Path: utzoo!utgpu!attcan!uunet!steinmetz!kbsvax!caldwell
From: caldwell@akhenaten.steinmetz.ge.com (James Caldwell)
Newsgroups: comp.lang.misc
Subject: Re: a simple miranda problem
Message-ID: 
Date: 10 Aug 88 13:45:42 GMT
References: 
Sender: news@steinmetz.ge.com
Reply-To: caldwell@akhenaten.steinmetz.ge.com
Distribution: comp
Organization: GE Corporate Research & Development Center. Schenectady, NY
Lines: 63
In-reply-to: feldmark@hanako.stars.flab.Fujitsu.JUNET's message of 9 Aug 88 02:47:27 GMT


twice f x = f (f x)
s x = x + 1
answer 	= twice twice twice s 0 
	= twice (twice twice) s 0
	= twice twice (twice twice s) 0
	= twice (twice (twice twice s)) 0
	= twice (twice twice s)((twice (twice twice s)) 0)
	= (twice twice s)((twice twice s))((twice (twice twice s)) 0)
	= twice (twice s)((twice twice s))((twice (twice twice s)) 0)
	= (twice s)((twice s)((twice twice s)))((twice (twice twice s)) 0)
	= s (s ((twice s)((twice twice s))))((twice (twice twice s)) 0)
	= s ((twice s)((twice twice s)))((twice (twice twice s)) 0) + 1
	= ((twice s)((twice twice s)))((twice (twice twice s)) 0) + 1 + 1
	= s (s (((twice twice s))))((twice (twice twice s)) 0) + 1 + 1
	= s (((twice twice s)))((twice (twice twice s)) 0) + 1 + 1 + 1
	= (twice twice s)((twice (twice twice s)) 0) + 1 + 1 + 1 + 1
	= twice (twice s)((twice (twice twice s)) 0) + 1 + 1 + 1 + 1
	= (twice s)((twice s)((twice (twice twice s)) 0)) + 1 + 1 + 1 + 1
	= (s (s((twice s)((twice (twice twice s)) 0)))) + 1 + 1 + 1 + 1
	= (s((twice s)((twice (twice twice s)) 0))) + 1 + 1 + 1 + 1 + 1
	= ((twice s)((twice (twice twice s)) 0))) + 1 + 1 + 1 + 1 + 1 + 1
	= (s (s (((twice (twice twice s)) 0)))) + 1 + 1 + 1 + 1 + 1 + 1
	= (s (((twice (twice twice s)) 0))) + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= ((twice (twice twice s)) 0) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= ((twice twice s) ((twice twice s) 0)) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= ((twice (twice s)) ((twice twice s) 0)) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= ((twice s) ((twice s) ((twice twice s) 0))) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= (s (s ((twice s) ((twice twice s) 0)))) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= (s ((twice s) ((twice twice s) 0))) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= ((twice s) ((twice twice s) 0)) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= (s (s ((twice twice s) 0))) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= (s ((twice twice s) 0)) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= ((twice twice s) 0) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= ((twice (twice s)) 0) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= ((twice s) ((twice s) 0)) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= (s (s ((twice s) 0))) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= (s ((twice s) 0)) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= ((twice s) 0) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= (s (s 0)) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= (s 0) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= 0 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= 2 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= 3 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= 4 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= 5 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= 6 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= 7 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= 8 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= 9 + 1 + 1 + 1 + 1 + 1 + 1 + 1
	= 10 + 1 + 1 + 1 + 1 + 1 + 1
	= 11 + 1 + 1 + 1 + 1 + 1
	= 12 + 1 + 1 + 1 + 1
	= 13 + 1 + 1 + 1
	= 14 + 1 + 1
	= 15 + 1
	= 16	     


--
  Jim Caldwell     caldwell%akhenaten@steinmetz.UUCP
                   uunet!steinmetz!akhenaten!caldwell