HOLCF = HOL + LCF

Olaf Müller, Tobias Nipkow, David von Oheimb, Oscar Slotosch

HOLCF is the definitional extension of Church's Higher-Order Logic with Scott's Logic for Computable Functions that has been implemented in the theorem prover Isabelle. This results in a flexible setup for reasoning about functional programs. HOLCF supports standard domain theory (in particular fixpoint reasoning and recursive domain equations) but also coinductive arguments about lazy datatypes. This paper describes in detail how domain theory is embedded in HOL and presents applications from functional programming, concurrency and denotational semantics.

BibTeX:

@article{MuellerNvOS99,
author=
{Olaf M\"uller and Tobias Nipkow and Oheimb, David von and Oskar Slotosch},
title={{HOLCF = HOL + LCF}},
journal={Journal of Functional Programming},volume=9,pages={191--223},
year=1999}

The corresponding Isabelle theories.