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list_binary_operands (f : expr) : expr → tactic (list expr)
| x@(expr.app (expr.app g a) b) := do some _ ← try_core (unify f g) | pure [x], as ← list_binary_operands a, bs ← list_binary_operands b, pure (as ++ bs) | a := pure [a]
def
tactic.list_binary_operands
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Given an expression `f` (likely a binary operation) and a further expression `x`, calling `list_binary_operands f x` breaks `x` apart into successions of applications of `f` until this can no longer be done and returns a list of the leaves of the process. This matches `f` up to semireducible unification. In particular...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
mk_theorem (n : name) (ls : list name) (t : expr) (e : expr) : declaration
declaration.thm n ls t (task.pure e)
def
tactic.mk_theorem
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`mk_theorem n ls t e` creates a theorem declaration with name `n`, universe parameters named `ls`, type `t`, and body `e`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
add_theorem_by (n : name) (ls : list name) (type : expr) (tac : tactic unit) : tactic expr
do ((), body) ← solve_aux type tac, body ← instantiate_mvars body, add_decl $ mk_theorem n ls type body, return $ expr.const n $ ls.map level.param
def
tactic.add_theorem_by
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`add_theorem_by n ls type tac` uses `tac` to synthesize a term with type `type`, and adds this to the environment as a theorem with name `n` and universe parameters `ls`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
eval_expr' (α : Type*) [reflected _ α] (e : expr) : tactic α
mk_app ``id [e] >>= eval_expr α
def
tactic.eval_expr'
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`eval_expr' α e` attempts to evaluate the expression `e` in the type `α`. This is a variant of `eval_expr` in core. Due to unexplained behavior in the VM, in rare situations the latter will fail but the former will succeed.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
mk_user_fresh_name : tactic name
do nm ← mk_fresh_name, return $ `user__ ++ nm.pop_prefix.sanitize_name ++ `user__
def
tactic.mk_user_fresh_name
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`mk_fresh_name` returns identifiers starting with underscores, which are not legal when emitted by tactic programs. `mk_user_fresh_name` turns the useful source of random names provided by `mk_fresh_name` into names which are usable by tactic programs. The returned name has four components which are all strings.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
has_attribute' (attr_name decl_name : name) : tactic bool
succeeds (has_attribute attr_name decl_name)
def
tactic.has_attribute'
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[ "succeeds" ]
`has_attribute' attr_name decl_name` checks whether `decl_name` exists and has attribute `attr_name`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
is_simp_lemma : name → tactic bool
has_attribute' `simp
def
tactic.is_simp_lemma
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Checks whether the name is a simp lemma
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
is_instance : name → tactic bool
has_attribute' `instance
def
tactic.is_instance
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Checks whether the name is an instance.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
local_decls : tactic (name_map declaration)
do e ← tactic.get_env, let xs := e.fold native.mk_rb_map (λ d s, if environment.in_current_file e d.to_name then s.insert d.to_name d else s), pure xs
def
tactic.local_decls
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`local_decls` returns a dictionary mapping names to their corresponding declarations. Covers all declarations from the current file.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
get_decls_from (fs : list (option string)) : tactic (name_map declaration)
do root ← unsafe_run_io $ io.env.get_cwd, let fs := fs.map (option.map $ λ path, root ++ "/" ++ path), err ← unsafe_run_io $ (fs.filter_map id).mfilter $ (<$>) bnot ∘ io.fs.file_exists, guard (err = []) <|> fail format!"File not found: {err}", e ← tactic.get_env, let xs := e.fold native.mk_rb_map (λ...
def
tactic.get_decls_from
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[ "path" ]
`get_decls_from` returns a dictionary mapping names to their corresponding declarations. Covers all declarations the files listed in `fs`, with the current file listed as `none`. The path of the file names is expected to be relative to the root of the project (i.e. the location of `leanpkg.toml` when it is present); ...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
get_unused_decl_name_aux (e : environment) (nm : name) : ℕ → tactic name | n
let nm' := nm.append_suffix ("_" ++ to_string n) in if e.contains nm' then get_unused_decl_name_aux (n+1) else return nm'
def
tactic.get_unused_decl_name_aux
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
If `{nm}_{n}` doesn't exist in the environment, returns that, otherwise tries `{nm}_{n+1}`
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
get_unused_decl_name (nm : name) : tactic name
get_env >>= λ e, if e.contains nm then get_unused_decl_name_aux e nm 2 else return nm
def
tactic.get_unused_decl_name
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Return a name which doesn't already exist in the environment. If `nm` doesn't exist, it returns that, otherwise it tries `nm_2`, `nm_3`, ...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
decl_mk_const (d : declaration) : tactic (expr × expr)
do subst ← d.univ_params.mmap $ λ u, prod.mk u <$> mk_meta_univ, let e : expr := expr.const d.to_name (prod.snd <$> subst), return (e, d.type.instantiate_univ_params subst)
def
tactic.decl_mk_const
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Returns a pair `(e, t)`, where `e ← mk_const d.to_name`, and `t = d.type` but with universe params updated to match the fresh universe metavariables in `e`. This should have the same effect as just ```lean do e ← mk_const d.to_name, t ← infer_type e, return (e, t) ``` but is hopefully faster.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
replace_univ_metas_with_univ_params (e : expr) : tactic expr
do e.list_univ_meta_vars.enum.mmap (λ n, do let n' := (`u).append_suffix ("_" ++ to_string (n.1+1)), unify (expr.sort (level.mvar n.2)) (expr.sort (level.param n'))), instantiate_mvars e
def
tactic.replace_univ_metas_with_univ_params
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Replace every universe metavariable in an expression with a universe parameter. (This is useful when making new declarations.)
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
mk_local (n : name) : expr
expr.local_const n n binder_info.default (expr.const n [])
def
tactic.mk_local
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`mk_local n` creates a dummy local variable with name `n`. The type of this local constant is a constant with name `n`, so it is very unlikely to be a meaningful expression.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
mk_psigma : list expr → tactic expr
| [] := mk_const ``punit | [x@(expr.local_const _ _ _ _)] := pure x | (x@(expr.local_const _ _ _ _) :: xs) := do y ← mk_psigma xs, α ← infer_type x, β ← infer_type y, t ← lambdas [x] β >>= instantiate_mvars, r ← mk_mapp ``psigma.mk [α,t], pure $ r x y | _ := fail "mk_psigma expects a list of ...
def
tactic.mk_psigma
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`mk_psigma [x,y,z]`, with `[x,y,z]` list of local constants of types `x : tx`, `y : ty x` and `z : tz x y`, creates an expression of sigma type: `⟨x,y,z⟩ : Σ' (x : tx) (y : ty x), tz x y`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
update_type : expr → tactic expr
| e@(expr.local_const ppname uname binfo _) := expr.local_const ppname uname binfo <$> infer_type e | e@(expr.mvar ppname uname _) := expr.mvar ppname uname <$> infer_type e | e := pure e
def
tactic.update_type
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Update the type of a local constant or metavariable. For local constants and metavariables obtained via, for example, `tactic.get_local`, the type stored in the expression is not necessarily the same as the type returned by `infer_type`. This tactic, given a local constant or metavariable, updates the stored type to ma...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
elim_gen_prod : nat → expr → list expr → list name → tactic (list expr × expr × list name)
| 0 e hs ns := return (hs.reverse, e, ns) | (n + 1) e hs ns := do t ← infer_type e, if t.is_app_of `eq then return (hs.reverse, e, ns) else do [(_, [h, h'], _)] ← cases_core e (ns.take 1), elim_gen_prod n h' (h :: hs) (ns.drop 1)
def
tactic.elim_gen_prod
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`elim_gen_prod n e _ ns` with `e` an expression of type `psigma _`, applies `cases` on `e` `n` times and uses `ns` to name the resulting variables. Returns a triple: list of new variables, remaining term and unused variable names.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
elim_gen_sum_aux : nat → expr → list expr → tactic (list expr × expr)
| 0 e hs := return (hs, e) | (n + 1) e hs := do [(_, [h], _), (_, [h'], _)] ← induction e [], swap, elim_gen_sum_aux n h' (h::hs)
def
tactic.elim_gen_sum_aux
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
elim_gen_sum (n : nat) (e : expr) : tactic (list expr)
do (hs, h') ← elim_gen_sum_aux n e [], gs ← get_goals, set_goals $ (gs.take (n+1)).reverse ++ gs.drop (n+1), return $ hs.reverse ++ [h']
def
tactic.elim_gen_sum
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`elim_gen_sum n e` applies cases on `e` `n` times. `e` is assumed to be a local constant whose type is a (nested) sum `⊕`. Returns the list of local constants representing the components of `e`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
extract_def (n : name) (trusted : bool) (elab_def : tactic unit) : tactic unit
do cxt ← list.map expr.to_implicit_local_const <$> local_context, t ← target, (eqns,d) ← solve_aux t elab_def, d ← instantiate_mvars d, t' ← pis cxt t, d' ← lambdas cxt d, let univ := t'.collect_univ_params, add_decl $ declaration.defn n univ t' d' (reducibility_hints.regular 1 tt) trusted, appl...
def
tactic.extract_def
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[ "expr.to_implicit_local_const" ]
Given `elab_def`, a tactic to solve the current goal, `extract_def n trusted elab_def` will create an auxiliary definition named `n` and use it to close the goal. If `trusted` is false, it will be a meta definition.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
exact_dec_trivial : tactic unit
`[exact dec_trivial]
def
tactic.exact_dec_trivial
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Attempts to close the goal with `dec_trivial`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
retrieve {α} (tac : tactic α) : tactic α
λ s, result.cases_on (tac s) (λ a s', result.success a s) result.exception
def
tactic.retrieve
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Runs a tactic for a result, reverting the state after completion.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
retrieve' {α} (tac : tactic α) : tactic α
λ s, result.cases_on (tac s) (λ a s', result.success a s) (λ msg pos s', result.exception msg pos s)
def
tactic.retrieve'
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Runs a tactic for a result, reverting the state after completion or error.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
repeat1 (t : tactic unit) : tactic unit
t; repeat t
def
tactic.repeat1
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Repeat a tactic at least once, calling it recursively on all subgoals, until it fails. This tactic fails if the first invocation fails.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
iterate_range : ℕ → ℕ → tactic unit → tactic unit
| 0 0 t := skip | 0 (n+1) t := try (t >> iterate_range 0 n t) | (m+1) n t := t >> iterate_range m (n-1) t
def
tactic.iterate_range
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`iterate_range m n t`: Repeat the given tactic at least `m` times and at most `n` times or until `t` fails. Fails if `t` does not run at least `m` times.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
replace_at (tac : expr → tactic (expr × expr)) (hs : list expr) (tgt : bool) : tactic bool
do to_remove ← hs.mfilter $ λ h, do { h_type ← infer_type h, succeeds $ do (new_h_type, pr) ← tac h_type, assert h.local_pp_name new_h_type, mk_eq_mp pr h >>= tactic.exact }, goal_simplified ← succeeds $ do { guard tgt, (new_t, pr) ← target >>= tac, replace_target new_t pr }, to_re...
def
tactic.replace_at
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[ "succeeds" ]
Given a tactic `tac` that takes an expression and returns a new expression and a proof of equality, use that tactic to change the type of the hypotheses listed in `hs`, as well as the goal if `tgt = tt`. Returns `tt` if any types were successfully changed.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
revert_after (e : expr) : tactic ℕ
do l ← local_context, [pos] ← return $ l.indexes_of e | pp e >>= λ s, fail format!"No such local constant {s}", let l := l.drop pos.succ, -- all local hypotheses after `e` revert_lst l
def
tactic.revert_after
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`revert_after e` reverts all local constants after local constant `e`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
revert_target_deps : tactic ℕ
do tgt ← target, ctx ← local_context, l ← ctx.mfilter (kdepends_on tgt), n ← revert_lst l, if l = [] then return n else do m ← revert_target_deps, return (m + n)
def
tactic.revert_target_deps
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`revert_target_deps` reverts all local constants on which the target depends (recursively). Returns the number of local constants that have been reverted.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
generalize' (e : expr) (n : name) : tactic expr
(generalize e n >> intro n) <|> note n none e
def
tactic.generalize'
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`generalize' e n` generalizes the target with respect to `e`. It creates a new local constant with name `n` of the same type as `e` and replaces all occurrences of `e` by `n`. `generalize'` is similar to `generalize` but also succeeds when `e` does not occur in the goal, in which case it just calls `assert`. In contra...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
intron_no_renames : ℕ → tactic unit
| 0 := pure () | (n+1) := do expr.pi pp_n _ _ _ ← target, intro pp_n, intron_no_renames n
def
tactic.intron_no_renames
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`intron_no_renames n` calls `intro` `n` times, using the pretty-printing name provided by the binder to name the new local constant. Unlike `intron`, it does not rename introduced constants if the names shadow existing constants.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
get_univ_level (t : expr) (md := semireducible) (unfold_ginductive := tt) : tactic level
do expr.sort u ← infer_type t >>= λ s, whnf s md unfold_ginductive | fail "get_univ_level: argument is not a type", return u
def
tactic.get_univ_level
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`get_univ_level t` returns the universe level of a type `t`
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
local_def_value (e : expr) : tactic expr
pp e >>= λ s, -- running `pp` here, because we cannot access it in the `type_context` monad. tactic.unsafe.type_context.run $ do lctx <- tactic.unsafe.type_context.get_local_context, some ldecl <- return $ lctx.get_local_decl e.local_uniq_name | tactic.unsafe.type_context.fail format!"No such hypothesis {s}.", ...
def
tactic.local_def_value
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`local_def_value e` returns the value of the expression `e`, assuming that `e` has been defined locally using a `let` expression. Otherwise it fails.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
is_local_def (e : expr) : tactic unit
do ctx ← unsafe.type_context.get_local_context.run, (some decl) ← pure $ ctx.get_local_decl e.local_uniq_name | fail format!"is_local_def: {e} is not a local constant", when decl.value.is_none $ fail format!"is_local_def: {e} is not a local definition"
def
tactic.is_local_def
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`is_local_def e` succeeds when `e` is a local definition (a local constant of the form `e : α := t`) and otherwise fails.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
local_defs : tactic (list expr)
do ctx ← unsafe.type_context.get_local_context.run, ctx' ← local_context, ctx'.mfilter $ λ h, do (some decl) ← pure $ ctx.get_local_decl h.local_uniq_name | fail format!"local_defs: local {h} not found in the local context", pure decl.value.is_some
def
tactic.local_defs
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Returns the local definitions from the context. A local definition is a local constant of the form `e : α := t`. The local definitions are returned in the order in which they appear in the context.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
partition_local_deps_aux {α} [decidable_eq α] (vs : list α) : list α → list α → list (list α)
| [] acc := [acc.reverse] | (l :: ls) acc := if l ∈ vs then acc.reverse :: partition_local_deps_aux ls [l] else partition_local_deps_aux ls (l :: acc)
def
tactic.partition_local_deps_aux
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
like `split_on_p p xs`, `partition_local_deps_aux vs xs acc` searches for matches in `xs` (using membership to `vs` instead of a predicate) and breaks `xs` when matches are found. whereas `split_on_p p xs` removes the matches, `partition_local_deps_aux vs xs acc` includes them in the following partition. Also, `partiti...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
partition_local_deps (vs : list expr) : tactic (list (list expr))
do ls ← local_context, pure (partition_local_deps_aux vs ls []).tail.reverse
def
tactic.partition_local_deps
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`partition_local_deps vs`, with `vs` a list of local constants, reorders `vs` in the order they appear in the local context together with the variables that follow them. If local context is `[a,b,c,d,e,f]`, and that we call `partition_local_deps [d,b]`, we get `[[d,e,f], [b,c]]`. The head of each list is one of the var...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
clear_value (vs : list expr) : tactic unit
do ls ← partition_local_deps vs, ls.mmap' $ λ vs, do { revert_lst vs, (expr.elet v t d b) ← target | fail format!"Cannot clear the body of {vs.head}. It is not a local definition.", let e := expr.pi v binder_info.default t b, type_check e <|> fail format!"Cannot clear the body of {vs.head}...
def
tactic.clear_value
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`clear_value [e₀, e₁, e₂, ...]` clears the body of the local definitions `e₀`, `e₁`, `e₂`, ... changing them into regular hypotheses. A hypothesis `e : α := t` is changed to `e : α`. The order of locals `e₀`, `e₁`, `e₂` does not matter as a permutation will be chosen so as to preserve type correctness. This tactic is c...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
context_has_local_def : tactic bool
do ctx ← local_context, ctx.many (succeeds ∘ local_def_value)
def
tactic.context_has_local_def
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[ "succeeds" ]
`context_has_local_def` is true iff there is at least one local definition in the context.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
context_upto_hyp_has_local_def (h : expr) : tactic bool
do ff ← succeeds (local_def_value h) | pure tt, ctx ← local_context, let ctx := ctx.take_while (≠ h), ctx.many (succeeds ∘ local_def_value)
def
tactic.context_upto_hyp_has_local_def
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[ "succeeds" ]
`context_upto_hyp_has_local_def h` is true iff any of the hypotheses in the context up to and including `h` is a local definition.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
subst' (h : expr) : tactic unit
do e ← do { -- we first find the variable being substituted away t ← infer_type h, let (f, args) := t.get_app_fn_args, if (f.const_name = `eq ∨ f.const_name = `heq) then do { let lhs := args.inth 1, let rhs := args.ilast, if rhs.is_local_constant then return rhs else if lhs.is_local_...
def
tactic.subst'
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
If the expression `h` is a local variable with type `x = t` or `t = x`, where `x` is a local constant, `tactic.subst' h` substitutes `x` by `t` everywhere in the main goal and then clears `h`. If `h` is another local variable, then we find a local constant with type `h = t` or `t = h` and substitute `t` for `h`. This ...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
simp_bottom_up' (post : expr → tactic (expr × expr)) (e : expr) (cfg : simp_config := {}) : tactic (expr × expr)
prod.snd <$> simplify_bottom_up () (λ _, (<$>) (prod.mk ()) ∘ post) e cfg
def
tactic.simp_bottom_up'
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
A variant of `simplify_bottom_up`. Given a tactic `post` for rewriting subexpressions, `simp_bottom_up post e` tries to rewrite `e` starting at the leaf nodes. Returns the resulting expression and a proof of equality.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
instance_cache
(α : expr) (univ : level) (inst : name_map expr)
structure
tactic.instance_cache
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Caches unary type classes on a type `α : Type.{univ}`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
mk_instance_cache (α : expr) : tactic instance_cache
do u ← mk_meta_univ, infer_type α >>= unify (expr.sort (level.succ u)), u ← get_univ_assignment u, return ⟨α, u, mk_name_map⟩
def
tactic.mk_instance_cache
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Creates an `instance_cache` for the type `α`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
get (c : instance_cache) (n : name) : tactic (instance_cache × expr)
match c.inst.find n with | some i := return (c, i) | none := do e ← mk_app n [c.α] >>= mk_instance, return (⟨c.α, c.univ, c.inst.insert n e⟩, e) end
def
tactic.instance_cache.get
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
If `n` is the name of a type class with one parameter, `get c n` tries to find an instance of `n c.α` by checking the cache `c`. If there is no entry in the cache, it tries to find the instance via type class resolution, and updates the cache.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
append_typeclasses : expr → instance_cache → list expr → tactic (instance_cache × list expr)
| (pi _ binder_info.inst_implicit (app (const n _) (var _)) body) c l := do (c, p) ← c.get n, return (c, p :: l) | _ c l := return (c, l)
def
tactic.instance_cache.append_typeclasses
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
If `e` is a `pi` expression that binds an instance-implicit variable of type `n`, `append_typeclasses e c l` searches `c` for an instance `p` of type `n` and returns `p :: l`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
mk_app (c : instance_cache) (n : name) (l : list expr) : tactic (instance_cache × expr)
do d ← get_decl n, (c, l) ← append_typeclasses d.type.binding_body c l, return (c, (expr.const n [c.univ]).mk_app (c.α :: l))
def
tactic.instance_cache.mk_app
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Creates the application `n c.α p l`, where `p` is a type class instance found in the cache `c`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
of_nat (c : instance_cache) (n : ℕ) : tactic (instance_cache × expr)
if n = 0 then c.mk_app ``has_zero.zero [] else do (c, ai) ← c.get ``has_add, (c, oi) ← c.get ``has_one, (c, one) ← c.mk_app ``has_one.one [], return (c, n.binary_rec one $ λ b n e, if n = 0 then one else cond b ((expr.const ``bit1 [c.univ]).mk_app [c.α, oi, ai, e]) ((expr.const ``bit0 [c.uni...
def
tactic.instance_cache.of_nat
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`c.of_nat n` creates the `c.α`-valued numeral expression corresponding to `n`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
of_int (c : instance_cache) : ℤ → tactic (instance_cache × expr)
| (n : ℕ) := c.of_nat n | -[1+ n] := do (c, e) ← c.of_nat (n+1), c.mk_app ``has_neg.neg [e]
def
tactic.instance_cache.of_int
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`c.of_int n` creates the `c.α`-valued numeral expression corresponding to `n`. The output is either a numeral or the negation of a numeral.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
local_proof (h : name) (p : expr) (tac₀ : tactic unit) : tactic (expr × list expr)
focus1 $ do h' ← assert h p, [g₀,g₁] ← get_goals, set_goals [g₀], tac₀, gs ← get_goals, set_goals [g₁], return (h', gs)
def
tactic.local_proof
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
A variation on `assert` where a (possibly incomplete) proof of the assertion is provided as a parameter. ``(h,gs) ← local_proof `h p tac`` creates a local `h : p` and use `tac` to (partially) construct a proof for it. `gs` is the list of remaining goals in the proof of `h`. The benefits over assert are: - unlike with...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
var_names : expr → list name
| (expr.pi n _ _ b) := n :: var_names b | _ := []
def
tactic.var_names
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`var_names e` returns a list of the unique names of the initial pi bindings in `e`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
subobject_names (struct_n : name) : tactic (list name × list name)
do env ← get_env, c ← match env.constructors_of struct_n with | [c] := pure c | [] := if env.is_inductive struct_n then fail format!"{struct_n} does not have constructors" else fail format!"{struct_n} is not an inductive type" | _ := fail "too many constructors" ...
def
tactic.subobject_names
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
When `struct_n` is the name of a structure type, `subobject_names struct_n` returns two lists of names `(instances, fields)`. The names in `instances` are the projections from `struct_n` to the structures that it extends (assuming it was defined with `old_structure_cmd false`). The names in `fields` are the standard fi...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
expanded_field_list' : name → tactic (dlist $ name × name) | struct_n
do (so,fs) ← subobject_names struct_n, ts ← so.mmap (λ n, do (_, e) ← mk_const (n.update_prefix struct_n) >>= infer_type >>= open_pis, expanded_field_list' $ e.get_app_fn.const_name), return $ dlist.join ts ++ dlist.of_list (fs.map $ prod.mk struct_n)
def
tactic.expanded_field_list'
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[ "dlist.join" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
expanded_field_list (struct_n : name) : tactic (list $ name × name)
dlist.to_list <$> expanded_field_list' struct_n
def
tactic.expanded_field_list
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`expanded_field_list struct_n` produces a list of the names of the fields of the structure named `struct_n`. These are returned as pairs of names `(prefix, name)`, where the full name of the projection is `prefix.name`. `struct_n` cannot be a synonym for a `structure`, it must be itself a `structure`
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
get_classes (e : expr) : tactic (list name)
attribute.get_instances `class >>= list.mfilter (λ n, succeeds $ mk_app n [e] >>= mk_instance)
def
tactic.get_classes
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[ "succeeds" ]
Return a list of all type classes which can be instantiated for the given expression.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
mk_conditional_instance (cond tgt : expr) : tactic (expr × expr)
do f ← mk_meta_var cond, e ← assertv `c cond f, swap, reset_instance_cache, inst ← mk_instance tgt, return (e, inst)
def
tactic.mk_conditional_instance
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Finds an instance of an implication `cond → tgt`. Returns a pair of a local constant `e` of type `cond`, and an instance of `tgt` that can mention `e`. The local constant `e` is added as an hypothesis to the tactic state, but should not be used, since it has been "proven" by a metavariable.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
mk_mvar_list : ℕ → tactic (list expr)
| 0 := pure [] | (succ n) := (::) <$> mk_mvar <*> mk_mvar_list n
def
tactic.mk_mvar_list
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Create a list of `n` fresh metavariables.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
get_goal : tactic expr
do gs ← get_goals, match gs with | [a] := return a | [] := fail "there are no goals" | _ := fail "there are too many goals" end
def
tactic.get_goal
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Returns the only goal, or fails if there isn't just one goal.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
iterate_at_most_on_all_goals : nat → tactic unit → tactic unit
| 0 tac := trace "maximal iterations reached" | (succ n) tac := tactic.all_goals' $ (do tac, iterate_at_most_on_all_goals n tac) <|> skip
def
tactic.iterate_at_most_on_all_goals
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`iterate_at_most_on_all_goals n t`: repeat the given tactic at most `n` times on all goals, or until it fails. Always succeeds.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
iterate_at_most_on_subgoals : nat → tactic unit → tactic unit
| 0 tac := trace "maximal iterations reached" | (succ n) tac := focus1 (do tac, iterate_at_most_on_all_goals n tac)
def
tactic.iterate_at_most_on_subgoals
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`iterate_at_most_on_subgoals n t`: repeat the tactic `t` at most `n` times on the first goal and on all subgoals thus produced, or until it fails. Fails iff `t` fails on current goal.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
lock_tactic_state {α} (t : tactic α) : tactic α
| s := match t s with | result.success a s' := result.success a s | result.exception msg pos s' := result.exception msg pos s end
def
tactic.lock_tactic_state
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
This makes sure that the execution of the tactic does not change the tactic state. This can be helpful while using rewrite, apply, or expr munging. Remember to instantiate your metavariables before you're done!
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
apply_list_expr (opt : apply_cfg) : list (tactic expr) → tactic unit
| [] := fail "no matching rule" | (h::t) := (do e ← h, interactive.concat_tags (apply e opt)) <|> apply_list_expr t
def
tactic.apply_list_expr
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`apply_list l`, for `l : list (tactic expr)`, tries to apply one of the lemmas generated by the tactics in `l` to the first goal, and fail if none succeeds.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
resolve_attribute_expr_list (attr_name : name) : tactic (list (tactic expr))
do l ← attribute.get_instances attr_name, list.map i_to_expr_for_apply <$> list.reverse <$> l.mmap (λ n, do c ← (mk_const n), return (pexpr.of_expr c))
def
tactic.resolve_attribute_expr_list
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Given the name of a user attribute, produces a list of `tactic expr`s, each of which is the application of `i_to_expr_for_apply` to a declaration with that attribute.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
apply_rules (args : list pexpr) (attrs : list name) (n : nat) (opt : apply_cfg) : tactic unit
do attr_exprs ← lock_tactic_state $ attrs.mfoldl (λ l n, list.append l <$> resolve_attribute_expr_list n) [], let args_exprs := args.map i_to_expr_for_apply ++ attr_exprs, -- `args_exprs` is a list of `tactic expr`, rather than just `expr`, because these expressions will -- be repeatedly applied against goals, ...
def
tactic.apply_rules
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`apply_rules args attrs n`: apply the lists of rules `args` (given as pexprs) and `attrs` (given as names of attributes) and the tactic `assumption` on the first goal and the resulting subgoals, iteratively, at most `n` times. Unlike `solve_by_elim`, `apply_rules` does not do any backtracking, and just greedily applie...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
replace (h : name) (p : pexpr) : tactic unit
do h' ← get_local h, p ← to_expr p, note h none p, clear h'
def
tactic.replace
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`replace h p` elaborates the pexpr `p`, clears the existing hypothesis named `h` from the local context, and adds a new hypothesis named `h`. The type of this hypothesis is the type of `p`. Fails if there is nothing named `h` in the local context.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
mk_iff_mp_app (iffmp : name) : expr → (nat → expr) → option expr
| (expr.pi n bi e t) f := expr.lam n bi e <$> mk_iff_mp_app t (λ n, f (n+1) (expr.var n)) | `(%%a ↔ %%b) f := some $ @expr.const tt iffmp [] a b (f 0) | _ f := none
def
tactic.mk_iff_mp_app
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Auxiliary function for `iff_mp` and `iff_mpr`. Takes a name, which should be either `` `iff.mp`` or `` `iff.mpr``. If the passed expression is an iterated function type eventually producing an `iff`, returns an expression with the `iff` converted to either the forwards or backwards implication, as requested.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
iff_mp_core (e ty: expr) : option expr
mk_iff_mp_app `iff.mp ty (λ_, e)
def
tactic.iff_mp_core
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`iff_mp_core e ty` assumes that `ty` is the type of `e`. If `ty` has the shape `Π ..., A ↔ B`, returns an expression whose type is `Π ..., A → B`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
iff_mpr_core (e ty: expr) : option expr
mk_iff_mp_app `iff.mpr ty (λ_, e)
def
tactic.iff_mpr_core
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`iff_mpr_core e ty` assumes that `ty` is the type of `e`. If `ty` has the shape `Π ..., A ↔ B`, returns an expression whose type is `Π ..., B → A`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
iff_mp (e : expr) : tactic expr
do t ← infer_type e, iff_mp_core e t <|> fail "Target theorem must have the form `Π x y z, a ↔ b`"
def
tactic.iff_mp
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Given an expression whose type is (a possibly iterated function producing) an `iff`, create the expression which is the forward implication.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
iff_mpr (e : expr) : tactic expr
do t ← infer_type e, iff_mpr_core e t <|> fail "Target theorem must have the form `Π x y z, a ↔ b`"
def
tactic.iff_mpr
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Given an expression whose type is (a possibly iterated function producing) an `iff`, create the expression which is the reverse implication.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
apply_iff (e : expr) : tactic (list (name × expr))
let ap e := tactic.apply e {new_goals := new_goals.non_dep_only} in ap e <|> (iff_mp e >>= ap) <|> (iff_mpr e >>= ap)
def
tactic.apply_iff
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Attempts to apply `e`, and if that fails, if `e` is an `iff`, try applying both directions separately.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
apply_any_opt extends apply_cfg
(use_symmetry : bool := tt) (use_exfalso : bool := tt)
structure
tactic.apply_any_opt
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Configuration options for `apply_any`: * `use_symmetry`: if `apply_any` fails to apply any lemma, call `symmetry` and try again. * `use_exfalso`: if `apply_any` fails to apply any lemma, call `exfalso` and try again. * `apply`: specify an alternative to `tactic.apply`; usually `apply := tactic.eapply`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
apply_any_thunk (lemmas : list (tactic expr)) (opt : apply_any_opt := {}) (tac : tactic unit := skip) (on_success : expr → tactic unit := (λ _, skip)) (on_failure : tactic unit := skip) : tactic unit
do let modes := [skip] ++ (if opt.use_symmetry then [symmetry] else []) ++ (if opt.use_exfalso then [exfalso] else []), modes.any_of (λ m, do m, lemmas.any_of (λ H, H >>= (λ e, do apply e opt.to_apply_cfg, on_success e, tac))) <|> (on_failure >> fail "apply_any tactic failed; no lemma could be applied...
def
tactic.apply_any_thunk
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
This is a version of `apply_any` that takes a list of `tactic expr`s instead of `expr`s, and evaluates these as thunks before trying to apply them. We need to do this to avoid metavariables getting stuck during subsequent rounds of `apply`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
apply_any (lemmas : list expr) (opt : apply_any_opt := {}) (tac : tactic unit := skip) : tactic unit
apply_any_thunk (lemmas.map pure) opt tac
def
tactic.apply_any
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`apply_any lemmas` tries to apply one of the list `lemmas` to the current goal. `apply_any lemmas opt` allows control over how lemmas are applied. `opt` has fields: * `use_symmetry`: if no lemma applies, call `symmetry` and try again. (Defaults to `tt`.) * `use_exfalso`: if no lemma applies, call `exfalso` and try aga...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
apply_assumption : tactic unit
local_context >>= apply_any
def
tactic.apply_assumption
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Try to apply a hypothesis from the local context to the goal.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
change_core (e : expr) : option expr → tactic unit
| none := tactic.change e | (some h) := do num_reverted : ℕ ← revert h, expr.pi n bi d b ← target, tactic.change $ expr.pi n bi e b, intron num_reverted
def
tactic.change_core
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`change_core e none` is equivalent to `change e`. It tries to change the goal to `e` and fails if this is not a definitional equality. `change_core e (some h)` assumes `h` is a local constant, and tries to change the type of `h` to `e` by reverting `h`, changing the goal, and reintroducing hypotheses.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
change_with_at (olde newe : pexpr) (hyp : name) : tactic unit
do h ← get_local hyp, tp ← infer_type h, olde ← to_expr olde, newe ← to_expr newe, let repl_tp := tp.replace (λ a n, if a = olde then some newe else none), when (repl_tp ≠ tp) $ change_core repl_tp (some h)
def
tactic.change_with_at
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`change_with_at olde newe hyp` replaces occurences of `olde` with `newe` at hypothesis `hyp`, assuming `olde` and `newe` are defeq when elaborated.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
metavariables : tactic (list expr)
expr.list_meta_vars <$> result
def
tactic.metavariables
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[ "expr.list_meta_vars" ]
Returns a list of all metavariables in the current partial proof. This can differ from the list of goals, since the goals can be manually edited.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sorry_if_contains_sorry : tactic unit
do g ← target, guard g.contains_sorry <|> fail "goal does not contain `sorry`", tactic.admit
def
tactic.sorry_if_contains_sorry
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`sorry_if_contains_sorry` will solve any goal already containing `sorry` in its type with `sorry`, and fail otherwise.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
no_mvars_in_target : tactic unit
expr.has_meta_var <$> target >>= guardb ∘ bnot
def
tactic.no_mvars_in_target
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Fail if the target contains a metavariable.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
propositional_goal : tactic unit
do g :: _ ← get_goals, is_proof g >>= guardb
def
tactic.propositional_goal
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Succeeds only if the current goal is a proposition.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
subsingleton_goal : tactic unit
do g :: _ ← get_goals, ty ← infer_type g >>= instantiate_mvars, to_expr ``(subsingleton %%ty) >>= mk_instance >> skip
def
tactic.subsingleton_goal
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Succeeds only if we can construct an instance showing the current goal is a subsingleton type.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
terminal_goal : tactic unit
propositional_goal <|> subsingleton_goal <|> do g₀ :: _ ← get_goals, mvars ← (λ L, list.erase L g₀) <$> metavariables, mvars.mmap' $ λ g, do t ← infer_type g >>= instantiate_mvars, d ← kdepends_on t g₀, monad.whenb d $ pp t >>= λ s, fail ("The current goal is not terminal: " ++ s.to_string +...
def
tactic.terminal_goal
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Succeeds only if the current goal is "terminal", in the sense that no other goals depend on it (except possibly through shared metavariables; see `independent_goal`).
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
independent_goal : tactic unit
no_mvars_in_target >> terminal_goal
def
tactic.independent_goal
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Succeeds only if the current goal is "independent", in the sense that no other goals depend on it, even through shared meta-variables.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
triv' : tactic unit
do c ← mk_const `trivial, exact c reducible
def
tactic.triv'
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`triv'` tries to close the first goal with the proof `trivial : true`. Unlike `triv`, it only unfolds reducible definitions, so it sometimes fails faster.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
iterate1 (t : tactic α) : tactic (list α)
do r ← decorate_ex "iterate1 failed: tactic did not succeed" t, L ← iterate t, return (r :: L)
def
tactic.iterate1
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Apply a tactic as many times as possible, collecting the results in a list. Fail if the tactic does not succeed at least once.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
check_target_changes (tac : tactic α) : tactic α
focus1 $ do t ← target, x ← tac, gs ← get_goals >>= list.mmap infer_type, (success_if_fail $ gs.mfirst $ unify t) <|> fail "Goal did not change", pure x
def
tactic.check_target_changes
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
A simple check: `check_target_changes tac` applies tactic `tac` and fails if the main target before applying the tactic `tac` unifies with one of the goals produced by the tactic itself. Useful to make sure that the tactic `tac` is actually making progress.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
intros1 : tactic (list expr)
iterate1 intro1
def
tactic.intros1
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Introduces one or more variables and returns the new local constants. Fails if `intro` cannot be applied.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
under_binders {α : Type} (t : tactic α) : tactic α
do v ← intros, r ← t, revert_lst v, return r
def
tactic.under_binders
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Run a tactic "under binders", by running `intros` before, and `revert` afterwards.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
under_binders (i : itactic) : itactic
tactic.under_binders i
def
tactic.interactive.under_binders
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[ "tactic.under_binders" ]
Run a tactic "under binders", by running `intros` before, and `revert` afterwards.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
successes (tactics : list (tactic α)) : tactic (list α)
list.filter_map id <$> monad.sequence (tactics.map (λ t, try_core t))
def
tactic.successes
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`successes` invokes each tactic in turn, returning the list of successful results.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
try_all {α : Type} (tactics : list (tactic α)) : tactic (list α)
λ s, result.success (tactics.map $ λ t : tactic α, match t s with | result.success a s' := [a] | _ := [] end).join s
def
tactic.try_all
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
try_all_sorted {α : Type} (tactics : list (tactic α)) (sort_by : tactic ℕ := num_goals) : tactic (list (α × ℕ))
λ s, result.success ((tactics.map $ λ t : tactic α, match (do a ← t, n ← sort_by, return (a, n)) s with | result.success a s' := [a] | _ := [] end).join.qsort (λ p q : α × ℕ, p.2 < q.2)) s
def
tactic.try_all_sorted
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Try all the tactics in a list, each time starting at the original `tactic_state`, returning the list of successful results sorted by the value produced by a subsequent execution of the `sort_by` tactic, and reverting to the original `tactic_state`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
target' : tactic expr
target >>= instantiate_mvars >>= whnf
def
tactic.target'
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Return target after instantiating metavars and whnf.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
fsplit : tactic unit
do [c] ← target' >>= get_constructors_for | fail "fsplit tactic failed, target is not an inductive datatype with only one constructor", mk_const c >>= λ e, apply e {new_goals := new_goals.all, auto_param := ff} >> skip
def
tactic.fsplit
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
injections_and_clear : tactic unit
do l ← local_context, results ← successes $ l.map $ λ e, injection e >> clear e, when (results.empty) (fail "could not use `injection` then `clear` on any hypothesis")
def
tactic.injections_and_clear
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Calls `injection` on each hypothesis, and then, for each hypothesis on which `injection` succeeds, clears the old hypothesis.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
case_bash : tactic unit
do l ← local_context, r ← successes (l.reverse.map (λ h, cases h >> skip)), when (r.empty) failed
def
tactic.case_bash
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
Calls `cases` on every local hypothesis, succeeding if it succeeds on at least one hypothesis.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
note_anon (t : option expr) (v : expr) : tactic expr
do h ← get_unused_name `h none, note h t v
def
tactic.note_anon
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
find_local (t : pexpr) : tactic expr
do t' ← to_expr t, (prod.snd <$> solve_aux t' assumption >>= instantiate_mvars) <|> fail format!"No hypothesis found of the form: {t'}"
def
tactic.find_local
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`find_local t` returns a local constant with type t, or fails if none exists.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
dependent_pose_core (l : list (expr × expr)) : tactic unit
do let lc := l.map prod.fst, let lm := l.map (λ⟨l, v⟩, (l.local_uniq_name, v)), old::other_goals ← get_goals, t ← infer_type old, new_goal ← mk_meta_var (t.pis lc), set_goals (old :: new_goal :: other_goals), exact ((new_goal.mk_app lc).instantiate_locals lm), return ()
def
tactic.dependent_pose_core
tactic
src/tactic/core.lean
[ "control.basic", "data.dlist.basic", "meta.expr", "system.io", "tactic.binder_matching", "tactic.interactive_expr", "tactic.lean_core_docs", "tactic.project_dir" ]
[]
`dependent_pose_core l`: introduce dependent hypotheses, where the proofs depend on the values of the previous local constants. `l` is a list of local constants and their values.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83