3b78ada5d8
This PR improves support for `Nat` in the `cutsat` procedure used in `grind`: - `cutsat` no longer *pollutes* the local context with facts of the form `-1 * NatCast.natCast x <= 0` for each `x : Nat`. These facts are now stored internally in the `cutsat` state. - A single context is now used for all `Nat` terms. The PR also introduces a mapping mechanism for all "foreign" types that can be converted to `Int`. Currently, only `Nat` is supported, but additional types will be added in the future.
78 lines
2 KiB
Text
78 lines
2 KiB
Text
opaque g : Nat → Nat
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set_option trace.Meta.debug true
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@[grind] def f (a : Nat) :=
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match a with
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| 0 => 10
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| x+1 => g (f x)
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set_option grind.debug true
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set_option grind.debug.proofs true
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set_option trace.grind.ematch.instance true
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set_option trace.grind.assert true
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/--
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info: [grind.assert] f (y + 1) = a
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[grind.assert] ¬a = g (f y)
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[grind.ematch.instance] f.eq_2: f y.succ = g (f y)
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[grind.assert] f (y + 1) = g (f y)
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-/
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#guard_msgs (info) in
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example : f (y + 1) = a → a = g (f y):= by
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grind
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@[grind] def app (xs ys : List α) :=
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match xs with
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| [] => ys
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| x::xs => x :: app xs ys
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/--
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info: [grind.assert] app [1, 2] ys = xs
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[grind.assert] ¬xs = 1 :: 2 :: ys
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[grind.ematch.instance] app.eq_2: app [1, 2] ys = 1 :: app [2] ys
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[grind.assert] app [1, 2] ys = 1 :: app [2] ys
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[grind.ematch.instance] app.eq_2: app [2] ys = 2 :: app [] ys
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[grind.assert] app [2] ys = 2 :: app [] ys
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[grind.ematch.instance] app.eq_1: app [] ys = ys
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[grind.assert] app [] ys = ys
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-/
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#guard_msgs (info) in
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example : app [1, 2] ys = xs → xs = 1::2::ys := by
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grind
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opaque p : Nat → Nat → Prop
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opaque q : Nat → Prop
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@[grind =] theorem pq : p x x ↔ q x := by sorry
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/--
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info: [grind.assert] p a a
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[grind.assert] ¬q a
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[grind.ematch.instance] pq: p a a ↔ q a
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[grind.assert] p a a = q a
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-/
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#guard_msgs (info) in
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example : p a a → q a := by
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grind
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opaque appV (xs : Vector α n) (ys : Vector α m) : Vector α (n + m) :=
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Vector.append xs ys
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@[grind =]
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theorem appV_assoc (a : Vector α n) (b : Vector α m) (c : Vector α n') :
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HEq (appV a (appV b c)) (appV (appV a b) c) := sorry
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/--
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info: [grind.assert] x1 = appV a_2 b
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[grind.assert] x2 = appV x1 c
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[grind.assert] x3 = appV b c
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[grind.assert] x4 = appV a_2 x3
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[grind.assert] ¬HEq x2 x4
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[grind.ematch.instance] appV_assoc: HEq (appV a_2 (appV b c)) (appV (appV a_2 b) c)
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[grind.assert] HEq (appV a_2 (appV b c)) (appV (appV a_2 b) c)
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-/
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#guard_msgs (info) in
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example : x1 = appV a b → x2 = appV x1 c → x3 = appV b c → x4 = appV a x3 → HEq x2 x4 := by
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grind
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