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Re: Re: exchanging 2 elements in a list (problem with Block)

• To: mathgroup at smc.vnet.net
• Subject: [mg27801] Re: [mg27631] Re: exchanging 2 elements in a list (problem with Block)
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Sat, 17 Mar 2001 05:41:27 -0500 (EST)
• References: <933FF20B19D8D411A3AB0006295069B0286951@dassne02.darmstadt.dsh.de> <3AAF97B7.8494FB81@cs.berkeley.edu> <000d01c0acc9$9995a8e0$9b16989e@machine1> <3AAFEA90.BA2302CD@cs.berkeley.edu>
• Sender: owner-wri-mathgroup at wolfram.com

Richard,

> I guess the examples of why Block is preferable to Module
> don't seem convincing to me.

The examples were of *some* uses for Block - not part of an argument that
Block is generally preferable - I don't think it is.

> The first example is   ....
>.....In my view, the result of Module is right

The first example was

    i=j;

    Table[i^j, {j,3}]

            {1, 4, 27}

    Module[{i},Table[i^j, {j,3}]]

            {i$1049, i$1049^2, i$1049^3}

    Block[{i},Table[i^j, {j,3}]]

            {j, j^2, j^3}

I wanted an expression that in the presence of the rule  i =j (really
of OwnValue  HoldPattern[i] :> j  ) would evaluate to  {j, j^2,
j^3} .
The use of Block seems a natural way to achieve this

The way that Module was used does not achieve this.
Of course, we could use Module on j instead of i.

    Module[{j},Table[i^j, {j,3}]]

            {j, j^2, j^3}

However this could fall foul of the rash introduction of variables reserved
symbols:

    $ModuleNumber =1;

     i=j$1;

    Module[{j},Table[i^j, {j,3}]]

            {1,4,27}

Here is another bit of bad programming:

    Clear[i]

    Module[{j},i=j;Table[i^j, {j,3}]]

        {1,4,27}

----------------------------------------------------------------------------

BLOCK AND NUMBER ARITHMETIC

> but not for Block[{Plus},Print[Plus[1,1]]]   (doesn't work).
> or  Block[{Times=Plus},4!]  (doesn't work[??])


Block does not block Plus or Times on numbers

      Block[{Plus}, Print[2+3]]

            5

But they are blocked on symbols.
Also: attributes are blocked
(note that c comes before b in the output).

    Block[{Plus},Print[Attributes[Plus]]; Print[c+b+a+a+2+3]]

            {}

            5+c+b+a+a

Temporary assignment works:

    x:= 2+3

    Block[{Plus= HeldPlus}, {2+3, x}]

            {HeldPlus[2,3],HeldPlus[2,3]}

Maybe number arithmetic goes directly to C.

But notice

        Block[{Subtract},Subtract[2,3] ]

        -1

Re: Block[{Times=Plus},4!]  (doesn't work[??])

        Block[{Times=Plus}, 4!]

            24

This may be because Factorial is not defined in Mathematica's language but is
passed on directly to C.

Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

----- Original Message -----
From: "Richard Fateman" <fateman at cs.berkeley.edu>
To: mathgroup at smc.vnet.net
Subject: [mg27801] Re: [mg27631] Re: exchanging 2 elements in a list (problem with
Block)


> I guess the examples of why Block is preferable to Module
> don't seem convincing to me.
> The first example is simply to avoid having the variable
> i evaluated.  In a language with single-level evaluation
> it should be possible to quote variables.  Thus
> Table [Quote[i]^j,{j,3}]   ; Hold[] in Mathematica is
> not the same as this.  I find Hold to be unuseable.  For
> reasons of the evaluation strategy in Mathematica, I
> suppose Quote[] is difficult.
> In my view, the result of Module is right, even though
> the printout is bad.  Establishing a local variable i and
> then squaring it should not return the variable associated
> with the global name i.
>
>
> I don't understand what example 2 does.  If the intention
> is to dynamically hide the definition
> of Dot and all its rules  by the Block[{Dot}...]
> then I suppose that is of some use.  I didn't know that
> would work for built-in "functions", and I suspect that it
> doesn't.  That is
> Foo[x_]:=foobar[x]
> Block[{Foo},Print[Foo[3]]]
>
> prints Foo[3] not foobar[3]  so the definition of Foo is
> blocked.  (works)
>
> And similarly for Block[{Sin},Print[Sin[1.2]]] (works)
>
> but not for Block[{Plus},Print[Plus[1,1]]]   (doesn't work).
> or  Block[{Times=Plus},4!]  (doesn't work[??])
>
> I think the point of the other examples is to use dynamic
> scope to hide definitions temporarily. That's OK if
> used with restraint.  Block[{D=3}, ...f[x]]  presumably
> breaks the Derivative function in the "call" to f[].
>
>
> The Module "bugs" though are related to the erroneous
> implementation of Module in mathematica.  Faking the
> module variables but by having equivalent user-syntax
> alternatives looks like an implementation or
> perhaps a design error.