73 lines
2.2 KiB
Lua
73 lines
2.2 KiB
Lua
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import("util.lua")
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function pibody(e)
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while (e:is_pi()) do
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local _, _, r = e:fields()
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e = r
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end
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return e
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end
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function funbody(e)
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while (e:is_lambda()) do
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local _, _, r = e:fields()
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e = r
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end
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return e
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end
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function hoptst(rule, target, expected)
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if expected == nil then
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expected = true
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end
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local th = parse_lean(rule)
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local p = pibody(th):arg(2)
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local t = funbody(parse_lean(target))
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local r = hop_match(p, t)
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if (r and not expected) or (not r and expected) then
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error("test failed: " .. tostring(rule) .. " === " .. tostring(target))
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end
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if r then
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local s = p:instantiate(r):beta_reduce()
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print "Solution:"
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for i = 1, #r do
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print("#" .. tostring(i) .. " <--- " .. tostring(r[i]))
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end
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print ""
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if s ~= t then
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print("Mismatch")
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print(s)
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print(t)
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end
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assert(s == t)
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end
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end
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parse_lean_cmds([[
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variable f : Nat -> Nat -> Nat
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variable g : Nat -> Nat
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variable p : Nat -> Bool
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]])
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hoptst([[forall (A : TypeU) (P Q : A -> Bool), (forall x : A, P x /\ Q x) = ((forall x : A, P x) /\ (forall x : A, Q x))]],
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[[forall x : Nat, p (f x 0) /\ f (f x x) 1 >= 0]])
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hoptst([[forall (F G : Nat -> Nat), (forall x y : Nat, F x = x /\ G y = y) = (F = G)]],
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[[(forall x y : Nat, f x (g x) = x /\ g (g (g y)) = y)]])
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hoptst([[forall (F G : Nat -> Nat), (forall x y : Nat, F x = x /\ G y = y) = (F = G)]],
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[[fun (a b c : Nat), (forall x y : Nat, f x (f (g b) c) = x /\ (f (g (g (f y c))) a) = y)]])
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hoptst([[forall (a b c : Bool), ((a /\ b) /\ c) = (a /\ (b /\ c))]],
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[[fun (p1 p2 p3 p4 p5 : Bool), (((p1 ∧ p2) ∧ p3) ∧ (p4 ∧ p2))]])
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hoptst([[forall (F G : Nat -> Bool), (forall x : Nat, F x = (F x ∧ G x)) = (F = G)]],
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[[forall x : Nat, p (f x x) = (p (f x x) ∧ p (f x 0))]])
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hoptst([[forall (F G : Nat -> Bool), (forall x : Nat, F x = (F x ∧ G x)) = (F = G)]],
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[[forall x : Nat, p (f x x) = (p (f (g x) x) ∧ p (f x 0))]], false)
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hoptst([[forall (F G : Nat -> Nat), (forall x y : Nat, F x = x /\ G y = y) = (F = G)]],
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[[fun (a b c : Nat), (forall x y : Nat, f x (f (g y) c) = x /\ (f (g (g (f y c))) a) = y)]], false)
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