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gen (α : Type u)
reader_t (ulift ℕ) rand α
def
slim_check.gen
testing.slim_check
src/testing/slim_check/gen.lean
[ "control.random", "control.uliftable", "data.list.big_operators.lemmas", "data.list.perm" ]
[ "rand" ]
Monad to generate random examples to test properties with. It has a `nat` parameter so that the caller can decide on the size of the examples.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
io.run_gen {α} (x : gen α) (i : ℕ) : io α
io.run_rand (x.run ⟨i⟩)
def
slim_check.io.run_gen
testing.slim_check
src/testing/slim_check/gen.lean
[ "control.random", "control.uliftable", "data.list.big_operators.lemmas", "data.list.perm" ]
[ "io.run_rand" ]
Execute a `gen` inside the `io` monad using `i` as the example size and with a fresh random number generator.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
choose_any [random α] : gen α
⟨ λ _, rand.random α ⟩
def
slim_check.gen.choose_any
testing.slim_check
src/testing/slim_check/gen.lean
[ "control.random", "control.uliftable", "data.list.big_operators.lemmas", "data.list.perm" ]
[ "rand.random", "random" ]
Lift `random.random` to the `gen` monad.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
choose [bounded_random α] (x y : α) (p : x ≤ y) : gen (x .. y)
⟨ λ _, rand.random_r x y p ⟩
def
slim_check.gen.choose
testing.slim_check
src/testing/slim_check/gen.lean
[ "control.random", "control.uliftable", "data.list.big_operators.lemmas", "data.list.perm" ]
[ "bounded_random", "rand.random_r" ]
Lift `random.random_r` to the `gen` monad.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
choose_nat (x y : ℕ) (p : x ≤ y) : gen (x .. y)
choose x y p
def
slim_check.gen.choose_nat
testing.slim_check
src/testing/slim_check/gen.lean
[ "control.random", "control.uliftable", "data.list.big_operators.lemmas", "data.list.perm" ]
[]
Generate a `nat` example between `x` and `y`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
choose_nat' (x y : ℕ) (p : x < y) : gen (set.Ico x y)
have ∀ i, x < i → i ≤ y → i.pred < y, from λ i h₀ h₁, show i.pred.succ ≤ y, by rwa succ_pred_eq_of_pos; apply lt_of_le_of_lt (nat.zero_le _) h₀, subtype.map pred (λ i (h : x+1 ≤ i ∧ i ≤ y), ⟨le_pred_of_lt h.1, this _ h.1 h.2⟩) <$> choose (x+1) y p
def
slim_check.gen.choose_nat'
testing.slim_check
src/testing/slim_check/gen.lean
[ "control.random", "control.uliftable", "data.list.big_operators.lemmas", "data.list.perm" ]
[ "set.Ico", "subtype.map" ]
Generate a `nat` example between `x` and `y`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sized (cmd : ℕ → gen α) : gen α
⟨ λ ⟨sz⟩, reader_t.run (cmd sz) ⟨sz⟩ ⟩
def
slim_check.gen.sized
testing.slim_check
src/testing/slim_check/gen.lean
[ "control.random", "control.uliftable", "data.list.big_operators.lemmas", "data.list.perm" ]
[]
Get access to the size parameter of the `gen` monad. For reasons of universe polymorphism, it is specified in continuation passing style.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
resize (f : ℕ → ℕ) (cmd : gen α) : gen α
⟨ λ ⟨sz⟩, reader_t.run cmd ⟨f sz⟩ ⟩
def
slim_check.gen.resize
testing.slim_check
src/testing/slim_check/gen.lean
[ "control.random", "control.uliftable", "data.list.big_operators.lemmas", "data.list.perm" ]
[]
Apply a function to the size parameter.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
vector_of : ∀ (n : ℕ) (cmd : gen α), gen (vector α n)
| 0 _ := return vector.nil | (succ n) cmd := vector.cons <$> cmd <*> vector_of n cmd
def
slim_check.gen.vector_of
testing.slim_check
src/testing/slim_check/gen.lean
[ "control.random", "control.uliftable", "data.list.big_operators.lemmas", "data.list.perm" ]
[]
Create `n` examples using `cmd`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
list_of (cmd : gen α) : gen (list α)
sized $ λ sz, do do ⟨ n ⟩ ← uliftable.up $ choose_nat 0 (sz + 1) dec_trivial, v ← vector_of n.val cmd, return v.to_list
def
slim_check.gen.list_of
testing.slim_check
src/testing/slim_check/gen.lean
[ "control.random", "control.uliftable", "data.list.big_operators.lemmas", "data.list.perm" ]
[ "uliftable.up" ]
Create a list of examples using `cmd`. The size is controlled by the size parameter of `gen`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
one_of (xs : list (gen α)) (pos : 0 < xs.length) : gen α
do ⟨⟨n, h, h'⟩⟩ ← uliftable.up $ choose_nat' 0 xs.length pos, list.nth_le xs n h'
def
slim_check.gen.one_of
testing.slim_check
src/testing/slim_check/gen.lean
[ "control.random", "control.uliftable", "data.list.big_operators.lemmas", "data.list.perm" ]
[ "uliftable.up" ]
Given a list of example generators, choose one to create an example.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
elements (xs : list α) (pos : 0 < xs.length) : gen α
do ⟨⟨n,h₀,h₁⟩⟩ ← uliftable.up $ choose_nat' 0 xs.length pos, pure $ list.nth_le xs n h₁
def
slim_check.gen.elements
testing.slim_check
src/testing/slim_check/gen.lean
[ "control.random", "control.uliftable", "data.list.big_operators.lemmas", "data.list.perm" ]
[ "uliftable.up" ]
Given a list of example generators, choose one to create an example.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
freq_aux : Π (xs : list (ℕ+ × gen α)) i, i < (xs.map (subtype.val ∘ prod.fst)).sum → gen α
| [] i h := false.elim (nat.not_lt_zero _ h) | ((i, x) :: xs) j h := if h' : j < i then x else freq_aux xs (j - i) (by { rw tsub_lt_iff_right (le_of_not_gt h'), simpa [list.sum_cons, add_comm] using h })
def
slim_check.gen.freq_aux
testing.slim_check
src/testing/slim_check/gen.lean
[ "control.random", "control.uliftable", "data.list.big_operators.lemmas", "data.list.perm" ]
[ "tsub_lt_iff_right" ]
`freq_aux xs i _` takes a weighted list of generator and a number meant to select one of the generators. If we consider `freq_aux [(1, gena), (3, genb), (5, genc)] 4 _`, we choose a generator by splitting the interval 1-9 into 1-1, 2-4, 5-9 so that the width of each interval corresponds to one of the number in the lis...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
freq (xs : list (ℕ+ × gen α)) (pos : 0 < xs.length) : gen α
let s := (xs.map (subtype.val ∘ prod.fst)).sum in have ha : 1 ≤ s, from (le_trans pos $ list.length_map (subtype.val ∘ prod.fst) xs ▸ (list.length_le_sum_of_one_le _ (λ i, by { simp, intros, assumption }))), have 0 ≤ s - 1, from le_tsub_of_add_le_right ha, uliftable.adapt_up gen.{0} gen.{u} (choose_nat 0 (s...
def
slim_check.gen.freq
testing.slim_check
src/testing/slim_check/gen.lean
[ "control.random", "control.uliftable", "data.list.big_operators.lemmas", "data.list.perm" ]
[ "le_tsub_iff_right", "le_tsub_of_add_le_right", "list.length_le_sum_of_one_le", "uliftable.adapt_up" ]
`freq [(1, gena), (3, genb), (5, genc)] _` will choose one of `gena`, `genb`, `genc` with probabilities proportional to the number accompanying them. In this example, the sum of those numbers is 9, `gena` will be chosen with probability ~1/9, `genb` with ~3/9 (i.e. 1/3) and `genc` with probability 5/9.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
permutation_of {α : Type u} : Π xs : list α, gen (subtype $ list.perm xs)
| [] := pure ⟨[], list.perm.nil ⟩ | (x :: xs) := do ⟨xs',h⟩ ← permutation_of xs, ⟨⟨n,_,h'⟩⟩ ← uliftable.up $ choose_nat 0 xs'.length dec_trivial, pure ⟨list.insert_nth n x xs', list.perm.trans (list.perm.cons _ h) (list.perm_insert_nth _ _ h').symm ⟩
def
slim_check.gen.permutation_of
testing.slim_check
src/testing/slim_check/gen.lean
[ "control.random", "control.uliftable", "data.list.big_operators.lemmas", "data.list.perm" ]
[ "list.perm", "list.perm_insert_nth", "uliftable.up" ]
Generate a random permutation of a given list.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sizeof_lt {α} [has_sizeof α] (x y : α)
sizeof x < sizeof y
def
slim_check.sizeof_lt
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
`sizeof_lt x y` compares the sizes of `x` and `y`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
shrink_fn (α : Type*) [has_sizeof α]
Π x : α, lazy_list { y : α // sizeof_lt y x }
def
slim_check.shrink_fn
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "lazy_list" ]
`shrink_fn α` is the type of functions that shrink an argument of type `α`
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sampleable
[wf : has_sizeof α] (sample [] : gen α) (shrink : Π x : α, lazy_list { y : α // @sizeof _ wf y < @sizeof _ wf x } := λ _, lazy_list.nil)
class
slim_check.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "lazy_list", "shrink" ]
`sampleable α` provides ways of creating examples of type `α`, and given such an example `x : α`, gives us a way to shrink it and find simpler examples.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sampleable_functor (F : Type u → Type v) [functor F]
[wf : Π α [has_sizeof α], has_sizeof (F α)] (sample [] : ∀ {α}, gen α → gen (F α)) (shrink : ∀ α [has_sizeof α], shrink_fn α → shrink_fn (F α)) (p_repr : ∀ α, has_repr α → has_repr (F α))
class
slim_check.sampleable_functor
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink" ]
`sampleable_functor F` makes it possible to create samples of and shrink `F α` given a sampling function and a shrinking function for arbitrary `α`
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sampleable_bifunctor (F : Type u → Type v → Type w) [bifunctor F]
[wf : Π α β [has_sizeof α] [has_sizeof β], has_sizeof (F α β)] (sample [] : ∀ {α β}, gen α → gen β → gen (F α β)) (shrink : ∀ α β [has_sizeof α] [has_sizeof β], shrink_fn α → shrink_fn β → shrink_fn (F α β)) (p_repr : ∀ α β, has_repr α → has_repr β → has_repr (F α β))
class
slim_check.sampleable_bifunctor
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "bifunctor", "shrink" ]
`sampleable_bifunctor F` makes it possible to create samples of and shrink `F α β` given a sampling function and a shrinking function for arbitrary `α` and `β`
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sampleable.mk_trivial_interp : tactic unit
tactic.refine ``(id)
def
slim_check.sampleable.mk_trivial_interp
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
This function helps infer the proxy representation and interpretation in `sampleable_ext` instances.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sampleable_ext (α : Sort u)
(proxy_repr : Type v) [wf : has_sizeof proxy_repr] (interp [] : proxy_repr → α . sampleable.mk_trivial_interp) [p_repr : has_repr proxy_repr] (sample [] : gen proxy_repr) (shrink : shrink_fn proxy_repr)
class
slim_check.sampleable_ext
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink" ]
`sampleable_ext` generalizes the behavior of `sampleable` and makes it possible to express instances for types that do not lend themselves to introspection, such as `ℕ → ℕ`. If we test a quantification over functions the counter-examples cannot be shrunken or printed meaningfully. For that purpose, `sampleable_ext` pr...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sampleable_ext.of_sampleable {α} [sampleable α] [has_repr α] : sampleable_ext α
{ proxy_repr := α, sample := sampleable.sample α, shrink := shrink }
instance
slim_check.sampleable_ext.of_sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sampleable.functor {α} {F} [functor F] [sampleable_functor F] [sampleable α] : sampleable (F α)
{ wf := _, sample := sampleable_functor.sample F (sampleable.sample α), shrink := sampleable_functor.shrink α sampleable.shrink }
instance
slim_check.sampleable.functor
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sampleable.bifunctor {α β} {F} [bifunctor F] [sampleable_bifunctor F] [sampleable α] [sampleable β] : sampleable (F α β)
{ wf := _, sample := sampleable_bifunctor.sample F (sampleable.sample α) (sampleable.sample β), shrink := sampleable_bifunctor.shrink α β sampleable.shrink sampleable.shrink }
instance
slim_check.sampleable.bifunctor
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "bifunctor", "shrink" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sampleable_ext.functor {α} {F} [functor F] [sampleable_functor F] [sampleable_ext α] : sampleable_ext (F α)
{ wf := _, proxy_repr := F (proxy_repr α), interp := functor.map (interp _), sample := sampleable_functor.sample F (sampleable_ext.sample α), shrink := sampleable_functor.shrink _ sampleable_ext.shrink, p_repr := sampleable_functor.p_repr _ sampleable_ext.p_repr }
instance
slim_check.sampleable_ext.functor
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sampleable_ext.bifunctor {α β} {F} [bifunctor F] [sampleable_bifunctor F] [sampleable_ext α] [sampleable_ext β] : sampleable_ext (F α β)
{ wf := _, proxy_repr := F (proxy_repr α) (proxy_repr β), interp := bifunctor.bimap (interp _) (interp _), sample := sampleable_bifunctor.sample F (sampleable_ext.sample α) (sampleable_ext.sample β), shrink := sampleable_bifunctor.shrink _ _ sampleable_ext.shrink sampleable_ext.shrink, p_repr := sampleable_bi...
instance
slim_check.sampleable_ext.bifunctor
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "bifunctor", "shrink" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
nat.shrink' (k : ℕ) : Π n : ℕ, n ≤ k → list { m : ℕ // has_well_founded.r m k } → list { m : ℕ // has_well_founded.r m k }
| n hn ls := if h : n ≤ 1 then ls.reverse else have h₂ : 0 < n, by linarith, have 1 * n / 2 < n, from nat.div_lt_of_lt_mul (nat.mul_lt_mul_of_pos_right (by norm_num) h₂), have n / 2 < n, by simpa, let m := n / 2 in have h₀ : m ≤ k, from le_trans (le_of_lt this) hn, have h₃ : 0 < m, ...
def
slim_check.nat.shrink'
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "nat.div_lt_of_lt_mul" ]
`nat.shrink' k n` creates a list of smaller natural numbers by successively dividing `n` by 2 and subtracting the difference from `k`. For example, `nat.shrink 100 = [50, 75, 88, 94, 97, 99]`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
nat.shrink (n : ℕ) : list { m : ℕ // has_well_founded.r m n }
if h : n > 0 then have ∀ k, 1 < k → n / k < n, from λ k hk, nat.div_lt_of_lt_mul (suffices 1 * n < k * n, by simpa, nat.mul_lt_mul_of_pos_right hk h), ⟨n/11, this _ (by norm_num)⟩ :: ⟨n/3, this _ (by norm_num)⟩ :: nat.shrink' n n le_rfl [] else []
def
slim_check.nat.shrink
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "le_rfl", "nat.div_lt_of_lt_mul" ]
`nat.shrink n` creates a list of smaller natural numbers by successively dividing by 2 and subtracting the difference from `n`. For example, `nat.shrink 100 = [50, 75, 88, 94, 97, 99]`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sampleable.lift (α : Type u) {β : Type u} [sampleable α] (f : α → β) (g : β → α) (h : ∀ (a : α), sizeof (g (f a)) ≤ sizeof a) : sampleable β
{ wf := ⟨ sizeof ∘ g ⟩, sample := f <$> sample α, shrink := λ x, have ∀ a, sizeof a < sizeof (g x) → sizeof (g (f a)) < sizeof (g x), by introv h'; solve_by_elim [lt_of_le_of_lt], subtype.map f this <$> shrink (g x) }
def
slim_check.sampleable.lift
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink", "subtype.map" ]
Transport a `sampleable` instance from a type `α` to a type `β` using functions between the two, going in both directions. Function `g` is used to define the well-founded order that `shrink` is expected to follow.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
nat.sampleable : sampleable ℕ
{ sample := sized $ λ sz, freq [(1, coe <$> choose_any (fin $ succ (sz^3))), (3, coe <$> choose_any (fin $ succ sz))] dec_trivial, shrink := λ x, lazy_list.of_list $ nat.shrink x }
instance
slim_check.nat.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "lazy_list.of_list", "shrink" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
iterate_shrink {α} [has_to_string α] [sampleable α] (p : α → Prop) [decidable_pred p] : α → option α
well_founded.fix has_well_founded.wf $ λ x f_rec, do trace sformat!"{x} : {(shrink x).to_list}" $ pure (), y ← (shrink x).find (λ a, p a), f_rec y y.property <|> some y.val
def
slim_check.iterate_shrink
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink" ]
`iterate_shrink p x` takes a decidable predicate `p` and a value `x` of some sampleable type and recursively shrinks `x`. It first calls `shrink x` to get a list of candidate sample, finds the first that satisfies `p` and recursively tries to shrink that one.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
fin.sampleable {n : ℕ} [ne_zero n] : sampleable (fin n)
sampleable.lift ℕ fin.of_nat' fin.val $ λ i, (mod_le _ _ : i % n ≤ i)
instance
slim_check.fin.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "fin.of_nat'", "ne_zero" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
fin.sampleable' {n} : sampleable (fin (succ n))
sampleable.lift ℕ fin.of_nat fin.val $ λ i, (mod_le _ _ : i % succ n ≤ i)
instance
slim_check.fin.sampleable'
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
pnat.sampleable : sampleable ℕ+
sampleable.lift ℕ nat.succ_pnat pnat.nat_pred $ λ a, by unfold_wf; simp only [pnat.nat_pred, succ_pnat, pnat.mk_coe, tsub_zero, succ_sub_succ_eq_sub]
instance
slim_check.pnat.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "nat.succ_pnat", "pnat.mk_coe", "pnat.nat_pred", "tsub_zero" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
int.has_sizeof : has_sizeof ℤ
⟨ int.nat_abs ⟩
def
slim_check.int.has_sizeof
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
Redefine `sizeof` for `int` to make it easier to use with `nat`
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
int.sampleable : sampleable ℤ
{ wf := _, sample := sized $ λ sz, freq [(1, subtype.val <$> choose (-(sz^3 + 1) : ℤ) (sz^3 + 1) (neg_le_self dec_trivial)), (3, subtype.val <$> choose (-(sz + 1)) (sz + 1) (neg_le_self dec_trivial))] dec_trivial, shrink := λ x, lazy_list.of_list $ (nat.shrink $ int.nat_...
instance
slim_check.int.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "lazy_list.of_list", "shrink" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
bool.sampleable : sampleable bool
{ wf := ⟨ λ b, if b then 1 else 0 ⟩, sample := do { x ← choose_any bool, return x }, shrink := λ b, if h : b then lazy_list.singleton ⟨ff, by cases h; unfold_wf⟩ else lazy_list.nil }
instance
slim_check.bool.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "lazy_list.singleton", "shrink" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
prod.shrink {α β} [has_sizeof α] [has_sizeof β] (shr_a : shrink_fn α) (shr_b : shrink_fn β) : shrink_fn (α × β)
| ⟨x₀,x₁⟩ := let xs₀ : lazy_list { y : α × β // sizeof_lt y (x₀,x₁) } := (shr_a x₀).map $ subtype.map (λ a, (a, x₁)) (λ x h, by dsimp [sizeof_lt]; unfold_wf; apply h), xs₁ : lazy_list { y : α × β // sizeof_lt y (x₀,x₁) } := (shr_b x₁).map $ subtype.map (λ a, (x₀, a...
def
slim_check.prod.shrink
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "lazy_list", "subtype.map" ]
Provided two shrinking functions `prod.shrink` shrinks a pair `(x, y)` by first shrinking `x` and pairing the results with `y` and then shrinking `y` and pairing the results with `x`. All pairs either contain `x` untouched or `y` untouched. We rely on shrinking being repeated for `x` to get maximally shrunken and then...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
prod.sampleable : sampleable_bifunctor.{u v} prod
{ wf := _, sample := λ α β sama samb, do { ⟨x⟩ ← (uliftable.up $ sama : gen (ulift.{max u v} α)), ⟨y⟩ ← (uliftable.up $ samb : gen (ulift.{max u v} β)), pure (x,y) }, shrink := @prod.shrink, p_repr := @prod.has_repr }
instance
slim_check.prod.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink", "uliftable.up" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sigma.sampleable {α β} [sampleable α] [sampleable β] : sampleable (Σ _ : α, β)
sampleable.lift (α × β) (λ ⟨x,y⟩, ⟨x,y⟩) (λ ⟨x,y⟩, ⟨x,y⟩) $ λ ⟨x,y⟩, le_rfl
instance
slim_check.sigma.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "le_rfl" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sum.shrink {α β} [has_sizeof α] [has_sizeof β] (shrink_α : shrink_fn α) (shrink_β : shrink_fn β) : shrink_fn (α ⊕ β)
| (sum.inr x) := (shrink_β x).map $ subtype.map sum.inr $ λ a, by dsimp [sizeof_lt]; unfold_wf; solve_by_elim | (sum.inl x) := (shrink_α x).map $ subtype.map sum.inl $ λ a, by dsimp [sizeof_lt]; unfold_wf; solve_by_elim
def
slim_check.sum.shrink
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "subtype.map" ]
shrinking function for sum types
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sum.sampleable : sampleable_bifunctor.{u v} sum
{ wf := _, sample := λ (α : Type u) (β : Type v) sam_α sam_β, (@uliftable.up_map gen.{u} gen.{max u v} _ _ _ _ (@sum.inl α β) sam_α <|> @uliftable.up_map gen.{v} gen.{max v u} _ _ _ _ (@sum.inr α β) sam_β), shrink := λ α β Iα Iβ shr_α shr_β, @sum.shrink _ _ Iα Iβ shr_α shr_β, p_repr := @s...
instance
slim_check.sum.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink", "uliftable.up_map" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
rat.sampleable : sampleable ℚ
sampleable.lift (ℤ × ℕ+) (λ x, prod.cases_on x rat.mk_pnat) (λ r, (r.num, ⟨r.denom, r.pos⟩)) $ begin intro i, rcases i with ⟨x,⟨y,hy⟩⟩; unfold_wf; dsimp [rat.mk_pnat], mono*, { rw [← int.coe_nat_le, int.coe_nat_abs, int.coe_nat_abs], apply int.abs_div_le_abs }, { change _ - 1 ≤ y-1, apply tsub_le_ts...
instance
slim_check.rat.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "int.abs_div_le_abs", "int.coe_nat_abs", "int.coe_nat_le", "rat.mk_pnat", "tsub_le_tsub_right" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sampleable_char (length : nat) (characters : string) : sampleable char
{ sample := do { x ← choose_nat 0 length dec_trivial, if x.val = 0 then do n ← sample ℕ, pure $ char.of_nat n else do i ← choose_nat 0 (characters.length - 1) dec_trivial, pure (characters.mk_iterator.nextn i)....
def
slim_check.sampleable_char
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink" ]
`sampleable_char` can be specialized into customized `sampleable char` instances. The resulting instance has `1 / length` chances of making an unrestricted choice of characters and it otherwise chooses a character from `characters` with uniform probabilities.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
char.sampleable : sampleable char
sampleable_char 3 " 0123abcABC:,;`\\/"
instance
slim_check.char.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
list.sizeof_drop_lt_sizeof_of_lt_length {xs : list α} {k} (hk : 0 < k) (hk' : k < xs.length) : sizeof (list.drop k xs) < sizeof xs
begin induction xs with x xs generalizing k, { cases hk' }, cases k, { cases hk }, have : sizeof xs < sizeof (x :: xs), { unfold_wf }, cases k, { simp only [this, list.drop] }, { simp only [list.drop], transitivity, { solve_by_elim [xs_ih, lt_of_succ_lt_succ hk', zero_lt_succ] }, { assumpt...
lemma
slim_check.list.sizeof_drop_lt_sizeof_of_lt_length
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
list.sizeof_cons_lt_right (a b : α) {xs : list α} (h : sizeof a < sizeof b) : sizeof (a :: xs) < sizeof (b :: xs)
by unfold_wf; assumption
lemma
slim_check.list.sizeof_cons_lt_right
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
list.sizeof_cons_lt_left (x : α) {xs xs' : list α} (h : sizeof xs < sizeof xs') : sizeof (x :: xs) < sizeof (x :: xs')
by unfold_wf; assumption
lemma
slim_check.list.sizeof_cons_lt_left
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
list.sizeof_append_lt_left {xs ys ys' : list α} (h : sizeof ys < sizeof ys') : sizeof (xs ++ ys) < sizeof (xs ++ ys')
begin induction xs, { apply h }, { unfold_wf, simp only [list.sizeof, add_lt_add_iff_left], exact xs_ih } end
lemma
slim_check.list.sizeof_append_lt_left
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
list.one_le_sizeof (xs : list α) : 1 ≤ sizeof xs
by cases xs; unfold_wf; linarith
lemma
slim_check.list.one_le_sizeof
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
list.shrink_removes (k : ℕ) (hk : 0 < k) : Π (xs : list α) n, n = xs.length → lazy_list { ys : list α // sizeof_lt ys xs }
| xs n hn := if hkn : k > n then lazy_list.nil else if hkn' : k = n then have 1 < xs.sizeof, by { subst_vars, cases xs, { contradiction }, unfold_wf, apply lt_of_lt_of_le, show 1 < 1 + has_sizeof.sizeof xs_hd + 1, { linarith }, { mono, apply list.one_le_sizeof, } }, ...
def
slim_check.list.shrink_removes
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "lazy_list", "lazy_list.singleton", "list.split_at", "list.split_at_eq_take_drop", "list.take_append_drop", "prod.mk.inj_iff", "subtype.map" ]
`list.shrink_removes` shrinks a list by removing chunks of size `k` in the middle of the list.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
list.shrink_one : shrink_fn (list α)
| [] := lazy_list.nil | (x :: xs) := lazy_list.append (subtype.map (λ x', x' :: xs) (λ a, list.sizeof_cons_lt_right _ _) <$> shr x) (subtype.map ((::) x) (λ _, list.sizeof_cons_lt_left _) <$> list.shrink_one xs)
def
slim_check.list.shrink_one
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "lazy_list.append", "subtype.map" ]
`list.shrink_one xs` shrinks list `xs` by shrinking only one item in the list.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
list.shrink_with (xs : list α) : lazy_list { ys : list α // sizeof_lt ys xs }
let n := xs.length in lazy_list.append ((lazy_list.cons n $ (shrink n).reverse.map subtype.val).bind (λ k, if hk : 0 < k then list.shrink_removes k hk xs n rfl else lazy_list.nil )) (list.shrink_one shr _)
def
slim_check.list.shrink_with
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "lazy_list", "lazy_list.append", "shrink" ]
`list.shrink_with shrink_f xs` shrinks `xs` by first considering `xs` with chunks removed in the middle (starting with chunks of size `xs.length` and halving down to `1`) and then shrinks only one element of the list. This strategy is taken directly from Haskell's QuickCheck
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
list.sampleable : sampleable_functor list.{u}
{ wf := _, sample := λ α sam_α, list_of sam_α, shrink := λ α Iα shr_α, @list.shrink_with _ Iα shr_α, p_repr := @list.has_repr }
instance
slim_check.list.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
Prop.sampleable_ext : sampleable_ext Prop
{ proxy_repr := bool, interp := coe, sample := choose_any bool, shrink := λ _, lazy_list.nil }
instance
slim_check.Prop.sampleable_ext
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
no_shrink (α : Type*)
α
def
slim_check.no_shrink
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
`no_shrink` is a type annotation to signal that a certain type is not to be shrunk. It can be useful in combination with other types: e.g. `xs : list (no_shrink ℤ)` will result in the list being cut down but individual integers being kept as is.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
no_shrink.inhabited {α} [inhabited α] : inhabited (no_shrink α)
⟨ (default : α) ⟩
instance
slim_check.no_shrink.inhabited
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
no_shrink.mk {α} (x : α) : no_shrink α
x
def
slim_check.no_shrink.mk
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
Introduction of the `no_shrink` type.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
no_shrink.get {α} (x : no_shrink α) : α
x
def
slim_check.no_shrink.get
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
Selector of the `no_shrink` type.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
no_shrink.sampleable {α} [sampleable α] : sampleable (no_shrink α)
{ sample := no_shrink.mk <$> sample α }
instance
slim_check.no_shrink.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
string.sampleable : sampleable string
{ sample := do { x ← list_of (sample char), pure x.as_string }, .. sampleable.lift (list char) list.as_string string.to_list $ λ _, le_rfl }
instance
slim_check.string.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "le_rfl" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
tree.sample (sample : gen α) : ℕ → gen (tree α) | n
if h : n > 0 then have n / 2 < n, from div_lt_self h (by norm_num), tree.node <$> sample <*> tree.sample (n / 2) <*> tree.sample (n / 2) else pure tree.nil
def
slim_check.tree.sample
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "div_lt_self", "tree" ]
implementation of `sampleable (tree α)`
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
rec_shrink {α : Type*} [has_sizeof α] (t : α) (sh : Π x : α, sizeof_lt x t → lazy_list { y : α // sizeof_lt y x }) : shrink_fn { t' : α // sizeof_lt t' t }
| ⟨t',ht'⟩ := (λ t'' : { y : α // sizeof_lt y t' }, ⟨⟨t''.val, lt_trans t''.property ht'⟩, t''.property⟩ ) <$> sh t' ht'
def
slim_check.rec_shrink
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "lazy_list" ]
`rec_shrink x f_rec` takes the recursive call `f_rec` introduced by `well_founded.fix` and turns it into a shrinking function whose result is adequate to use in a recursive call.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
tree.one_le_sizeof {α} [has_sizeof α] (t : tree α) : 1 ≤ sizeof t
by cases t; unfold_wf; linarith
lemma
slim_check.tree.one_le_sizeof
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "tree" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
rec_shrink_with [has_sizeof α] (shrink_a : Π x : α, shrink_fn { y : α // sizeof_lt y x } → list (lazy_list { y : α // sizeof_lt y x })) : shrink_fn α
well_founded.fix (sizeof_measure_wf _) $ λ t f_rec, lazy_list.join (lazy_list.of_list $ shrink_a t $ λ ⟨t', h⟩, rec_shrink _ f_rec _)
def
slim_check.rec_shrink_with
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "lazy_list", "lazy_list.join", "lazy_list.of_list" ]
Recursion principle for shrinking tree-like structures.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
rec_shrink_with_eq [has_sizeof α] (shrink_a : Π x : α, shrink_fn { y : α // sizeof_lt y x } → list (lazy_list { y : α // sizeof_lt y x })) (x : α) : rec_shrink_with shrink_a x = lazy_list.join (lazy_list.of_list $ shrink_a x $ λ t', rec_shrink _ (λ x h', rec_shrink_with shrink_a x) _)
begin conv_lhs { rw [rec_shrink_with, well_founded.fix_eq], }, congr, ext ⟨y, h⟩, refl end
lemma
slim_check.rec_shrink_with_eq
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "lazy_list", "lazy_list.join", "lazy_list.of_list" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
tree.shrink_with [has_sizeof α] (shrink_a : shrink_fn α) : shrink_fn (tree α)
rec_shrink_with $ λ t, match t with | tree.nil := λ f_rec, [] | (tree.node x t₀ t₁) := λ f_rec, have h₂ : sizeof_lt tree.nil (tree.node x t₀ t₁), by clear _match; have := tree.one_le_sizeof t₀; dsimp [sizeof_lt, sizeof, has_sizeof.sizeof] at *; unfold_wf; linarith, have h₀ : sizeof_lt t₀ (tree.nod...
def
slim_check.tree.shrink_with
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "lazy_list.of_list", "tree" ]
`tree.shrink_with shrink_f t` shrinks `xs` by using the empty tree, each subtrees, and by shrinking the subtree to recombine them. This strategy is taken directly from Haskell's QuickCheck
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sampleable_tree : sampleable_functor tree
{ wf := _, sample := λ α sam_α, sized $ tree.sample sam_α, shrink := λ α Iα shr_α, @tree.shrink_with _ Iα shr_α, p_repr := @tree.has_repr }
instance
slim_check.sampleable_tree
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink", "tree" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
small (α : Type*)
α
def
slim_check.small
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "small" ]
Type tag that signals to `slim_check` to use small values for a given type.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
small.mk {α} (x : α) : small α
x
def
slim_check.small.mk
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "small" ]
Add the `small` type tag
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
large (α : Type*)
α
def
slim_check.large
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
Type tag that signals to `slim_check` to use large values for a given type.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
large.mk {α} (x : α) : large α
x
def
slim_check.large.mk
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
Add the `large` type tag
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
small.functor : functor small
id.monad.to_functor
instance
slim_check.small.functor
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "small" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
large.functor : functor large
id.monad.to_functor
instance
slim_check.large.functor
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
small.inhabited [inhabited α] : inhabited (small α)
⟨ (default : α) ⟩
instance
slim_check.small.inhabited
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "small" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
large.inhabited [inhabited α] : inhabited (large α)
⟨ (default : α) ⟩
instance
slim_check.large.inhabited
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
small.sampleable_functor : sampleable_functor small
{ wf := _, sample := λ α samp, gen.resize (λ n, n / 5 + 5) samp, shrink := λ α _, id, p_repr := λ α, id }
instance
slim_check.small.sampleable_functor
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink", "small" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
large.sampleable_functor : sampleable_functor large
{ wf := _, sample := λ α samp, gen.resize (λ n, n * 5) samp, shrink := λ α _, id, p_repr := λ α, id }
instance
slim_check.large.sampleable_functor
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
ulift.sampleable_functor : sampleable_functor ulift.{u v}
{ wf := λ α h, ⟨ λ ⟨x⟩, @sizeof α h x ⟩, sample := λ α samp, uliftable.up_map ulift.up $ samp, shrink := λ α _ shr ⟨x⟩, (shr x).map (subtype.map ulift.up (λ a h, h)), p_repr := λ α h, ⟨ @repr α h ∘ ulift.down ⟩ }
instance
slim_check.ulift.sampleable_functor
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink", "subtype.map", "uliftable.up_map" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
nat_le.sampleable {y} : slim_check.sampleable { x : ℕ // x ≤ y }
{ sample := do { ⟨x,h⟩ ← slim_check.gen.choose_nat 0 y dec_trivial, pure ⟨x, h.2⟩}, shrink := λ ⟨x, h⟩, (λ a : subtype _, subtype.rec_on a $ λ x' h', ⟨⟨x', le_trans (le_of_lt h') h⟩, h'⟩) <$> shrink x }
instance
slim_check.nat_le.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink", "slim_check.gen.choose_nat", "slim_check.sampleable" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
nat_ge.sampleable {x} : slim_check.sampleable { y : ℕ // x ≤ y }
{ sample := do { (y : ℕ) ← slim_check.sampleable.sample ℕ, pure ⟨x+y, by norm_num⟩ }, shrink := λ ⟨y, h⟩, (λ a : { y' // sizeof y' < sizeof (y - x) }, subtype.rec_on a $ λ δ h', ⟨⟨x + δ, nat.le_add_right _ _⟩, lt_tsub_iff_left.mp h'⟩) <$> shrink (y - x) }
instance
slim_check.nat_ge.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink", "slim_check.sampleable" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
nat_gt.sampleable {x} : slim_check.sampleable { y : ℕ // x < y }
{ sample := do { (y : ℕ) ← slim_check.sampleable.sample ℕ, pure ⟨x+y+1, by linarith⟩ }, shrink := λ x, shrink _ }
instance
slim_check.nat_gt.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "shrink", "slim_check.sampleable" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
le.sampleable {y : α} [sampleable α] [linear_ordered_add_comm_group α] : slim_check.sampleable { x : α // x ≤ y }
{ sample := do { x ← sample α, pure ⟨y - |x|, sub_le_self _ (abs_nonneg _) ⟩ }, shrink := λ _, lazy_list.nil }
instance
slim_check.le.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "abs_nonneg", "linear_ordered_add_comm_group", "shrink", "slim_check.sampleable" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
ge.sampleable {x : α} [sampleable α] [linear_ordered_add_comm_group α] : slim_check.sampleable { y : α // x ≤ y }
{ sample := do { y ← sample α, pure ⟨x + |y|, by norm_num [abs_nonneg]⟩ }, shrink := λ _, lazy_list.nil }
instance
slim_check.ge.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "abs_nonneg", "linear_ordered_add_comm_group", "shrink", "slim_check.sampleable" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
int_le.sampleable {y : ℤ} : slim_check.sampleable { x : ℤ // x ≤ y }
sampleable.lift ℕ (λ n, ⟨y - n, int.sub_left_le_of_le_add $ by simp⟩) (λ ⟨i, h⟩, (y - i).nat_abs) (λ n, by unfold_wf; simp [int_le.sampleable._match_1]; ring)
instance
slim_check.int_le.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "ring", "slim_check.sampleable" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
int_ge.sampleable {x : ℤ} : slim_check.sampleable { y : ℤ // x ≤ y }
sampleable.lift ℕ (λ n, ⟨x + n, by simp⟩) (λ ⟨i, h⟩, (i - x).nat_abs) (λ n, by unfold_wf; simp [int_ge.sampleable._match_1]; ring)
instance
slim_check.int_ge.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "ring", "slim_check.sampleable" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
int_lt.sampleable {y} : slim_check.sampleable { x : ℤ // x < y }
sampleable.lift ℕ (λ n, ⟨y - (n+1), int.sub_left_lt_of_lt_add $ by linarith [int.coe_nat_nonneg n]⟩) (λ ⟨i, h⟩, (y - i - 1).nat_abs) (λ n, by unfold_wf; simp [int_lt.sampleable._match_1]; ring)
instance
slim_check.int_lt.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "int.coe_nat_nonneg", "ring", "slim_check.sampleable" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
int_gt.sampleable {x} : slim_check.sampleable { y : ℤ // x < y }
sampleable.lift ℕ (λ n, ⟨x + (n+1), by linarith⟩) (λ ⟨i, h⟩, (i - x - 1).nat_abs) (λ n, by unfold_wf; simp [int_gt.sampleable._match_1]; ring)
instance
slim_check.int_gt.sampleable
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "ring", "slim_check.sampleable" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
perm.slim_check {xs : list α} : slim_check.sampleable { ys : list α // list.perm xs ys }
{ sample := permutation_of xs, shrink := λ _, lazy_list.nil }
instance
slim_check.perm.slim_check
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "list.perm", "shrink", "slim_check.sampleable" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
perm'.slim_check {xs : list α} : slim_check.sampleable { ys : list α // list.perm ys xs }
{ sample := subtype.map id (@list.perm.symm α _) <$> permutation_of xs, shrink := λ _, lazy_list.nil } setup_tactic_parser
instance
slim_check.perm'.slim_check
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "list.perm", "list.perm.symm", "shrink", "slim_check.sampleable", "subtype.map" ]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
print_samples {t : Type u} [has_repr t] (g : gen t) : io unit
do xs ← io.run_rand $ uliftable.down $ do { xs ← (list.range 10).mmap $ g.run ∘ ulift.up, pure ⟨xs.map repr⟩ }, xs.mmap' io.put_str_ln
def
slim_check.print_samples
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[ "io.run_rand", "uliftable.down" ]
Print (at most) 10 samples of a given type to stdout for debugging.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
mk_generator (e : expr) : tactic (expr × expr)
do t ← infer_type e, match t with | `(gen %%t) := do repr_inst ← mk_app ``has_repr [t] >>= mk_instance, pure (repr_inst, e) | _ := do samp_inst ← to_expr ``(sampleable_ext %%e) >>= mk_instance, repr_inst ← mk_mapp ``sampleable_ext.p_repr [e, samp_inst], gen ← mk_mapp ``sampleable_ext.sample [none, samp_inst],...
def
slim_check.mk_generator
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
Create a `gen α` expression from the argument of `#sample`
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
sample_cmd (_ : parse $ tk "#sample") : lean.parser unit
do e ← texpr, of_tactic $ do e ← i_to_expr e, (repr_inst, gen) ← mk_generator e, print_samples ← mk_mapp ``print_samples [none, repr_inst, gen], sample ← eval_expr (io unit) print_samples, unsafe_run_io sample
def
slim_check.sample_cmd
testing.slim_check
src/testing/slim_check/sampleable.lean
[ "data.lazy_list.basic", "data.tree", "data.pnat.basic", "control.bifunctor", "control.ulift", "testing.slim_check.gen", "tactic.linarith" ]
[]
`#sample my_type`, where `my_type` has an instance of `sampleable`, prints ten random values of type `my_type` of using an increasing size parameter. ```lean #sample nat -- prints -- 0 -- 0 -- 2 -- 24 -- 64 -- 76 -- 5 -- 132 -- 8 -- 449 -- or some other sequence of numbers #sample list int -- prints -- [] -- [1, 1] -...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
test_result (p : Prop) | success : (psum unit p) → test_result | gave_up {} : ℕ → test_result | failure : ¬ p → (list string) → ℕ → test_result
inductive
slim_check.test_result
testing.slim_check
src/testing/slim_check/testable.lean
[ "testing.slim_check.sampleable" ]
[]
Result of trying to disprove `p` The constructors are: * `success : (psum unit p) → test_result` succeed when we find another example satisfying `p` In `success h`, `h` is an optional proof of the proposition. Without the proof, all we know is that we found one example where `p` holds. With a pr...
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
test_result.to_string {p} : test_result p → string
| (test_result.success (psum.inl ())) := "success (without proof)" | (test_result.success (psum.inr h)) := "success (with proof)" | (test_result.gave_up n) := sformat!"gave up {n} times" | (test_result.failure a vs _) := sformat!"failed {vs}"
def
slim_check.test_result.to_string
testing.slim_check
src/testing/slim_check/testable.lean
[ "testing.slim_check.sampleable" ]
[]
format a `test_result` as a string.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
slim_check_cfg
(num_inst : ℕ := 100) -- number of examples (max_size : ℕ := 100) -- final size argument (trace_discarded : bool := ff) -- enable the printing out of discarded samples (trace_success : bool := ff) -- enable the printing out of successful tests (trace_shrink : ...
structure
slim_check.slim_check_cfg
testing.slim_check
src/testing/slim_check/testable.lean
[ "testing.slim_check.sampleable" ]
[]
configuration for testing a property
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
printable_prop (p : Prop)
(print_prop : option string)
class
slim_check.printable_prop
testing.slim_check
src/testing/slim_check/testable.lean
[ "testing.slim_check.sampleable" ]
[]
`printable_prop p` allows one to print a proposition so that `slim_check` can indicate how values relate to each other.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
default_printable_prop {p} : printable_prop p
⟨ none ⟩
instance
slim_check.default_printable_prop
testing.slim_check
src/testing/slim_check/testable.lean
[ "testing.slim_check.sampleable" ]
[]
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83
testable (p : Prop)
(run [] (cfg : slim_check_cfg) (minimize : bool) : gen (test_result p))
class
slim_check.testable
testing.slim_check
src/testing/slim_check/testable.lean
[ "testing.slim_check.sampleable" ]
[]
`testable p` uses random examples to try to disprove `p`.
https://github.com/leanprover-community/mathlib
65a1391a0106c9204fe45bc73a039f056558cb83