lambda-calculus factorial

gistfile1.rb

True = ->(a,b) {a}
False = ->(a,b) {b}

#Church encodings
zero = ->(f){->(x) {x}} 
one =  ->(f){->(x) { f.(x)}}
two =  ->(f){->(x) { f.(f.(x))}}
three =->(f){->(x) { f.(f.(f.(x)))}}

#operations
multi = ->(n1,n2) {->(f) {n2.(n1.(f))}}
pred = ->(number) { ->(f) { ->(x) { number.(->(g) {->(h) {h.(g.(f))}}).(->(u) {x}).(->(u) {u})}}}
sub = ->(n1,n2) {n2.(pred.(n1))}

iszero = ->(number) {number.(->(x) {False}).(True)}

y_combinator = ->(f) { ( ->(x) { f.( ->(v) { x.(x).(v) } ) } ).( ->(x) { f.(->(v) { x.(x).(v) } ) } ) }

#non-strict if-else is missing
factorial =  y_combinator.(->(y_factorial) { ->(n) { iszero.(n) == True ? one : multi.(n, y_factorial.(sub.(n,one))) } })


show = ->(number) {puts number.(->(x) {x + 1}).(0)}


show.(factorial.(three))