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Article #3

Re: Copmaring Power (Expressivity) of Two Languages

#3
From: Joe Armstrong
Date: Tue, 27 Oct 1992 09:18
53 lines
2198 bytes
|> In article <1992Oct23.132146.20784@eua.ericsson.se> joe@erix.ericsson.se (Joe Armstrong) writes:
|> >How about:
|> >
|> >	language L1 is move expressive than L2 for solving the problem P iff:
|> >	#(min_prog(L1, P)) < #(min_prog(L2, P))
|> >	# is the number of characters in the program
|> >	min_prog(L, P) is the shortest algorithm in langage L which solves
|> >    problem P.
|> 
|> Boy howdy!
|> 
|> So why haven't replaced C with Cterse:
|> 
|> i m(){
|>   i x;
|>   f(x=0;(x<10);x++){
|>     pf("%d\n",x);
|>   }
|> }
|> 
|> Boy, you've hit the nail on the head. Clearly the reduction of the
|> number of characters needed to express a program is proportional
|> to the increase in power. 
|> 
|> Cosmic.
|> 

	Nit picking

Several people have critisised my earlier definition so ....

	let  O  = observer
	     P  = set of programs which O might with to write
	     Pi = element of P
	     L  = Langauge
	     
	and  prog(O, Pi, L) = a reasonable straight forward, clear and
beautiful program written in language L written by  O to solve Pi.

	Then from O`s point of view.

	Li is more expressive than Lj iff:

	ForAll Pi in P sum(#prog(O, Pi, Li)) < sum(#prog(*O, Pi, Lj))

	Where # is a function which from O`s point of view gives a numerical
measure of the ease with which Pi could be written.

Notes: 1) I'm not interested in the shortest program only a program which is
reasonable clear and gets the job done with a minimum of fuss.
       2) Expressibility is in the eye of the beholder.

	Joe
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Message-ID: <1992Oct27.091848.13551@eua.ericsson.se>
Path: arc1-ca.pugleaf.net!sparky!uunet!mcsun!sunic!sics.se!eua.ericsson.se!erix.ericsson.se!joe
References: <1992Oct20.193129.251@thinkage.on.ca> <BwJ4Ms.1Mo@rice.edu> <1992Oct23.132146.20784@eua.ericsson.se> <Bwqs8L.1v3@phage.cshl.org>

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Path: arc1-ca.pugleaf.net!sparky!uunet!mcsun!sunic!sics.se!eua.ericsson.se!erix.ericsson.se!joe
From: joe@erix.ericsson.se (Joe Armstrong)
Subject: Re: Copmaring Power (Expressivity) of Two Languages
Message-ID: <1992Oct27.091848.13551@eua.ericsson.se>
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References: <1992Oct20.193129.251@thinkage.on.ca> <BwJ4Ms.1Mo@rice.edu> <1992Oct23.132146.20784@eua.ericsson.se> <Bwqs8L.1v3@phage.cshl.org>
Date: Tue, 27 Oct 1992 09:18:48 GMT
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