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CORR
2010
Springer
140views Education» more  CORR 2010»
13 years 4 months ago
Refinement Types for Logical Frameworks and Their Interpretation as Proof Irrelevance
Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. We present a system of refinement types for...
William Lovas, Frank Pfenning
CORR
2011
Springer
170views Education» more  CORR 2011»
12 years 8 months ago
A Modular Type-checking algorithm for Type Theory with Singleton Types and Proof Irrelevance
We define a logical framework with singleton types and one universe of small types. We give the semantics using a PER model; it is used for constructing a normalisation-by-evaluat...
Andreas Abel, Thierry Coquand, Miguel Pagano
CADE
2006
Springer
14 years 5 months ago
Combining Type Theory and Untyped Set Theory
Abstract. We describe a second-order type theory with proof irrelevance. Within this framework, we give a representation of a form of Mac Lane set theory and discuss automated supp...
Chad E. Brown
IJCAI
2003
13 years 6 months ago
Weak Conditional Logics of Normality
A default conditional α → β has most often been informally interpreted as a defeasible version of a classical conditional, usually the material conditional. That is, the intui...
James P. Delgrande
CADE
2005
Springer
14 years 5 months ago
Reflecting Proofs in First-Order Logic with Equality
Our general goal is to provide better automation in interactive proof assistants such as Coq. We present an interpreter of proof traces in first-order multi-sorted logic with equal...
Evelyne Contejean, Pierre Corbineau