An Explicit Substitution

An Explicit Substitution Notation in a Prolog Implementation

Explicit substitution calculi with de Bruijn indices and intersection type systems

Explicit substitution calculi propose solutions to the main drawback of the λ-calculus: substitutiondefined as a meta-operation in the system. By making explicit the process of substitution, thetheoretical system gets closer to an eventual implementation. Furthermore, for implementationpurposes, many explicit substitution systems are written with de Bruijn indices. The λ-calculus<lb...

The Soundness of Explicit Substitution with Nameless Variables

We show the soundness of a-calculus B where de Bruijn indices are used, substitution is explicit, and reduction is step-wise. This is done by interpreting B in the classical calculus where the explicit substitution becomes implicit and de Bruijn indices become named variables. This is the rst at semantics of explicit substitution and step-wise reduction and the rst clear account of exactly when...

Explicit substitutions for control operators ?

The-calculus is a-calculus with a local operator closely related to normal-isation procedures in classical logic and control operators in functional programming. We introduce exp, an explicit substitution calculus for , show it preserves strong normali-sation and that its simply typed version is strongly normalising. Interestingly, exp is the rst example for which the decency method of showing ...

Explicit substitution for graphs

We present an atomic decomposition of substitution into erasure, duplication and (for bound variables) scoping.