42 lines
1.4 KiB
Lua
42 lines
1.4 KiB
Lua
local env = hott_environment()
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assert(not env:impredicative())
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assert(not env:prop_proof_irrel())
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local l = param_univ("l")
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local U_l = mk_sort(l)
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local A = Local("A", U_l)
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local list_l = Const("list", {l})
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-- In HoTT environments, we don't need to use max(l, 1) trick
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-- in the following definition
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env = add_inductive(env,
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"list", {l}, 1, Pi(A, U_l),
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"nil", Pi(A, list_l(A)),
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"cons", Pi(A, mk_arrow(A, list_l(A), list_l(A))))
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local l1 = param_univ("l1")
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local l2 = param_univ("l2")
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local U_l1 = mk_sort(l1)
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local U_l2 = mk_sort(l2)
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local U_l1l2 = mk_sort(max_univ(l1, l2))
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local A = Local("A", U_l1)
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local B = Local("B", U_l2)
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local a = Local("a", A)
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local b = Local("b", B)
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local sigma_l1l2 = Const("sigma", {l1, l2})
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env = add_inductive(env,
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"sigma", {l1, l2}, 2, Pi(A, B, U_l1l2),
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"pair", Pi(A, B, a, b, sigma_l1l2(A, B)))
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local coproduct_l1l2 = Const("coproduct", {l1, l2})
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env = add_inductive(env,
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"coproduct", {l1, l2}, 2, Pi(A, B, U_l1l2),
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"inl", Pi(A, B, a, coproduct_l1l2(A, B)),
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"inr", Pi(A, B, b, coproduct_l1l2(A, B)))
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env:for_each_decl(function(d)
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print(tostring(d:name()) .. " : " .. tostring(d:type()))
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end
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)
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