61 lines
2.3 KiB
Lua
61 lines
2.3 KiB
Lua
local env = environment()
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local env = environment()
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local l = mk_param_univ("l")
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local A = Const("A")
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local U_l = mk_sort(l)
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local U_l1 = mk_sort(max_univ(l, 1)) -- Make sure U_l1 is not Bool/Prop
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local nat = Const({"nat", "nat"})
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local vec_l = Const({"vec", "vec"}, {l}) -- vec.{l}
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local zero = Const({"nat", "zero"})
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local succ = Const({"nat", "succ"})
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local one = succ(zero)
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local list_l = Const({"list", "list"}, {l}) -- list.{l}
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env = add_inductive(env,
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name("nat", "nat"), Type,
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name("nat", "zero"), nat,
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name("nat", "succ"), mk_arrow(nat, nat))
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env:for_each(function(d) print(d:name()) end)
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env = add_aliases(env, "nat", "natural")
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assert(get_alias(env, {"natural", "zero"}) == zero)
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assert(get_alias(env, {"natural", "nat"}) == nat)
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assert(is_aliased(env, nat) == name("natural", "nat"))
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env = add_inductive(env,
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name("list", "list"), {l}, 1, Pi(A, U_l, U_l1),
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name("list", "nil"), Pi({{A, U_l, true}}, list_l(A)),
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name("list", "cons"), Pi({{A, U_l, true}}, mk_arrow(A, list_l(A), list_l(A))))
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env = add_aliases(env, "list", "lst")
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print(get_alias(env, {"lst", "list_rec"}))
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env = add_aliases(env, "list")
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print(get_alias(env, "list_rec"))
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assert(get_alias(env, "list_rec"))
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assert(get_alias(env, {"lst", "list_rec"}))
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env = add_aliases(env, "list", "lnat", {{"A", nat}})
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print(get_alias(env, {"lnat", "list"}))
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print(get_alias(env, {"lnat", "cons"}))
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assert(get_alias(env, {"lnat", "cons"}) == Const({"list", "cons"}, { mk_level_placeholder() })(nat))
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local A = Local("A", mk_sort(1))
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local R = Local("R", mk_arrow(A, A, Bool))
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local a = Local("a", A)
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local b = Local("b", A)
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env = add_decl(env, mk_var_decl({"foo", "pred"}, Pi({A, R, a, b}, Bool)))
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env = add_aliases(env, "foo", nil, {{"A", nat}, {"a", zero}})
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local Rn = Local("R", mk_arrow(nat, nat, Bool))
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local bn = Local("b", nat)
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local a1 = get_alias(env, "pred")
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local a2 = Fun({Rn, bn}, Const({"foo", "pred"})(nat, Rn, zero, bn))
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print(a1)
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print(a2)
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assert(a1 == a2)
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env = add_aliases(env, "foo", nil, {{"A", nat}, {"a", zero}, {"b", one}})
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print(get_alias(env, "pred"))
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env = add_alias(env, "z", zero)
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assert(get_alias(env, "z") == zero)
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assert(not get_alias(env, "zz"))
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