Implementing HOL in an Higher Order Logic Programming Language

Cvetan Dunchev (1) , Claudio Sacerdoti Coen (1) , Enrico Tassi (2)

1 DISI - Department of Computer Science and Engineering [Bologna]
2 MARELLE - Mathematical, Reasoning and Software

We present a proof-of-concept prototype of a (constructive variant of an) HOL interactive theorem prover written in a Higher Order Logic Programming (HOLP) language, namely an extension of λProlog. The prototype is meant to support the claim, that we reinforce , that HOLP is the class of languages that provides the right abstraction level and programming primitives to obtain concise implementations of theorem provers. We identify and advocate for a programming technique, that we call semi-shallow embedding, while at the same time identifying the reasons why pure λProlog is not sufficient to support that technique, and it needs to be extended.

Mots clés: Higher Order Logic Programming; HOL; CR-number [subcategory]:; third-level; Keywords λProlog; Constraints

Domaines: Logique en informatique [cs.LO]; Logiciel mathématique [cs.MS]

Cvetan Dunchev, Claudio Sacerdoti Coen, Enrico Tassi. Implementing HOL in an Higher Order Logic Programming Language. Logical Frameworks and Meta Languages: Theory and Practice, Jun 2016, Porto, Portugal. pp.10, ⟨10.1145/2966268.2966272⟩. ⟨hal-01394686⟩