HOL theorem prover

HOL (Higher Order Logic) denotes a family of interactive theorem proving systems using similar (higher-order) logics and implementation strategies. Systems in this family follow the LCF approach as they are implemented as a library in some programming language. This library implements an abstract data type of proven theorems so that new objects of this type can only be created using the functions in the library which correspond to inference rules in higher-order logic. As long as these functions are correctly implemented, all theorems proven in the system must be valid. In this way, a large system can be built on top of a small trusted kernel.

Systems in the HOL family use the ML programming language or its successors. ML was originally developed along with LCF to serve the purpose of a meta-language for theorem proving systems; in fact, the name stands for "Meta-Language".

There are four HOL systems (sharing essentially the same logic) that are still maintained and developed.

HOL is a predecessor of Isabelle.

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