Some Church encodings

ChurchEncodings.worksheet.sc

type Boolian = (Any, Any) => Any

val troo = (a: Any, _: Any) => a
val fols = (_: Any, b: Any) => b

// Logic

val not = (b: Boolian) => b(fols, troo)

not(troo) == fols
not(fols) == troo

val and = (b1: Boolian, b2: Boolian) => b1(b2(troo, fols), fols)

and(troo, troo) == troo
and(troo, fols) == fols
and(fols, troo) == fols
and(fols, fols) == fols

val or = (b1: Boolian, b2: Boolian) => b1(troo, b2(troo, fols))

or(troo, troo) == troo
or(troo, fols) == troo
or(fols, troo) == troo
or(fols, fols) == fols

// Branching

val eef = (p: Boolian, p1: Any, p2: Any) => p(p1, p2)

eef(troo, "yay", "nay")
eef(fols, "yay", "nay")

val yourNameIsJosh: Boolian = troo
val yourNameIsNotJosh: Boolian = fols

val youAreFromNY: Boolian = troo
val youAreNotFromNY: Boolian = fols

val areYouJoshFromNY = (isYourNameJosh: Boolian, areYouFromNY: Boolian) =>
  and(isYourNameJosh, areYouFromNY).asInstanceOf[Boolian]

eef(areYouJoshFromNY(yourNameIsJosh, youAreFromNY), "yay", "nay")
eef(areYouJoshFromNY(yourNameIsJosh, youAreNotFromNY), "yay", "nay")