javascript boolean matches (and / nand / or / nor / xor / iff / all / any / none )

booleans.js

function id(x) {
  // id :: a -> a
  return x }

function anyBool(pred,bool,xs) {
  /* a better name would be - if predicate is True then bool, else not bool.
  using basic logic we can now create logic functions that compute only as much as required */
  // anyBool :: (a -> Bool) -> Bool -> [a] -> Bool
  for (var i = 0; i < xs.length; i++) {
    if (pred(xs[i]) === bool) {
      return bool }}
  return !bool }

function or(xs) {
  // or :: [Bool] -> Bool
  return anyBool(id,true,xs) }
  
function nor(xs) {
  // nor :: [Bool] -> Bool
  return !or(xs) }

function and(xs) {
  // and :: [Bool] -> Bool
  return anyBool(id,false,xs) }
  
function nand(xs) {
  // nand :: [Bool] -> Bool
  return !and(xs) }
  
function xor(xs) {
  // xor :: [Bool] -> Bool
  return or(xs) && nand(xs) }

function iff(xs) {
  // xor :: [Bool] -> Bool
  return !xor(xs) }

function any(pred,xs) {
  // returns TRUE after FIRST match - else returns FALSE after iteration 
  // any :: (a -> Bool) -> [a] -> Bool
  return anyBool(pred,true,xs) }

function all(pred,xs) {
  // returns FALSE after FIRST failed match - else returns TRUE after iteration  
  // all :: (a -> Bool) -> [a] -> Bool
  return anyBool(pred,false,xs) }

function none(pred,xs) {
  // returns FALSE after FIRST match - else returns TRUE after iteration
  // none :: (a -> Bool) -> [a] -> Bool  
  return !any(pred,xs) }

// some examples.

or([true,true]) === true
or([true,false]) === true
or([false,false]) === false
or([false,true]) === true

nor([true,true]) === false
nor([true,false]) === false
nor([false,false]) === true
nor([false,true]) === false

xor([true,true]) === false
xor([true,false]) === true
xor([false,false]) === false
xor([false,true]) === true

and([true,true]) === true
and([true,false]) === false
and([false,false]) === false
and([false,true]) === false

nand([true,true]) === false
nand([true,false]) === true
nand([false,false]) === true
nand([false,true]) === true

any(function(x) { return x === "a" }, ["a","b"])  === true
any(function(x) { return x === "c" }, ["a","b"])  === false

all(function(x) { return x === "a" }, ["a","a"])  === true
all(function(x) { return x === "a" }, ["a","b"])  === false

none(function(x) { return x === "c" }, ["a","b"])  === true
none(function(x) { return x === "a" }, ["a","b"])  === false