Typed representation of objects by functions

A systematic representation of objects grouped into types by constructions similar to the composition of sets in mathematics is proposed. The representation is by lambda expressions, which supports the representation of objects from function spaces. The representation is related to a rather conventional language of type descriptions in a way that is believed to be new. Ordinary control-expressions (i.e.,case- and let-expressions) are derived from the proposed representation.

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

[2]  H. B. Curry,et al.  Combinatory Logic, Volume I. , 1961 .

[3]  Peter Henderson,et al.  Functional programming - application and implementation , 1980, Prentice Hall International Series in Computer Science.

[4]  Dana S. Scott,et al.  Data Types as Lattices , 1976, SIAM J. Comput..

[5]  Corrado Böhm,et al.  Automatic Synthesis of Typed Lambda-Programs on Term Algebras , 1985, Theor. Comput. Sci..

[6]  James B. Morris,et al.  Programming by semantic refinement , 1973, SIGPLAN-SIGOPS Interface Meeting.

[7]  William A. Howard,et al.  The formulae-as-types notion of construction , 1969 .

[8]  Per Martin-Löf,et al.  Constructive mathematics and computer programming , 1984 .

[9]  Henk Barendregt,et al.  The Lambda Calculus: Its Syntax and Semantics , 1985 .

[10]  Haskell B. Curry,et al.  Combinatory Logic, Volume I , 1959 .

[11]  Peter Wegner,et al.  Classification in object-oriented systems , 1986, OOPWORK '86.

[12]  Daniel Leivant.  Reasoning about functional programs and complexity classes associated with type disciplines , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[13]  James H. Morris,et al.  Types are not sets , 1973, POPL.

[14]  Jørgen Steensgaard-Madsen,et al.  A Statement-Oriented Approach to Data Abstraction , 1981, TOPL.

[15]  Robin Milner,et al.  A proposal for standard ML , 1984, LFP '84.

[16]  Mitchell Wand,et al.  Final Algebra Semantics and Data Type Extensions , 1979, J. Comput. Syst. Sci..

[17]  D. Neel,et al.  Correctness Proofs of Syntax-Directed Processing Descriptions by Attributes , 1979, J. Comput. Syst. Sci..

[18]  Samuel N. Kamin.  Final Data Types and Their Specification , 1983, TOPL.

[19]  Marcel Crabbé.  H. B. Curry, J. R. Hindley, J. P. Seldin, Combinatory Logic. Vol. II , 1974 .