Lambda Calc

Lambda Calc

λf.(λx.f(xx))(λx.f(xx))


ZERO  = λfx.x                           | f -> x -> x
ONE   = λfx.fx                          | f -> x -> f(x)
TWO   = λfx.f(fx)                       | f -> x -> f(f(x))
THREE = λfx.f(f(fx))                    | f -> x -> f(f(f(x)))

SUCC = λnfx.nfx                         | n -> f -> x -> n(f)(x)
ADD  = λmnfx.mf(nfx) || λmn.n succ m    | m -> n -> f -> x -> m(n(f))(x)
MULt = λmnfx.m(nf)x  || λmnf.m(nf)      | m -> n -> f -> m(n(f))
PRED = λnfx.n(λgh.h(gf))(λu.x)(λu.u)    | n -> f -> x -> (g -> h -> h(g(f)))(u -> x)(u -> u)

TRUE  = λab.a                           | a -> b -> a
FALSE = λab.b                           | a -> b -> b
IF    = λpab.pab                        | p -> a -> b -> p(a)(b)
AND   = λpq.pqp                         | p -> q -> p(q)(p)
OR    = λpq.ppq                         | p -> q -> p(p)(q)
NOT   = λpab.pba                        | p -> a -> b -> p(b)(a)
XOR   = λab.a(NOT b)b                   | a -> b -> a(NOT(b))(b)

ISZERO   = λn.(n (λx.FALSE) TRUE)         | n -> n(x -> FALSE)(TRUE)
LEQ = <= = λmn.(ISZERO (MINUS m n))
EQ  = == = λmn.(AND (LEQ m n) (LEQ n m))

IF QUIBIT DEAD ALIVE
λpab.pab QUIBIT DEAD ALIVE
λab.(QUIBIT a b) DEAD ALIVE
λb.(QUIBIT DEAD b) ALIVE
QUIBIT DEAD ALIVE

QUIBIT = TRUE = λab.a | QUBIT = FALSE = λab.b
QUIBIT DEAD ALIVE     | QUIBIT DEAD ALIVE
λab.a DEAD ALIVE      | λab.b DEAD ALIVE
λb.DEAD ALIVE         | λb.b ALIVE
DEAD                  | ALIVE

DEAD  = FALSE
ALIVE = TRUE

QUBIT DEAD ALIVE  | QUBIT DEAD ALIVE
TRUE FALSE TRUE   | FALSE FALSE TRUE
λab.a FALSE TRUE  | λab.b FALSE TRUE
λb.FALSE TRUE     | λb.b TRUE
FALSE             | TRUE

Y = λf.(λx.f(xx))(λx.f(xx))                | f -> (x -> f(x(x)))(x -> f(x(x)))



var rawr = (n) ->
  n == 0
    ? 0
    : n * rawr(n-1)



FACT = λfn.(IF (ISZERO n) ONE (MULTI n (f f (PRED n))))

FACT FACT ZERO
λn.(IF (ISZERO n) ONE (MULTI n (FACT FACT (PRED n)))) ZERO
IF (ISZERO ZERO) ONE (MULTI n (FACT FACT (PRED n)))

ISZERO ZERO
ZERO λx.FALSE TRUE
λfx.x λx.FALSE TRUE
λx.x TRUE
TRUE

IF TRUE ONE (MULTI ZERO (FACT FACT (PRED ZERO)))
λpab.pab TRUE ONE (MULTI ZERO FACT (FACT (PRED ZERO)))
λab.(TRUE a b) ONE (MULTI ZERO FACT (PRED ZERO)))
λb.(TRUE ONE b) (MULTI ZERO FACT (FACT (PRED ZERO)))
TRUE ONE (MULTI ZERO (FACT FACT (PRED ZERO)))
λab.a ONE (MULTI ZERO (FACT FACT (PRED ZERO)))
λb.ONE (MULTI ZERO (FACT FACT (PRED ZERO)))
ONE


FACT FACT ONE
λn.(IF (ISZERO n) ZERO (MULTI n (FACT FACT (PRED n)))) ONE
IF (ISZERO ONE) ZERO (MULTI ONE (FACT FACT (PRED ONE)))
IF FALSE ZERO (MULTI ONE (FACT FACT (PRED ONE)))
MULTI ONE (FACT FACT (PRED ONE))
MULTI ONE (FACT FACT ZERO)
MULTI ONE ONE
ONE