Re: Funny Behavior of Module

*To*: mathgroup at smc.vnet.net*Subject*: [mg124770] Re: Funny Behavior of Module*From*: "Nasser M. Abbasi" <nma at 12000.org>*Date*: Sat, 4 Feb 2012 06:35:06 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jgg195$bnb$1@smc.vnet.net>*Reply-to*: nma at 12000.org

On 2/3/2012 1:10 AM, Louis Talman wrote: > I know that Module exhibits some funny behavior, but this behavior is > something I've never seen before. It seems wrong to me. > > In a new kernel session enter > > f[x_] := Module[{a},a = x^2; x = y; a] > > f[z] > > z > > Mathematica returns y for z, as it ought to. (In fact, the purpose of > the code was to demonstrate to students what can happen when a Module > monkeys with its formal parameters.) > > But f[z] returns y^2. It seems to me that it should return z^2, but that > for some reason it's interpreting the first Set instruction in the body > of the Module as a SetDelayed instruction. (We get exactly the same > behavior if we replace that Set with SetDelayed in the code.) > > Can anyone explain what's going on here? ITABOAF? > > > --Lou Talman > Department of Mathematical& Computer Sciences > Metropolitan State College of Denver > > <http://rowdy.mscd.edu/%7Etalmanl> > The program is not really a valid Mathematica code, inside the function, the pattern x_ should always show up on the RHS of any assignment, not on the LHS. In your example this line x=y is not valid, since the pattern x shows on the left side of an assignment not on the right side. As what happens when you wrote it the way you did: a=x^2 ===> this becomes a=z^2 since x is z next, you say x=y, which became z=y, since x is z. next, the last thing you have is 'a'. Now Mathematica will evaluate 'a', which is z^2. But now 'z' is 'y', so it does one more transformation rule, Hence 'a' which is 'z^2' evaluates to 'y^2' And this is what you see. This is no different than writing ------------------ Remove["Global`*"] a=z^2; z=y; a ------------------- and now you'll see that 'a' is y^2 and not z^2. Since 'a' evaluates 'a' to z^2, and 'z' evaluates to 'y^2', and now the evaluator stops, since there is no more transformation rules to apply. One way to do what you did is by introducing a local symbol ----------------------- Remove["Global`*"] f[$x_] := Module[{a, x = $x}, a = x^2; x = y; a] f[z] -------------------------- now it returns z^2. The reason the above returns z^2 and not y^2, is because: a=x^2 ===> this becomes a=z^2 since x is z next, x=y, but now x is the local x and not z. So, x becomes y. next, we have'a'. Now Mathematica will evaluate 'a', which is z^2, and no more. z still is z. So what you get is z^2. --Nasser