When are two effectively given domains identical?
In this paper, we will observe that the notion of computability in an effectively given domain is dependent on the indexing of its basis. This indicates that we cannot identify two effectively given domains just because they are order isomorphic. We propose a suitable notion of effective isomorphism to compensate for this deficiency. Also we show that, for every recursion domain equation, there is an effectively given domain which is an initial solution to within effective isomorphism.
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- Egli-Constable, Computability concepts for programming language semantics, Theoritical Computer Science, Vol. 2 (1976).Google Scholar
- Kanda. A, Data types as effective objects, Theory of Computation Report No.22, Warwick University, (1977).Google Scholar
- Markowsky-Rosen, Bases for chain complete posets, IBM Journal of Research and Development, Vol.20, No.2, (1979).Google Scholar
- Plotkin. G, A power domain construction, SIAM Journal on Computing, Vol.5, (1976).Google Scholar
- Rogers, H. Theory of recursive functions and effective computability, McGraw Hill, New York, (1967).Google Scholar
- Tang. A, Recrusion theory and descriptive set theory in effectively given To-spaces, Ph.D. theesis, Princeton Univ. (1974).Google Scholar
- Scott. D, Outline of the mathematical theory of computation, Proc. of the 4th Princeton Conference on Information Science, (1970).Google Scholar
- Smyth. M, Effectively given domains, Theoretical Computer Science, Vol. 5 (1977).Google Scholar
- Smyth-Plotkin, The categorical solution of recursive domain equattions, Proc. of the 18th IEEE FOCS Conference, (1977).Google Scholar