PyLambda is a simple hybrid lambda / Python expression evaluator.

It evaluates lambda expressions by binding python arguments to its variables. Behind the scenes it converts a lambda expression into a python expression consisting of anonymous functions (defined using lambda) and then combines it with the python arguments.

For information on lambda expressions, see http://wikipedia.org/wiki/Lambda_calculus.

The program presents itself as a REPL (read-evaluate-print-loop). Start it up and just enter expressions. When you are finished, enter Ctrl-D to exit.

Lambda expressions should be entered using the standard notation, except instead of using the 'λ' symbol, use 'L'.

The identity function. The general form is lambda-expression:python-arguments:

Lx.x:(2)
2

Note the need to bracket each argument:

Lx.Ly.y:(2)(3)
3

Lambda expressions are not particularly interesting unless at least one of the arguments passed in is a function (defined using lambda):

Lf.Lx.f x:(lambda x:x+1)(2)
3

This last is an example of the Y-combinator. Because the python evaluator has applicative order (eager evaluation), the normal Y-combinator expression has been converted to a form which implements lazy evaluation:

Lf.(Lx.x x)(Lx.Lv.(f x x)v):(lambda f:(lambda n:1 if n==0 else n*f(n-1)))(5)
120

The Y-combinator expression here converts the single-step factorial function into a fully recursive factorial, which calculates 5! = 120.

PyLambda requires PLY 3.4, which must be installed prior to PyLambda installation.

Evaluation using normal order without requiring any explicit syntax.