Implementing Baker's SUBTYPEP decision procedure

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Abstract

The Common Lisp language provides a predicate functionSUBTYPEP, for instrospecting sub-type relationship. In some situations, and given the type system of this languageknowing whether a type is a sub-type of another would require enumerating all the element of that type, possibly an infinite number of them. Because of that, SUBTYPEP is allowed to return the two values (NIL NIL), indicating that it couldn't answer the question. Common Lisp implementations have a tendency to frequently not answereven in situations where they could. Such an abusive behavior prevents potential optimizations to occur, or even leads to violating the standard. In his paper entitled “A Decision Procedure for Common Lisp's SUBTYPEP Predicate”Henry Baker proposes an algorithm that he claims to be both more accurate and more efficient than the average SUBTYPEP implementation. We present here the current state the current state of our implementation and discuss one potential improvement based on R-trees of Baker's algorithm.