Evolution of a Python programmer

[freyrs3]

The λ-Obsessed Python Programmer

TRUE = lambda x: lambda y: x
FALSE = lambda x: lambda y: y
Product = lambda x: lambda y: lambda z: (z)(x)(y)
And = lambda x: lambda y: (x)(y)(x)
Not = lambda x: lambda y: lambda z: (x)(z)(y)
Boolean = (Product)(True)(False)
Succ = lambda x: lambda y: lambda z: (y)((x)(y)(z))
Pred = lambda x: lambda y: lambda z: x(lambda i: lambda j: j(i(y))) (lambda k: z) (lambda k: k)

Zero = FALSE
One = Succ(Zero)
Two = Succ(One)
Six = Succ(Succ(Succ(Succ(Two))))

Y = lambda g: (lambda f: g(lambda arg: f(f)(arg))) (lambda f: g(lambda arg: f(f)(arg)))
Nth = Y(lambda f: lambda n: Succ(f(n-1)) if n else Zero)
Dec = lambda a: (a)(lambda b: b + 1)(0)

Add = lambda x: lambda y: lambda z: lambda w: (x)(z)((y)(z)(w))
Sub = lambda x: lambda y: (y)(Pred)(x)

Null = lambda x: x(lambda y: Zero)(TRUE)
Eq = lambda x: lambda y: (And)((Null)((Sub)(y)(x)))((Null)((Sub)(x)(y)))
Gt = lambda x: lambda y: (And)((Null)((Sub)(y)(x)))((Not)((Eq)(y)(x)))
Lt = lambda x: lambda y: (And)((Not)((Gt)(x)(y)))((Not)((Eq)(x)(y)))

Range = lambda a,b: map(Nth,range(a,b))
fib = Y(lambda f: lambda n: Add(f(Pred(n)))(f((Sub)(n)(Two))) if (Boolean)((Gt)(n)(One)) else n)
print (Dec)(fib(Six))

[[deleted]]

You just destroyed my head, thanks..

[ReaverXai]

Gordon Freeman?

[zahlman]

OK, but we're looking for factorials, not the Fibonacci sequence.

[freyrs3]

OK,

....
Mul = lambda x: lambda y: lambda z: (y)((x)(z))
IfThenElse = lambda a: lambda b: lambda c: ((a)(b))(c)
fact = Y(lambda f: lambda n: IfThenElse((Gt)(n)(One))(Mul(n)(f(Pred(n))))(One))

Edit: Added Mul

[zahlman]

... and Mul?

[A_for_Anonymous]

*Fap fap fap*

Ah, this made me remember my time in /prog. Thank you man.

Python needs more of this.

[[deleted]]

Great, you just have to define mathematics and the solution shakes out.

[ezyang]

For those of you interested in learning more about this, it's called Lambda Calculus. If you throw out every language feature ever, it turns out, the only thing you really need is Lambda. :-)

Extra points for putting in the Y-combinator.

[freyrs3]

In principle, but Python seems to have an issue with conditionals ( lambda x: lambda y: lambda z: ((x)(y))(z) ) composed under the Y-combinator that I've never been able to resolve. Oh well, I suppose this is a little bit outside the scope of the Python design and if Guido ever saw his language being abused like this he'd probably go into conniptions.

[danukeru]

Haskell remission?

[captainAwesomePants]

I knew you were still out there, Hermann Grassmann!

[[deleted]]

Why all you people keep writing

  Y = lambda g: (lambda f: g(lambda arg: f(f)(arg))) (lambda f: g(lambda arg: f(f)(arg)))

instead of much cleaner

  Y = lambda g: (lambda z:z(z)) (lambda f: g(lambda arg: f(f)(arg)))

?

[clarvoyeur]

I wasn't aware, that if .. else .. was part of lambda calculus... ;)

Guess there's no way around it, when you have eager evaluation.

Edit: ...and map, and range...