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example 1

we can use Information , but can not use ?

Sin // Information

Sin // ?

example 2

we can use StringJoin but cannot use <>

"aa" <> 1 <> 2 <> "Ab" <> 123 <> "aend" /. <>-> ~~

"aa" <> 1 <> 2 <> "Ab" <> 123 <> "aend" /. StringJoin -> StringExpression

share|improve this question
~~ is not a symbol, but a binary infix operator that needs 2 arguments, so foo // ~~ doesn't make sense, because it is incomplete. a ~~ b is parsed to StringExpression[a, b], but ~~ (without any arguments) does not parse to StringExpression. – R. M. Jun 28 '13 at 6:28
@rm-rf Yes, my post was not so exactly. Sometimes, my first response to do those // /. things is ? <> because I've got used to do ?Sin,a<>b, rather that Information[]. Actually I found this also couldn't been done ?/@{Sin} – HyperGroups Jun 28 '13 at 7:44
That's because ? is not an operator for Information. It so happens that just ?foo by itself is parsed as Information[foo], but otherwise, it does not behave like any other operator. To see that ?foo is not actually a short form for Information[foo], try f[x_Symbol] := ?x and then evaluate, say, f[Sin]. You'd expect it to be the same as ?Sin, right? Check for yourself what happens. Besides, ? is the operator for PatternTest. – R. M. Jun 28 '13 at 8:04
Just to make it clear: if ? had been an operator for Information it would have to be entered in prefix form as ?@Sin or ?[Sin] instead of ?Sin. Only if the operator is called as op@arg can you postfix it as arg//op. – István Zachar Jun 28 '13 at 11:37
@rm-rf well Actually in my first post, there is no such word Operator...Anyway, good to learn that. – HyperGroups Jun 28 '13 at 15:09

Input Expressions

There exists a definite grammar which specifies how your input should be converted to an internal form.

There are several operators which basically are overloads for internal functions:

^  -> Power
+  -> Plus
~~ -> StringExpression

What these operators all have in common is that they are binary operators, meaning their equivalent is a function taking two parameters.

The only two forms that do support binary operators are:

f[x, y]     -> standard form
x ~~ f ~~ y -> infix form

The other two forms support unary operators and they are special cases because of their precedence. When you write:

f @ x + y  ==> f[x] + y
x + y // f ==> f[x + y]

But you could write f[x, y] in prefix form, due to its higher precedence: f@(x+y).

The last example x + y // f shows perfectly the problem here. It is translated to f[x + y] but if f would be the equivalent to ~~ it would be incomplete and therefore a syntax error.

I highly doubt that ? is the operator equivalent for Information

I hope this answers your question.

share|improve this answer
I'm not sure the equivalence of ? and Information, Sometimes I use Definition, when I cannot use ? in such case ?/@{Sin,Cos}. One reason about why I ask this question is that some newbie like me know only ? in the beginning, and then after a long time, I know Information and Definition, what a bad thing. – HyperGroups Jun 28 '13 at 7:48
Information prints the same information as ??. Information is a function taking a symbol as a parameter, whereas ?? is not. ? and ?? are just input escapes. – Stefan Jun 28 '13 at 12:13

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