134 lines
4.2 KiB
Lua
134 lines
4.2 KiB
Lua
-- Create names for commonly used constants
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local Or = Const("or")
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local Not = Const("not")
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local False = Const("false")
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function init_env(env)
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-- Populate environment when declarations used by resolve_macro.
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-- This is a 'fake' environment used only for testing.
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local a = Local("a", Prop)
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local b = Local("b", Prop)
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local c = Local("c", Prop)
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local Ha = Local("Ha", a)
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local Hb = Local("Hb", b)
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env = add_decl(env, mk_var_decl("or", mk_arrow(Prop, Prop, Prop)))
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env = add_decl(env, mk_var_decl("not", mk_arrow(Prop, Prop)))
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env = add_decl(env, mk_var_decl("false", Prop))
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env = add_decl(env, mk_axiom({"or", "elim"}, Pi(a, b, c, mk_arrow(Or(a, b), mk_arrow(a, c), mk_arrow(b, c), c))))
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env = add_decl(env, mk_axiom({"or", "intro_left"}, Pi(a, Ha, b, Or(a, b))))
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env = add_decl(env, mk_axiom({"or", "intro_right"}, Pi(b, a, Hb, Or(a, b))))
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env = add_decl(env, mk_axiom("absurd_elim", Pi(a, b, mk_arrow(a, Not(a), b))))
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return env
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end
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function decl_bools(env, ls)
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for i = 1, #ls do
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env = add_decl(env, mk_var_decl(ls[i]:data(), Prop))
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end
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return env
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end
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function Consts(s)
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-- Auxiliary function for creating multiple constants
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local r = {}
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local i = 1
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for c in string.gmatch(s, '[^ ,;\t\n]+') do
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r[i] = Const(c)
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i = i + 1
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end
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return unpack(r)
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end
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function OR(...)
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-- Nary Or
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local arg = {...}
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if #arg == 0 then
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return False
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elseif #arg == 1 then
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return arg[1]
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else
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local r = arg[#arg]
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for i = #arg-1, 1, -1 do
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r = Or(arg[i], r)
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end
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return r
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end
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end
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function print_types(env, ...)
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local arg = {...}
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local tc = type_checker(env)
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for i = 1, #arg do
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print(tostring(arg[i]) .. " : " .. tostring(tc:check(arg[i])))
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end
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end
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function assert_some_axioms(env)
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-- Assert some clauses
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local l1, l2, l3, l4, l5, l6 = Consts("l1 l2 l3 l4 l5 l6")
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env = decl_bools(env, {l1, l2, l3, l4, l5})
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env = add_decl(env, mk_definition("l6", Prop, l3, {opaque=false})) -- l6 is alias for l3
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env = add_decl(env, mk_axiom("H1", OR(l1, l2, Not(l3))))
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env = add_decl(env, mk_axiom("H2", OR(l2, l3, l4)))
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env = add_decl(env, mk_axiom("H3", OR(Not(l1), l2, l4, l5)))
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env = add_decl(env, mk_axiom("H4", OR(l4, l6, Not(l5))))
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env = add_decl(env, mk_axiom("H5", OR(Not(l4), l3)))
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env = add_decl(env, mk_axiom("H6", Not(l3)))
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env = add_decl(env, mk_axiom("H7", Not(l2)))
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return env
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end
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local env = bare_environment({trust_lvl=1})
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env = init_env(env)
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env = assert_some_axioms(env)
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local l1, l2, l3, l4, l5, l6 = Consts("l1 l2 l3 l4 l5 l6")
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local H1, H2, H3, H4, H5, H6, H7 = Consts("H1 H2 H3 H4 H5 H6 H7")
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local tc = type_checker(env)
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print(tc:check(Or))
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print(tc:check(Const("absurd_elim")))
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print(tc:check(H4))
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local Pr1 = resolve_macro(l6, H2, H1)
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local Pr2 = resolve_macro(l1, Pr1, H3)
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assert(Pr1:is_macro())
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assert(Pr1:macro_num_args() == 3)
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assert(Pr1:macro_arg(0) == l6)
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assert(Pr1:macro_def() == Pr2:macro_def())
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assert(Pr1:data() == Pr1:macro_def())
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assert(Pr1 == mk_macro(Pr1:macro_def(), {Pr1:macro_arg(0), Pr1:macro_arg(1), Pr1:macro_arg(2)}))
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assert(Pr1:macro_def():name() == name("resolve"))
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assert(Pr1:macro_def():trust_level() >= 0)
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print(Pr1:macro_def():hash())
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print(Pr1:macro_def())
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print("-----------")
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print(tc:check(H2))
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print(tc:check(H1))
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print(tc:check(Pr1))
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print(tc:check(H3))
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print(tc:check(Pr2))
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local Pr3 = resolve_macro(l4, resolve_macro(l5, Pr2, H4), H5)
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print(tc:check(Pr3))
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local Pr4 = resolve_macro(l2, resolve_macro(l3, Pr3, H6), H7)
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print("-----------")
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print("proof for false: ")
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print_types(env, H1, H2, H3, H4, H5, H6, H7)
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print(tostring(Pr4) .. " : " .. tostring(tc:check(Pr4)))
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print("----------------")
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print("Type checking again, but using trust_lvl=0, macros will be expanded during type checking")
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local env = bare_environment({trust_lvl=0})
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env = init_env(env)
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env = assert_some_axioms(env)
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local tc = type_checker(env)
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-- Since the trust_lvl is 0, the macro will be expanded during type checking
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print(tc:whnf(Pr1))
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print(tc:check(Pr1))
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print(tc:check(Pr4))
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print(env:normalize(Pr4))
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local a = Const("a")
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assert(not pcall(function() a:macro_num_args() end))
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assert(not pcall(function() a:let_name() end))
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assert(not pcall(function() mk_arrow(a) end))
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