Typing algorithm in type theory with inheritance
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Coercive subtyping for the calculus of constructions
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Implicit Coercions in Type Systems
TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
Coercion Synthesis in Computer Implementations of Type-Theoretic Frameworks
TYPES '96 Selected papers from the International Workshop on Types for Proofs and Programs
A Logical Framework with Dependently Typed Records
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
Manifest Fields and Module Mechanisms in Intensional Type Theory
Types for Proofs and Programs
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Packaging Mathematical Structures
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
The Matita interactive theorem prover
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Interfacing Coq + SSReflect with GAP
Electronic Notes in Theoretical Computer Science (ENTCS)
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We address the problem of representing mathematical structures in a proof assistant which: 1) is based on a type theory with dependent types, telescopes and a computational version of Leibniz equality; 2) implements coercive subtyping, accepting multiple coherent paths between type families; 3) implements a restricted form of higher order unification and type reconstruction. We show how to exploit the previous quite common features to reduce the "syntactic" gap between pen&paper and formalised algebra. However, to reach our goal we need to propose unification and type reconstruction heuristics that are slightly different from the ones usually implemented. We have implemented them in Matita.