predicates.js

import {and, not, True, False} from './booleans'
import {sub} from './numerals'

isZero takes a value and returns Church encoded True if it is a Church encoded zero and False otherwise

isZero(zero) // => True
isZero(one) // => False

export const isZero = a => a(_ => False)(True)

lte takes two numerals and returns True if the first is less than or equal to the first and False otherwise

lte(two)(three) // => True
lte(three)(three) // => True
lte(four)(three) // => False

export const lte = a => b => isZero(sub(a)(b))

gte takes two numerals and returns True if the first is greater than or equal to the first and False otherwise

gte(two)(three) // => False
gte(three)(three) // => True
gte(four)(three) // => True

export const gte = a => b => isZero(sub(b)(a))

lt takes two numerals and returns True if the first is less than the first and False otherwise

lt(two)(three) // => True
lt(three)(three) // => False
lt(four)(three) // => False

export const lt = a => b => not(gte(a)(b))

gt takes two numerals and returns True if the first is greater than the first and False otherwise

gt(two)(three) // => False
gt(three)(three) // => False
gt(four)(three) // => True

export const gt = a => b => not(lte(a)(b))

eq takes two numerals and returns True if the first is equal to the first and False otherwise

eq(three)(three) // => True
eq(four)(three) // => False

export const eq = a => b => and(lte(a)(b))(lte(b)(a))