tech►Lisp

logical operators from lisp ifs

Mentioning my progress in learning Lisp during a check-in today got us into expressing AND OR and NOT with the Lisp if expression.
AND Logic Gate

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; AND -> A and B can be any expression returning T or NIL
(if A
  B
  A)

;equivalent of
(and A B)

Think of it! If A is returns T then our if expression returns the return value of the expression B. Otherwise if A returns NIL the if expression returns A .. which we already know, is NIL.

example: even AND divisibleBy4

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(defparameter n 8) ;would return T
(defparameter n 6) ;would return NIL

(if (= (mod n 2) 0)
  (= (mod n 2) 0); return the result of the even check
  (= (mod n 4) 0)); return the result of the divisibleBy4 check

for non-lispers out there here’s an implementation in javascript.

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let checkIfEvenAndDivisibleBy4 = n => {
  if (n%2 === 0) {
    return (n%4 === 0)
  }else {
    return (n%2 === 0)
  }
}

checkIfEvenAndDivisibleBy4(8) //true
checkIfEvenAndDivisibleBy4(6) //false

//equivalent of
(n%2 === 0) && (n%4 === 0)

Beyond AND

of course this also works for OR:

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(if A
  A
  B)

since we only need one of the two expressions to be T, we don’t even have to evaluate expression B if A is already T.

To describe NOT though we would need the lisp primitives:

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(if A
  NIL
  T)

That said, here’s how a NAND would look like

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(if ((if A
    B
    A))
  NIL
  T)

You probably know that everything can be built from nand

Like and AND is built by chaining a NOT after a NAND like this ;)

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(defun my-overcomplicated-and (a b)
  (if (if (if a b a)
      NIL
      T)
    NIL
    T))

yes .. this is stupid :)
Thanks Nick.