# On Stepwise Explicit Substitution

@article{Kamareddine1993OnSE, title={On Stepwise Explicit Substitution}, author={Fairouz Kamareddine and R. P. Nederpelt}, journal={Int. J. Found. Comput. Sci.}, year={1993}, volume={4}, pages={197-240} }

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 substitution steps, giving rise to different versions of β-reduction including local and global…

## 54 Citations

### Reductions, intersection types, and explicit substitutions

- MathematicsMathematical Structures in Computer Science
- 2003

It is shown that the terms that normalise by leftmost reduction and the terms by head reduction can each be characterised as the terms typable in a certain system, and refine and strengthen the classical normalisation theorems.

### Generalized -reduction and Explicit Substitutions

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- 1996

Extending the-calculus with either explicit substitution or generalised reduction has been the subject of extensive research recently which still has many open problems. Due to this reason, the…

### Generalised -reduction and Explicit Substitutions 8th International Conference on Programming

- Computer Science
- 1996

This paper presents such a calculus sg and shows that it is a desirable extension of the-calculus and preserves strong normalisation, is sound and it simulates classical-reduction.

### A Flexible Framework for Visualisation of Computational Properties of General Explicit Substitutions Calculi

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### Comparing and implementing calculi of explicit substitutions with eta-reduction

- Computer ScienceAnn. Pure Appl. Log.
- 2005

### Preservation of strong normalisation in named lambda calculi with explicit substitution and garbage collection

- Computer Science
- 1995

It is shown that xgc is a conservative extension which preserves strong normalisation (PSN) of the untyped-calculus, which has two distinguishing features: rst, it retains the use of traditional variable names, specifying terms modulo renaming; this simpliies the reduction system.

### Extending a λ-calculus with explicit substitution which preserves strong normalisation into a confluent calculus on open terms

- MathematicsJournal of Functional Programming
- 1997

This paper extends the λ-calculus with explicit substitutions to a confluent calculus on open terms and considers that this extended method is a useful tool to obtain confluence when strong normalisation of the subcalculus of substitutions is not available.

### Comparing Calculi of Explicit Substitutions with Eta-reduction

- MathematicsElectron. Notes Theor. Comput. Sci.
- 2002

### A useful ?-notation

- Computer Science
- 1996

This article shows that deenitions such as compatibility, the heart of a term and-redexes become simpler in item notation and shows that with this item notation, reduction can be generalised in a nice way.

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