lean2/tests/lua/simp1.lua
Leonardo de Moura bbf6e6a256 feat(builtin/kernel): create default rule set in the kernel, and adjust unit tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-19 11:24:20 -08:00

43 lines
1 KiB
Lua

add_rewrite_rules({"Nat", "add_zerol"})
add_rewrite_rules({"Nat", "add_zeror"})
parse_lean_cmds([[
variable f : Nat -> Nat -> Nat
variable g : Nat -> Nat
variable b : Nat
definition a := 1
theorem a_eq_1 : a = 1
:= refl a
definition c := 1
set_opaque a true
axiom f_id (x : Nat) : f x 1 = 2*x
axiom g_g_x (x : Nat) : (not (x = 0)) -> g (g x) = 0
]])
add_rewrite_rules("a_eq_1")
add_rewrite_rules("f_id")
add_rewrite_rules("eq_id")
-- set_option({"lean", "pp", "implicit"}, true)
e, pr = simplify(parse_lean('fun x, f (f x (0 + a)) (g (b + 0))'))
print(e)
print(pr)
local env = get_environment()
print(env:type_check(pr))
e, pr = simplify(parse_lean('forall x, let d := a + 1 in f x a >= d'))
print(e)
print(pr)
local env = get_environment()
print(env:type_check(pr))
e, pr = simplify(parse_lean('(fun x, f (f x (0 + a)) (g (b + 0))) b'))
print(e)
print(pr)
local env = get_environment()
print(env:type_check(pr))
e, pr = simplify(parse_lean('(fun x y, f x y) = f'))
print(e)
print(pr)
local env = get_environment()
print(env:type_check(pr))