Module lambda_calculus::data::num::church

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Church numerals

Functions§

  • add
    Applied to two Church-encoded numbers it produces their sum.
  • div
    Applied to two Church-encoded numbers it returns a Church-encoded pair with the result of their division - the quotient and the remainder.
  • eq
    Applied to two Church-encoded numbers it returns a lambda-encoded boolean indicating whether its first argument is equal to the second one.
  • fac
    Applied to a Church-encoded number it yields its Church-encoded factorial.
  • geq
    Applied to two Church-encoded numbers it returns a lambda-encoded boolean indicating whether its first argument is greater than or equal to the second one.
  • gt
    Applied to two Church-encoded numbers it returns a lambda-encoded boolean indicating whether its first argument is greater than the second one.
  • is_even
    Applied to a Church-encoded number it produces a lambda-encoded boolean, indicating whether its argument is even.
  • is_odd
    Applied to a Church-encoded number it produces a lambda-encoded boolean, indicating whether its argument is odd.
  • is_zero
    Applied to a Church-encoded number it produces a lambda-encoded boolean, indicating whether its argument is equal to zero.
  • leq
    Applied to two Church-encoded numbers it returns a lambda-encoded boolean indicating whether its first argument is less than or equal to the second one.
  • lt
    Applied to two Church-encoded numbers it returns a lambda-encoded boolean indicating whether its first argument is less than the second one.
  • max
    Applied to two Church-encoded numbers it returns the greater one.
  • min
    Applied to two Church-encoded numbers it returns the smaller one.
  • mul
    Applied to two Church-encoded numbers it yields their product.
  • neq
    Applied to two Church-encoded numbers it returns a lambda-encoded boolean indicating whether its first argument is not equal to the second one.
  • one
    Produces a Church-encoded number one.
  • pow
    Applied to two Church-encoded numbers it raises the first one to the power of the second one.
  • pred
    Applied to a Church-encoded number it produces its predecessor.
  • quot
    Applied to two Church-encoded numbers it returns a Church-encoded quotient of their division.
  • rem
    Applied to two Church-encoded numbers it returns a Church-encoded remainder of their division.
  • shl
    Applied to two Church-encoded numbers a and b it returns the left logical shift of a performed b times.
  • shr
    Applied to two Church-encoded numbers a and b it returns the right logical shift of a performed b times.
  • sub
    Applied to two Church-encoded numbers it subtracts the second one from the first one.
  • succ
    Applied to a Church-encoded number it produces its successor.
  • to_parigot
    Applied to a Church-encoded number it produces the equivalent Parigot-encoded number.
  • to_scott
    Applied to a Church-encoded number it produces the equivalent Scott-encoded number.
  • to_stumpfu
    Applied to a Church-encoded number it produces the equivalent Stump-Fu-encoded number.
  • zero
    Produces a Church-encoded number zero; equivalent to boolean::fls.