Introduction to higher order categorical logic
Introduction to higher order categorical logic
Proofs and types
Isomorphisms of types: from &lgr;-calculus to information retrieval and language design
Isomorphisms of types: from &lgr;-calculus to information retrieval and language design
Combining algebraic rewriting, extensional lambda calculi, and fixpoints
ICALP '94 Selected papers from the 21st international colloquium on Automata, languages and programming
Term rewriting and all that
Theoretical Computer Science - Special issue on theories of types and proofs
A Complete Axiom System for Isomorphism of Types in Closed Categories
LPAR '93 Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning
Remarks on Isomorphisms in Typed Lambda Calculi with Empty and Sum Types
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
On Mints' Reduction for ccc-Calculus
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
On the Power of Simple Diagrams
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Rewriting with Extensional Polymorphic Lambda-Calculus
CSL '95 Selected Papers from the9th International Workshop on Computer Science Logic
Commutation, Transformation, and Termination
Proceedings of the 8th International Conference on Automated Deduction
A Deciding Algorithm for Linear Isomorphism of Types with Complexity O (n log2(n))
CTCS '97 Proceedings of the 7th International Conference on Category Theory and Computer Science
An insertion operator preserving infinite reduction sequences
Mathematical Structures in Computer Science
Computations in graph rewriting: inductive types and pullbacks in DPO approach
CEE-SET'09 Proceedings of the 4th IFIP TC 2 Central and East European conference on Advances in Software Engineering Techniques
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We study isomorphisms of inductive types (that is, recursive types satisfying a condition of strict positivity) in an extensional simply typed $\lambda$-calculus with product and unit types. We first show that the calculus enjoys strong normalisation and confluence. Then we extend it with new conversion rules ensuring that all inductive representations of the product and unit types are isomorphic, and such that the extended reduction remains convergent. Finally, we define the notion of a faithful copy of an inductive type and a corresponding conversion relation that also preserves the good properties of the calculus.