Logical Relations for PCF


Title: Logical Relations for PCF
Author: Peter Gammie
Submission date: 2012-07-01
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.
  author  = {Peter Gammie},
  title   = {Logical Relations for PCF},
  journal = {Archive of Formal Proofs},
  month   = jul,
  year    = 2012,
  note    = {\url{http://isa-afp.org/entries/PCF.shtml},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.