Swapping: a natural bridge between named and indexed explicit substitution calculi

Swapping: a natural bridge between named and indexed explicit substitution calculi

This article is devoted to the presentation of λ rex, an explicit substitution calculus with de Bruijn indexes and a simple notation. By being isomorphic to λex – a recent formalism with variable names –, λ rex accomplishes simulation of β -reduction (Sim), preservation of β -strong normalization (PSN) and meta-confluence (MC), among other desirable properties. Our calculus is based on a novel ...

Preservation of Strong Normalisation in Named Lambda Calculi with Explicit Substitution and Garbage Collection

In this paper we introduce and study a new-calculus with explicit substitution, xgc, which has two distinguishing features: rst, it retains the use of traditional variable names, specifying terms modulo renaming; this simpliies the reduction system. Second, it includes reduction rules for explicit garbage collection; this simpliies several proofs. We show that xgc is a conservative extension wh...

On strong normalization of explicit substitution calculi

We present a counterexample to the strong normalization—also called termination—of the underlying calculus of explicit substitution of λτ . This problem was open.

Simple Proofs of Characterizing Strong Normalization for Explicit Substitution Calculi

We present a method of lifting to explicit substitution calculi some characterizations of the strongly normalizing terms of λ-calculus by means of intersection type systems. The method is first illustrated by applying to a composition-free calculus of explicit substitutions, yielding a simpler proof than the previous one by Lengrand et al. Then we present a new intersection type system in the s...

Normalization for Typed Lambda Calculi with Explicit Substitution