3 ms·
> A single point basis [...] is not in itself a combinator. > A combinator [...] must have all lambdas in leading position. What's your opinion on: ωabcd =
by a1369209993 6y ago
> A single point basis [...] is not in itself a combinator.
> A combinator [...] must have all lambdas in leading position.
What's your opinion on:
ωabcd = bd(cd) if a has no normal form[0][1]
or = c if b has no normal form
or = d if c has no normal form
or = dd otherwise
where
SII = ωωωω
Ω = SII(SII) = ωωωω(ωωωω)
S = ωΩ = ω(ωωωω(ωωωω))
K = ωωΩ = ωω(ωωωω(ωωωω))
I = ωωωΩ = ωωω(ωωωω(ωωωω))
as a single-'combinator' basis?
0: Aka, does not halt.
1: Evaluation diverges if a (or b or c, if queried) is somthing like:
SII(C(C(B(ωωx(KI)K)(SII))Ω)I)
(from https://en.wikipedia.org/wiki/Combinatory_logic#Undecidability_of_combinatorial_calculus https://en.wikipedia.org/wiki/Combinatory_logic#Undecidabili...) that tries to diagonalize ω.
- tromp 6y agoSuch a combinator ω cannot exist.