A Typeless Lambda cAlculus Simulator
Currently finished in C#, still developing in C++17, template is really hard.
##Usage
You should know the Nicolas de Bruijin representation of lambda first. (Using number to represent each variable)
the number k represents the variable that enclosed by the kth lambda
for example:
\a.a can be represented as \.0
\f.\s.s can be represented as \.\.0
and \f.\s.fs is same as \.\.10
when it comes to free variable, first, give it a unique number that is greater than the number of lambdas, then when using it in the lambda expression, add it by the number of lamndas which surround it.
for example:
Mapping of free variable to number:
y -> 3
then
\w.y w is represented as \.4 0, in which 4 comes from the origin number of free variable 3 + the number of lambda that surround the variable 1
##Usage in code (C#)
construct your lambda with static class Operation or just new it.
var succ = Abs(Abs(Abs(Var(1) * (Var(2) * Var(1) * Var(0)))));Abs means abstraction, namely function
you can use operator* to replace construction of Application
then you evaluate
Console.WriteLine($"one: {(succ*zero).Eval()}");or see a step by step evaluation
Console.WriteLine($"one: {(succ*zero).EvalOnce()}");the parameter Context is currently not used
all the method is pure method and objecs are immutable, so you need to store it in a temporary reference or use chained invocation.