LCF examples in HOL

LCF Examples in HOL

The LCF system provides a logic of xed point theory and is useful to reason about nontermination, recursive deenitions and innnite-valued types such as lazy lists. Because of continual presence of bottom elements, it is clumsy for reasoning about nite-valued types and strict functions. The HOL system provides set theory and supports reasoning about nite-valued types and total functions well. In...

Holcf=hol+lcf

HOLCF is the de nitional 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 exible setup for reasoning about functional programs HOLCF supports stan dard domain theory in particular xpoint reasoning and recursive domain equations but also coinductive arguments about lazy datatypes This p...

From LCF to HOL: a short history

The original LCF system was a proof-checking program developed at Stanford University by Robin Milner in 1972. Descendents of LCF now form a thriving paradigm in computer assisted reasoning. Many of the developments of the last 25 years have been due to Robin Milner, whose influence on the field of automated reasoning has been diverse and profound. One of the descendents of LCF is HOL, a proof ...

Miscellaneous HOL Examples

An LCF-Style Interface between HOL and First-Order Logic

Performing interactive proof in the HOL theorem prover [3] involves reducing goals to simpler subgoals. It turns out that many of these subgoals can be efficiently ‘finished off’ by an automatic first-order prover. To fill this niche, Harrison implemented a version of the MESON procedure [4] with the ability to translate proofs to higher-order logic. This was integrated as a HOL tactic in 1996,...