Extracting &ohgr;'s programs from proofs in the calculus of constructions
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Handbook of logic in computer science (vol. 2)
Proceedings of the 26th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Intensionality, Extensionality, and Proof Irrelevance in Modal Type Theory
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Call-by-value is dual to call-by-name
ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
The Girard—Reynolds isomorphism (second edition)
Theoretical Computer Science
Erasure and polymorphism in pure type systems
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Parametricity and dependent types
Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
Realizability and parametricity in pure type systems
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Canonicity for 2-dimensional type theory
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proofs for free: Parametricity for dependent types
Journal of Functional Programming
A Computational Interpretation of Parametricity
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Transporting functions across ornaments
Proceedings of the 17th ACM SIGPLAN international conference on Functional programming
Proceedings of the 17th ACM SIGPLAN international conference on Functional programming
Names for free: polymorphic views of names and binders
Proceedings of the 2013 ACM SIGPLAN symposium on Haskell
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Dependent type-theory aims to become the standard way to formalize mathematics at the same time as displacing traditional platforms for high-assurance programming. However, current implementations of type theory are still lacking, in the sense that some obvious truths require explicit proofs, making type-theory awkward to use for many applications, both in formalization and programming. In particular, notions of erasure are poorly supported. In this paper we propose an extension of type-theory with colored terms, color erasure and interpretation of colored types as predicates. The result is a more powerful type-theory: some definitions and proofs may be omitted as they become trivial, it becomes easier to program with precise types, and some parametricity results can be internalized.