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Quantifier Heuristics in HOL4

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If you have a question about this talk, please contact William Denman.

Automatically guessing instantiations for quantifiers is often very useful. Using the Unwind library, HOL4 ’s simplifier can simplify terms like ∀x y. P (x,y) ∧ (x = 2) ⇒ Q x to ∀y. P (2,y) ⇒ Q 2 . However, even slightly more complicated terms like ∀x. (∃y. P (x,y) ∧ (x = 2)) ⇒ Q x cannot be simplified.

In this talk, I present the quantifier heuristics library. In contrast to the Unwind library, the quantifier heuristics library does not use a fixed set of term patterns. Instead, an extensible set of heuristics produce guesses for subterms. These guesses are then combined for larger terms.

The quantifier heuristics library can simplify more complicated terms than the Unwind library. Moreover, it is easily extensible by adding new heuristics. An interesting feature is partial instantiations, i.e. instantiations that introduce new quantifiers. This allows to simplify for examples the term ∀x. IS_SOME x ⇒ P x to ∀x_x. P (SOME x_x).

I will try to present the library without referring to too many HOL4 details. However, it’s a talk about the concrete implementation in HOL4 . The theoretical ideas behind the library are very simple.

This talk is part of the Computer Laboratory Automated Reasoning Group Lunches series.

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