11

I ran into unexpected behavior in my code based on an errant assumption. Namely, I thought that:

ClearAll[aa, bb, cc, dd, ee, ff];
Thread[Equal[{aa, bb, cc}, {dd, ee, ff}]]
Thread[SameQ[{aa, bb, cc}, {dd, ee, ff}]]

would result in:

{aa == dd, bb == ee, cc == ff}
{False, False, False}

What I get instead is:

{aa == dd, bb == ee, cc == ff}
False

Which I can argue makes sense, since the lists aren't equivalent. But why doesn't Thread work? What's the precedence argument here? How can I get the answer I want ({False, False, False}) from a similar construct?

István Zachar
  • 47,032
  • 20
  • 143
  • 291
tkott
  • 4,939
  • 25
  • 44
  • 3
    To get {False,False,False} you can use MapThread[SameQ, {{aa, bb, cc}, {dd, ee, ff}}]. – kglr Apr 18 '12 at 02:19

2 Answers2

18

Thread doesn't hold its arguments. You can check its attributes.

So, before doing any threading, it evaluates its arguments.

Now, understanding the behaviour you describe requires understanding the difference between Equal and SameQ. Equal is meant for math reasoning. For expressing an equality, which might involve a variable that at the time you don't yet know it's value. So, for example, x==8 returns unevaluated if x isn't defined.

SameQ however is a predicate. It will always return either True or False if the constructs are exactly the same (after evaluation).

So, Thread[SameQ[{aa, bb, cc}, {dd, ee, ff}]] -> Thread[False]-> False

One can see this by running (thanks @rcollyer)

Trace[Thread[SameQ[{aa, bb, cc}, {dd, ee, ff}]], 
 TraceInternal -> True]

Out[1] = {{{aa, bb, cc} === {dd, ee, ff}, False}, Thread[False], False}

If you want to thread SameQ without evaluation, just use Unevaluated

Thread[Unevaluated@SameQ[{aa, bb, cc}, {dd, ee, ff}]]

{False, False, False}

Another construction that gives the result you want is the one suggested by @kguler in his comment and supported by @rcoller and his upvoters: MapThread. I'd suggest you search the docs if you don't know it

MapThread[SameQ, {{aa, bb, cc}, {dd, ee, ff}}]
Rojo
  • 42,601
  • 7
  • 96
  • 188
11

I use Part for this sort of thing.

data = Transpose[{{aa, bb, cc}, {dd, ee, ff}}]
{{aa, dd}, {bb, ee}, {cc, ff}}

Now change the heads:

data[[All, 0]] = Equal;
data
{aa == dd, bb == ee, cc == ff}

and:

data[[All, 0]] = SameQ;
data
{False, False, False}
Mike Honeychurch
  • 37,541
  • 3
  • 85
  • 158
  • I like the use of the 0th part to replace the head :) – tkott Apr 18 '12 at 10:24
  • I only started using it a couple of months ago but now use it a fair bit due to it being nice and concise. – Mike Honeychurch Apr 18 '12 at 11:48
  • An interesting replacement for Equal @@@ data, although in this case, I think Apply wins in character count. But, definitely something to keep in mind when working with deeper nesting. – rcollyer Apr 18 '12 at 13:17