Executing Higher Order Logic

Berghofer, Stefan; Nipkow, Tobias

doi:10.1007/3-540-45842-5_2

Cited by 68 publications

(41 citation statements)

References 13 publications

(16 reference statements)

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“…8 These effective operations on Base allow us to reason in the programming language, where in the past we resorted to reflection in the logic [6].…”

Section: Canonical Form Testsmentioning

confidence: 99%

“…An obvious question is then, could we build a verified compiler for Nuprl in Nuprl that generates reasonably fast code? Modern proof assistants that implement constructive type theories such as Coq [9,1], Isabelle [8,7], or Nuprl rely on unverified compilers. Even though the programs they generate, e.g., by extraction from proofs, are correct-by-construction, one could argue whether the machine code obtained after compilation is still correct.…”

Section: Introductionmentioning

confidence: 99%

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Formal Program Optimization in Nuprl Using Computational Equivalence and Partial Types

Rahli

Bickford

Anand

2013

Interactive Theorem Proving

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Abstract. This paper extends the proof methods used by the Nuprl proof assistant to reason about the computational behavior of its untyped programs. We have implemented new methods to prove non-trivial bisimulations between programs and have successfully applied these methods to formally optimize distributed programs such as our synthesized and verified version of Paxos, a widely used protocol to achieve software based replication. We prove new results about the basic computational equality relation on terms, and we extend the theory of partial types as the basis for stating internal results about the computation system that were previously treated only in the meta theory of Nuprl. All the lemmas presented in this paper have been formally proved in Nuprl.

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“…8 These effective operations on Base allow us to reason in the programming language, where in the past we resorted to reflection in the logic [6].…”

Section: Canonical Form Testsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Formal Program Optimization in Nuprl Using Computational Equivalence and Partial Types

Rahli

Bickford

Anand

2013

Interactive Theorem Proving

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“…We now describe our new translation from Minlog terms into Haskell programs (there is also limited support for translating into Scheme). Coq [17], Isabelle/HOL [5] and Agda [26] provide similar features.…”

Section: Translation To a General-purpose Programming Languagementioning

confidence: 99%

Program Extraction from Nested Definitions

Miyamoto

Forsberg

Schwichtenberg

2013

Interactive Theorem Proving

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Abstract. Minlog is a proof assistant which automatically extracts computational content in an extension of Gödel's T from formalized proofs. We report on extending Minlog to deal with predicates defined using a particular combination of induction and coinduction, via so-called nested definitions. In order to increase the efficiency of the extracted programs, we have also implemented a feature to translate terms into Haskell programs. To illustrate our theory and implementation, a formalisation of a theory of uniformly continuous functions due to Berger is presented.

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“…Several works have attempted to overcome this weakness of inductive relations by providing mechanisms that transform inductively defined relations in a proof assistant based on type theory into recursive programs in a typed functional language, see e.g. [5]. While such a translation allows users to specify and verify inductively defined functions, and to extract an executable program for computing the result of the functions, it forces computations to take place outside the proof assistant.…”

Section: Applications To Relationsmentioning

confidence: 99%

Defining and Reasoning About Recursive Functions: A Practical Tool for the Coq Proof Assistant

Barthe

Forest

Pichardie

et al. 2006

Functional and Logic Programming

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Abstract. We present a practical tool for defining and proving properties of recursive functions in the Coq proof assistant. The tool generates from pseudo-code the graph of the intended function as an inductive relation. Then it proves that the relation actually represents a function, which is by construction the function that we are trying to define. Then, we generate induction and inversion principles, and a fixpoint equation for proving other properties of the function. Our tool builds upon stateof-the-art techniques for defining recursive functions, and can also be used to generate executable functions from inductive descriptions of their graph. We illustrate the benefits of our tool on two case studies.

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Executing Higher Order Logic

Cited by 68 publications

References 13 publications

Formal Program Optimization in Nuprl Using Computational Equivalence and Partial Types

Formal Program Optimization in Nuprl Using Computational Equivalence and Partial Types

Program Extraction from Nested Definitions

Defining and Reasoning About Recursive Functions: A Practical Tool for the Coq Proof Assistant

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