Re: How to tell Mathematica to stop conditional testing in an If statment if one condition is niether True or False? McCarthy evaluation rules? 'and then' test?

• To: mathgroup at smc.vnet.net
• Subject: [mg69551] Re: [mg69525] How to tell Mathematica to stop conditional testing in an If statment if one condition is niether True or False? McCarthy evaluation rules? 'and then' test?
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Fri, 15 Sep 2006 06:45:37 -0400 (EDT)
• References: <200609141057.GAA21660@smc.vnet.net>

```On Sep 14, 2006, at 6:57 AM, Nasser Abbasi wrote:

> I can better describe this with simple example:
>
> ------------- code ------------
>
> Remove["Global`*"];
> xc = Table[i, {i, 1, 3}]
> x = 5;
> If[x == b && xc[[10]] == 4, Print["True"], Print["False"], Print
> ["Can't
> decide"]]
>
> ----- end code -------------
> In the above, 'x==b' is neither True nor False, since 'b' has no
> numerical
> value.
>
> But what I want is when this happens, for Mathematica to NOT
> continue with
> the  testing if xc[[10]]==4  is True (because even if it is True,
> it will
> not change the outcome, which is can't decide.
>
> I am looking for something like 'and then'  which says to test the
> next
> condition only if the one just tested was true.
> The interesting thing is that if 'b' had a value, say 7, which
> makes the
> first test (the x==b) to be False, then Mathematica does the right
> thing,
> and will not try to check the xc[[10]]==4 condition.  I need it to
> do the
> same thing when also the result of the check is 'undecided', not just
> 'False' or 'True'.

And does work like and then, but it only short circuits evaluation if
the result of that argument was False.

The expression If[x==b,xc[[10]]==4,,False,x==b] will behave as you
want.  Thus you can make your own operator:

andThen[term_,{}]:=term

andThen[term_,{terms__}]:=If[term,andThen[First[{terms}],Rest
[{terms}]],False,term]

andThen[a__]:=If[Length[{a}]==1,First[{a}],andThen[First[{a}],Rest
[{a}]]]

so that

If[andThen[x==b,xc[[10]]==4],Print["True"], Print["False"], Print
["Can't decide"]]

will work as you want.

> It is clear to me that the way Mathematica does it now is not the
> right way.

&& is the And from Boolean logic so it only makes sense when its
arguments only have the values True or False.  You want a different
form of logic and unfortunately have to write your own operators.

> I do not see why it tries to check for xc[[10]]==4 when it will not
> make a
> difference to the final result.

Because it is not designed to work with logics other than Boolean.

Regards,

Ssezi

```

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