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:
“It would be disingenuous, however, not to point out that some things are considered as morally certain, that is, as having sufficient certainty for application to ordinary life, even though they may be uncertain in relation to the absolute power of God.”
—René Descartes (1596–1650)
“Whoever has a keen eye for profits, is blind in relation to his craft.”
—Sophocles (497–406/5 B.C.)
“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 (1928–1974)