Comment by cphoover | Hacker News Reader

Comment by cphoover | Hacker News Reader

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I think I was confused about the when function... I was at first thinking of when as when in clojure which is essentially just a macro for

(if .. do ..)

(macroexpand '(when 1 2 3 4)) (if 1 (do 2 3 4))

but that is not what it seems to do in PM-Lisp take the example of `=` definition:

(def = (and (when A B) (when B A)))

If this were the same functionality clojure it would be testing the truthyness of the evaluation of each when expression

so If I had (and (when 3 5) (when 5 3)) it would evaluate to (and 5 3) which would evaluate to 3 which is truthy.

So that got me stuck in the article. But it seems that when is more like a test/assertion... (when x z) saying for all values of x ... z is implied (i.e. the same way one mathematical rule implies another).

I'm going to reread this article and try to understand better.

Don't know about clojure (is that a lisp?), here when is therefore in formal logic - "A implies B". Ex, "If it's raining, the streets are wet".

It doesn't "do" anything, just sets a constraint which can be matched against later. I took a class on Prolog in school, which works by back-matching against conditionals like that. I remember just sorting a list being mind-bendingly recursive.

I still think there's some funny business going on in the intersection of computable functions, infinite sets and "there exists a _" style conditionals. Can't put my finger on why "there exists a number of the form 2n + 1" feels fine, but "there exists a function in the set of all possible functions" feels wrong.

The imperative if in programming is different from the logical if. But it isn't disconnected from logic.

In fact, it is closely related to the logical and: it is and with short-circuiting, enabling the left expression to control effects in the right.

In Lisp, the two-form if, namely (if x y), can be replaced by (and x y), because and has the right logic and result value, and also the short-circuiting semantics that y is not evaluated if x is false.

If we want the logical if, we can use the equivalent expression (or (not x) y), which has the same truth table:

     x     y  | (if x y)  |  (or (not x) y)
  ------------+-----------+----------------
   nil   nil  |    nil    |     t
   nil     t  |    nil    |     t
     t   nil  |    nil    |   nil
     t     t  |      t    |     t

The if/and relationship of course shows up in other languages:

   if (pointer != NULL) {
      if (pointer->foo == 42)
        do();
   }

-->

  if (pointer != NULL && pointer->foo)
    do();

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