Untyping Typed Algebraic Structures
نویسنده
چکیده
Algebraic structures sometimes need to be typed. For example, matrices over a ring form a ring, but the product is a only a partial operation: dimensions have to agree. Therefore, an easy way to look at matrices algebraically is to consider “typed rings”. We prove some “untyping” theorems: in some algebras (semirings, Kleene algebras, residuated monoids), types can be reconstructed from valid untyped equalities. As a consequence, the corresponding untyped decision procedures can be extended to the typed setting.
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