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Code generation from Isabelle/HOL theories
, 2008
"... This tutorial gives a motivationdriven introduction to a generic code generator framework in Isabelle for generating executable code in functional programming languages from logical specifications. ..."
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This tutorial gives a motivationdriven introduction to a generic code generator framework in Isabelle for generating executable code in functional programming languages from logical specifications.
Animating the Formalised Semantics of a Javalike Language
"... Abstract. Considerable effort has gone into the techniques of extracting executable code from formal specifications and animating them. We show how to apply these techniques to the large JinjaThreads formalisation. It models a substantial subset of multithreaded Java source and bytecode in Isabelle/ ..."
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Abstract. Considerable effort has gone into the techniques of extracting executable code from formal specifications and animating them. We show how to apply these techniques to the large JinjaThreads formalisation. It models a substantial subset of multithreaded Java source and bytecode in Isabelle/HOL and focuses on proofs and modularity whereas code generation was of little concern in its design. Employing Isabelle’s code generation facilities, we obtain a verified Java interpreter that is sufficiently efficient for running small Java programs. To this end, we present refined implementations for common notions such as the reflexive transitive closure and Russell’s definite description operator. From our experience, we distill simple guidelines on how to develop future formalisations with executability in mind. 1
Smart testing of functional programs in Isabelle
"... Abstract. We present a novel counterexample generator for the interactive theorem prover Isabelle based on a compiler that synthesizes test data generators for functional programming languages (e.g. ML, Haskell) from specifications in Isabelle. In contrast to naive typebased test data generators, t ..."
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Abstract. We present a novel counterexample generator for the interactive theorem prover Isabelle based on a compiler that synthesizes test data generators for functional programming languages (e.g. ML, Haskell) from specifications in Isabelle. In contrast to naive typebased test data generators, the smart generators take the preconditions into account and only generate tests that fulfill the preconditions. The smart generators are constructed by a compiler that reformulates the preconditions as logic programs and analyzes them with an enriched mode inference. From this inference, the compiler can construct the desired generators in the functional programming language. Applying these test data generators reduces the number of tests significantly and enables us to find errors in specifications where naive random and exhaustive testing fail. 1
Formalizing Bounded Increase ⋆
"... Abstract. Bounded increase is a termination technique where it is tried to find an argument x of a recursive function that is increased repeatedly until it reaches a bound b, which might be ensured by a condition x < b. Since the predicates like < may be arbitrary userdefined recursive functi ..."
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Abstract. Bounded increase is a termination technique where it is tried to find an argument x of a recursive function that is increased repeatedly until it reaches a bound b, which might be ensured by a condition x < b. Since the predicates like < may be arbitrary userdefined recursive functions, an induction calculus is utilized to prove conditional constraints. In this paper, we present a full formalization of bounded increase in the theorem prover Isabelle/HOL. It fills one large gap in the penandpaper proof, and it includes generalized inference rules for the induction calculus as well as variants of the Babylonian algorithm to compute square roots. These algorithms were required to write executable functions which can certify untrusted termination proofs from termination tools that make use of bounded increase. And indeed, the resulting certifier was already useful: it detected an implementation error that remained undetected since 2007. 1
Certification of nontermination proofs
 In Proc. ITP 2012, volume 7406 of LNCS
, 2012
"... Abstract Automatic tools for proving (non)termination of term rewrite systems, if successful, deliver proofs as justification. In this work, we focus on how to certify nontermination proofs. Besides some techniques that allow to reduce the number of rules, the main way of showing nontermination is t ..."
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Abstract Automatic tools for proving (non)termination of term rewrite systems, if successful, deliver proofs as justification. In this work, we focus on how to certify nontermination proofs. Besides some techniques that allow to reduce the number of rules, the main way of showing nontermination is to find a loop, a finite derivation of a special shape that implies nontermination. For standard termination, certifying loops is easy. However, it is not at all trivial to certify whether a given loop also implies innermost nontermination. To this end, a complex decision procedure has been developed in [1]. We formalized this decision procedure in Isabelle/HOL and were able to simplify some parts considerably. Furthermore, from our formalized proofs it is easy to obtain a low complexity bound. Along the way of presenting our formalization, we report on generally applicable ideas that allow to reduce the formalization effort and improve the efficiency of our certifier.
Smart test data generators via logic programming ∗
"... We present a novel counterexample generator for the interactive theorem prover Isabelle based on a compiler that synthesizes test data generators for functional programming languages (e.g. Standard ML, OCaml) from specifications in Isabelle. In contrast to naive typebased test data generators, the ..."
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We present a novel counterexample generator for the interactive theorem prover Isabelle based on a compiler that synthesizes test data generators for functional programming languages (e.g. Standard ML, OCaml) from specifications in Isabelle. In contrast to naive typebased test data generators, the smart generators take the preconditions into account and only generate tests that fulfill the preconditions. The smart generators are constructed by a compiler that reformulates the preconditions as logic programs and analyzes them by an enriched mode inference. From this inference, the compiler can construct the desired generators in the functional programming language. These test data generators are applied to find errors in specifications, as we show in a case study of a hotel key card system.
A Solution to the PoplMark Challenge using de Bruijn indices in Isabelle/HOL
"... We present a solution to the PoplMark challenge designed by Aydemir et al., which has as a goal the formalization of the metatheory of System F<:. The formalization is carried out in the theorem prover Isabelle/HOL using an encoding based on de Bruijn indices. We start with a relatively simple ..."
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We present a solution to the PoplMark challenge designed by Aydemir et al., which has as a goal the formalization of the metatheory of System F<:. The formalization is carried out in the theorem prover Isabelle/HOL using an encoding based on de Bruijn indices. We start with a relatively simple formalization covering only the basic features of System F<:, and explain how it can be extended to also cover records and more advanced binding constructs. We also discuss different styles of formalizing the evaluation relation, and how this choice influences executability of the specification.
Lem: reusable engineering of realworld semantics
"... Recent years have seen remarkable successes in rigorous engineering: using mathematically rigorous semantic models (not just idealised calculi) of realworld processors, programming languages, protocols, and security mechanisms, for testing, proof, analysis, and design. Building these models is chal ..."
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Recent years have seen remarkable successes in rigorous engineering: using mathematically rigorous semantic models (not just idealised calculi) of realworld processors, programming languages, protocols, and security mechanisms, for testing, proof, analysis, and design. Building these models is challenging, requiring experimentation, dialogue with vendors or standards bodies, and validation; their scale adds engineering issues akin to those of programming to the task of writing clear and usable mathematics. But language and tool support for specification is lacking. Proof assistants can be used but bring their own difficulties, and a model produced in one, perhaps requiring many personyears effort and maintained over an extended period, cannot be used by those familiar with another. We introduce Lem, a language for engineering reusable largescale semantic models. The Lem design takes inspiration both from functional programming languages and from proof assistants, and Lem definitions are translatable into OCaml for testing, Coq, HOL4, and Isabelle/HOL for proof, and LaTeX and HTML for presentation. This requires a delicate balance of expressiveness, careful library design, and implementation of transformations – akin to compilation, but subject to the constraint of producing usable and humanreadable code for each target. Lem’s effectiveness is demonstrated by its use in practice.