### Abstract

We apply Andy Pitts's methods of defining relations over domains to several classical results in the literature. We show that the Y combinator coincides with the domain-theoretic fixpoint operator, that parallel-or and the Plotkin existential are not definable in PCF, that the continuation semantics for PCF coincides with the direct semantics, and that our domain-theoretic semantics for PCF is adequate for reasoning about contextual equivalence in an operational semantics. Our version of PCF is untyped and has both strict and non-strict function abstractions. The development is carried out in HOLCF.

### License

BSD License

### Topics

- Computer science/Programming languages/Lambda calculi

### Session PCF

- Basis
- Logical_Relations
- PCF
- OpSem
- Continuations
- SmallStep

## Cite

×

PCF-AFP

    @article{PCF-AFP,
      author  = {Peter Gammie},
      title   = {Logical Relations for PCF},
      journal = {Archive of Formal Proofs},
      month   = {July},
      year    = {2012},
      note    = {\url{https://isa-afp.org/entries/PCF.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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