Heyting Algebra Validation

heyting-validation.js

const all = (...preds) => (obj) => preds.map(f => f(obj)).reduce((a, b) => a && b, true)
const any = (...preds) => (obj) => preds.map(f => f(obj)).reduce((a, b) => a || b, false)
const oneOf = (...preds) => (obj) => preds.map(f => f(obj)).reduce((a, b) => a ? !b : b, false)
const has = (prop) => (obj) => obj[prop] !== undefined
const not = (pred) => (obj) => !pred(obj)
const equals = (prop, val) => (obj) => obj[prop] === val
const implies = (f, g) => (obj) => !f(obj) || g(obj);

const validate = all(implies(has('selectedIndex'), equals('isOpen', true)))

validate({}) // true; passes all 'implications'
validate({'selectedIndex': 3}) // false; isOpen !== true!
validate({'selectedIndex': 3, isOpen: true}) // true; passes all implications


// more complex example
const complexValidate = all(
  implies(equals('mode', 'indexed'),
    all(
      has('selectedIndex'),
      obj => obj['selectedIndex'] <= 5
    )
  ),
  implies(equals('mode', 'disabled'), not(has('selectedIndex')))
)

Stealing the hack from 2ality you can (almost) have it like in Purescript
using +/* instead of &&/||

// see https://gist.github.com/matthieubulte/53ed96c5c5ee2297347e730804486918

const complexValidate =
  implies(
    equals('mode', 'indexed'),
    has('selectedIndex') * (obj => obj['selectedIndex'] <= 5)
  )
  * implies(equals('mode', 'disabled'), not(has('selectedIndex')));

mkP(complexValidate)({'mode':'enabled', 'selectedIndex':3}) // = true

😉

I just discovered Heyting today. I'm confused as to what makes this a Heyting algebra? implies? Would not(not(equals(mode', 'indexed')) make this a boolean algebra?