D. J. Howe. Reasoning about functional programs in Nuprl. In Functional Programming, Concurrency, Simulation and Reasoning, number 693 in Lecture Notes in Computer Science, pages 145-164, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....via the fixed point combinator Y. This is possible because Nuprl s underlying computation system is an untyped # calculus. This possibility for the Nuprl type system was first noted by Allen in 1984 who realized that applications of Y could be assigned a type. Based on Allen s proof, Howe [6, 7] developed the current methodology for defining and using general recursive functions in Nuprl. Jackson [8, 9] incorporated Howe s methodology into his tactics for Nuprl 4. We will only present details of Nuprl s type theory here as necessary. A hypertext account of the type theory is available ....

Douglas J. Howe. Reasoning about functional programs in Nuprl. In Functional Programming, Concurrency, Simulation and Automated Reasoning, volume 693 of Lecture Notes in Computer Science, Berlin, 1993. Springer Verlag.

....functions via the xed point combinator Y. This is possible because Nuprl s underlying computation system is an untyped calculus. This possibility for the Nuprl type system was rst noted by Allen in 1984 who realized that applications of Y could be assigned a type. Based on Allen s proof, Howe [6, 7] developed the current methodology for de ning and using general recursive functions in Nuprl. Jackson [8, 9] incorporated Howe s methodology into his tactics for Nuprl 4. We will only present details of Nuprl s type theory here as necessary. A hypertext account of the type theory is available ....

Douglas J. Howe. Reasoning about functional programs in Nuprl. In Functional Programming, Concurrency, Simulation and Automated Reasoning, volume 693 of Lecture Notes in Computer Science, Berlin, 1993. Springer Verlag.

....computing by proof and programmingby proof. Computing by proof is concerned with computations, the object of functional programming languages such as LISP or SML. Programming is mainly concerned with actions such as sorting a disk file. In this case, classical program synthesizing systems such as [7, 14, 16, 19, 21, 22, 23] are not adapted because they rely on more or less classical logics and produce expressions. Even if imperative execution can be modeled with functions, it is not realistic. Logics and actions. Classical and even intuitionistic logics are also not adapted for processing actions unless we use the ....

HOWE, D. Reasoning about functional programs in nuprl. In Functional Programming, Concurrency, Simulation, and Automated Reasoning (1991), vol. 693 of Lecture Notes in Computer Science, Springer-verlag, pp. 145--164.

....same that [Pol94] to construct proof and program at the same time but the framework different. In Nuprl [Con86] one can prove directly that a program realizes a specification. The logic allows the user to hide the logical information and include as much computational information as needed (see [How93] for examples) 6. Conclusion We have defined a new extraction function for the Calculus of Inductive Constructions called the weak extraction. Weak extracted terms are condensed forms of proofs. They are F Ind programs annotated with specifications. A new notion of typing has been defined ....

D. Howe. Reasoning About Functional Programs in Nuprl. In Functional Programming, Concurrency, Simulation and Automated Reasoning, volume 693 of LNCS, 1993.

....a member of the formal methods group at NASA Langley Research Center. The author is currently visiting Cornell University, and can be contacted at 4116 Upson Hall, Cornell University, Ithaca, NY, 14850. in an attempt to improve the efficiency, readability, and understanding of extracted programs [11, 5, 12]. This paper presents a methodology for specification and proof in the Nuprl system that yields clean recursive programs as extracts. The methodology for directly defining recursive functions and proving properties about them is well established in Nuprl practice. Indeed many of the pieces for the ....

....and proof in the Nuprl system that yields clean recursive programs as extracts. The methodology for directly defining recursive functions and proving properties about them is well established in Nuprl practice. Indeed many of the pieces for the new methodology described here are already present in [5]. The approach described here makes it possible to extract programs from proofs that can be uniformly manipulated by the Nuprl system using current methodology. Although it has always been possible in Nuprl to approach program development from either side, i.e. via verification or extraction, the ....

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D. J. Howe. Reasoning about functional programs in Nuprl. In Functional Programming, Concurrency, Simulation and Automated Reasoning, volume 693 of Lecture Notes in Computer Science, Berlin, 1993. Springer Verlag.

....its computation system is untyped. The typing rules describe when a term inhabits a type, and are expressive enough to permit typing judgements about terms without always having to assign types to every subterm. In particular, general recursive functions can be defined using Curry s Y combinator [27]. This method is useful for generating readable and efficient extracts. Additionally, theorems stating induction principles can be proved so that the computational content of their proofs are efficient recursion schemes. The typing ensures that the recursion is well founded. In [8] a letrec form ....

D.J. Howe. Reasoning about functional programs in Nuprl. In P.F. Lauer, editor, Functional Programming, Concurrency, Simulation and Automated Reasoning, pages 145--164. Springer-Verlag, 1993.

....if the type theory had included a subtyping predicate. Fortunately, I think that much of the theory development and all the proof tool development would remain intact if a type theory were adopted with these or equivalent changes. Howe has put much thought into how such changes might be achieved [How93, HS94] However, part of the problems are inherent in the constructivist agenda of seeing potential computational content in every logical proposition. The constructivist makes many subtle distinctions that a classical mathematician ignores. Then, to make the presentation of the mathematics ....

Douglas J. Howe. Reasoning about functional programs in Nuprl. Functional Programming, Concurrency, Simulation and Automated Reasoning, Lecture Notes in Computer Science, 1993.

....Second, Nuprl s computation system is untyped. The typing rules describe when a term inhabits a type, and are complex enough to permit typing judge22 ments about terms with untypable subterms. In particular, we can define functions using Curry s Y combinator to describe recursion directly [25]. We can then show that such a function inhabits a type representing an induction principle. The recursive function then can be used as the computational content of the induction principle; the typing ensures that the recursion is well founded. This technique is described in some depth in [8] ....

D.J. Howe. Reasoning about functional programs in Nuprl. Functional Programming, Concurrency, Simulation and Automated Reasoning, Lecture Notes in Computer Science, 1993.

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D. J. Howe. Reasoning about functional programs in Nuprl. In Functional Programming, Concurrency, Simulation and Reasoning, number 693 in Lecture Notes in Computer Science, pages 145-164, 1993.

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Douglas J. Howe. Reasoning about functional programs in Nuprl. Functional Programming, Concurrency, Simulation and Automated Reasoning, Lecture Notes in Computer Science, 1993.

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Howe, D. Reasoning about functional programs in nuprl. In Functional Programming, Concurrency, Simulation, and Automated Reasoning (1991), vol. 693 of LNCS, Springer-verlag, pp. 145164. 21

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Douglas J. Howe. Reasoning about functional programs in Nuprl. Functional Programming, Concurrency, Simulation and Automated Reasoning, Lecture Notes in Computer Science, Vol. 693, Springer, Berlin, 1993.

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