ON STEPWISE EXPLICIT SUBSTITUTION

On Stepwise Explicit Substitution

This paper starts by setting the ground for a lambda calculus notation that strongly mirrors the two fundamental operations of term construction, namely abstraction and application. In particular, we single out those parts of a term, called items in the paper, that are added during abstraction and application. This item notation proves to be a powerful device for the representation of basic sub...

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.

Explicit substitution for graphs

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

An Explicit Substitution

Extending the Explicit Substitution Paradigm

We present a simple term language with explicit operators for erasure, duplication and substitution enjoying a sound and complete correspondence with the intuitionistic fragment of Linear Logic’s Proof Nets. We establish the good operational behaviour of the language by means of some fundamental properties such as confluence, preservation of strong normalisation, strong normalisation of well-ty...