Re: Assertions in Mathematica?

*To*: mathgroup at smc.vnet.net*Subject*: [mg113448] Re: Assertions in Mathematica?*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Fri, 29 Oct 2010 06:27:48 -0400 (EDT)

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 recommend. (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 evaluation. 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