λ-Calculus Online Playground

Try writing your lambda expression! We've defined some basic expressions for you:

Y = λf.(λx.f (x x)) λx.f (x x)

I = λz.z

T = λx.λy.x

F = λx.λy.y

O = λf.λx.x

S = λn.λf.λx.f (n f x)

P = λn.λf.λx.n (λg.λh.h (g f)) (λu.x) λu.u

One = λf.λx.f x

Two = λf.λx.f (f x)

Plus = λn.λm.λf.λx.n f (m f x)

Mul = λn.λm.λf.λx.n (m f) x

Exp = λn.λm.n (Mul m) One

IfThenElse = λe.λx.λy.e x y

IsZero = λn.n (λx.F) T

Fact = λf.λn.IsZero n One (Mul n (f (P n)))

You can click on underlined part to make beta reduction, or click on predefined named variables to expand them.