Relation To Non-constructive Logic
The Curry-Howard correspondence between proofs and programs relates call/cc to Peirce's law, which extends intuitionistic logic to non-constructive, classical logic: ((α → β) → α) → α. Here, ((α → β) → α) is the type of the function f, which can either return a value of type α directly or apply an argument to the continuation of type (α → β). Since the existing context is deleted when the continuation is applied, the type β is never used and may be taken to be ⊥.
The principle of double negative elimination ((α → ⊥) → ⊥) → α is comparable to a variant of call-cc which expects its argument f to always evaluate the current continuation without normally returning a value.
Embeddings of classical logic into intuitionistic logic are related to continuation passing style translation.
Read more about this topic: Call-with-current-continuation
Famous quotes containing the words relation to, relation and/or logic:
“Concord is just as idiotic as ever in relation to the spirits and their knockings. Most people here believe in a spiritual world ... in spirits which the very bullfrogs in our meadows would blackball. Their evil genius is seeing how low it can degrade them. The hooting of owls, the croaking of frogs, is celestial wisdom in comparison.”
—Henry David Thoreau (18171862)
“Among the most valuable but least appreciated experiences parenthood can provide are the opportunities it offers for exploring, reliving, and resolving ones own childhood problems in the context of ones relation to ones child.”
—Bruno Bettelheim (20th century)
“Somebody who should have been born
is gone.
Yes, woman, such logic will lead
to loss without death. Or say what you meant,
you coward . . . this baby that I bleed.”
—Anne Sexton (19281974)