init", "Lean.Elab.Exception", "Batteries.Lean.NameMapAttribute", "Batteries.Tactic.Lint" ]
Mathlib/Tactic/Simps/NotationClass.lean
AutomaticProjectionData
Data needed to generate automatic projections. This data is associated to a name of a projection in a structure that must be used to trigger the search.
private TerminalReplacementOutcome where | success (stx : TSyntax `tactic) | remainingGoals (stx : TSyntax `tactic) (goals : List MessageData) | error (stx : TSyntax `tactic) (msg : MessageData) open Elab.Command
inductive
Tactic
[ "Mathlib.Tactic.TacticAnalysis", "Mathlib.Tactic.ExtractGoal", "Mathlib.Tactic.MinImports", "Lean.Elab.Tactic.Meta", "Lean.Elab.Command" ]
Mathlib/Tactic/TacticAnalysis/Declarations.lean
TerminalReplacementOutcome
Helper structure for the return type of the `test` function in `terminalReplacement`.
terminalReplacement (oldTacticName newTacticName : String) (oldTacticKind : SyntaxNodeKind) (newTactic : Syntax → MVarId → MetaM (TSyntax `tactic)) (reportFailure : Bool := true) (reportSuccess : Bool := false) (reportSlowdown : Bool := false) (maxSlowdown : Float := 1) : TacticAnalysis.Config := .ofComplex { out := TerminalReplacementOutcome ctx := Syntax trigger _ stx := if stx.getKind == oldTacticKind then .accept stx else .skip test stx goal := do let tac ← newTactic stx goal try let (goals, _) ← Lean.Elab.runTactic goal tac match goals with | [] => return .success tac | _ => do let goalsMessages ← goals.mapM fun g => do let e ← instantiateMVars (← g.getType) pure m!"⊢ {MessageData.ofExpr e}\n" return .remainingGoals tac goalsMessages catch _e => let name ← mkAuxDeclName `extracted let ((sig, _, modules), _) ← (Mathlib.Tactic.ExtractGoal.goalSignature name goal).run let imports := modules.toList.map (s!"import {·}") return .error tac m!"{"\n".intercalate imports}\n\ntheorem {sig} := by\n fail_if_success {tac}\n {stx}" tell stx _ oldHeartbeats new newHeartbeats := match new with | .error _ msg => if reportFailure then let msg := m!"`{newTacticName}` failed where `{oldTacticName}` succeeded.\n" ++ m!"Original tactic:{indentD stx}\n" ++ m!"Counterexample:{indentD msg}" return msg else return none | .remainingGoals newStx goals => if reportFailure then let msg := m!"`{newTacticName}` left unsolved goals where `{oldTacticName}` succeeded.\n" ++ m!"Original tactic:{indentD stx}\n" ++ m!"Replacement tactic:{indentD newStx}\n" ++ m!"Unsolved goals:{indentD goals}" return msg else return none | .success newStx => do let msg := if (← liftCoreM <| PrettyPrinter.ppTactic newStx).pretty = newTacticName then m!"`{newTacticName}` can replace `{stx}`" else m!"`{newTacticName}` can replace `{stx}` using `{newStx}`" ...
def
Tactic
[ "Mathlib.Tactic.TacticAnalysis", "Mathlib.Tactic.ExtractGoal", "Mathlib.Tactic.MinImports", "Lean.Elab.Tactic.Meta", "Lean.Elab.Command" ]
Mathlib/Tactic/TacticAnalysis/Declarations.lean
terminalReplacement
Define a pass that tries replacing one terminal tactic with another. `newTacticName` is a human-readable name for the tactic, for example "linarith". This can be used to group messages together, so that `ring`, `ring_nf`, `ring1`, ... all produce the same message. `oldTacticKind` is the `SyntaxNodeKind` for the tactic's main parser, for example `Mathlib.Tactic.linarith`. `newTactic stx goal` selects the new tactic to try, which may depend on the old tactic invocation in `stx` and the current `goal`.
grindReplacementWith (tacticName : String) (tacticKind : SyntaxNodeKind) (reportFailure : Bool := true) (reportSuccess : Bool := false) (reportSlowdown : Bool := false) (maxSlowdown : Float := 1) : TacticAnalysis.Config := terminalReplacement tacticName "grind" tacticKind (fun _ _ => `(tactic| grind)) reportFailure reportSuccess reportSlowdown maxSlowdown
def
Tactic
[ "Mathlib.Tactic.TacticAnalysis", "Mathlib.Tactic.ExtractGoal", "Mathlib.Tactic.MinImports", "Lean.Elab.Tactic.Meta", "Lean.Elab.Command" ]
Mathlib/Tactic/TacticAnalysis/Declarations.lean
grindReplacementWith
Define a pass that tries replacing a specific tactic with `grind`. `tacticName` is a human-readable name for the tactic, for example "linarith". This can be used to group messages together, so that `ring`, `ring_nf`, `ring1`, ... all produce the same message. `tacticKind` is the `SyntaxNodeKind` for the tactic's main parser, for example `Mathlib.Tactic.linarith`.
@[tacticAnalysis linter.tacticAnalysis.regressions.linarithToGrind, inherit_doc linter.tacticAnalysis.regressions.linarithToGrind] linarithToGrindRegressions := grindReplacementWith "linarith" `Mathlib.Tactic.linarith
def
Tactic
[ "Mathlib.Tactic.TacticAnalysis", "Mathlib.Tactic.ExtractGoal", "Mathlib.Tactic.MinImports", "Lean.Elab.Tactic.Meta", "Lean.Elab.Command" ]
Mathlib/Tactic/TacticAnalysis/Declarations.lean
linarithToGrindRegressions
null
@[tacticAnalysis linter.tacticAnalysis.regressions.ringToGrind, inherit_doc linter.tacticAnalysis.regressions.ringToGrind] ringToGrindRegressions := grindReplacementWith "ring" `Mathlib.Tactic.RingNF.ring
def
Tactic
[ "Mathlib.Tactic.TacticAnalysis", "Mathlib.Tactic.ExtractGoal", "Mathlib.Tactic.MinImports", "Lean.Elab.Tactic.Meta", "Lean.Elab.Command" ]
Mathlib/Tactic/TacticAnalysis/Declarations.lean
ringToGrindRegressions
null
@[tacticAnalysis linter.tacticAnalysis.regressions.omegaToCutsat, inherit_doc linter.tacticAnalysis.regressions.omegaToCutsat] omegaToCutsatRegressions := terminalReplacement "omega" "cutsat" ``Lean.Parser.Tactic.omega (fun _ _ => `(tactic| cutsat)) (reportSuccess := false) (reportFailure := true)
def
Tactic
[ "Mathlib.Tactic.TacticAnalysis", "Mathlib.Tactic.ExtractGoal", "Mathlib.Tactic.MinImports", "Lean.Elab.Tactic.Meta", "Lean.Elab.Command" ]
Mathlib/Tactic/TacticAnalysis/Declarations.lean
omegaToCutsatRegressions
null
@[tacticAnalysis linter.tacticAnalysis.omegaToCutsat, inherit_doc linter.tacticAnalysis.omegaToCutsat] omegaToCutsat := terminalReplacement "omega" "cutsat" ``Lean.Parser.Tactic.omega (fun _ _ => `(tactic| cutsat)) (reportSuccess := true) (reportFailure := false)
def
Tactic
[ "Mathlib.Tactic.TacticAnalysis", "Mathlib.Tactic.ExtractGoal", "Mathlib.Tactic.MinImports", "Lean.Elab.Tactic.Meta", "Lean.Elab.Command" ]
Mathlib/Tactic/TacticAnalysis/Declarations.lean
omegaToCutsat
null
@[tacticAnalysis linter.tacticAnalysis.rwMerge, inherit_doc linter.tacticAnalysis.rwMerge] rwMerge : TacticAnalysis.Config := .ofComplex { out := (List MVarId × Array Syntax) ctx := (Array (Array Syntax)) trigger ctx stx := match stx with | `(tactic| rw [$args,*]) => .continue ((ctx.getD #[]).push args) | _ => if let some args := ctx then if args.size > 1 then .accept args else .skip else .skip test ctx goal := withOptions (fun opts => opts.set `grind.warning false) do let ctxT : Array (TSyntax `Lean.Parser.Tactic.rwRule) := ctx.flatten.map (⟨·⟩) let tac ← `(tactic| rw [$ctxT,*]) try let (goals, _) ← Lean.Elab.runTactic goal tac return (goals, ctxT.map (↑·)) catch _e => -- rw throws an error if it fails to pattern-match. return ([goal], ctxT.map (↑·)) tell _stx _old _oldHeartbeats new _newHeartbeats := pure <| if new.1.isEmpty then m!"Try this: rw {new.2}" else none }
def
Tactic
[ "Mathlib.Tactic.TacticAnalysis", "Mathlib.Tactic.ExtractGoal", "Mathlib.Tactic.MinImports", "Lean.Elab.Tactic.Meta", "Lean.Elab.Command" ]
Mathlib/Tactic/TacticAnalysis/Declarations.lean
rwMerge
null
@[tacticAnalysis linter.tacticAnalysis.mergeWithGrind, inherit_doc linter.tacticAnalysis.mergeWithGrind] mergeWithGrind : TacticAnalysis.Config where run seq := do if let #[(preCtx, preI), (_postCtx, postI)] := seq[0:2].array then if postI.stx.getKind == ``Lean.Parser.Tactic.grind then if let [goal] := preI.goalsBefore then let goals ← try preCtx.runTacticCode preI goal postI.stx catch _e => pure [goal] if goals.isEmpty then logWarningAt preI.stx m!"'{preI.stx}; grind' can be replaced with 'grind'"
def
Tactic
[ "Mathlib.Tactic.TacticAnalysis", "Mathlib.Tactic.ExtractGoal", "Mathlib.Tactic.MinImports", "Lean.Elab.Tactic.Meta", "Lean.Elab.Command" ]
Mathlib/Tactic/TacticAnalysis/Declarations.lean
mergeWithGrind
null
@[tacticAnalysis linter.tacticAnalysis.terminalToGrind, inherit_doc linter.tacticAnalysis.terminalToGrind] terminalToGrind : TacticAnalysis.Config where run seq := do let threshold := 3 let mut replaced : List (TSyntax `tactic) := [] let mut success := false let mut oldHeartbeats := 0 let mut newHeartbeats := 0 for (ctx, i) in seq.reverse do if replaced.length >= threshold - 1 && i.stx.getKind != ``Lean.Parser.Tactic.grind then if let [goal] := i.goalsBefore then let suffix := ⟨i.stx⟩ :: replaced let seq ← `(tactic| $suffix.toArray;*) let (oldGoals, heartbeats) ← withHeartbeats <| try ctx.runTacticCode i goal seq catch _e => pure [goal] if !oldGoals.isEmpty then logWarningAt i.stx m!"Original tactics failed to solve the goal: {seq}" oldHeartbeats := heartbeats let tac ← `(tactic| grind) let (newGoals, heartbeats) ← withHeartbeats <| try ctx.runTacticCode i goal tac catch _e => pure [goal] newHeartbeats := heartbeats if newGoals.isEmpty then success := true else break else break replaced := ⟨i.stx⟩ :: replaced if h : replaced.length >= threshold ∧ success then let stx := replaced[0] let seq ← `(tactic| $replaced.toArray;*) logWarningAt stx m!"replace the proof with 'grind': {seq}" if oldHeartbeats * 2 < newHeartbeats then logWarningAt stx m!"'grind' is slower than the original: {oldHeartbeats} -> {newHeartbeats}"
def
Tactic
[ "Mathlib.Tactic.TacticAnalysis", "Mathlib.Tactic.ExtractGoal", "Mathlib.Tactic.MinImports", "Lean.Elab.Tactic.Meta", "Lean.Elab.Command" ]
Mathlib/Tactic/TacticAnalysis/Declarations.lean
terminalToGrind
null
@[tacticAnalysis linter.tacticAnalysis.introMerge, inherit_doc linter.tacticAnalysis.introMerge] introMerge : TacticAnalysis.Config := .ofComplex { out := Option (TSyntax `tactic) ctx := Array (Array Term) trigger ctx stx := match stx with | `(tactic| intro%$x $args*) => .continue ((ctx.getD #[]).push <| if args.size = 0 then #[⟨mkHole x⟩] else args) | _ => if let some args := ctx then if args.size > 1 then .accept args else .skip else .skip test ctx goal := do let ctxT := ctx.flatten let tac ← `(tactic| intro $ctxT*) try let _ ← Lean.Elab.runTactic goal tac return some tac catch _e => -- if for whatever reason we can't run `intro` here. return none tell _stx _old _oldHeartbeats new _newHeartbeats := pure <| if let some tac := new then m!"Try this: {tac}" else none}
def
Tactic
[ "Mathlib.Tactic.TacticAnalysis", "Mathlib.Tactic.ExtractGoal", "Mathlib.Tactic.MinImports", "Lean.Elab.Tactic.Meta", "Lean.Elab.Command" ]
Mathlib/Tactic/TacticAnalysis/Declarations.lean
introMerge
null
@[to_additive /-- Addition is commutative -/] mul_comm' {α} [CommSemigroup α] (x y : α) : x * y = y * x := CommSemigroup.mul_comm ``` The transport tries to do the right thing in most cases using several heuristics described below. However, in some cases it fails, and requires manual intervention. Use the `to_additive existing` syntax to use an existing additive declaration, instead of automatically generating it. Use the `(reorder := ...)` syntax to reorder the arguments in the generated additive declaration. This is specified using cycle notation. For example `(reorder := 1 2, 5 6)` swaps the first two arguments with each other and the fifth and the sixth argument and `(reorder := 3 4 5)` will move the fifth argument before the third argument. This is mostly useful to translate declarations using `Pow` to those using `SMul`. Use the `(attr := ...)` syntax to apply attributes to both the multiplicative and the additive version: ``` @[to_additive (attr := simp)] lemma mul_one' {G : Type*} [Group G] (x : G) : x * 1 = x := mul_one x ``` For `simps` this also ensures that some generated lemmas are added to the additive dictionary. `@[to_additive (attr := to_additive)]` is a special case, where the `to_additive` attribute is added to the generated lemma only, to additivize it again. This is useful for lemmas about `Pow` to generate both lemmas about `SMul` and `VAdd`. Example: ``` @[to_additive (attr := to_additive VAdd_lemma, simp) SMul_lemma]
theorem
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
mul_comm'
An attribute that tells `@[to_additive]` that certain arguments of this definition are not involved when using `@[to_additive]`. This helps the heuristic of `@[to_additive]` by also transforming definitions if `ℕ` or another fixed type occurs as one of these arguments. -/ syntax (name := to_additive_ignore_args) "to_additive_ignore_args" (ppSpace num)* : attr /-- This attribute is deprecated. Use `to_additive (relevant_arg := ...)` instead. -/ syntax (name := to_additive_relevant_arg) "to_additive_relevant_arg " num : attr /-- An attribute that stores all the declarations that deal with numeric literals on variable types. Numeral literals occur in expressions without type information, so in order to decide whether `1` needs to be changed to `0`, the context around the numeral is relevant. Most numerals will be in an `OfNat.ofNat` application, though tactics can add numeral literals inside arbitrary functions. By default we assume that we do not change numerals, unless it is in a function application with the `to_additive_change_numeral` attribute. `@[to_additive_change_numeral n₁ ...]` should be added to all functions that take one or more numerals as argument that should be changed if `additiveTest` succeeds on the first argument, i.e. when the numeral is only translated if the first argument is a variable (or consists of variables). The arguments `n₁ ...` are the positions of the numeral arguments (starting counting from 1). -/ syntax (name := to_additive_change_numeral) "to_additive_change_numeral" (ppSpace num)* : attr /-- The `to_additive_dont_translate` attribute, used to specify types that should be translated by `to_additive`, but its operations should remain multiplicative. Usage notes: * Apply this together with the `to_additive` attribute. * The name generation of `to_additive` is not aware that the operations on this type should not be translated, so you generally have to specify the name itself, if the name should remain multiplicative. -/ syntax (name := to_additive_dont_translate) "to_additive_dont_translate" : attr /-- An `attr := ...` option for `to_additive`. -/ syntax toAdditiveAttrOption := &"attr" " := " Parser.Term.attrInstance,* /-- `reorder := ...` reorders the arguments/hypotheses in the generated declaration. It uses cycle notation. For example `(reorder := 1 2, 5 6)` swaps the first two arguments with each other and the fifth and the sixth argument and `(reorder := 3 4 5)` will move the fifth argument before the third argument. This is used in `to_dual` to swap the arguments in `≤`, `<` and `⟶`. It is also used in `to_additive` to translate from `^` to `•`. -/ syntax toAdditiveReorderOption := &"reorder" " := " (num+),+ /-- the `relevant_arg := ...` option tells which argument is a type where this declaration uses the multiplicative structure. This is inferred automatically using the function `findMultiplicativeArg`, but it can also be overwritten using this syntax. If there are multiple arguments with a multiplicative structure, we typically tag the first one. If this argument contains a fixed type, this declaration will not be additivized. See the Heuristics section of the `to_additive` doc-string for more details. If a declaration is not tagged, it is presumed that the first argument is relevant. To indicate that there is no relevant argument, set it to a number that is out of bounds, i.e. larger than the number of arguments, e.g. `(relevant_arg := 100)`. Implementation note: we only allow exactly 1 relevant argument, even though some declarations (like `Prod.instGroup`) have multiple arguments with a multiplicative structure on it. The reason is that whether we additivize a declaration is an all-or-nothing decision, and we will not be able to additivize declarations that (e.g.) talk about multiplication on `ℕ × α` anyway. -/ syntax toAdditiveRelevantOption := &"relevant_arg" " := " num /-- `dont_translate := ...` takes a list of type variables (separated by spaces) that should not be considered for translation. For example in ``` lemma foo {α β : Type} [Group α] [Group β] (a : α) (b : β) : a * a⁻¹ = 1 ↔ b * b⁻¹ = 1 ``` we can choose to only additivize `α` by writing `to_additive (dont_translate := β)`. -/ syntax toAdditiveDontTranslateOption := &"dont_translate" " := " ident+ /-- Options to `to_additive`. -/ syntax toAdditiveOption := "(" toAdditiveAttrOption <|> toAdditiveReorderOption <|> toAdditiveRelevantOption <|> toAdditiveDontTranslateOption ")" /-- An `existing` or `self` name hint for `to_additive`. -/ syntax toAdditiveNameHint := (ppSpace (&"existing" <|> &"self"))? /-- Remaining arguments of `to_additive`. -/ syntax toAdditiveRest := toAdditiveNameHint (ppSpace toAdditiveOption)* (ppSpace ident)? (ppSpace (str <|> docComment))? /-- The attribute `to_additive` can be used to automatically transport theorems and definitions (but not inductive types and structures) from a multiplicative theory to an additive theory. To use this attribute, just write: ``` @[to_additive] theorem mul_comm' {α} [CommSemigroup α] (x y : α) : x * y = y * x := mul_comm x y ``` This code will generate a theorem named `add_comm'`. It is also possible to manually specify the name of the new declaration: ``` @[to_additive add_foo] theorem foo := sorry ``` An existing documentation string will _not_ be automatically used, so if the theorem or definition has a doc string, a doc string for the additive version should be passed explicitly to `to_additive`. ``` /-- Multiplication is commutative
Pow_lemma ... := ``` In the above example, the `simp` is added to all 3 lemmas. All other options to `to_additive` (like the generated name or `(reorder := ...)`) are not passed down, and can be given manually to each individual `to_additive` call.
lemma
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
Pow_lemma
null
findTranslation? (env : Environment) : Name → Option Name := (ToAdditive.translations.getState env).find?
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
findTranslation
Linter, mostly used by `@[to_additive]`, that checks that the source declaration doesn't have certain attributes -/ register_option linter.existingAttributeWarning : Bool := { defValue := true descr := "Linter, mostly used by `@[to_additive]`, that checks that the source declaration \ doesn't have certain attributes" } /-- Linter to check that the `to_additive` attribute is not given manually -/ register_option linter.toAdditiveGenerateName : Bool := { defValue := true descr := "Linter used by `@[to_additive]` that checks if `@[to_additive]` automatically \ generates the user-given name" } /-- Linter to check whether the user correctly specified that the additive declaration already exists -/ register_option linter.toAdditiveExisting : Bool := { defValue := true descr := "Linter used by `@[to_additive]` that checks whether the user correctly specified that the additive declaration already exists" } /-- Linter to check that the `relevant_arg` attribute is not given manually -/ register_option linter.toAdditiveRelevantArg : Bool := { defValue := true descr := "Linter to check that the `relevant_arg` attribute is not given manually." } @[inherit_doc to_additive_ignore_args] initialize ignoreArgsAttr : NameMapExtension (List Nat) ← registerNameMapAttribute { name := `to_additive_ignore_args descr := "Auxiliary attribute for `to_additive` stating that certain arguments are not additivized." add := fun _ stx ↦ do let ids ← match stx with | `(attr| to_additive_ignore_args $[$ids:num]*) => pure <| ids.map (·.1.isNatLit?.get!) | _ => throwUnsupportedSyntax return ids.toList } /-- An extension that stores all the declarations that need their arguments reordered when applying `@[to_additive]`. It is applied using the `to_additive (reorder := ...)` syntax. -/ initialize reorderAttr : NameMapExtension (List (List Nat)) ← registerNameMapExtension _ @[inherit_doc to_additive_relevant_arg] initialize relevantArgAttr : NameMapExtension Nat ← registerNameMapAttribute { name := `to_additive_relevant_arg descr := "Auxiliary attribute for `to_additive` stating \ which arguments are the types with a multiplicative structure." add := fun | _, stx@`(attr| to_additive_relevant_arg $id) => do Linter.logLintIf linter.toAdditiveRelevantArg stx m!"This attribute is deprecated. Use `@[to_additive (relevant_arg := ...)]` instead." pure <| id.getNat.pred | _, _ => throwUnsupportedSyntax } @[inherit_doc to_additive_dont_translate] initialize dontTranslateAttr : NameMapExtension Unit ← registerNameMapAttribute { name := `to_additive_dont_translate descr := "Auxiliary attribute for `to_additive` stating \ that the operations on this type should not be translated." add := fun | _, `(attr| to_additive_dont_translate) => return | _, _ => throwUnsupportedSyntax } @[inherit_doc to_additive_change_numeral] initialize changeNumeralAttr : NameMapExtension (List Nat) ← registerNameMapAttribute { name := `to_additive_change_numeral descr := "Auxiliary attribute for `to_additive` that stores functions that have numerals as argument." add := fun | _, `(attr| to_additive_change_numeral $[$arg]*) => pure <| arg.map (·.1.isNatLit?.get!.pred) |>.toList | _, _ => throwUnsupportedSyntax } /-- Maps multiplicative names to their additive counterparts. -/ initialize translations : NameMapExtension Name ← registerNameMapExtension _ /-- Get the multiplicative → additive translation for the given name.
findPrefixTranslation (env : Environment) (nm : Name) : Name := nm.mapPrefix (findTranslation? env)
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
findPrefixTranslation
Get the multiplicative → additive translation for the given name, falling back to translating a prefix of the name if the full name can't be translated. This allows translating automatically generated declarations such as `IsRegular.casesOn`.
insertTranslation (src tgt : Name) (failIfExists := true) : CoreM Unit := do if let some tgt' := findTranslation? (← getEnv) src then if failIfExists then throwError "The translation {src} ↦ {tgt'} already exists" else trace[to_additive] "The translation {src} ↦ {tgt'} already exists" return modifyEnv (ToAdditive.translations.addEntry · (src, tgt)) trace[to_additive] "Added translation {src} ↦ {tgt}"
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
insertTranslation
Add a (multiplicative → additive) name translation to the translations map.
ArgInfo where /-- The arguments that should be reordered by `to_additive`, using cycle notation. -/ reorder : List (List Nat) := [] /-- The argument used to determine whether this constant should be translated. -/ relevantArg : Nat := 0
structure
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
ArgInfo
`ArgInfo` stores information about how a constant should be translated.
insertTranslationAndInfo (src tgt : Name) (argInfo : ArgInfo) (failIfExists := true) : CoreM Unit := do insertTranslation src tgt failIfExists if argInfo.reorder != [] then trace[to_additive] "@[to_additive] will reorder the arguments of {tgt} by {argInfo.reorder}." reorderAttr.add src argInfo.reorder if argInfo.relevantArg != 0 then trace[to_additive_detail] "Setting relevant_arg for {src} to be {argInfo.relevantArg}." relevantArgAttr.add src argInfo.relevantArg
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
insertTranslationAndInfo
Add a name translation to the translations map and add the `argInfo` information to `src`.
Config : Type where /-- View the trace of the to_additive procedure. Equivalent to `set_option trace.to_additive true`. -/ trace : Bool := false /-- The name of the target (the additive declaration). -/ tgt : Name := Name.anonymous /-- An optional doc string. -/ doc : Option String := none /-- If `allowAutoName` is `false` (default) then `@[to_additive]` will check whether the given name can be auto-generated. -/ allowAutoName : Bool := false /-- The arguments that should be reordered by `to_additive`, using cycle notation. -/ reorder : List (List Nat) := [] /-- The argument used to determine whether this constant should be translated. -/ relevantArg? : Option Nat := none /-- The attributes which we want to give to both the multiplicative and additive versions. For `simps` this will also add generated lemmas to the translation dictionary. -/ attrs : Array Syntax := #[] /-- A list of type variables that should not be translated by `to_additive`. -/ dontTranslate : List Ident := [] /-- The `Syntax` element corresponding to the original multiplicative declaration (or the `to_additive` attribute if it is added later), which we need for adding definition ranges. -/ ref : Syntax /-- An optional flag stating that the additive declaration already exists. If this flag is wrong about whether the additive declaration exists, `to_additive` will raise a linter error. Note: the linter will never raise an error for inductive types and structures. -/ existing : Bool := false /-- An optional flag stating that the target of the translation is the target itself. This can be used to reorder arguments, such as in `attribute [to_dual self (reorder := 3 4)] LE.le`. It can also be used to give a hint to `additiveTest`, such as in `attribute [to_additive self] Unit`. If `self := true`, we should also have `existing := true`. -/ self : Bool := false deriving Repr attribute [nolint unusedArguments] instReprConfig.repr
structure
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
Config
`Config` is the type of the arguments that can be provided to `to_additive`.
etaExpandN (n : Nat) (e : Expr) : MetaM Expr := do forallBoundedTelescope (← inferType e) (some n) fun xs _ ↦ mkLambdaFVars xs (mkAppN e xs)
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
etaExpandN
Eta expands `e` at most `n` times.
expand (e : Expr) : MetaM Expr := do let env ← getEnv let reorderFn : Name → List (List ℕ) := fun nm ↦ (reorderAttr.find? env nm |>.getD []) let e₂ ← Lean.Meta.transform (input := e) (skipConstInApp := true) (post := fun e => return .done e) fun e ↦ e.withApp fun f args ↦ do match f with | .proj n i s => let some info := getStructureInfo? (← getEnv) n | return .continue -- e.g. if `n` is `Exists` let some projName := info.getProjFn? i | unreachable! if findTranslation? env projName |>.isNone then return .continue return .visit <| (← whnfD (← inferType s)).withApp fun sf sargs ↦ mkAppN (mkApp (mkAppN (.const projName sf.constLevels!) sargs) s) args | .const c _ => let reorder := reorderFn c if reorder.isEmpty then return .continue let needed_n := reorder.flatten.foldr Nat.max 0 + 1 if needed_n ≤ args.size then return .continue else let e' ← etaExpandN (needed_n - args.size) e trace[to_additive_detail] "expanded {e} to {e'}" return .continue e' | _ => return .continue if e != e₂ then trace[to_additive_detail] "expand:\nBefore: {e}\nAfter: {e₂}" return e₂
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
expand
`e.expand` eta-expands all expressions that have as head a constant `n` in `reorder`. They are expanded until they are applied to one more argument than the maximum in `reorder.find n`. It also expands all kernel projections that have as head a constant `n` in `reorder`.
unsafe additiveTestUnsafe (env : Environment) (e : Expr) (dontTranslate : Array FVarId) : Option (Name ⊕ FVarId) := let rec visit (e : Expr) (inApp := false) : OptionT (StateM (PtrSet Expr)) (Name ⊕ FVarId) := do if e.isConst then if (dontTranslateAttr.find? env e.constName).isNone && (inApp || (findTranslation? env e.constName).isSome) then failure else return .inl e.constName if (← get).contains e then failure modify fun s => s.insert e match e with | x@(.app e a) => visit e true <|> do guard !x.isConstantApplication if let some n := e.getAppFn.constName? then if let some l := ignoreArgsAttr.find? env n then if e.getAppNumArgs + 1 ∈ l then failure visit a | .lam _ _ t _ => visit t | .forallE _ _ t _ => visit t | .letE _ _ e body _ => visit e <|> visit body | .mdata _ b => visit b | .proj _ _ b => visit b | .fvar fvarId => if dontTranslate.contains fvarId then return .inr fvarId else failure | _ => failure Id.run <| (visit e).run' mkPtrSet
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
additiveTestUnsafe
Implementation function for `additiveTest`. Failure means that in that subexpression there is no constant that blocks `e` from being translated. We cache previous applications of the function, using an expression cache using ptr equality to avoid visiting the same subexpression many times. Note that we only need to cache the expressions without taking the value of `inApp` into account, since `inApp` only matters when the expression is a constant. However, for this reason we have to make sure that we never cache constant expressions, so that's why the `if`s in the implementation are in this order. Note that this function is still called many times by `applyReplacementFun` and we're not remembering the cache between these calls.
additiveTest (env : Environment) (e : Expr) (dontTranslate : Array FVarId := #[]) : Option (Name ⊕ FVarId) := unsafe additiveTestUnsafe env e dontTranslate
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
additiveTest
`additiveTest e` tests whether the expression `e` contains a constant `nm` that is not applied to any arguments, and such that `translations.find?[nm] = none`. This is used in `@[to_additive]` for deciding which subexpressions to transform: we only transform constants if `additiveTest` applied to their relevant argument returns `true`. This means we will replace expression applied to e.g. `α` or `α × β`, but not when applied to e.g. `ℕ` or `ℝ × α`. We ignore all arguments specified by the `ignore` `NameMap`.
_root_.List.swapFirstTwo {α : Type _} : List α → List α | [] => [] | [x] => [x] | x::y::l => y::x::l
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
_root_.List.swapFirstTwo
Swap the first two elements of a list
changeNumeral : Expr → Expr | .lit (.natVal 1) => mkRawNatLit 0 | e => e
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
changeNumeral
Change the numeral `nat_lit 1` to the numeral `nat_lit 0`. Leave all other expressions unchanged.
applyReplacementFun (e : Expr) (dontTranslate : Array FVarId := #[]) : MetaM Expr := do let e' := aux (← getEnv) (← getBoolOption `trace.to_additive_detail) (← expand e) e'.forEach fun | .const n .. => do if !(← hasConst (skipRealize := false) n) && isReservedName (← getEnv) n then executeReservedNameAction n | _ => pure () return e' where /-- Implementation of `applyReplacementFun`. -/ aux (env : Environment) (trace : Bool) : Expr → Expr := let reorderFn : Name → List (List ℕ) := fun nm ↦ (reorderAttr.find? env nm |>.getD []) let relevantArg : Name → ℕ := fun nm ↦ (relevantArgAttr.find? env nm).getD 0 Lean.Expr.replaceRec fun r e ↦ Id.run do if trace then dbg_trace s!"replacing at {e}" match e with | .const n₀ ls₀ => do let n₁ := findPrefixTranslation env n₀ let ls₁ : List Level := if 0 ∈ (reorderFn n₀).flatten then ls₀.swapFirstTwo else ls₀ if trace then if n₀ != n₁ then dbg_trace s!"changing {n₀} to {n₁}" if 0 ∈ (reorderFn n₀).flatten then dbg_trace s!"reordering the universe variables from {ls₀} to {ls₁}" return some <| .const n₁ ls₁ | .app g x => do let mut gf := g.getAppFn if gf.isBVar && x.isLit then if trace then dbg_trace s!"applyReplacementFun: Variables applied to numerals are not changed {g.app x}" return some <| g.app x let mut gAllArgs := e.getAppArgs let some nm := gf.constName? | return mkAppN (← r gf) (← gAllArgs.mapM r) /- Test if the head should not be replaced. -/ let relevantArgId := relevantArg nm if h : relevantArgId < gAllArgs.size then if let some fxd := additiveTest env gAllArgs[relevantArgId] dontTranslate then if trace then match fxd with | .inl fxd => dbg_trace s!"The application of {nm} contains the fixed type \ {fxd}, so it is not changed." | .inr _ => dbg_trace s!"The application of {nm} contains a fixed \ variable so it is not changed." else gf ← r gf /- Test if arguments should be reordered. -/ let reorder := reorderFn nm if !reorder.isEmpty then gAllArgs := gAllArgs.permute! reorder if trace then dbg_trace s!"reordering the arguments of {nm} using the cyclic permutations {reorder}" ...
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
applyReplacementFun
`applyReplacementFun e` replaces the expression `e` with its additive counterpart. It translates each identifier (inductive type, defined function etc) in an expression, unless * The identifier occurs in an application with first argument `arg`; and * `test arg` is false. However, if `f` is in the dictionary `relevant`, then the argument `relevant.find f` is tested, instead of the first argument. It will also reorder arguments of certain functions, using `reorderFn`: e.g. `g x₁ x₂ x₃ ... xₙ` becomes `g x₂ x₁ x₃ ... xₙ` if `reorderFn g = some [1]`.
renameBinderNames (src : Expr) : Expr := src.mapForallBinderNames fun | .str p s => .str p (guessName s) | n => n
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
renameBinderNames
Rename binder names in pi type.
reorderForall (reorder : List (List Nat)) (src : Expr) : MetaM Expr := do if let some maxReorder := reorder.flatten.max? then forallBoundedTelescope src (some (maxReorder + 1)) fun xs e => do if xs.size = maxReorder + 1 then mkForallFVars (xs.permute! reorder) e else throwError "the permutation\n{reorder}\nprovided by the `(reorder := ...)` option is \ out of bounds, the type{indentExpr src}\nhas only {xs.size} arguments" else return src
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
reorderForall
Reorder pi-binders. See doc of `reorderAttr` for the interpretation of the argument
reorderLambda (reorder : List (List Nat)) (src : Expr) : MetaM Expr := do if let some maxReorder := reorder.flatten.max? then let maxReorder := maxReorder + 1 lambdaBoundedTelescope src maxReorder fun xs e => do if xs.size = maxReorder then mkLambdaFVars (xs.permute! reorder) e else forallBoundedTelescope (← inferType e) (maxReorder - xs.size) fun ys _ => do mkLambdaFVars ((xs ++ ys).permute! reorder) (mkAppN e ys) else return src
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
reorderLambda
Reorder lambda-binders. See doc of `reorderAttr` for the interpretation of the argument
applyReplacementForall (dontTranslate : List Nat) (e : Expr) : MetaM Expr := do if let some maxDont := dontTranslate.max? then forallBoundedTelescope e (some (maxDont + 1)) fun xs e => do let xs := xs.map (·.fvarId!) let dontTranslate := dontTranslate.filterMap (xs[·]?) |>.toArray let mut e ← applyReplacementFun e dontTranslate for x in xs.reverse do let decl ← x.getDecl let xType ← applyReplacementFun decl.type dontTranslate e := .forallE decl.userName xType (e.abstract #[.fvar x]) decl.binderInfo return e else applyReplacementFun e #[]
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
applyReplacementForall
Run `applyReplacementFun` on an expression `∀ x₁ .. xₙ, e`, making sure not to translate type-classes on `xᵢ` if `i` is in `dontTranslate`.
applyReplacementLambda (dontTranslate : List Nat) (e : Expr) : MetaM Expr := do if let some maxDont := dontTranslate.max? then lambdaBoundedTelescope e (maxDont + 1) fun xs e => do let xs := xs.map (·.fvarId!) let dontTranslate := dontTranslate.filterMap (xs[·]?) |>.toArray let mut e ← applyReplacementFun e dontTranslate for x in xs.reverse do let decl ← x.getDecl let xType ← applyReplacementFun decl.type dontTranslate e := .lam decl.userName xType (e.abstract #[.fvar x]) decl.binderInfo return e else applyReplacementFun e #[]
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
applyReplacementLambda
Run `applyReplacementFun` on an expression `fun x₁ .. xₙ ↦ e`, making sure not to translate type-classes on `xᵢ` if `i` is in `dontTranslate`.
declUnfoldAuxLemmas (decl : ConstantInfo) : MetaM ConstantInfo := do let mut decl := decl decl := decl.updateType <| ← unfoldAuxLemmas decl.type if let some v := decl.value? then trace[to_additive] "value before unfold:{indentExpr v}" decl := decl.updateValue <| ← unfoldAuxLemmas v trace[to_additive] "value after unfold:{indentExpr decl.value!}" else if let .opaqueInfo info := decl then -- not covered by `value?` decl := .opaqueInfo { info with value := ← unfoldAuxLemmas info.value } return decl
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
declUnfoldAuxLemmas
Unfold auxlemmas in the type and value.
getDontTranslates (given : List Ident) (type : Expr) : MetaM (List Nat) := do forallTelescope type fun xs _ => do given.mapM fun id => withRef id.raw <| do let fvarId ← getFVarFromUserName id.getId return (xs.idxOf? fvarId).get!
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
getDontTranslates
Given a list of variable local identifiers that shouldn't be translated, determine the arguments that shouldn't be translated. TODO: Currently, this function doesn't deduce any `dont_translate` types from `type`. In the future we would like that the presence of `MonoidAlgebra k G` will automatically flag `k` as a type to not be translated.
updateDecl (tgt : Name) (srcDecl : ConstantInfo) (reorder : List (List Nat)) (dont : List Ident) : MetaM ConstantInfo := do let mut decl := srcDecl.updateName tgt if 0 ∈ reorder.flatten then decl := decl.updateLevelParams decl.levelParams.swapFirstTwo let dont ← getDontTranslates dont srcDecl.type decl := decl.updateType <| ← reorderForall reorder <| ← applyReplacementForall dont <| renameBinderNames decl.type if let some v := decl.value? then decl := decl.updateValue <| ← reorderLambda reorder <| ← applyReplacementLambda dont v else if let .opaqueInfo info := decl then -- not covered by `value?` decl := .opaqueInfo { info with value := ← reorderLambda reorder <| ← applyReplacementLambda dont info.value } return decl
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
updateDecl
Run applyReplacementFun on the given `srcDecl` to make a new declaration with name `tgt`
declAbstractNestedProofs (decl : ConstantInfo) : MetaM ConstantInfo := do if decl matches .defnInfo _ then return decl.updateValue <| ← withDeclNameForAuxNaming decl.name do Meta.abstractNestedProofs decl.value! else return decl
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
declAbstractNestedProofs
Abstracts the nested proofs in the value of `decl` if it is a def.
findTargetName (env : Environment) (src pre tgt_pre : Name) : CoreM Name := /- This covers auxiliary declarations like `match_i` and `proof_i`. -/ if let some post := pre.isPrefixOf? src then return tgt_pre ++ post /- This covers equation lemmas (for other declarations). -/ else if let some post := privateToUserName? src then match findTranslation? env post.getPrefix with | none => return src | some addName => return src.updatePrefix <| mkPrivateName env addName else if src.hasMacroScopes then mkFreshUserName src.eraseMacroScopes else throwError "internal @[to_additive] error."
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
findTargetName
Find the target name of `pre` and all created auxiliary declarations.
findAuxDecls (e : Expr) (pre : Name) : NameSet := e.foldConsts ∅ fun n l ↦ if n.getPrefix == pre || isPrivateName n || n.hasMacroScopes then l.insert n else l
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
findAuxDecls
Returns a `NameSet` of all auxiliary constants in `e` that might have been generated when adding `pre` to the environment. Examples include `pre.match_5` and `_private.Mathlib.MyFile.someOtherNamespace.someOtherDeclaration._eq_2`. The last two examples may or may not have been generated by this declaration. The last example may or may not be the equation lemma of a declaration with the `@[to_additive]` attribute. We will only translate it if it has the `@[to_additive]` attribute. Note that this function would return `proof_nnn` aux lemmas if we hadn't unfolded them in `declUnfoldAuxLemmas`.
partial transformDeclAux (cfg : Config) (pre tgt_pre : Name) : Name → CoreM Unit := fun src ↦ do let env ← getEnv trace[to_additive_detail] "visiting {src}" if (findTranslation? env src).isSome && src != pre then return if src != pre && !src.isInternalDetail then throwError "The declaration {pre} depends on the declaration {src} which is in the namespace \ {pre}, but does not have the `@[to_additive]` attribute. This is not supported.\n\ Workaround: move {src} to a different namespace." let tgt ← findTargetName env src pre tgt_pre if env.contains tgt then if tgt == src then trace[to_additive_detail] "Auxiliary declaration {src} will be translated to itself." else trace[to_additive_detail] "Already visited {tgt} as translation of {src}." return let srcDecl ← getConstInfo src let srcDecl ← MetaM.run' do declUnfoldAuxLemmas srcDecl for n in findAuxDecls srcDecl.type pre do transformDeclAux cfg pre tgt_pre n if let some value := srcDecl.value? then for n in findAuxDecls value pre do transformDeclAux cfg pre tgt_pre n if let .opaqueInfo {value, ..} := srcDecl then for n in findAuxDecls value pre do transformDeclAux cfg pre tgt_pre n if !pre.isPrefixOf src then insertTranslation src tgt let trgDecl : ConstantInfo ← MetaM.run' <| if src == pre then updateDecl tgt srcDecl cfg.reorder cfg.dontTranslate else updateDecl tgt srcDecl [] [] let value ← match trgDecl with | .thmInfo { value, .. } | .defnInfo { value, .. } | .opaqueInfo { value, .. } => pure value | _ => throwError "Expected {tgt} to have a value." trace[to_additive] "generating\n{tgt} : {trgDecl.type} :=\n {value}" try MetaM.run' <| check value catch | Exception.error _ msg => throwError "@[to_additive] failed. \ The translated value is not type correct. For help, see the docstring \ of `to_additive.attr`, section `Troubleshooting`. \ Failed to add declaration\n{tgt}:\n{msg}" | _ => panic! "unreachable" let trgDecl ← MetaM.run' <| declAbstractNestedProofs trgDecl /- If `src` is explicitly marked as `noncomputable`, then add the new decl as a declaration but do not compile it, and mark is as noncomputable. Otherwise, only log errors in compiling if `src` has executable code. Note that `noncomputable section` does not explicitly mark noncomputable definitions as ...
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
transformDeclAux
Transform the declaration `src` and all declarations `pre._proof_i` occurring in `src` using the transforms dictionary. `replace_all`, `trace`, `ignore` and `reorder` are configuration options. `pre` is the declaration that got the `@[to_additive]` attribute and `tgt_pre` is the target of this declaration.
copyInstanceAttribute (src tgt : Name) : CoreM Unit := do if let some prio ← getInstancePriority? src then let attr_kind := (← getInstanceAttrKind? src).getD .global trace[to_additive_detail] "Making {tgt} an instance with priority {prio}." addInstance tgt attr_kind prio |>.run'
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
copyInstanceAttribute
Copy the instance attribute in a `to_additive` [todo] it seems not to work when the `to_additive` is added as an attribute later.
warnAttrCore (stx : Syntax) (f : Environment → Name → Bool) (thisAttr attrName src tgt : Name) : CoreM Unit := do if f (← getEnv) src then Linter.logLintIf linter.existingAttributeWarning stx <| m!"The source declaration {src} was given attribute {attrName} before calling @[{thisAttr}]. \ The preferred method is to use `@[{thisAttr} (attr := {attrName})]` to apply the \ attribute to both {src} and the target declaration {tgt}." ++ if thisAttr == `to_additive then m!"\nSpecial case: If this declaration was generated by @[to_additive] \ itself, you can use @[to_additive (attr := to_additive, {attrName})] on the original \ declaration." else ""
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
warnAttrCore
Warn the user when the multiplicative declaration has an attribute.
warnAttr {α β : Type} [Inhabited β] (stx : Syntax) (attr : SimpleScopedEnvExtension α β) (f : β → Name → Bool) (thisAttr attrName src tgt : Name) : CoreM Unit := warnAttrCore stx (f <| attr.getState ·) thisAttr attrName src tgt
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
warnAttr
Warn the user when the multiplicative declaration has a simple scoped attribute.
warnParametricAttr {β : Type} [Inhabited β] (stx : Syntax) (attr : ParametricAttribute β) (thisAttr attrName src tgt : Name) : CoreM Unit := warnAttrCore stx (attr.getParam? · · |>.isSome) thisAttr attrName src tgt
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
warnParametricAttr
Warn the user when the multiplicative declaration has a parametric attribute.
additivizeLemmas {m : Type → Type} [Monad m] [MonadError m] [MonadLiftT CoreM m] (names : Array Name) (argInfo : ArgInfo) (desc : String) (t : Name → m (Array Name)) : m Unit := do let auxLemmas ← names.mapM t let nLemmas := auxLemmas[0]!.size for (nm, lemmas) in names.zip auxLemmas do unless lemmas.size == nLemmas do throwError "{names[0]!} and {nm} do not generate the same number of {desc}." for (srcLemmas, tgtLemmas) in auxLemmas.zip <| auxLemmas.eraseIdx! 0 do for (srcLemma, tgtLemma) in srcLemmas.zip tgtLemmas do insertTranslationAndInfo srcLemma tgtLemma argInfo
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
additivizeLemmas
`additivizeLemmas names argInfo desc t` runs `t` on all elements of `names` and adds translations between the generated lemmas (the output of `t`). `names` must be non-empty.
findMultiplicativeArg (nm : Name) : MetaM Nat := do forallTelescopeReducing (← getConstInfo nm).type fun xs ty ↦ do let env ← getEnv let multArg? (tgt : Expr) : Option Nat := do let c ← tgt.getAppFn.constName? guard (findTranslation? env c).isSome let relevantArg := (relevantArgAttr.find? env c).getD 0 let arg ← tgt.getArg? relevantArg xs.findIdx? (arg.containsFVar ·.fvarId!) let arg ← OptionT.run <| xs.firstM fun x ↦ OptionT.mk do forallTelescope (← inferType x) fun _ys tgt ↦ return multArg? tgt let arg := arg <|> multArg? ty trace[to_additive_detail] "findMultiplicativeArg: {arg}" return arg.getD 0
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
findMultiplicativeArg
Find the argument of `nm` that appears in the first multiplicative (type-class) argument. Returns 1 if there are no types with a multiplicative class as arguments. E.g. `Prod.instGroup` returns 1, and `Pi.instOne` returns 2. Note: we only consider the relevant argument (`(relevant_arg := ...)`) of each type-class. E.g. `[Pow A N]` is a multiplicative type-class on `A`, not on `N`.
targetName (cfg : Config) (src : Name) : CoreM Name := do if cfg.self then if cfg.tgt != .anonymous then throwError m!"`to_additive self` ignores the provided name {cfg.tgt}" return src let .str pre s := src | throwError "to_additive: can't transport {src}" trace[to_additive_detail] "The name {s} splits as {s.splitCase}" let tgt_auto := guessName s let depth := cfg.tgt.getNumParts let pre := findPrefixTranslation (← getEnv) pre let (pre1, pre2) := pre.splitAt (depth - 1) let res := if cfg.tgt == .anonymous then pre.str tgt_auto else pre1 ++ cfg.tgt if res == src then throwError "to_additive: the generated additivised name equals the original name '{src}', \ meaning that no part of the name was additivised.\n\ If this is intentional, use the `@[to_additive self]` syntax.\n\ Otherwise, check that your declaration name is correct \ (if your declaration is an instance, try naming it)\n\ or provide an additivised name using the `@[to_additive my_add_name]` syntax." if cfg.tgt == pre2.str tgt_auto && !cfg.allowAutoName then Linter.logLintIf linter.toAdditiveGenerateName cfg.ref m!"\ to_additive correctly autogenerated target name for {src}.\n\ You may remove the explicit argument {cfg.tgt}." if cfg.tgt != .anonymous then trace[to_additive_detail] "The automatically generated name would be {pre.str tgt_auto}" return res
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
targetName
Return the provided target name or autogenerate one if one was not provided.
proceedFieldsAux (src tgt : Name) (argInfo : ArgInfo) (f : Name → Array Name) : CoreM Unit := do let srcFields := f src let tgtFields := f tgt if srcFields.size != tgtFields.size then throwError "Failed to map fields of {src}, {tgt} with {srcFields} ↦ {tgtFields}.\n \ Lengths do not match." for srcField in srcFields, tgtField in tgtFields do insertTranslationAndInfo srcField tgtField argInfo
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
proceedFieldsAux
if `f src = #[a_1, ..., a_n]` and `f tgt = #[b_1, ... b_n]` then `proceedFieldsAux src tgt f` will insert translations from `a_i` to `b_i`.
proceedFields (src tgt : Name) (argInfo : ArgInfo) : CoreM Unit := do let env ← getEnv let aux := proceedFieldsAux src tgt argInfo aux fun declName ↦ if isStructure env declName then let info := getStructureInfo env declName Array.ofFn (n := info.fieldNames.size) (info.getProjFn? · |>.get!) else #[] aux fun declName ↦ if isStructure env declName then getStructureInfo env declName |>.parentInfo |>.filterMap fun c ↦ if !c.subobject then c.projFn else none else #[] aux fun declName ↦ match env.find? declName with | some (ConstantInfo.inductInfo { ctors, .. }) => ctors.toArray | _ => #[]
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
proceedFields
Add the structure fields of `src` to the translations dictionary so that future uses of `to_additive` will map them to the corresponding `tgt` fields.
elabToAdditive : Syntax → CoreM Config | `(attr| to_additive%$tk $[?%$trace]? $existing? $[$opts:toAdditiveOption]* $[$tgt]? $[$doc]?) => do let mut attrs := #[] let mut reorder := [] let mut relevantArg? := none let mut dontTranslate := [] for opt in opts do match opt with | `(toAdditiveOption| (attr := $[$stxs],*)) => attrs := attrs ++ stxs | `(toAdditiveOption| (reorder := $[$[$reorders:num]*],*)) => for cycle in reorders do if h : cycle.size = 1 then throwErrorAt cycle[0] "\ invalid cycle `{cycle[0]}`, a cycle must have at least 2 elements.\n\ `(reorder := ...)` uses cycle notation to specify a permutation.\n\ For example `(reorder := 1 2, 5 6)` swaps the first two arguments with each other \ and the fifth and the sixth argument and `(reorder := 3 4 5)` will move \ the fifth argument before the third argument." let cycle ← cycle.toList.mapM fun n => match n.getNat with | 0 => throwErrorAt n "invalid position `{n}`, positions are counted starting from 1." | n+1 => pure n reorder := cycle :: reorder | `(toAdditiveOption| (relevant_arg := $n)) => if let some arg := relevantArg? then throwErrorAt opt "cannot specify `relevant_arg` multiple times" else relevantArg? := n.getNat.pred | `(toAdditiveOption| (dont_translate := $[$types:ident]*)) => dontTranslate := dontTranslate ++ types.toList | _ => throwUnsupportedSyntax let (existing, self) := match existing? with | `(toAdditiveNameHint| existing) => (true, false) | `(toAdditiveNameHint| self) => (true, true) | _ => (false, false) if self && !attrs.isEmpty then throwError "invalid `(attr := ...)` after `self`, \ as there is only one declaration for the attributes.\n\ Instead, you can write the attributes in the usual way." trace[to_additive_detail] "attributes: {attrs}; reorder arguments: {reorder}" let doc ← doc.mapM fun | `(str|$doc:str) => open Linter in do if getLinterValue linter.deprecated (← getLinterOptions) then let hintSuggestion := { diffGranularity := .none toTryThisSuggestion := { suggestion := "/-- " ++ doc.getString.trim ++ " -/" } } let sugg ← Hint.mkSuggestionsMessage #[hintSuggestion] doc (codeActionPrefix? := "Update to: ") (forceList := false) logWarningAt doc <| .tagged ``Linter.deprecatedAttr ...
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
elabToAdditive
Elaboration of the configuration options for `to_additive`.
partial applyAttributes (stx : Syntax) (rawAttrs : Array Syntax) (thisAttr src tgt : Name) (argInfo : ArgInfo) : TermElabM (Array Name) := do copyInstanceAttribute src tgt if src != tgt && linter.existingAttributeWarning.get (← getOptions) then let appliedAttrs ← getAllSimpAttrs src if appliedAttrs.size > 0 then let appliedAttrs := ", ".intercalate (appliedAttrs.toList.map toString) Linter.logLintIf linter.existingAttributeWarning stx m!"\ The source declaration {src} was given the simp-attribute(s) {appliedAttrs} before \ calling @[{thisAttr}].\nThe preferred method is to use something like \ `@[{thisAttr} (attr := {appliedAttrs})]`\nto apply the attribute to both \ {src} and the target declaration {tgt}." warnAttr stx Lean.Elab.Tactic.Ext.extExtension (fun b n => (b.tree.values.any fun t => t.declName = n)) thisAttr `ext src tgt warnAttr stx Lean.Meta.Rfl.reflExt (·.values.contains ·) thisAttr `refl src tgt warnAttr stx Lean.Meta.Symm.symmExt (·.values.contains ·) thisAttr `symm src tgt warnAttr stx Batteries.Tactic.transExt (·.values.contains ·) thisAttr `trans src tgt warnAttr stx Lean.Meta.coeExt (·.contains ·) thisAttr `coe src tgt warnParametricAttr stx Lean.Linter.deprecatedAttr thisAttr `deprecated src tgt warnParametricAttr stx simpsAttr thisAttr `simps src tgt warnAttrCore stx Term.elabAsElim.hasTag thisAttr `elab_as_elim src tgt let attrs ← elabAttrs rawAttrs let (additiveAttrs, attrs) := attrs.partition (·.name == `to_additive) let nestedDecls ← match additiveAttrs.size with | 0 => pure #[] | 1 => addToAdditiveAttr tgt (← elabToAdditive additiveAttrs[0]!.stx) additiveAttrs[0]!.kind | _ => throwError "cannot apply {thisAttr} multiple times." let allDecls := #[src, tgt] ++ nestedDecls if attrs.size > 0 then trace[to_additive_detail] "Applying attributes {attrs.map (·.stx)} to {allDecls}" for attr in attrs do withRef attr.stx do withLogging do if attr.name == `simps then additivizeLemmas allDecls argInfo "simps lemmas" (simpsTacFromSyntax · attr.stx) return let env ← getEnv match getAttributeImpl env attr.name with | Except.error errMsg => throwError errMsg | Except.ok attrImpl => let runAttr := do for decl in allDecls do attrImpl.add decl attr.stx attr.kind let elaborator := attrImpl.ref if (← getInfoState).enabled && (← getEnv).contains elaborator then withInfoContext (mkInfo := return .ofCommandInfo { elaborator, stx := attr.stx }) do try runAttr finally if attr.stx[0].isIdent || attr.stx[0].isAtom then pushInfoLeaf <| .ofCommandInfo { elaborator, stx := attr.stx[0] } else runAttr ...
def
Tactic
[ "Batteries.Tactic.Trans", "Lean.Compiler.NoncomputableAttr", "Lean.Elab.Tactic.Ext", "Lean.Meta.Tactic.Rfl", "Lean.Meta.Tactic.Symm", "Lean.Meta.Tactic.TryThis", "Mathlib.Data.Array.Defs", "Mathlib.Data.Nat.Notation", "Mathlib.Lean.Expr.ReplaceRec", "Mathlib.Lean.Meta.Simp", "Mathlib.Lean.Name",...
Mathlib/Tactic/ToAdditive/Frontend.lean
applyAttributes
Apply attributes to the multiplicative and additive declarations.