lean2/tests/lua/tc2.lua

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local env = environment()
local l = mk_param_univ("l")
local A = Local("A", mk_sort(l))
local a = Local("a", A)
local b = Local("b", A)
local P = Local("P", mk_arrow(A, Bool))
env = add_decl(env, mk_definition("id", {l},
Pi(A, mk_arrow(A, mk_arrow(A, Bool))),
Fun(A, a, b, Pi(P, mk_arrow(P(a), P(b))))))
local id_l = Const("id", {l})
local H = Local("H", P(a))
env = add_decl(env, mk_theorem("refl", {l},
Pi(A, a, id_l(A, a, a)),
Fun(A, a, P, H, H)))
local H1 = Local("H1", id_l(A, a, b))
local H2 = Local("H2", P(a))
env = add_decl(env, mk_theorem("subst", {l},
Pi(A, P, a, b, H1, H2, P(b)),
Fun(A, P, a, b, H1, H2, H1(P, H2))))
local refl_l = Const("refl", {l})
local subst_l = Const("subst", {l})
local x = Local("x", A)
local H = Local("H", id_l(A, a, b))
env = add_decl(env, mk_theorem("symm", {l},
Pi(A, a, b, H, id_l(A, b, a)),
Fun(A, a, b, H,
subst_l(A, Fun(x, id_l(A, x, a)), a, b, H, refl_l(A, a)))))
local c = Local("c", A)
local H1 = Local("H1", id_l(A, a, b))
local H2 = Local("H2", id_l(A, b, c))
env = add_decl(env, mk_theorem("trans", {l},
Pi(A, a, b, c, H1, H2, id_l(A, a, c)),
Fun(A, a, b, c, H1, H2,
subst_l(A, Fun(x, id_l(A, a, x)), b, c, H2, H1))))
local symm_l = Const("symm", {l})
local trans_l = Const("trans", {l})
print(env:get("trans"):value())
env = env:add_universe("u")
local u = mk_global_univ("u")
local tc = type_checker(env)
print(tc:check(Const("trans", {u})))
local id_u = Const("id", {u})
local refl_u = Const("refl", {u})
local subst_u = Const("subst", {u})
local symm_u = Const("symm", {u})
local trans_u = Const("trans", {u})
local A = Local("A", mk_sort(u))
local d = Local("d", A)
local H1 = Local("H1", id_u(A, b, a))
local H2 = Local("H2", id_u(A, b, c))
local H3 = Local("H3", id_u(A, c, d))
print(tc:check(Fun(A, a, b, c, d, H1, H2, H3,
trans_u(A, a, b, d,
symm_u(A, b, a, H1),
trans_u(A, b, c, d, H2, H3)))))
local g = name_generator("tst")
local tc2 = type_checker(env, g)
print("=================")
local A = Local("A", mk_sort(u))
local mf_ty = mk_metavar("f_ty", Pi(A, mk_sort(mk_meta_univ("l_f"))))
local f = Local("f", mf_ty(A))
local a = Local("a", A)
local mA1 = mk_metavar("A1", Pi(A, f, a, mk_sort(mk_meta_univ("l_A1"))))
print(tc2:check(Fun(A, f, a,
id_u(mA1(A, f, a), f(a), a))))