lean2/tests/lua/env5.lua

local env    = bare_environment()
local l_name = name("l")
local l      = mk_param_univ(l_name)
local U_l    = mk_sort(l)
local x      = Const("x")
local A      = Local("A", U_l)
local x      = Local("x", A)
local A2A    = mk_arrow(A, A)
local id_ty  = Pi(A, mk_arrow(A, A))
local id_def = Fun(A, Fun(x, x))
env = add_decl(env, mk_definition(env, "id", {l_name}, id_ty, id_def, {opaque=false}))
local ok, ex = pcall(function()
                        env = add_decl(env, mk_definition(env, "id2", {"l2"}, id_ty, id_def, {opaque=false}))
                     end
)
assert(not ok)
print(ex:what())
local tc     = type_checker(env)
local ok, ex = pcall(function()
                        local id     = Const("id")
                        tc:check(id)
                     end
)
assert(not ok)
print(ex:what())
local id_1 = Const("id", {mk_level_one()})
print(tc:check(id_1))
assert(not pcall(function()
                    id_u = Const("id", {mk_global_univ("u")})
                    print(tc:check(id_u))
                 end
))
assert(not pcall(function()
                    id_1_1 = Const("id", {mk_level_one(), mk_level_one()})
                    print(tc:check(id_1_1))
                 end
))
local env2 = env:add_universe("u")
assert(env2:is_descendant(env))
assert(not env:is_descendant(env2))
local tc2 = type_checker(env2)
id_u = Const("id", {mk_global_univ("u")})
print(tc2:check(id_u))
local tmp = tc2:check(id_u)
print(tc2:check(tmp))
local tmp1 = tc2:check(id_u)
local tmp2 = tc2:check(tmp1)
print(tc2:check(tmp2))
env2 = add_decl(env2, mk_var_decl("a", Type))
local tc2  = type_checker(env2)
local a    = Const("a")
local id_2 = Const("id", {mk_level_succ(mk_level_one())})
print(tc2:check(id_2(Type, a)))
assert(tc2:check(id_2(Type, a)) == Type)
assert(not pcall(function() print(tc2:check(id_1(Type, a))) end))
assert(tc2:whnf(id_2(Type, a)) == a)
assert(tc2:whnf(id_2(Type, id_2(Type, a))) == a)
local tc3 = type_checker(env, name_generator("foo"), {extra_opaque=name_set("id")})
assert(tc3:whnf(id_2(Type, id_2(Type, a))) == id_2(Type, id_2(Type, a)))
print(id_2(Type, id_2(Type, a)))