# ---------------------------------------------------------------------------
# - 0806.als                                                                -
# - afnix example : chapter 8 : example 06                                  -
# ---------------------------------------------------------------------------
# - This program is free software;  you can redistribute it  and/or  modify -
# - it provided that this copyright notice is kept intact.                  -
# -                                                                         -
# - This program  is  distributed in  the hope  that it will be useful, but -
# - without  any  warranty;  without  even   the   implied    warranty   of -
# - merchantability or fitness for a particular purpose.  In no event shall -
# - the copyright holder be liable for any  direct, indirect, incidental or -
# - special damages arising in any way out of the use of this software.     -
# ---------------------------------------------------------------------------
# - copyright (c) 1999-2007 amaury darsch                                   -
# ---------------------------------------------------------------------------

# Y combinator with factorial

# factorial - as a combinator
const c-fact (f) {
  println "creating factorial gamma expression"
  gamma (n) (f) {
    println "evaluating the factorial gamma with n = " n
    if (== n 1) 1 (* n (f (- n 1)))
  }
}

# the Y combinator
const Y (f) ((gamma (g) (f) (f (gamma (x) (g) ((g g) x)))) 
             (gamma (g) (f) (f (gamma (x) (g) ((g g) x)))))

# let do the math
println "fact 5 = " ((Y c-fact) 5)