90 lines
4.3 KiB
Lua
90 lines
4.3 KiB
Lua
local env = environment()
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local l = param_univ("l")
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local nat = Const("nat")
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local real = Const("real")
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local one = Const("one")
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local Ul = mk_sort(l)
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local lst_l = Const("lst", {l})
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local vec_l = Const("vec", {l})
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local mat_l = Const("mat", {l})
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local A = Local("A", Ul)
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local n = Local("n", nat)
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local ll = Local("ll", lst_l(A))
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local len_l = Const("len", {l})
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local lst_1 = Const("lst", {1})
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local l1 = param_univ("l1")
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local l2 = param_univ("l2")
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local m = Local("m", nat)
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env = add_decl(env, mk_constant_assumption("nat", Type))
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env = add_decl(env, mk_constant_assumption("real", Type))
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env = add_decl(env, mk_constant_assumption("one", nat))
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env = add_decl(env, mk_constant_assumption("lst", {l}, mk_arrow(Ul, Ul)))
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env = add_decl(env, mk_constant_assumption("len", {l}, Pi(A, mk_arrow(lst_l(A), nat))))
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env = add_decl(env, mk_constant_assumption("vec", {l}, mk_arrow(Ul, nat, Ul)))
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env = add_decl(env, mk_constant_assumption("mat", {l}, mk_arrow(Ul, nat, nat, Ul)))
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env = add_decl(env, mk_constant_assumption("dlst", {l1, l2}, mk_arrow(mk_sort(l1), mk_sort(l2), mk_sort(max_univ(l1, l2)))))
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env = add_decl(env, mk_constant_assumption("vec2lst", {l}, Pi(A, n, mk_arrow(vec_l(A, n), lst_l(A)))))
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env = add_decl(env, mk_constant_assumption("lst2vec", {l}, Pi(A, ll, vec_l(A, len_l(A, ll)))))
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env = add_decl(env, mk_constant_assumption("vec2mat", {l}, Pi(A, n, mk_arrow(vec_l(A, n), mat_l(A, n, one)))))
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env = add_decl(env, mk_constant_assumption("mat2dlst", {l}, Pi(A, n, m, mk_arrow(mat_l(A, n, m), Const("dlst", {l, 1})(A, nat)))))
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env = add_decl(env, mk_constant_assumption("nat2lst", mk_arrow(nat, lst_1(nat))))
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env = add_coercion(env, "lst2vec")
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assert(is_coercion(env, Const("lst2vec", {l})))
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assert(has_coercions_from(env, "lst"))
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local lst_nat = lst_1(nat)
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function display_coercions(coes)
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if not coes:is_nil() then
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print(coes:head())
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display_coercions(coes:tail())
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end
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end
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display_coercions(get_coercions(env, lst_nat, "vec"))
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env = add_coercion(env, "vec2mat")
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display_coercions(get_coercions(env, lst_nat, "mat"))
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assert(env:type_check(get_coercions(env, lst_nat, "mat"):head()))
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for_each_coercion_user(env, function(C, D, f) print(tostring(C) .. " >-> " .. tostring(D) .. " : " .. tostring(f)) end)
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env = add_coercion(env, "nat2lst")
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print("---------")
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for_each_coercion_user(env, function(C, D, f) print(tostring(C) .. " >-> " .. tostring(D) .. " : " .. tostring(f)) end)
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print(get_coercions(env, nat, "mat"):head())
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assert(env:type_check(get_coercions(env, nat, "mat"):head()))
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env = add_coercion(env, "mat2dlst")
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print("---------")
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for_each_coercion_user(env, function(C, D, f) print(tostring(C) .. " >-> " .. tostring(D) .. " : " .. tostring(f)) end)
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print(get_coercions(env, lst_nat, "dlst"):head())
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assert(env:type_check(get_coercions(env, lst_nat, "dlst"):head()))
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env:export("coe1_mod.olean")
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local env2 = import_modules("coe1_mod")
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print(get_coercions(env2, lst_nat, "dlst"):head())
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assert(env2:type_check(get_coercions(env2, lst_nat, "dlst"):head()))
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assert(is_coercion(env2, "vec2mat"))
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assert(is_coercion(env2, "lst2vec"))
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env2 = add_decl(env2, mk_constant_assumption("lst2vec2", {l}, Pi(A, ll, vec_l(A, len_l(A, ll)))))
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print("======")
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env2 = add_coercion(env2, "lst2vec2")
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print("======")
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print(get_coercions(env2, lst_nat, "dlst"):head())
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print("---------")
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for_each_coercion_user(env2, function(C, D, f) print(tostring(C) .. " >-> " .. tostring(D) .. " : " .. tostring(f)) end)
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env2 = add_coercion(env2, "vec2lst")
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env2 = add_decl(env2, mk_constant_assumption("lst2nat", {l}, Pi(A, mk_arrow(lst_l(A), nat))))
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env2 = add_coercion(env2, "lst2nat")
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print("---------")
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for_each_coercion_user(env2, function(C, D, f) print(tostring(C) .. " >-> " .. tostring(D)) end)
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for_each_coercion_user(env2, function(C, D, f) print(tostring(C) .. " >-> " .. tostring(D) .. " : " .. tostring(f)) end)
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assert(has_coercions_from(env2, lst_nat))
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assert(not has_coercions_from(env2, Const("foo")))
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assert(not has_coercions_from(env2, Const("lst", {1})))
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assert(has_coercions_from(env2, Const("vec", {1})(nat, one)))
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assert(not has_coercions_from(env2, Const("vec", {1})(nat)))
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assert(not has_coercions_from(env2, Const("vec")(nat, one)))
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print("Coercions (vec nat one): ")
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cs = get_coercions_from(env2, Const("vec", {1})(nat, one))
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for i = 1, #cs do
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print(tostring(cs[i][2]) .. " : " .. tostring(cs[i][4]) .. " : " .. tostring(cs[i][3]))
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end
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