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      A Scheme for Defining Partial Higher-Order Functions by Recursion

      3rd Irish Workshop on Formal Methods (IWFM)

      Formal Methods

      1st - 2nd July 1999

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          Abstract

          This paper describes a scheme for defining partial higher-order functions as the least fixed points of monotone functionals. The scheme can be used to define both single functions by recursion and systems of functions by mutual recursion. The scheme is implemented in the IMPS Interactive Mathematical Proof System. The IMPS implementation includes an automatic syntactic check for monotonicity that succeeds for many common recursive definitions.

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          Most cited references 9

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          A lattice-theoretical fixpoint theorem and its applications

           Alfred Tarski (1955)
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            A formulation of the simple theory of types

             Alonzo Church (1940)
            The purpose of the present paper is to give a formulation of the simple theory of types which incorporates certain features of the calculus of λ-conversion. A complete incorporation of the calculus of λ-conversion into the theory of types is impossible if we require that λx and juxtaposition shall retain their respective meanings as an abstraction operator and as denoting the application of function to argument. But the present partial incorporation has certain advantages from the point of view of type theory and is offered as being of interest on this basis (whatever may be thought of the finally satisfactory character of the theory of types as a foundation for logic and mathematics).
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              PVS: A prototype verification system

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                Author and article information

                Contributors
                Conference
                July 1999
                July 1999
                : 1-13
                Affiliations
                St. Cloud State University

                St. Cloud, Minnesota, USA
                Article
                10.14236/ewic/IWFM1999.5
                © William M. Farmer. Published by BCS Learning and Development Ltd. 3rd Irish Workshop on Formal Methods

                This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

                3rd Irish Workshop on Formal Methods
                IWFM
                3
                Galway, Ireland
                1st - 2nd July 1999
                Electronic Workshops in Computing (eWiC)
                Formal Methods
                Product
                Product Information: 1477-9358BCS Learning & Development
                Self URI (journal page): https://ewic.bcs.org/
                Categories
                Electronic Workshops in Computing

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