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View all- Downey PSethi R(1975)Correct computation rules for recursive languagesProceedings of the 16th Annual Symposium on Foundations of Computer Science10.1109/SFCS.1975.10(48-56)Online publication date: 13-Oct-1975
Computability concepts for programming language semantics
Pages 98 - 106
Abstract
This paper is about mathematical problems in programming language semantics and their influence on recursive function theory. We define a notion of computability on continuous higher types (for all types) and show its equivalence to effective operators. This result shows that our computable operators can model mathematically (i.e. extensionally) everything that can be done in an operational semantics. These new recursion theoretic concepts which are appropriate to semantics also allow us to construct Scott models for the λ-calculus which contain all and only computable elements. Depending on the choice of the initial cpo, our general theory yields a theory for either strictly determinate or else arbitrary non-deterministic objects (parallelism).
The formal theory is developed in part II of this paper. Part I gives motivation and comparison with related work.
References
[1]
Cadiou, J.M., "Recursive Definitions of Partial Functions and their Computations", Ph.D. Thesis, AIM-163/CS-266, Dept. of Computer Science, Stanford University (1972).
[2]
Constable, R.L. and D. Gries, "On Classes of Program Schemata", SIAM J. Computing, 1, 1, March 1972.
[3]
Egli, H., "An Analysis of Scott's &lgr;-Calculus Models", TR 73-191, Cornell University (1973).
[4]
Egli, H., "Programming Language Semantics Using Extensional &lgr;-Calculus Models", TR 74-206, Cornell University (1974).
[5]
Gandy, R.O., "Computable Functionals of Finite Type I", Sets, Models and Recursion Theory, ed. Crossley, North-Holland, (1967).
[6]
Harrison, J., "Equivalence of the Effective Operations and the Hereditarily Recursively Continuous Functionals", Foundations of Classical Analysis, Stanford Summer Seminar 1963, App. VC
[7]
Kleene, S.C., "Introduction to Meta-mathematics", D. Van Nostrand, Princeton, (1952).
[8]
Kleene, S.C., "Countable Functionals", Constructivity in Mathematics, ed.A. Heyting, North-Holland, (1959).
[9]
Kreisel, G., D. Lacombe and J.R. Schönfield, "Partial Recursive Functionals and Effective Operations", same as {8}.
[10]
Milner, R., "Models of LCF", AIM-186/CS-332, Computer Science Department, Stanford University, (1973).
[11]
Milner, R., "Implementation and Application of Scott's Logic for Computable Functions", Proc. ACM Conf. on Proving Assertions about Programs, Las Cruces, New Mexico (1972).
[12]
Rogers, H., "Theory of Recursive Functions and Effective Computability" McGraw-Hill, New York (1967).
[13]
Scott, D., "Continuous Lattices", Proc. Dalhousie Conference on Toposes, Algebraic Geometry and Logic, Springer Lecture Notes in Mathematics 274, Springer Verlag Berlin (1972).
[14]
Scott, D. and C. Strachey, "Toward a Mathematical Semantics for Computer Languages", Proc. of a Symposium on Computer and Automata, New York, Polytechnic Institute of Brooklin, (1971).
[15]
Scott, D., "Data Types as Lattices", Lecture Notes of the Kiel Summer Seminar (July 1974). To be published in Springer Lecture Notes.
Index Terms
- Computability concepts for programming language semantics
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Published In
May 1975
265 pages
ISBN:9781450374194
DOI:10.1145/800116
Copyright © 1975 ACM.
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Published: 05 May 1975
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STOC '75 Paper Acceptance Rate 31 of 87 submissions, 36%;
Overall Acceptance Rate 1,469 of 4,586 submissions, 32%
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View all- Downey PSethi R(1975)Correct computation rules for recursive languagesProceedings of the 16th Annual Symposium on Foundations of Computer Science10.1109/SFCS.1975.10(48-56)Online publication date: 13-Oct-1975
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