Handbook of logic in computer science (vol. 2)
Parallel reductions in &lgr;-calculus
Information and Computation
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The Relevance of Proof-Irrelevance
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
A short and flexible proof of Strong Normalization for the Calculus of Constructions
TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
A Generic Normalisation Proof for Pure Type Systems
TYPES '96 Selected papers from the International Workshop on Types for Proofs and Programs
A Generic Strong Normalization Argument: Application to the Calculus of Constructions
CSL '93 Selected Papers from the 7th Workshop on Computer Science Logic
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Extensional Equality in Intensional Type Theory
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Intensionality, Extensionality, and Proof Irrelevance in Modal Type Theory
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
The Formal Semantics of PVS
Journal of Automated Reasoning
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Lectures on the Curry-Howard Isomorphism, Volume 149 (Studies in Logic and the Foundations of Mathematics)
Formal verification of a realistic compiler
Communications of the ACM - Barbara Liskov: ACM's A.M. Turing Award Winner
Formal Verification of Avionics Software Products
FM '09 Proceedings of the 2nd World Congress on Formal Methods
seL4: formal verification of an operating-system kernel
Communications of the ACM
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
The not so simple proof-irrelevant model of CC
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
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
The implicit calculus of constructions as a programming language with dependent types
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Safe to the last instruction: automated verification of a type-safe operating system
PLDI '10 Proceedings of the 2010 ACM SIGPLAN conference on Programming language design and implementation
Irrelevance in type theory with a heterogeneous equality judgement
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
The Matita interactive theorem prover
CADE'11 Proceedings of the 23rd international conference on Automated deduction
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We extend Pure Type Systems with a function turning each term M of type A into a dummy |M| of the same type (|.| is not an identity, in that M ≠ |M|). Intuitively, a dummy represents an unknown, canonical object of the given type: dummies are opaque (cannot be internally inspected), and irrelevant in the sense that dummies of a same type are convertible to each other. This latter condition makes convertibility in PTS with dummies (DPTS) stronger than usual, hence raising not trivial consistency issues. DPTS offer an alternative approach to (proof) irrelevance, tagging irrelevant information at the level of terms and not of types, and avoiding the annoying syntactical duplication of products, abstractions and applications into an explicit and an implicit version, typical of systems like ICC*.