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Data types as lattices: Retractions, closures and projections. (English) Zbl 0394.03019


MSC:

03B40 Combinatory logic and lambda calculus
03D25 Recursively (computably) enumerable sets and degrees
03D60 Computability and recursion theory on ordinals, admissible sets, etc.

Citations:

Zbl 0337.02018
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References:

[1] 1. P. CRAWLEY, The Isomorphism Theorem in Compactly Generated Lattices, Bull. Amer. Math. Soc., 65, 1959, pp. 377-379. Zbl0094.01702 MR106860 · Zbl 0094.01702 · doi:10.1090/S0002-9904-1959-10384-0
[2] 2. C. J. EVERETT, Closure Operators and Galois Theory in Lattices, Trans. Amer. Math. Soc., 55, 1944, pp. 514-525. Zbl0060.06205 MR10556 · Zbl 0060.06205 · doi:10.2307/1990306
[3] 3. O. ORE, Galois Connexions, Trans. Amer. Math. Soc., 55, 1944, pp. 493-513. Zbl0060.06204 MR10555 · Zbl 0060.06204 · doi:10.2307/1990305
[4] 4. J. C. REYNOLDS, Towards a Theory of Type Structure in Programming Symposium Proceedings, Lecture Notes in Computer Science 19, April 1974, pp. 408-425, Springer Verlag. Zbl0309.68016 MR458988 · Zbl 0309.68016
[5] 5. J. C. REYNOLDS, On the Relation between Direct and Continuation Semantics, in Automata, Languages and Programming 2nd Colloquium, University of Saarbrucken, Lecture Notes in Computer Science 14, 1974, pp. 141-156, Springer Verlag. Zbl0313.68023 MR443409 · Zbl 0313.68023
[6] 6. D. SCOTT, Continuous Lattices, in Toposes, Algebraic Geometry and Logic, Lecture Notes in Mathematics 274, pp. 96-136, Springer Verlag. Zbl0239.54006 MR404073 · Zbl 0239.54006
[7] 7. D. SCOTT, Data Types as Lattices, S.I.A.M. Journal on Computing, 5, 1976, pp. 522-587. Zbl0337.02018 MR437330 · Zbl 0337.02018 · doi:10.1137/0205037
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