README.md

Install LambLamb

git clone https://github.com/GarrisonJ/LambLamb.git
cd LambLamb 
cabal install

Using LambLamb

LambLamb
(\s.\z.s(z))(\w.(\y.(\x.y(wyx))))(\s.\z.s(z))
λy.λx.(y)((y)(x))

Lambda Calculus:

\ or λ  Denotes lambda  
.       Denotes dot  
()      Denotes order  
a-z     Denotes names  

Church encoding:

\x.x              # Unit  
\s.\z.z           # Zero  
\s.\z.s(z)        # One  
\s.\z.s(s(z))     # Two  
\f.\x.f(f(f(x)))  # Three
\x.\y.x           # True  
\x.\y.y           # False  

Addition

(\w.(\y.(\x.y(wyx))))  

Multiplication

(\x.(\y.(\z.x(yz))))  

Division

(\n.((\f.(\x.xx)(\x.f(xx)))(\c.\n.\m.\f.\x.(\d.(\n.n(\x.(\a.\b.b))(\a.\b.a))d((\f.\x.x)fx)(f(cdmfx)))((\m.\n.n(\n.\f.\x.n(\g.\h.h(gf))(\u.x)(\u.u))m)nm)))((\n.\f.\x.f(nfx))n))  

9/3 is written as follows:

(\n.((\f.(\x.xx)(\x.f(xx)))(\c.\n.\m.\f.\x.(\d.(\n.n(\x.(\a.\b.b))(\a.\b.a))d((\f.\x.x)fx)(f(cdmfx)))((\m.\n.n(\n.\f.\x.n(\g.\h.h(gf))(\u.x)(\u.u))m)nm)))((\n.\f.\x.f(nfx))n))(\f.\x.f(f(f(f(f(f(f(f(fx)))))))))(\f.\x.f(f(fx)))

Which evaluates to:

\f.\x.f(f(f(x)))