Results 1  10
of
14
Ribbon Proofs for Separation Logic
"... Abstract—We present a diagrammatic system for constructing and presenting readable program proofs in separation logic. A program proof should not merely certify that a program is correct; it should explain why it is correct. By examining a proof, one should gain understanding of both the program bei ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Abstract—We present a diagrammatic system for constructing and presenting readable program proofs in separation logic. A program proof should not merely certify that a program is correct; it should explain why it is correct. By examining a proof, one should gain understanding of both the program being considered and the proof technique being used. To
Unified decision procedures for regular expression equivalence. http://www.in.tum.de/∼nipkow/pubs/regex equiv. pdf
, 2014
"... Abstract. We formalize a unified framework for verified decision procedures for regular expression equivalence. Five recently published formalizations of such decision procedures (three based on derivatives, two on marked regular expressions) can be obtained as instances of the framework. We discov ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We formalize a unified framework for verified decision procedures for regular expression equivalence. Five recently published formalizations of such decision procedures (three based on derivatives, two on marked regular expressions) can be obtained as instances of the framework. We discover that the two approaches based on marked regular expressions, which were previously thought to be the same, are different, and we prove a quotient relation between the automata produced by them. The common framework makes it possible to compare the performance of the different decision procedures in a meaningful way. 1
Certified Parsing of Regular Languages
"... Abstract. We report on a certified parser generator for regular languages using the Agda programming language. Specifically, we programmed a transformation of regular expressions into a Booleanmatrix based representation of nondeterministic finite automata (NFAs). And we proved (in Agda) that a st ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We report on a certified parser generator for regular languages using the Agda programming language. Specifically, we programmed a transformation of regular expressions into a Booleanmatrix based representation of nondeterministic finite automata (NFAs). And we proved (in Agda) that a string matches a regular expression if and only if the NFA accepts it. The proof of the ifpart is effectively a function turning acceptance of a string into a parse tree while the onlyif part gives a function turning rejection into a proof of impossibility of a parse tree. 1
A Locale for Minimal Bad Sequences
"... We present a locale that abstracts over the necessary ingredients for constructing a minimal bad sequence, as required in classical proofs of Higman’s lemma and Kruskal’s tree theorem. 1 ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
We present a locale that abstracts over the necessary ingredients for constructing a minimal bad sequence, as required in classical proofs of Higman’s lemma and Kruskal’s tree theorem. 1
Theoretical Informatics and Applications Informatique Théorique et Applications Will be set by the publisher A FORMALISATION OF THE MYHILLNERODE THEOREM BASED ON REGULAR EXPRESSIONS ∗
"... Abstract. There are numerous textbooks on regular languages. Nearly all of them introduce the subject by describing finite automata and only mentioning on the side a connection with regular expressions. Unfortunately, automata are difficult to formalise in HOLbased theorem provers. The reason is th ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. There are numerous textbooks on regular languages. Nearly all of them introduce the subject by describing finite automata and only mentioning on the side a connection with regular expressions. Unfortunately, automata are difficult to formalise in HOLbased theorem provers. The reason is that they need to be represented as graphs, matrices or functions, none of which are inductive datatypes. Also convenient operations for disjoint unions of graphs, matrices and functions are not easily formalisiable in HOL. In contrast, regular expressions can be defined conveniently as a datatype and a corresponding reasoning infrastructure comes for free. We show in this paper that a central result from formal language theory—the MyhillNerode Theorem—can be recreated using only regular expressions. From this theorem many closure properties of regular languages follow. 1991 Mathematics Subject Classification. 68Q45. 1.
4 ɛclosure and moves 5 Discussion and ConclusionsA compact proof of decidability for regular expression equivalence Content
"... A compact proof of decidability for regular expression equivalence A compact proof of decidability for regular expression equivalence ITP 2012 ..."
Abstract
 Add to MetaCart
A compact proof of decidability for regular expression equivalence A compact proof of decidability for regular expression equivalence ITP 2012
Ribbon Proofs for Separation Logic A verification pearl
"... We present ribbon proofs, a diagrammatic proof system for separation logic. Inspired by an eponymous system due to Bean, ribbon proofs emphasise the structure of a proof, so are intelligible and hence useful pedagogically. Because they contain less redundancy than proof outlines, and allow each proo ..."
Abstract
 Add to MetaCart
(Show Context)
We present ribbon proofs, a diagrammatic proof system for separation logic. Inspired by an eponymous system due to Bean, ribbon proofs emphasise the structure of a proof, so are intelligible and hence useful pedagogically. Because they contain less redundancy than proof outlines, and allow each proof step to be checked locally, they are highly scalable (and we illustrate this with a ribbon proof of the Version 7 Unix memory manager). Where proof outlines are cumbersome to modify, ribbon proofs can be visually manoeuvred to yield proofs of variant programs. This paper introduces the ribbon proof system, proves its soundness and completeness, and outlines a prototype tool for validating the diagrams in Isabelle. 1.