The Polymorphic Rewriting-calculus

Authors:
Luigi Liquori;Benjamin Wack
Affiliations:
INRIA Sophia Antipolis;LORIA & Universitéé Henri Poincaré, Nancy
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2005

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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 fea- tures higher-order functions (from Lambda-calculus) and pattern-matching (from Term Rewriting Systems). In this paper, we study extensively a second-order Rho-calculus a la Church (RhoF) that enjoys subject reduction, type uniqueness, and decidability of typing. Then we apply a classical type-erasing function to RhoF, to obtain an untyped Rho-calculus a la Curry (uRhoF). The related type inference system is isomorphic to RhoF and enjoys subject reduction. Both RhoF and uRhoF systems can be considered as minimal calculi for polymorphic rewriting-based program- ming languages. We discuss the possibility of a logic existing underneath the type systems via a Curry-Howard Isomorphism.