HOL Light
HOL Light is a member of the HOL theorem prover family. Like the other members, it is a proof assistant for classical higher order logic. Compared with other HOL systems, HOL Light is intended to have relatively simple foundations. HOL Light is authored and maintained by the mathematician and computer scientist John Harrison. HOL Light is released under the simplified BSD license.
Logical foundations
HOL Light is based on a formulation of type theory with equalityas the only primitive notion. The primitive rules of inference
are the following:
| REFL | reflexivity of equality | |
| TRANS | transitivity of equality | |
| MK_COMB | congruence of equality | |
| ABS | abstraction of equality | |
| BETA | connection of abstraction and function application | |
| ASSUME | assuming, prove | |
| EQ_MP | relation of equality and deduction | |
| DEDUCT_ANTISYM_RULE | deduce equality from 2-way deducibility | |
| INST | instantiate variables in assumptions and conclusion of theorem | |
| INST_TYPE | instantiate type variables in assumptions and conclusion of theorem |
This formulation of type theory is very close to the one described in
section II.2 of .