<λ++>

turing-complete idiom to express types in C++

see https://github.com/neu-rah/yolanda for a runtime/compile time alternative to this.

Based on lambda calculus, therefor using functional paradigm on top of modern C++ metaprogramming. Expressions on this idiom are metaprogramming and evaluate at compile time, yelding C++ types as a result.

inspired by the excellent videos of @glebec (https://youtu.be/3VQ382QG-y4) (thank you!)

Scope

This idiom uses lambda calculus as its background on a close cope with c++ templates. It only operates at compile time.
Results in β normal form translate to C++ types (native or user defined).
So this expressions can only be used in replacement of C++ types.
A layer to provide constexpr values is available through dependent types. It is therefor a turing-complete idiom to decide types at compile time. Types have to be extracted after expression evaluation (::App) to yeld valid C++ types. Using Lazyness, static immutable "data" (here expressed as c++ types) and partial application.

lambda base

lambda calculus base lambda core doc.

lpp

Syntatic sugar for "lambda.h"

because Head<L2> looks much better that Expr<Head,L2>::App

LPP doc.

r-lambda

RCurry (runtime curry) turns regular c++ functions into curry versions.

A C++ function that accepts lets say 2 arguments a and b, and returns c is then turned into a function that accepts one argument a and return a second function that accepts b and returns c (considering the previous a).

curry is the only part implemented, and still testing. No lambda calculus yet

#include <iostream>
using namespace std;

#include <r-lambda.h>//runtime lambda core
using namespace rlambda;

template<typename I>
inline I _id(I i) {return i;}
template<typename I>
constexpr auto id=RCurry<decltype(_id<I>),_id,I>();

//regular function with single param
int _d(int x){return x<<1;}
constexpr auto d=RCurry<decltype(_d),_d,int>();
// constexpr auto d=typename decltype(fun(_d))::template curried<decltype(_d),_d>;

//regular function with multiple param
int _m(int x,int y){return x*y;}
constexpr auto m=RCurry<decltype(_m),_m,int,int>();

template<typename O> constexpr auto _true=rK<O>;

template<typename O> O __false(O,O o) {return o;}
template<typename O> constexpr auto _false=RCurry<decltype(__false<O>),__false<O>,O,O>();

int main(int argc, char **argv) {
  cout<<"d(2):"<<d(2)<<endl;
  cout<<"m(2)(3):"<<m(2)(3)<<endl;
  auto x=d(d);
  cout<<"x(2):"<<x(2)<<endl;
  cout<<"id<int>(d)(1967:"<<id<int>(d)(1967)<<endl;
  cout<<"m(d)(5)(3):"<<m(d)(5)(3)<<endl;
  cout<<"d(m)(2)(3):"<<d(m)(2)(3)<<endl;
  cout<<"m(5)(d)(3):"<<m(5)(d)(3)<<endl;
  cout<<"d(m)(10)(2):"<<d(m)(10)(2)<<endl;
  cout<<"d(m(10))(2):"<<d(m(10))(2)<<endl;//same as above
  cout<<"d(m)(5)(m)(3)(2):"<<d(m)(5)(m)(3)(2)<<endl;
  cout<<_true<const char*>("Ok")("Fail")<<endl;
  cout<<_false<const char*>("Fail")("Ok")<<endl;
  return 0;
}