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)
   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 ""
      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
]])

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)