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Re: Assertions in Mathematica?

kj wrote:
> What's the best to implement assertions in Mathematica?  By assertions
> I mean statements like assert(exp) in C, which generate an error
> if exp evaluates to false.
> This *should* be trivial, but it's Mathematica, so...
> Naively, I tried defining:
> Assert[exp_, msg__] := If[!exp, Message[msg]; Abort[]]
> ...which, of course, failed to work (as I've learned to expect);
> instead it produced a cryptic error "Message::name : Message name
> ... is not of the form symbol::name or symbol::name::language."
> I tried many other things, but after wasting 1 hour on this
> ridiculously trivial programming task, I'm reduced to begging for
> help.  (This, by the way, is always the way it is with me and
> Mathematica, and I've been using it on-and-off for almost 20 years.
> The documentation is as useless to me today as it was 20 years ago.
> I find it as horrible as the rest of Mathematica is brilliant.)
> I've posted desperate questions over programming mind-numbing
> trivialities like this one in Mathematica before, i.e. questions
> that seem so elementary and fundamental that no one who has access
> to the documentation and who can read should *ever* have to ask
> them.  I ask them less wanting to get the answer to the questions
> themselves than hoping to learn how I could have answered such
> questions by myself.  But I've never found how to do this.  Those
> who know the answers *already* can give them to me if they feel so
> inclined.  (And how they got to know the answer to begin with, I
> don't know; I imagine it took years of sustained Mathematica
> programming.  Or maybe they asked a similar question before to
> someone who already knew the answer...)  But no one has been able
> to tell me how someone who *doesn't* know the answers to such questions
> already can figure it out without outside help. 
> But hope springs eternal!  If someone is kind enough to tell me
> how I could implement my Assert, I'd be most grateful.  If someone
> can tell me how I could have arrived at this answer by myself by
> consulting the documentation, I'd be ecstatic.
> TIA,
> kj

I'm sure better responses will come your way. Here are some things I'd 

(1) Check the documentation for the correct syntax/usage of Message.

(2) Consider using Print instead of Message. It might be more what you 
want. (Hard to say, without seeing a concrete example from you).

(3) Make the function have attribute HoldAll or HoldRest. That way the 
second argument is not evaluated unless the assertion triggers. Example:

assert[exp_, msg__] := If[!exp, Print[msg]; Abort[]]

In[42]:= assert[5==5., aa=bb]

In[43]:= aa
Out[43]= bb

Notice it evaluated the second argument even though the assertion was 
not triggered. In contrast, the held variant below does not do such 

In[53]:= SetAttributes[assert2,HoldAll]

In[54]:= assert2[exp_, msg__] := If[!exp, Print[msg]; Abort[]]

In[55]:= assert2[5==5., xx=yy]

In[56]:= xx
Out[56]= xx

(4) Implement your "Assert" with a lower case 'a', e.g. assert[]. One 
excellent reason to do this is that it woun't give you a shadowing 
problem if you get version 8 of Mathematica, as that has Assert[].

Daniel Lichtblau
Wolfram Research

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