2014-05-25 18:15:25 +00:00
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local env = environment()
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local l = param_univ("l")
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env = add_decl(env, mk_var_decl("group", {l}, mk_sort(l+1)))
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env = add_decl(env, mk_var_decl("abelian_group", {l}, mk_sort(l+1)))
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env = add_decl(env, mk_var_decl("ring", {l}, mk_sort(l+1)))
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env = add_decl(env, mk_var_decl("abelian_ring", {l}, mk_sort(l+1)))
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local group = Const("group", {l})
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local ring = Const("ring", {l})
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local ab_group = Const("abelian_group", {l})
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local ab_ring = Const("abelian_ring", {l})
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env = add_decl(env, mk_var_decl("carrier", {l}, mk_arrow(group, mk_sort(l))))
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env = add_coercion(env, "carrier")
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env = add_decl(env, mk_var_decl("ag2g", {l}, mk_arrow(ab_group, group)))
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env = add_decl(env, mk_var_decl("r2g", {l}, mk_arrow(ring, group)))
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env = add_decl(env, mk_var_decl("ar2r", {l}, mk_arrow(ab_ring, ring)))
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env = add_decl(env, mk_var_decl("ar2ag", {l}, mk_arrow(ab_ring, ab_group)))
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env = add_coercion(env, "ag2g")
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env = add_coercion(env, "r2g")
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env = add_coercion(env, "ar2r")
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env = add_coercion(env, "ar2ag")
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for_each_coercion_sort(env, function(C, f) print(tostring(C) .. " >-> sort : " .. tostring(f)) end)
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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_coercion_to_sort(env, Const("abelian_ring", {1})))
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assert(env:type_check(get_coercion_to_sort(env, Const("abelian_ring", {1}))))
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2014-06-13 05:18:27 +00:00
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print("Coercions (abelian ring): ")
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cs = get_user_coercions(env, ab_ring)
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for i = 1, #cs do
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print(tostring(cs[i][1]) .. " : " .. tostring(cs[i][3]) .. " : " .. tostring(cs[i][2]))
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end
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