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Conference Papers Year : 2003

Rewriting Calculus with Fixpoints: Untyped and First-order Systems


The rewriting calculus, also called ρ-calculus, is a framework embedding λ-calculus and rewriting capabilities, by allowing abstraction not only on variables but also on patterns. The higher-order mechanisms of the λ-calculus and the pattern matching facilities of the rewriting are then both available at the same level. Many type systems for the λ-calculus can be generalized to the ρ-calculus: in this paper, we study extensively a first-order ρ-calculus à la Church, called ρstk→ . The type system of ρstk→ allows one to type (object oriented flavored) fixpoints, leading to an expressive and safe calculus. In particular, using pattern matching, one can encode and typecheck term rewriting systems in a natural and automatic way. Therefore, we can see our framework as a starting point for the theoretical basis of a powerful typed rewriting-based language.
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inria-00100113 , version 1 (07-05-2015)



Horatiu Cirstea, Luigi Liquori, Benjamin Wack. Rewriting Calculus with Fixpoints: Untyped and First-order Systems. Types for Proofs and Programs International Workshop, TYPES 2003, Torino, Italy, April 30 - May 4, 2003, Revised Selected Papers, Apr 2003, Turin, Italy. pp.147-161, ⟨10.1007/978-3-540-24849-1_10⟩. ⟨inria-00100113⟩
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