# Combining First Order Algebraic Rewriting Systems, Recursion and Extensional Lambda Calculi

@inproceedings{Cosmo1994CombiningFO, title={Combining First Order Algebraic Rewriting Systems, Recursion and Extensional Lambda Calculi}, author={Roberto Di Cosmo and Delia Kesner}, booktitle={ICALP}, year={1994} }

It is well known that confluence and strong normalization are preserved when combining left-linear algebraic rewriting systems with the simply typed lambda calculus. It is equally well known that confluence fails when adding either the usual extensional rule for η, or recursion together with the usual contraction rule for surjective pairing.

## 20 Citations

Combining Algebraic Rewriting, Extensional Lambda Calculi, and Fixpoints

- MathematicsTheor. Comput. Sci.
- 1996

Expanding Extensional Polymorphism

- MathematicsTLCA
- 1995

We prove the confluence and strong normalization properties for second order lambda calculus equipped with an expansive version of η-reduction. Our proof technique, based on a simple abstract lemma…

On Modular Properties of Higher Order Extensional Lambda Calculi

- MathematicsICALP
- 1997

We prove that confluence and strong normalisation are both modular properties for the addition of algebraic term rewriting systems to Girard's F ω equipped with either β-equality or βη-equality.

Combining Algebraic Rewriting with the Second-order Extensional Polymorphic Lambda Calculus

- Mathematics
- 2007

We prove that strong normalisation and connuence properties are conserved when a left-linear canonical rst-order algebraic rewriting system is combined with the second-order polymorphic-calculus with…

Reasoning about Layered, Wildcard and Product Patterns

- MathematicsALP
- 1994

A confluent reduction system is obtained by turning the extensional axioms as expansion rules, and then adding some restrictions to these expansions in order to avoid reduction loops.

An extensional operational and axiomatic semantics for type-inference with recursion and algebraic data types

- Computer Science
- 2013

This is the first satisfactory treatment of a polymorphic type inference systems in the presence of extensionality, and it is shown how to add, using some simple but powerful lemmas from the theory of rewriting, algebraic data types and recursion preserving confluence of the system under very liberal conditions.

Simulating eta-expansions with beta-reductions in the Second-Order Polymorphic lambda-calculus

- MathematicsLFCS
- 1997

A modular proof is presented that the second-order polymorphic λ-calculus with an expansive version of η-reduction is strong normalizing and confluent and shows that other rewriting systems are also strongly normalizing after expanded with certain versions ofη-expansion.

Confluence Properties of Extensional and Non-Extensional lambda-Calculi with Explicit Substitutions (Extended Abstract)

- MathematicsRTA
- 1996

A general scheme for explicit substitutions is proposed which describes those abstract properties that are sufficient to guarantee confluence in λ-calculi, and makes it possible to treat at the same time many well-known calculi, or some other new calculi that are proposed in this paper.

Labeling techniques and typed fixed-point operators

- Mathematics
- 1999

Labeling techniques for untyped lambda calculus were developed by Levy, Hyland, Wadsworth and others in the 1970's. A typical application is the proof of confluence from finiteness of de- velopments:…

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