125 lines
4.3 KiB
Lua
125 lines
4.3 KiB
Lua
import("util.lua")
|
|
|
|
function pibody(e)
|
|
while (e:is_pi()) do
|
|
local _, _, r = e:fields()
|
|
e = r
|
|
end
|
|
return e
|
|
end
|
|
|
|
function funbody(e)
|
|
while (e:is_lambda()) do
|
|
local _, _, r = e:fields()
|
|
e = r
|
|
end
|
|
return e
|
|
end
|
|
|
|
function hoptst(rule, target, expected)
|
|
if expected == nil then
|
|
expected = true
|
|
end
|
|
local th = parse_lean(rule)
|
|
local p = pibody(th):arg(2)
|
|
local t = funbody(parse_lean(target))
|
|
local r = hop_match(p, t)
|
|
-- print(p, t)
|
|
if (r and not expected) or (not r and expected) then
|
|
error("test failed: " .. tostring(rule) .. " === " .. tostring(target))
|
|
end
|
|
if r then
|
|
local s = p:instantiate(r):beta_reduce()
|
|
print "Solution:"
|
|
for i = 1, #r do
|
|
print("#" .. tostring(i) .. " <--- " .. tostring(r[i]))
|
|
end
|
|
print ""
|
|
t = t:beta_reduce()
|
|
if s ~= t then
|
|
print("Mismatch")
|
|
print(s)
|
|
print(t)
|
|
end
|
|
assert(s == t)
|
|
end
|
|
end
|
|
|
|
parse_lean_cmds([[
|
|
variable f : Nat -> Nat -> Nat
|
|
variable g : Nat -> Nat
|
|
variable p : Nat -> Bool
|
|
variable n : Nat
|
|
]])
|
|
|
|
hoptst([[forall (h : Nat -> Nat), (forall x : Nat, h 0 = h x) = true]],
|
|
[[fun (ff : Nat -> Nat), forall x : Nat, ff 0 = ff x]])
|
|
|
|
hoptst([[forall (h : Nat -> Nat -> Nat) (a : Nat), (forall x : Nat, (h x a) = a) = true]],
|
|
[[fun (a b c : Nat), (forall x : Nat, (f x b) = b)]])
|
|
|
|
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))]],
|
|
[[forall x : Nat, p (f x 0) /\ f (f x x) 1 >= 0]])
|
|
|
|
hoptst([[forall (F G : Nat -> Nat), (forall x y : Nat, F x = x /\ G y = y) = (F = G)]],
|
|
[[(forall x y : Nat, f x (g x) = x /\ g (g (g y)) = y)]])
|
|
|
|
hoptst([[forall (F G : Nat -> Nat), (forall x y : Nat, F x = x /\ G y = y) = (F = G)]],
|
|
[[fun (a b c : Nat), (forall x y : Nat, f x (f (g b) c) = x /\ (f (g (g (f y c))) a) = y)]])
|
|
|
|
hoptst([[forall (a b c : Bool), ((a /\ b) /\ c) = (a /\ (b /\ c))]],
|
|
[[fun (p1 p2 p3 p4 p5 : Bool), (((p1 ∧ p2) ∧ p3) ∧ (p4 ∧ p2))]])
|
|
|
|
hoptst([[forall (F G : Nat -> Bool), (forall x : Nat, F x = (F x ∧ G x)) = (F = G)]],
|
|
[[forall x : Nat, p (f x x) = (p (f x x) ∧ p (f x 0))]])
|
|
|
|
hoptst([[forall (F G : Nat -> Bool), (forall x : Nat, F x = (F x ∧ G x)) = (F = G)]],
|
|
[[forall x : Nat, p (f x x) = (p (f (g x) x) ∧ p (f x 0))]], false)
|
|
|
|
hoptst([[forall (F G : Nat -> Nat), (forall x y : Nat, F x = x /\ G y = y) = (F = G)]],
|
|
[[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)
|
|
|
|
hoptst([[forall (a : Bool), (a /\ true) = a]],
|
|
[[fun (p1 p2 p3 : Bool), (p1 /\ p2) /\ true]])
|
|
|
|
hoptst([[forall (a : Bool), (a /\ true) = a]],
|
|
[[fun (p1 p2 p3 : Bool), (p1 /\ p2) /\ false]], false)
|
|
|
|
hoptst([[forall (h : Nat -> Nat) (a : Nat), (h a) = a]],
|
|
[[fun (a b c : Nat), f a b]])
|
|
|
|
hoptst([[forall (a : Nat), (g a) = a]],
|
|
[[fun (a b c : Nat), f a b]], false)
|
|
|
|
hoptst([[forall (A : Type) (a : A), (a = a) = true]],
|
|
[[fun (a b : Nat), b = b]])
|
|
|
|
hoptst([[forall (h : Nat -> Nat), (forall x : Nat, h x = h 0) = true]],
|
|
[[fun (ff : Nat -> Nat), forall x : Nat, ff x = ff 0]])
|
|
|
|
hoptst([[forall (h : Nat -> Nat), (forall x : Nat, h x = h 0) = true]],
|
|
[[fun (ff : Nat -> Nat) (a b c : Nat), forall x : Nat, ff x = ff 0]])
|
|
|
|
hoptst([[forall (h : Nat -> Nat -> Bool), (forall x : Nat, h x x) = true]],
|
|
[[fun (a b : Nat), forall x : Nat, f x x]])
|
|
|
|
hoptst([[forall (h : Nat -> Nat -> Bool), (forall x : Nat, h x x) = true]], -- this is not a higher-order pattern
|
|
[[fun (a b : Nat), forall x : Nat, f (f x) (f x)]], false)
|
|
|
|
hoptst([[forall (h : Nat -> Nat -> Bool), (forall x : Nat, h n x) = true]],
|
|
[[fun (ff : Nat -> Nat -> Bool) (a b : Nat), forall x : Nat, ff n x]])
|
|
|
|
hoptst([[forall (h : Nat -> Nat -> Bool), (forall x : Nat, h n x) = true]], -- this is not a higher-order pattern
|
|
[[fun (ff : Nat -> Nat -> Bool) (a b : Nat), forall x : Nat, ff n (g x)]], false)
|
|
|
|
hoptst([[forall (h : Nat -> Bool), (forall x y : Nat, h x) = true]],
|
|
[[fun (a b : Nat), forall x y : Nat, (fun z : Nat, z + x) (fun w1 w2 : Nat, w1 + w2 + x)]])
|
|
|
|
hoptst([[forall (h : Nat -> Bool), (forall x y : Nat, h y) = true]],
|
|
[[fun (a b : Nat), forall x y : Nat, (fun z : Nat, z + y) (fun w1 w2 : Nat, w1 + w2 + y)]])
|
|
|
|
|
|
|
|
|
|
|
|
|