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