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