Programmer Humor

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The PHP part never gets old (toggl.com)

submitted 2 weeks ago by muhyb@programming.dev to c/programmer_humor@programming.dev

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[–] tetris11@feddit.uk 11 points 2 weeks ago* (last edited 2 weeks ago)

The Fixed Point Expression / Y Combinator expressed in horses:

    Y = (λ f. (λ x. f(xx))(λ x. f(xx)))
    ;; so then, give Y a horse argument with apple parameters:
    Y🐎️ = (λ f. (λ 🍎.  f(🍎🍎)) (λ 🍎. f(🍎🍎))) 🐎️   ;; [1]
        =       (λ 🍎. 🐎️(🍎🍎)) (λ 🍎. 🐎️(🍎🍎))      ;; [2]
        = 🐎️(   (λ 🍎. 🐎️(🍎🍎)) (λ 🍎. 🐎️(🍎🍎))   )  ;; [3]
        = 🐎️(Y🐎️)                                       ;; [4]

Explanation

1: x is 🍎, but could be anything. It's just a function parameter nested within another.
2: λf gets executed and vanishes from the left, substituting f internally with 🐎️. This is now a new function, with left group as the function body, and right group as the function argument, despite being identical.
3: λ🍎 gets executed and vanishes from the left, substituting 🍎 with (λ 🍎. 🐎️(🍎🍎))
4: Everything within the main brackets at [3] has been seen before at [1], but with f being 🐎. Thus we have bred a new horse. We can breed infinite horses this way