The Polymorphic Rewriting Calculus: Type checking vs. Type inference
Abstract
The rewriting calculus (rho-calculus), is a minimal framework embedding lambda-calculus and term rewriting systems, by allowing abstraction on variables and patterns. The rho-calculus features higher-order functions (from lambda-calculus) and pattern-matching (from term rewriting systems). In this paper, we study extensively a second-order rho-calculus à la Church (Rho F) that enjoys subject reduction, type uniqueness and decidability of typing. Then we apply a classical type-erasing function to rho 2, to obtain an untyped rho-calculus à la Curry (uRho F). The related type inference system is isomorphic to Rho F and enjoys subject reduction. Both Rho F and uRho F systems can be considered as minimal calculi for polymorphic rewriting-based programming languages. We discuss the possibility of a logic existing underneath the type systems via a Curry-Howard Isomorphism.
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