Editing HOL (proof assistant) (section)

{{Short description|Interactive theorem proving systems}}
{{Infobox programming language
| name = HOL
| designer = [[Michael J C Gordon]]
| license = [[BSD licenses|Modified (3-clause) BSD license]]
| website = {{url|hol-theorem-prover.org}}
| file_ext = .sml
}}

'''HOL''' ('''Higher Order Logic''') denotes a family of [[Proof assistant|interactive theorem proving systems]] using similar [[Higher-order logic|(higher-order)]] logics and implementation strategies. Systems in this family follow the [[LCF (theorem prover)|LCF]] (Logic for Computable Functions) approach as they are implemented as a library which defines an [[abstract data type]] of proven [[theorem]]s such that new objects of this type can only be created using the functions in the library which correspond to [[inference rule]]s in [[higher-order logic]]. As long as these functions are correctly implemented, all theorems proven in the system must be valid. As such, a large system can be built on top of a small trusted kernel.

Systems in the HOL family use [[ML (programming language)|ML]] or its successors. ML was originally developed along with LCF as a meta-language for theorem proving systems; in fact, the name stands for "Meta-Language".