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TOCL
2012
235views Formal Methods» more  TOCL 2012»
7 years 1 months ago
Topological and Simplicial Models of Identity Types
racting these leads us to introduce the notion of a path object category. This is a relatively simple axiomatic framework, which is nonetheless sufficiently strong to allow the con...
Benno van den Berg, Richard Garner
CORR
2010
Springer
121views Education» more  CORR 2010»
8 years 9 months ago
MiniAgda: Integrating Sized and Dependent Types
Sized types are a modular and theoretically well-understood tool for checking termination of recursive and productivity of corecursive definitions. The essential idea is to track ...
Andreas Abel
ENTCS
2007
102views more  ENTCS 2007»
8 years 11 months ago
Encoding Functional Relations in Scunak
We describe how a set-theoretic foundation for mathematics can be encoded in the new system Scunak. We then discuss an encoding of the construction of functions as functional relat...
Chad E. Brown
ENTCS
2008
92views more  ENTCS 2008»
8 years 11 months ago
Redundancy Elimination for LF
We present a type system extending the dependent type theory LF, whose terms are more amenable to compact representation. This is achieved by carefully omitting certain subterms w...
Jason Reed
ENTCS
2008
128views more  ENTCS 2008»
8 years 11 months ago
Towards Formalizing Categorical Models of Type Theory in Type Theory
This note is about work in progress on the topic of "internal type theory" where we investigate the internal formalization of the categorical metatheory of constructive ...
Alexandre Buisse, Peter Dybjer
ESOP
2008
Springer
9 years 27 days ago
A Realizability Model for Impredicative Hoare Type Theory
We present a denotational model of impredicative Hoare Type Theory, a very expressive dependent type theory in which one can and reason about mutable abstract data types. The model...
Rasmus Lerchedahl Petersen, Lars Birkedal, Aleksan...
CSL
2000
Springer
9 years 3 months ago
Interactive Programs in Dependent Type Theory
We introduce basic concepts from object-oriented programming into dependent type theory based on the idea of modelling objects as interactive programs. We consider methods, interf...
Peter Hancock, Anton Setzer
CSL
2004
Springer
9 years 4 months ago
A Dependent Type Theory with Names and Binding
We consider the problem of providing formal support for working tract syntax involving variable binders. Gabbay and Pitts have shown in their work on Fraenkel-Mostowski (FM) set th...
Ulrich Schöpp, Ian Stark
MKM
2007
Springer
9 years 5 months ago
Formal Representation of Mathematics in a Dependently Typed Set Theory
Abstract. We have formalized material from an introductory real analysis textbook in the proof assistant Scunak. Scunak is a system based on set theory encoded in a dependent type ...
Feryal Fulya Horozal, Chad E. Brown
TPHOL
2008
IEEE
9 years 5 months ago
First-Class Type Classes
Abstract. Type Classes have met a large success in Haskell and Isabelle, as a solution for sharing notations by overloading and for specith abstract structures by quantification o...
Matthieu Sozeau, Nicolas Oury
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