Implementing HOL in an Higher Order Logic Programming Language

Abstract : 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.
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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⟩

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