50 lines
1.8 KiB
Lua
50 lines
1.8 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 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_decl(function(d) print(d:name()) end)
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env = add_aliases(env, "nat", "natural")
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assert(get_alias_exprs(env, {"natural", "zero"}):head() == zero)
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assert(get_alias_exprs(env, {"natural", "nat"}):head() == nat)
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assert(is_aliased(env, nat) == name("natural", "nat"))
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local A = Local("A", U_l)
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env = add_inductive(env,
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name("list", "list"), {l}, 1, Pi(A, U_l1),
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name("list", "nil"), Pi(A, list_l(A)),
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name("list", "cons"), Pi(A, mk_arrow(A, list_l(A), list_l(A))))
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env = add_aliases(env, "list", "lst")
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print(not get_alias_exprs(env, {"lst", "list_rec"}):is_nil())
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env = add_aliases(env, "list")
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print(get_alias_exprs(env, "list_rec"):head())
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assert(not get_alias_exprs(env, "list_rec"):is_nil())
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assert(not get_alias_exprs(env, {"lst", "list_rec"}):is_nil())
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env = add_aliases(env, "list", "l")
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print(get_alias_exprs(env, {"l", "list"}):head())
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print(get_alias_exprs(env, {"l", "cons"}):head())
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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_alias(env, "z", zero)
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assert(get_alias_exprs(env, "z"):head() == zero)
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assert(get_alias_exprs(env, "zz"):is_nil())
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