Partiality and recursion in interactive theorem provers–an overview
The use of interactive theorem provers to establish the correctness of critical parts of a
software development or for formalizing mathematics is becoming more common and …
software development or for formalizing mathematics is becoming more common and …
Modelling general recursion in type theory
A Bove, V Capretta - Mathematical Structures in Computer Science, 2005 - cambridge.org
Constructive type theory is an expressive programming language in which both algorithms
and proofs can be represented. A limitation of constructive type theory as a programming …
and proofs can be represented. A limitation of constructive type theory as a programming …
Automating recursive definitions and termination proofs in higher-order logic
A Krauss - 2009 - mediatum.ub.tum.de
The aim of this thesis is to provide an infrastructure for general recursive function definitions
in a proof assistant based on higher-order logic (HOL) that has no native support for …
in a proof assistant based on higher-order logic (HOL) that has no native support for …
Partial and nested recursive function definitions in higher-order logic
A Krauss - Journal of Automated Reasoning, 2010 - Springer
Based on inductive definitions, we develop a tool that automates the definition of partial
recursive functions in higher-order logic (HOL) and provides appropriate proof rules for …
recursive functions in higher-order logic (HOL) and provides appropriate proof rules for …
Function definition in higher-order logic
K Slind - International Conference on Theorem Proving in …, 1996 - Springer
We use a formally proven wellfounded recursion theorem as the basis upon which to build a
function definition facility for Higher Order Logic. This approach offers flexibility in the choice …
function definition facility for Higher Order Logic. This approach offers flexibility in the choice …
Reasoning about partial functions in the formal development of programs
CB Jones - Electronic Notes in Theoretical Computer Science, 2006 - Elsevier
Partial functions and operators are used extensively in the formal development of programs
and thus development methods have to clarify how to reason about them. There are a …
and thus development methods have to clarify how to reason about them. There are a …
General recursion in type theory
A Bove - International Workshop on Types for Proofs and …, 2002 - Springer
In this work, a method to formalise general recursive algorithms in constructive type theory is
presented throughout examples. The method separates the computational and logical parts …
presented throughout examples. The method separates the computational and logical parts …
Treating partiality in a logic of total functions
O Müller, K Slind - The computer journal, 1997 - academic.oup.com
The need to use partial functions arises frequently in formal descriptions of computer
systems. However, most proof assistants are based on logics of total functions. One way to …
systems. However, most proof assistants are based on logics of total functions. One way to …
The 5 colour theorem in Isabelle/Isar
G Bauer, T Nipkow - Theorem Proving in Higher Order Logics: 15th …, 2002 - Springer
The 5 Colour Theorem in Isabelle/Isar Page 1 The 5 Colour Theorem in Isabelle/Isar Gertrud
Bauer and Tobias Nipkow Technische Universität München Institut für Informatik, Arcisstrasse …
Bauer and Tobias Nipkow Technische Universität München Institut für Informatik, Arcisstrasse …
Another look at nested recursion
K Slind - International Conference on Theorem Proving in …, 2000 - Springer
Functions specified by nested recursions are difficult to define and reason about. We present
several ameliorative techniques that use deduction in a classical higher-order logic. First, we …
several ameliorative techniques that use deduction in a classical higher-order logic. First, we …