68 lines
1.6 KiB
Text
68 lines
1.6 KiB
Text
open tactic conv
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open tactic
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run_command mk_simp_attr `foo
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run_command mk_simp_attr `bla
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constant f : nat → nat → nat
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@[foo] lemma f_lemma : ∀ x, f x x = 0 :=
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sorry
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constant g : nat → nat
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@[bla] lemma g_lemma : ∀ x, g x = x :=
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sorry
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example (a b c : nat) : (λ x, g (f (a + 0) (sizeof x))) a = 0 :=
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by conversion $
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whnf >>
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trace_lhs >>
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apply_simp_set `bla >>
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dsimp >>
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trace "after defeq simplifier" >>
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trace_lhs >>
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change `(f a a) >>
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trace_lhs >>
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apply_simp_set `foo >>
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trace_lhs
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set_option trace.app_builder true
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attribute [simp] sizeof_nat_eq
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example (a b c : nat) : (λ x, g (f x (sizeof x))) = (λ x, 0) :=
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by conversion $
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funext $ do
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trace_lhs,
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apply_simp_set `bla,
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dsimp,
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apply_simp_set `foo
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constant h : nat → nat → nat
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lemma ex (a : nat) : (λ a, h (f a (sizeof a)) (g a)) = (λ a, h 0 a) :=
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by conversion $
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bottom_up $
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(apply_simp_set `foo <|> apply_simp_set `bla <|> dsimp)
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lemma ex2 {A : Type} [comm_group A] (a b : A) : b * 1 * a = a * b :=
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by conversion $
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bottom_up (apply_simp_set `default)
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lemma ex3 (p q r : Prop) : (p ∧ true ∧ p) = p :=
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by conversion $
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bottom_up (apply_propext_simp_set `default)
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print "---------"
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lemma ex4 (a b c : nat) : g (g (g (f (f (g (g a)) (g (g a))) a))) = g (g (g (f (f a a) a))) :=
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by conversion $
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findp `(λ x, f (g x) (g x)) $
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trace "found pattern" >> trace_lhs >>
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bottom_up (apply_simp_set `bla)
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lemma ex5 (a b c : nat) : g (g (g (f (f (g (g a)) (g (g a))) a))) = g (g (g (f (f a a) a))) :=
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by conversion $
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find $
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match_expr `(λ x, f (g x) (g x)) >>
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trace "found pattern" >> trace_lhs >>
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bottom_up (apply_simp_set `bla)
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