feat(rules): add implication normalisation rules #597
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Adds the following normalisation rules for implication: + Contrapositive `!p -> !q ~~> q->p where p,q are safe` + Negation `!(p -> q) ~~> p/\ !q where p->q is safe` + Left distributivity: `(r->p) -> (r->q) ~~> (r -> (p ~> q))` + Import-export / uncurrying: `p -> (q->r) ~~> (p/\q) -> r` Import-export has a lower priority of 8400 to allow distributivity to apply first. For example, we want to do: ``` ((r -> p) -> (r -> q)) ~> (r -> (p -> q)) [left-distributivity] (r -> (p -> q)) ~> (r/\p) ~> q [uncurry] ``` not ``` ((r->p) -> (r->q)) ~> ((r->p) /\ r) -> q) ~> [uncurry] ```
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Closes: #511 |
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6 tasks
ozgurakgun
approved these changes
Jan 20, 2025
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Adds the following normalisation rules for implication:
Contrapositive
!p -> !q ~~> q->p where p,q are safeNegation
!(p -> q) ~~> p/\ !q where p->q is safeLeft distributivity:
(r->p) -> (r->q) ~~> (r -> (p ~> q))Import-export / uncurrying:
p -> (q->r) ~~> (p/\q) -> rImport-export has a lower priority of 8400 to allow distributivity to apply first.
For example, we want to do:
not