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
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.