The Interpretation of Textual Forms
|ToExpression[input]||create an expression by interpreting strings or boxes|
Converting from strings or boxes to expressions.
This takes a string and interprets it as an expression.
Here is the box structure corresponding to the textual form of an expression in StandardForm
interprets this box structure and yields the original expression again.
In any Mathematica
is always effectively using ToExpression
to interpret the textual form of your input as an actual expression to evaluate.
If you use the notebook front end for Mathematica
, then the interpretation only takes place when the contents of a cell are sent to the kernel, say for evaluation. This means that within a notebook there is no need for the textual forms you set up to correspond to meaningful Mathematica
expressions; this is only necessary if you want to send these forms to the kernel.
The hierarchy of forms for standard Mathematica input.
Here is an expression entered in FullForm
Here is the same expression entered in InputForm
Built into Mathematica
is a collection of standard rules for use by ToExpression
in converting textual forms to expressions.
These rules define the grammar
. They state, for example, that x+y
should be interpreted as Plus[x, y]
, and that xy
should be interpreted as Power[x, y]
. If the input you give is in FullForm
, then the rules for interpretation are very straightforward: every expression consists just of a head followed by a sequence of elements enclosed in brackets. The rules for InputForm
are slightly more sophisticated: they allow operators such as +
, and ->
, and understand the meaning of expressions where these operators appear between operands. StandardForm
involves still more sophisticated rules, which allow operators and operands to be arranged not just in a one-dimensional sequence, but in a full two-dimensional structure.
is set up so that FullForm
form a strict hierarchy: anything you can enter in FullForm
will also work in InputForm
, and anything you can enter in InputForm
will also work in StandardForm
If you use a notebook front end for Mathematica
, then you will typically want to use all the features of StandardForm
. If you use a text-based interface, however, then you will typically be able to use only features of InputForm
When you use StandardForm
in a Mathematica
notebook, you can enter directly two-dimensional forms such as x2
or annotated graphics. But InputForm
allows only one-dimensional forms.
If you copy a StandardForm
expression whose interpretation can be determined without evaluation, then the expression will be pasted into external applications as InputForm
. Otherwise, the text is copied in a linear form that precisely represents the two-dimensional structure using \!\(...\)
. When you paste this linear form back into a Mathematica
notebook, it will automatically "snap" into two-dimensional form.
|ToExpression[input,form]||attempt to create an expression assuming that input is given in the specified textual form|
Importing from other textual forms.
and its subsets FullForm
provide precise ways to represent any Mathematica
expression in textual form. And given such a textual form, it is always possible to convert it unambiguously to the expression it represents.
is an example of a textual form intended primarily for output. It is possible to take any Mathematica
expression and display it in TraditionalForm
. But TraditionalForm
does not have the precision of StandardForm
, and as a result there is in general no unambiguous way to go back from a TraditionalForm
representation and get the expression it represents.
Nevertheless, ToExpression[input, TraditionalForm]
takes text in TraditionalForm
and attempts to interpret it as an expression.
the same string would mean a product of terms.
output is generated as the result of a computation, the actual collection of boxes that represent the output typically contains special Interpretation
objects or other specially tagged forms which specify how an expression can be reconstructed from the TraditionalForm
The same is true of TraditionalForm
that is obtained by explicit conversion from StandardForm
. But if you edit TraditionalForm
extensively, or enter it from scratch, then Mathematica
will have to try to interpret it without the benefit of any additional embedded information.