61 lines
2.6 KiB
Lua
61 lines
2.6 KiB
Lua
local env = environment()
|
|
local N = Const("N")
|
|
local p = Const("p")
|
|
local q = Const("q")
|
|
local a = Const("a")
|
|
local b = Const("b")
|
|
local f = Const("f")
|
|
local H1 = Const("H1")
|
|
local H2 = Const("H2")
|
|
local And = Const("and")
|
|
local and_intro = Const("and_intro")
|
|
local A = Local("A", Bool)
|
|
local B = Local("B", Bool)
|
|
env = add_decl(env, mk_var_decl("N", Type))
|
|
env = add_decl(env, mk_var_decl("p", mk_arrow(N, N, Bool)))
|
|
env = add_decl(env, mk_var_decl("q", mk_arrow(N, Bool)))
|
|
env = add_decl(env, mk_var_decl("f", mk_arrow(N, N)))
|
|
env = add_decl(env, mk_var_decl("a", N))
|
|
env = add_decl(env, mk_var_decl("b", N))
|
|
env = add_decl(env, mk_var_decl("and", mk_arrow(Bool, Bool, Bool)))
|
|
env = add_decl(env, mk_var_decl("and_intro", Pi({A, B}, mk_arrow(A, B, And(A, B)))))
|
|
env = add_decl(env, mk_var_decl("foo_intro", Pi({A, B}, mk_arrow(B, B))))
|
|
env = add_decl(env, mk_var_decl("foo_intro2", Pi({A, B}, mk_arrow(B, B))))
|
|
env = add_decl(env, mk_axiom("Ax1", q(a)))
|
|
env = add_decl(env, mk_axiom("Ax2", q(a)))
|
|
env = add_decl(env, mk_axiom("Ax3", q(b)))
|
|
local Ax1 = Const("Ax1")
|
|
local Ax2 = Const("Ax2")
|
|
local Ax3 = Const("Ax3")
|
|
local foo_intro = Const("foo_intro")
|
|
local foo_intro2 = Const("foo_intro2")
|
|
local cs = {}
|
|
local ng = name_generator("foo")
|
|
local tc = type_checker(env, ng, function (c) print(c); cs[#cs+1] = c end)
|
|
local m1 = mk_metavar("m1", Bool)
|
|
print("before is_def_eq")
|
|
assert(not tc:is_def_eq(and_intro(m1, q(a)), and_intro(q(a), q(b))))
|
|
assert(#cs == 0)
|
|
local cs = {}
|
|
local tc = type_checker(env, ng, function (c) print(c); cs[#cs+1] = c end)
|
|
assert(tc:is_def_eq(foo_intro(m1, q(a), Ax1), foo_intro(q(a), q(a), Ax2)))
|
|
assert(#cs == 1) -- constraint is used, but there is an alternative that does not use it
|
|
assert(cs[1]:lhs() == m1)
|
|
assert(cs[1]:rhs() == q(a))
|
|
cs = {}
|
|
local tc = type_checker(env, ng, function (c) print(c); cs[#cs+1] = c end)
|
|
assert(tc:is_def_eq(foo_intro(m1, q(a), Ax1), foo_intro2(q(a), q(a), Ax2)))
|
|
assert(#cs == 0) -- constraint should be ignored since we have shown definitional equality using proof irrelevance
|
|
cs = {}
|
|
local tc = type_checker(env, ng, function (c) print(c); cs[#cs+1] = c end)
|
|
print("before failure")
|
|
assert(not pcall(function() print(tc:check(and_intro(m1, q(a), Ax1, Ax3))) end))
|
|
assert(#cs == 0) -- the check failed, so the constraints should be preserved
|
|
cs = {}
|
|
print("before success")
|
|
print(tc:check(and_intro(m1, q(a), Ax1, Ax2)))
|
|
assert(#cs == 1) -- the check succeeded, and we must get one constraint
|
|
|
|
-- Demo: infer method may generate constraints
|
|
-- local m2 = mk_metavar("m2", mk_metavar("ty_m2", mk_sort(mk_meta_univ("s_m2"))))
|
|
-- print(tc:infer(mk_pi("x", m2, Var(0))))
|