4 ms·
Likely an absence of an incentive to investigate alternatives along with the fact that an infinite number of fixed point combinators exist in addition to social
by potiuper 4y ago
Likely an absence of an incentive to investigate alternatives along with the fact that an infinite number of fixed point combinators exist in addition to social capital/inertia. One of the two people who is regarded as originating combinators even though the K combinator is Peirce's Law (1885) and the S combinator is Hypothetical Syllogism published the first fixed point combinator as the Y combinator (Curry 1930) and by association has been promoted as "the" fixed point operator (example). Also, Ω is a Greek (Unicode) and not a standard Latin (ASCII) character. The X combinator is similar to Ω in that they are the shorter basis and fixed point definitions respectively at a cost of a small number of additional steps in some proof applications.
- martyalain 4y agoThank you.
- potiuper 4y agoEdit: The S combinator is not exactly Hypothetical Syllogism, which is also known as double implication elimination, but may be used to derive each other with simplification and implication elimination: https://en.wikipedia.org/wiki/Hypothetical_syllogism#Alternative_forms https://en.wikipedia.org/wiki/Hypothetical_syllogism#Alterna... and the K combinator is simplification and not Peirce's Law: https://en.wikipedia.org/wiki/Hilbert_system#Further_connections https://en.wikipedia.org/wiki/Hilbert_system#Further_connect... Also, the first exact instance of S is likely P3 in Frege's propositional calculus.
- deleted 4y ago[deleted]