# On the Power of Simple Diagrams

@inproceedings{Cosmo1996OnTP, title={On the Power of Simple Diagrams}, author={Roberto Di Cosmo}, booktitle={RTA}, year={1996} }

In this paper we focus on a set of abstract lemmas that are easy to apply and turn out to be quite valuable in order to establish confluence and/or normalization modularly, especially when adding rewriting rules for extensional equalities to various calculi. We show the usefulness of the lemmas by applying them to various systems, ranging from simply typed lambda calculus to higher order lambda calculi, for which we can establish systematically confluence and/or normalization (or decidability…

## 15 Citations

### Isomorphisms of simple inductive types through extensional rewriting

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### Some Algebraic Structures in Lambda-Calculus with Inductive Types

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### Life without the Terminal Type

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### On Modular Properties of Higher Order Extensional Lambda Calculi

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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.

### The Journal of Functional and Logic Programming the Journal of Functional and Logic Programming Reasoning about Redundant Patterns

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This thesis explains how the adjunction of three features to System Fω allows writing programs in a modular way in an explicit system a la Church, while keeping a style that is similar to ML modules.…

### Higher-Order Rewriting with Dependent Types

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This dissertation studies a theory of Higher-order Term Rewriting for the LF calculus, on which Twelf is based, and presents applications to Milner's Action and Process Calculi, Category Theory, and Proof Theory.

### A brief history of rewriting with extensionality

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• A survey of confluence, decidability and normalization results for typed λ-calculi with extensional rules • A survey of the proof techniques • Some applications

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