The rewriting logic CRWL has been proposed as a semantic framework for higher-order functional logic programming, using applicative rewriting systems as programs and lazy narrowing as the goal solving procedure. We present an extension of CRWL with a polymorphic type system, and we investigate the consequences of type discipline both at the semantic level and at the operational level. Semantically, models must be extended to incorporate a type universe. Operationally, lazy narrowing must maintain suitable type information in goals, in order to guarantee well-typed computed answers.
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