Logical Foundations
HOL Light is based on a formulation of type theory with equality as the only primitive notion. The primitive rules of inference are the following:
REFL | reflexivity of equality | |
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TRANS | transitivity of equality |
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MK_COMB | congruence of equality |
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ABS | abstraction of equality ( must not be free in ) |
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BETA | connection of abstraction and function application |
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ASSUME | assuming, prove |
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EQ_MP | relation of equality and deduction |
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DEDUCT_ANTISYM_RULE | deduce equality from 2-way deducibility |
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INST | instantiate variables in assumptions and conclusion of theorem |
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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 Lambek & Scott (1986).
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