1fd7206f00
This PR implements `match`-expressions in `grind` using `match` congruence equations. The goal is to minimize the number of `cast` operations that need to be inserted, and avoid `cast` over functions. The new approach support `match`-expressions of the form `match h : ... with ...`.
62 lines
1.4 KiB
Text
62 lines
1.4 KiB
Text
def g (xs : List α) (ys : List α) :=
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match xs, ys with
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| [], _ => ys
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| _::_::_, [ ] => []
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| x::xs, ys => x :: g xs ys
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attribute [simp] g
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set_option trace.grind.assert true
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set_option trace.grind.split.candidate true
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set_option trace.grind.split.resolved true
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/--
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trace: [grind.assert] (match as, bs with
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| [], x => bs
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| head :: head_1 :: tail, [] => []
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| x :: xs, ys => x :: g xs ys) =
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d
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[grind.split.candidate] match as, bs with
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| [], x => bs
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| head :: head_1 :: tail, [] => []
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| x :: xs, ys => x :: g xs ys
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[grind.assert] bs = []
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[grind.assert] a₁ :: f 0 = as
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[grind.assert] f 0 = a₂ :: f 1
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[grind.assert] ¬d = []
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[grind.assert] (match as, bs with
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| [], x => bs
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| head :: head_1 :: tail, [] => []
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| x :: xs, ys => x :: g xs ys) =
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[]
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-/
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#guard_msgs (trace) in
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example (f : Nat → List Nat) : g as bs = d → bs = [] → a₁ :: f 0 = as → f 0 = a₂ :: f 1 → d = [] := by
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unfold g
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grind
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example : g as bs = d → as = [] → d = bs := by
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unfold g
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grind
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def f (x : List α) : Bool :=
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match x with
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| [] => true
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| _::_ => false
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example : f a = b → a = [] → b = true := by
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unfold f
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grind
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def f' (x : List Nat) : Bool :=
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match x with
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| [] => true
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| _::_ => false
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attribute [simp] f'
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#check f'.match_1.eq_1
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example : f' a = b → a = [] → b = true := by
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unfold f'
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grind
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