Abstract

The meaning of many kinds of expressions in programming languages can be taken as elements of certain spaces of “partial” objects. In this report these spaces are modeled in one universal domain ${\bf P} \omega $, the set of all subsets of the integers. This domain renders the connection of this semantic theory with the ordinary theory of number theoretic (especially general recursive) functions clear and straightforward.

Keywords

  1. programming language semantics
  2. lattice
  3. continuous lattice
  4. algebraic lattice
  5. computability
  6. retract
  7. combinatory logic
  8. lambda calculus
  9. recursion theorem
  10. enumeration degrees
  11. continuous function
  12. fixed-point theorem

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cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 522 - 587
ISSN (online): 1095-7111

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Submitted: 23 May 1975
Published online: 31 July 2006

Keywords

  1. programming language semantics
  2. lattice
  3. continuous lattice
  4. algebraic lattice
  5. computability
  6. retract
  7. combinatory logic
  8. lambda calculus
  9. recursion theorem
  10. enumeration degrees
  11. continuous function
  12. fixed-point theorem

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