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Challenge that might make the omega more preferable: define an omega usable with strict evaluation similar to the relationship of the Z combinator for the Y alo

Challenge that might make the omega more preferable: define an omega usable with strict evaluation similar to the relationship of the Z combinator for the Y along with the corresponding polyvadic combinator using the X combinator ref http://www.cs.uu.nl/research/techreps/repo/CS-1989/1989-14.pdf http://www.cs.uu.nl/research/techreps/repo/CS-1989/1989-14.p...

martyalain 4y ago
Thank you for the link. I am afraid I am not equipped to understand this paper. What is your opinion on the choice of the Y-combinator rather than the Ω-combinator?
- 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 ago
    Thank you.
  - potiuper 4y ago
    Edit: 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]

martyalain 4y ago

Thank you for the link. I am afraid I am not equipped to understand this paper. What is your opinion on the choice of the Y-combinator rather than the Ω-combinator?

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 ago
  Thank you.
- potiuper 4y ago
  Edit: 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]