22 lines
1.2 KiB
Lua
22 lines
1.2 KiB
Lua
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local env = environment()
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local l1 = param_univ("l1")
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local l2 = param_univ("l2")
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env = add_decl(env, mk_var_decl("functor", {l1, l2}, mk_arrow(mk_sort(l1), mk_sort(l2), mk_sort(imax_univ(l1, l2)))))
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local A = Local("A", mk_sort(l1))
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local B = Local("B", mk_sort(l2))
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local functor = Const("functor", {l1, l2})
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env = add_decl(env, mk_var_decl("to_fun", {l1, l2}, Pi({A, B}, mk_arrow(functor(A, B), mk_arrow(A, B)))))
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env = add_coercion(env, "to_fun", "functor")
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for_each_coercion_fun(env, function(C, f) print(tostring(C) .. " >-> function : " .. tostring(f)) end)
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env = add_decl(env, mk_var_decl("nat", Type))
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env = add_decl(env, mk_var_decl("real", Type))
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local nat = Const("nat")
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local real = Const("real")
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env = add_decl(env, mk_var_decl("f1", Const("functor", {1, 1})(nat, real)))
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print(get_coercion_to_fun(env, Const("functor", {1, 1})(nat, real)))
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env = add_decl(env, mk_var_decl("sfunctor", {l1}, mk_arrow(mk_sort(l1), mk_sort(l1))))
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env = add_decl(env, mk_var_decl("sf2f", {l1}, Pi(A, mk_arrow(Const("sfunctor", {l1})(A), Const("functor", {l1, l1})(A, A)))))
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env = add_coercion(env, "sf2f")
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print(get_coercion_to_fun(env, Const("sfunctor", {1})(nat)))
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assert(env:type_check(get_coercion_to_fun(env, Const("sfunctor", {1})(nat))))
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