nandi / braket

#!/usr/bin/env python3
"""
Small program built from function-defects.

Program:
  square_plus_one(n) = add (mul n n) 1

Everything is expressed through the current function-defect layer in church.py.
"""

from church import add, mul, normal_form, succ


def apply2(fn, a, b):
    """Apply a curried binary function-defect to two arguments."""
    return fn.apply(a).apply(b)


def square(n):
    """square(n) = mul n n"""
    return apply2(mul(), n, n)


def square_plus_one(n):
    """square_plus_one(n) = add (mul n n) 1"""
    return apply2(add(), square(n), normal_form(1))


def demo() -> None:
    two = normal_form(2)
    three = normal_form(3)

    print("=" * 60)
    print("DEFECT PROGRAM")
    print("=" * 60)
    print()
    print("Program:")
    print("  square_plus_one(n) = add (mul n n) 1")
    print()
    print(f"  input 2 = {two}")
    print(f"  square(2) = {square(two)}")
    print(f"  square_plus_one(2) = {square_plus_one(two)}")
    print()
    print(f"  input 3 = {three}")
    print(f"  square(3) = {square(three)}")
    print(f"  square_plus_one(3) = {square_plus_one(three)}")
    print()
    print("Extra:")
    print(f"  succ(square_plus_one(2)) = {succ().apply(square_plus_one(two))}")


if __name__ == "__main__":
    demo()