IMPS: An Interactive Mathematical Proof System

imps is an Interactive Mathematical Proof System intended as a general purpose tool for formulating and applying mathematics in a familiar fashion. The logic of imps is based on a version of simple type theory with partial functions and subtypes. Mathematical specication and inference are performed relative to axiomatic theories, which can be related to one another via inclusion and theory interpretation. imps provides relatively large primitive inference steps to facilitate human control of the deductive process and human comprehension of the resulting proofs. An initial theory library containing almost a thousand repeatable proofs covers signicant portions of logic, algebra and analysis, and provides some support for modeling applications in computer science.

[1]  Alonzo Church,et al.  A formulation of the simple theory of types , 1940, Journal of Symbolic Logic.

[2]  Joseph R. Shoenfield,et al.  Mathematical logic , 1967 .

[3]  Joseph A. Goguen,et al.  Principles of parameterized programming , 1989 .

[4]  Sentot Kromodimoeljo,et al.  m-NEVER System Summary , 1988, CADE.

[5]  P. Martin-Löf.  Constructive mathematics and computer programming , 1984 .

[6]  Stewart Shapiro,et al.  Second-order languages and mathematical practice , 1985, Journal of Symbolic Logic.

[7]  Michael J. C. Gordon,et al.  Edinburgh LCF: A mechanised logic of computation , 1979 .

[8]  Yiannis N. Moschovakis,et al.  Abstract recursion as a foundation for the theory of algorithms , 1984 .

[9]  William M. Farmer,et al.  A partial functions version of Church's simple theory of types , 1990, Journal of Symbolic Logic.

[10]  Luca Cardelli,et al.  On understanding types, data abstraction, and polymorphism , 1985, CSUR.

[11]  Jim Grundy,et al.  Window Inference In The HOL System , 1991, 1991., International Workshop on the HOL Theorem Proving System and Its Applications.

[12]  J. Dieudonne.  Foundations of Modern Analysis , 1969 .

[13]  Thierry Coquand,et al.  The Calculus of Constructions , 1988, Inf. Comput..

[14]  B. Russell.  Mathematical Logic as Based on the Theory of Types , 1908 .

[15]  Robert S. Boyer,et al.  Integrating decision procedures into heuristic theorem provers: a case study of linear arithmetic , 1988 .

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

[17]  Sentot Kromodimoeljo,et al.  EVES: An Overview , 1991, VDM Europe.

[18]  Peter B. Andrews.  An introduction to mathematical logic and type theory - to truth through proof , 1986, Computer science and applied mathematics.

[19]  Joseph A. Goguen,et al.  Introducing Institutions , 1983, Logic of Programs.

[20]  G. Boolos.  On second-order logic , 1975 .

[21]  Yiannis N. Moschovakis,et al.  Elementary induction on abstract structures , 1974 .

[22]  Gerhard Gentzen,et al.  Investigations into Logical Deduction , 1970 .

[23]  Herbert B. Enderton,et al.  A mathematical introduction to logic , 1972 .

[24]  Leon Henkin,et al.  Completeness in the theory of types , 1950, Journal of Symbolic Logic.

[25]  Solomon Feferman,et al.  Systems of predicative analysis , 1964, Journal of Symbolic Logic.

[26]  J. D. Monk,et al.  Mathematical Logic , 1976 .

[27]  M. Gordon.  HOL: A Proof Generating System for Higher-Order Logic , 1988 .