Question

I’m interested in actual examples of using fixed point combinators (such as the y-combinator in C++. Have you ever used a fixed point combinator with egg or bind in real live code?

I found this example in egg a little dense:

void egg_example() {     using bll::_1;     using bll::_2;      int r =         fix2(             bll::ret<int>(                 // \(f,a) -> a == 0 ? 1 : a * f(a-1)                 bll::if_then_else_return( _2 == 0,                     1,                     _2 * lazy(_1)(_2 - 1)                 )             )         ) (5);      BOOST_CHECK(r == 5*4*3*2*1); } 

Can you explain how this all works?

Is there a nice simple example perhaps using bind with perhaps fewer dependancies than this one?

Answer 1

Here is the same code converted into boost::bind notice the y-combinator and its application site in the main function. I hope this helps.

#include <boost/function.hpp> #include <boost/bind.hpp> #include <iostream>  // Y-combinator compatible factorial int fact(boost::function<int(int)> f,int v) {   if(v == 0)     return 1;   else     return v * f(v -1); }  // Y-combinator for the int type boost::function<int(int)>     y(boost::function<int(boost::function<int(int)>,int)> f) {   return boost::bind(f,boost::bind(&y,f),_1); }   int main(int argc,char** argv) {   boost::function<int(int)> factorial = y(fact);   std::cout << factorial(5) << std::endl;   return 0; }