Views: a way for pattern matching to cohabit with data abstraction
POPL '87 Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Type theory and functional programming
Type theory and functional programming
Analogy in Inductive Theorem Proving
Journal of Automated Reasoning
Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
A Natural Language Explanation for Formal Proofs
LACL '96 Selected papers from the First International Conference on Logical Aspects of Computational Linguistics
Using Reflection to Build Efficient and Certified Decision Procedures
TACS '97 Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Equational Reasoning via Partial Reflection
TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
A Prototype Proof Translator from HOL to Coq
TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
Fix-Point Equations for Well-Founded Recursion in Type Theory
TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
Representing Proof Transformations for Program Optimizations
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Hybrid Interactive Theorem Proving Using Nuprl and HOL
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
Automating changes of data type in functional programs
KBSE '95 Proceedings of The 10th Knowledge-Based Software Engineering Conference
The specialization and transformation of constructive existence proofs
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 1
A computational view of implicit coercions in type theory
Mathematical Structures in Computer Science
Constructive Membership Predicates as Index Types
Electronic Notes in Theoretical Computer Science (ENTCS)
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In type-theory based proof systems that provide inductive structures, computation tools are automatically associated to inductive definitions. Choosing a particular representation for a given concept has a strong influence on proof structure. We propose a method to make the change from one representation to another easier, by systematically translating proofs from one context to another. Weshow how this method works by using it on natural numbers, for which a unary representation (based on Peano axioms) and a binary representation are available. This method leads to an automatic translation tool that we have implemented in Coq and successfully applied to several arithmetical theorems.