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» Type theory in type theory using quotient inductive types
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AISC
2010
Springer
13 years 9 months ago
Structured Formal Development with Quotient Types in Isabelle/HOL
General purpose theorem provers provide sophisticated proof methods, but lack some of the advanced structuring mechanisms found in specification languages. This paper builds on pr...
Maksym Bortin, Christoph Lüth
JSAT
2007
95views more  JSAT 2007»
13 years 5 months ago
An Abstract Decision Procedure for a Theory of Inductive Data Types
Clark Barrett, Igor Shikanian, Cesare Tinelli
CORR
2011
Springer
170views Education» more  CORR 2011»
12 years 9 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
ASIAN
2006
Springer
91views Algorithms» more  ASIAN 2006»
13 years 9 months ago
A Type-Theoretic Framework for Formal Reasoning with Different Logical Foundations
Abstract. A type-theoretic framework for formal reasoning with different logical foundations is introduced and studied. With logic-enriched type theories formulated in a logical fr...
Zhaohui Luo
CADE
1998
Springer
13 years 9 months ago
Admissibility of Fixpoint Induction over Partial Types
Partial types allow the reasoning about partial functions in type theory. The partial functions of main interest are recursively computed functions, which are commonly assigned ty...
Karl Crary