My PEG

lambdaness.peg

{
  function id(x){ return x; }
  function cf(x){ return function(y) { return x; }; }
}

start
  = sp V:fn { return (V(null))(2); }

sum
  = L:term "+" sp R:sum { return function(x){ return L(x)+R(x); }; }
  / pow / term

sp = [ \t\n]*

pow
  = L:primary "^" sp R:primary
  { return Math.pow(L,R); }

term
  = L:primary "*" sp R:term { return function(x) { return L(x)*R(x); } }
  / primary 

primary = apply / fn / paren / var / integer


paren = "(" sp V:sum ")" sp { return V; }

callable = fn / var / paren

apply =
      F:callable  V:paren { return function(x) { return (F(x))(V(x)); }; }

fn
  = "{" sp V:sum "}" sp
  { return function(x) { return V; } }


integer "integer"
  = digits:[0-9]+ sp
 { return cf(parseInt(digits.join(""), 10)); }

var =
    letter:[A-Za-z] sp { return id; }