#include <string>
#include <set>

using namespace std;

typedef string variable;

class term {
  virtual set<variable> freeVariables();
  virtual term substitute(variable, term);
  virtual bool alphaEquivalent(term);
  virtual string pretty();
};

class var : public term {
  variable name;
public:
  var(variable name) : name(name) {};
};

class lam : public term {
  variable binding;
  term body;
public:
  lam(variable binding, term body) : binding(binding), body(body) {};
};

class app : public term {
  term function;
  term argument;
public:
  app(term function, term argument) : function(function), argument(argument) {};
};

int main(int argc, char** argv) {
  term example1 = lam("x", app(var("x"), var("y")));
  term example2 = app(var("f"),lam("f",app(example1,var("f"))));
  return 0;
}