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Hoare Logics for Recursive Procedures and Unbounded Nondeterminism
 COMPUTER SCIENCE LOGIC (CSL 2002), VOLUME 2471 OF LNCS
, 2002
"... This paper presents sound and complete Hoare logics for partial and total correctness of recursive parameterless procedures in the context of unbounded nondeterminism. For total correctness, the literature so far has either restricted recursive procedures to be deterministic or has studied unbounde ..."
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Cited by 26 (3 self)
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This paper presents sound and complete Hoare logics for partial and total correctness of recursive parameterless procedures in the context of unbounded nondeterminism. For total correctness, the literature so far has either restricted recursive procedures to be deterministic or has studied unbounded nondeterminism only in conjunction with loops rather than procedures. We consider both single procedures and systems of mutually recursive procedures. All proofs have been checked with the theorem prover Isabelle/HOL.
Finding lexicographic orders for termination proofs in Isabelle/HOL
 Theorem Proving in Higher Order Logics: TPHOLs 2007, volume 4732 of Lecture Notes in Computer Science
, 2007
"... Abstract. We present a simple method to formally prove termination of recursive functions by searching for lexicographic combinations of size measures. Despite its simplicity, the method turns out to be powerful enough to solve a large majority of termination problems encountered in daily theorem pr ..."
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Cited by 14 (5 self)
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Abstract. We present a simple method to formally prove termination of recursive functions by searching for lexicographic combinations of size measures. Despite its simplicity, the method turns out to be powerful enough to solve a large majority of termination problems encountered in daily theorem proving practice. 1
A Survey on Embedding Programming Logics in a Theorem Prover
 Institute of Information and Computing Sciences Utrecht University
, 2002
"... Theorem provers were also called 'proof checkers' because that is what they were in the beginning. They have grown powerful, however, capable in many cases to automatically produce complicated proofs. In particular, higher order logic based theorem provers such as HOL and PVS became popular because ..."
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Cited by 8 (2 self)
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Theorem provers were also called 'proof checkers' because that is what they were in the beginning. They have grown powerful, however, capable in many cases to automatically produce complicated proofs. In particular, higher order logic based theorem provers such as HOL and PVS became popular because the logic is well known and very expressive. They are generally considered to be potential platforms to embed a programming logic for the purpose of formal verification. In this paper we investigate a number of most commonly used methods of embedding programming logics in such theorem provers and expose problems we discover. We will also propose an alternative approach: hybrid embedding.
Mechanising Procedures in HOL
, 1999
"... In this paper we present an approach for modelling procedures (as they occur in imperative programs) in a weakest precondition semantics. We show how this approach can be implemented in the mechanisation of the refinement calculus theory in the HOL system. That makes it possible to derive a number o ..."
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In this paper we present an approach for modelling procedures (as they occur in imperative programs) in a weakest precondition semantics. We show how this approach can be implemented in the mechanisation of the refinement calculus theory in the HOL system. That makes it possible to derive a number of correctness and refinement properties of procedures. Finally, we show how our method for procedure handling can be integrated into a tool for transformational reasoning about programs  the Refinement Calculator.