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.
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Here is the box structure corresponding to the textual form of an expression in
StandardForm.
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ToExpression interprets this box structure and yields the original expression again.
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In any
Mathematica session,
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.
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Here is the same expression entered in
InputForm.
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Built into
Mathematica is a collection of standard rules for use by
ToExpression in converting textual forms to expressions.
These rules define the
grammar of
Mathematica. They state, for example, that
should be interpreted as
Plus
, and that
should be interpreted as
Power
. 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.
Mathematica is set up so that
FullForm,
InputForm, and
StandardForm 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
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.
StandardForm and its subsets
FullForm and
InputForm 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.
TraditionalForm 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.
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In
StandardForm the same string would mean a product of terms.
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When
TraditionalForm 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 that specify how an expression can be reconstructed from the
TraditionalForm output.
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.
