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MathGroup Archive 2007

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Re: Transformation rules - explain please

  • To: mathgroup at smc.vnet.net
  • Subject: [mg74140] Re: [mg74023] Transformation rules - explain please
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Mon, 12 Mar 2007 22:05:57 -0500 (EST)
  • References: <200703061032.FAA02186@smc.vnet.net>

On 6 Mar 2007, at 11:32, wooks wrote:

> This is supposed to substitute the first occurrence of old1 or old2
> with new.
>
> Why does this work
>
> Clear[old1, old, old2, lat, MySubst]
> lat = {banana, ice, cream, smeared, chocolate, topping};
> MySubst[new_, old1_, old2_, {x___, old_, r___}] := {x, new, r} /;
> Or[old == old1, old == old2];
> MySubst[strawberry, chocolate, cream, lat]
>
> but not this (with the conditional on the lhs).
>
> Clear[old1, old, old2, lat, MySubst]
> lat = {banana, ice, cream, smeared, chocolate, topping};
> MySubst[new_, old1_, old2_, {x___, old_, r___} /; Or[old = old1, old
> =  old2]] := {x, new, r};
> MySubst[strawberry, chocolate, cream, lat]
>
> I like the idea of using conditional rules like this but have found it
> very hit and miss. Often times things don't work so I am seeking
> further enlightment.
>
> I'd be interested to see what would need to be done to make the
> conditional work on the lhs.
>
>

Your definition with Condition on the RHS is equivalent to the 
following defintion with Condition on the LHS, which also works:

MySubst[new_, old1_, old2_, {x___, old_, r___} ] /; Or[old == old1, old
==  old2] := {x, new, r};


The problem with your attempt

> MySubst[new_, old1_, old2_, {x___, old_, r___} /; Or[old = old1, old
> =  old2]] := {x, new, r};


  is not that Condition is on the left, but that it is being used to 
test a pattern
{x___, old_, r___} /; old == old1 =E2=88=A8 old == old2, which can never 
match until old1 or old2 has been assigned a value. To see that 
better note that the following (rather pointless) defintion actually 
"works":

Clear[old1, old, old2, lat, MySubst]
lat = {banana, ice, cream, smeared, chocolate, topping};

MySubst[new_, old1_, old2_, {x___, old_, r___} /; Or[old == 
chocolate, old
==  old2]] := {x, new, r}


MySubst[strawberry, chocolate, cream,  lat]


{banana,ice,cream,smeared,strawberry,topping}


This time the pattern {x___, old_, r___} /; Or[old == chockolate, 
old 
==  old2] matched even before old2 had any value and the rule was 

applied.

Andrzej Kozlowski


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