_signed.py

from ._bool import NOT, TRUE, XOR, XNOR
from ._natural import ADD, LTE, DIFF, MUL
from ._pair import CONS, CAR, CDR

# signed numbers
SIGN   = lambda n: CONS(TRUE)(n)
NEG    = lambda p: CONS(NOT(CAR(p)))(CDR(p))
ISPOS  = lambda p: CAR(p)
ISNEG  = lambda p: NOT(CAR(p))
UNSIGN = lambda p: CDR(p)
SADD   = lambda a: lambda b: (
    XNOR(CAR(a))(CAR(b))
    (CONS(CAR(a))(ADD(CDR(a))(CDR(b))))  # same sign
    (
        CONS    # opposite sign
        (XOR(CAR(a))(LTE(CDR(a))(CDR(b))))  # calculate sign
        (DIFF(CDR(a))(CDR(b)))   # calculate value
    )
)
SSUB = lambda a: lambda b: SADD(a)(CONS(NOT(CAR(b)))(CDR(b)))
SMUL = lambda a: lambda b: CONS(XNOR(CAR(a))(CAR(b)))(MUL(CDR(a))(CDR(b)))