Re: scope all wrong? in Mathematica 4.1

*To*: mathgroup at smc.vnet.net*Subject*: [mg31832] Re: scope all wrong? in Mathematica 4.1*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Fri, 7 Dec 2001 05:55:44 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hi, > Consider the mathematica definition > > rr[x_] := Block[{x}, x = 5; Print["x is ", x]] > > what do you expect here? A disaster ? a complete crash of the system ? The destruction of Mathematica's memory management ? Future unpredicted results form Mathematica ? (That happens in early versions of Mathematica in such a case) > > rr[z] --> x is 5 is printed. > but you might not expect > > rr[4] --> "Block::"lvsym": "Local variable specification{4} contains 4 > which is not a symbol or an assignment to a symbol." > > If you use Module instead of Block, you get > the same. Wow ! Mathematica is so smart -- one of the most clever programs I have ever seen. You type complete nonsense and assign a value to a pattern and you only get an error message -- it is great ! You should definitely try to assign a value to a pattern to Mathematica version 1.2 ! A pattern stand for "all things like ..." and you can't say "all things" are 5. > > However, > Block[{x = 4}, Block[{x}, x = 5; Print["x is ", x]]] > > prints x is 5 > > Using pattern matching for > substituting 4 for x in rr[4] even when x is bound seems > to be counter to what most programming language designers > would expect. A pattern is *not* a variable on the stack of a C-program ! A pattern is a general form and can't have a value. > > Now look at > > uu[x_?((x = 5; Print["x is ", x]; True) &)] := x > > Usually when one defines a program, nothing is printed. > Here, we get > x is 5 > 5 > x is 5 My Mathematica 4.1 prints nothing. > > If we do this: > x =400 > uu[70] > x is 5 printed > the value returned is 70 > and the global x is 5. > This is absolutely correct. What whould you expect from uu[canBeAnyExpression_?((x = 5; Print["x is ", x]; True) &)] := x (?) the behaviour that you report ! That you just like to say that "any expression" has the name "x" on the right hand side can't affect the transformation rule. > Try this: > Module[{x}, uu[x_?((x = 5; Print["x is ", x]; True) &)] := x; > Print["in Module, x is " , x]] > > The expectation in a system supporting lexical scope > with Module > is that no use of x inside the module would escape. > But it does. The global x is set to 5. No ! You have typed all you examples but you have not cleared uu and x before you enter the last example: Try x =.; Clear[uu]; Module[{x}, uu[x_?((x = 5; Print["x is ", x]; True) &)] := x; Print[DownValues[uu]]; Print["in Module, x is ", x]] x and your global x is unchanged. > > The reason this all came up is in correspondence suggesting > that programs in one computer algebra system could be > translated into another. If you have a Mathematica code, there is no reason to translate it to an other system. But is a noble idea to translate the code from other systems to Mathematica. > If systems are semantically > "surprising", it is more difficult. I wonder how much > of mathematica internally depends on wrong scope, or how > much of the code is susceptible to bugs because of unexpected > capture of names. (I suspect that this has caused a proliferation > of package names e.g. MySecretNameSpace`x in Mathematica > routines). And *I* wonder how much of your work depends on such sloppy "observations". Please be a bit more careful *before* you make a wild guesses about the internal structure of Mathematica ! Regards Jens