Expressing program developments in a design calculus

The present paper describes a step in the study of means to express software developments. This study is also related to approaches where programs are extracted from proofs, and it is influenced by the spirit and the techniques of constructive logic.

[1]  John Darlington,et al.  A Transformation System for Developing Recursive Programs , 1977, J. ACM.

[2]  Michel Sintzoff.  Proof-oriented and applicative valuations in definitions of algorithms , 1981, FPCA '81.

[3]  Peter Pepper,et al.  Program Transformation and Programming Environments , 1984, NATO ASI Series.

[4]  J. C. Shepherdson,et al.  Mathematical Logic and Programming Languages , 1985 .

[5]  Hans Hermes,et al.  Introduction to mathematical logic , 1973, Universitext.

[6]  Bengt Nordström,et al.  Programming in Constructive Set Theory: Some examples , 1981, FPCA '81.

[7]  Hans-Dieter Ehrich.  On the Theory of Specification, Implementation, and Parametrization of Abstract Data Types , 1982, JACM.

[8]  Nicolas Bourbaki,et al.  Théorie des ensembles , 1954 .

[9]  Thierry Coquand,et al.  Constructions: A Higher Order Proof System for Mechanizing Mathematics , 1985, European Conference on Computer Algebra.

[10]  Neil V. Murray.  Completely Non-Clausal Theorem Proving , 1982, Artif. Intell..

[11]  J. Abrial.  Programming as a mathematical exercise , 1984, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[12]  Douglas R. Smith,et al.  Top-Down Synthesis of Divide-and-Conquer Algorithms , 1985, Artif. Intell..

[13]  Kathleen McKeown,et al.  Discourse Strategies for Generating Natural-Language Text , 1985, Artif. Intell..

[14]  Friedrich L. Bauer,et al.  The Munich Project CIP , 1988, Lecture Notes in Computer Science.

[15]  Jonathan Traugott,et al.  Nested Resolution , 1986, CADE.

[16]  R. Milner,et al.  The use of machines to assist in rigorous proof , 1984, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[17]  Amy P. Felty,et al.  An Integration of Resolution and Natural Deduction Theorem Proving , 1986, AAAI.

[18]  Keith Hanna,et al.  Purely Functional Implementation of a Logic , 1986, CADE.

[19]  J. Roger Hindley,et al.  Introduction to combinators and λ-calculus , 1986, Acta Applicandae Mathematicae.

[20]  M. A. Nait Abdallah.  Procedures in Horn-Clause Programming , 1986, ICLP.

[21]  Michel Sintzoff.  Suggestions for Composing and Specifying Program Design Decisions , 1980, Symposium on Programming.

[22]  S. C. Kleene,et al.  Introduction to Metamathematics , 1952 .

[23]  de Ng Dick Bruijn.  Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem , 1972 .

[24]  M. Sintzoff,et al.  Understanding and Expressing Software Construction , 1984 .

[25]  L. Cardelli.  A Polymorphic λ-calculus with Type:Type , 1986 .

[26]  John C. Mitchell,et al.  Representation independence and data abstraction , 1986, POPL '86.

[27]  C. Goad.  Computational uses of the manipulation of formal proofs , 1980 .

[28]  Rance Cleaveland,et al.  Implementing mathematics with the Nuprl proof development system , 1986 .

[29]  Kurt Schütte.  Proof theory , 1977 .

[30]  Cliff B. Jones,et al.  Systematic software development using VDM , 1986, Prentice Hall International Series in Computer Science.

[31]  David Gries,et al.  The Science of Programming , 1981, Text and Monographs in Computer Science.

[32]  Zohar Manna,et al.  Special relations in automated deduction , 1985, JACM.

[33]  de Ng Dick Bruijn,et al.  A survey of the project Automath , 1980 .