33 lines
1.2 KiB
Lua
33 lines
1.2 KiB
Lua
local env = environment()
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env = env:begin_section_scope()
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env = env:begin_section_scope()
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local nat = Const("nat")
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env = add_inductive(env,
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"nat", Type,
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"zero", nat,
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"succ", mk_arrow(nat, nat))
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local zero = Const("zero")
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local succ = Const("succ")
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local one = succ(zero)
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env = env:add_global_level("l")
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local l = mk_global_univ("l")
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env = env:add(check(env, mk_var_decl("A", mk_sort(l))), binder_info(true))
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env = env:add(check(env, mk_var_decl("B", mk_sort(l))), binder_info(true))
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local A = Const("A")
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local l1 = mk_param_univ("l1")
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local D = Const("D", {l1})
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local n = Local("n", nat)
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env = add_inductive(env,
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"D", {l1}, 1, mk_arrow(nat, nat, mk_sort(max_univ(l1, l, 1))),
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"mk1", Pi(n, mk_arrow(A, D(n, one))),
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"mk0", Pi(n, mk_arrow(A, A, D(n, zero))))
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print(env:find("D_rec"):type())
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env = env:end_scope()
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env = env:end_scope()
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print(env:find("D_rec"):type())
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local l = mk_param_univ("l")
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local A = Local("A", mk_sort(l))
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local D = Const("D", {l, l1})
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print(env:find("mk1"):type())
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assert(env:find("mk1"):type() == Pi({A, n}, mk_arrow(A, D(A, n, one))))
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