30 lines
1 KiB
Lua
30 lines
1 KiB
Lua
function display_type(env, t)
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print(tostring(t) .. " : " .. tostring(env:normalize(env:type_check(t))))
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end
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local env = environment()
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local l = 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 Prop
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local A = Local("A", U_l)
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local list_l = Const("list", {l})
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local env1 = add_inductive(env,
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"list", {l}, 1, Pi(A, U_l1),
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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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display_type(env1, Const("list_rec", {1, 1}))
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-- Slightly different definition where A : Type.{l} is an index
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-- instead of a global parameter
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local U_sl = mk_sort(succ_univ(l))
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local env2 = add_inductive(env,
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"list", {l}, 0, Pi(A, U_sl), -- The resultant type must live in the universe succ(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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display_type(env2, Const("list_rec", {1, 1}))
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