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ToExpression

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

ToExpression[input]
    parses input (a String) as Mathilda input and returns the resulting
    expression after evaluation.
ToExpression[input, form]
    uses interpretation rules for the specified form. form may be
    InputForm or FullForm (both currently use the same parser).
ToExpression[input, form, h]
    wraps the head h around the parsed expression before evaluation;
    use h = Hold to obtain the unevaluated parsed form.
Returns $Failed if a syntax error is encountered.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= ToExpression["1+1"]
Out[1]= 2

In[2]:= ToExpression["1+1", InputForm, Hold]
Out[2]= Hold[1 + 1]

In[3]:= ToExpression["x+"]
Out[3]= $Failed

Implementation notes

builtin_toexpression (src/core.c) feeds a string argument to parse_expression (the Pratt parser, src/parse.c) and returns the parsed tree for the evaluator to reduce. An optional second argument (InputForm/FullForm/StandardForm) is accepted but ignored, since the parser is form-agnostic; an optional third argument is a head h wrapped around the result (commonly Hold). A parse failure returns $Failed; non-string input returns NULL. The symbol is Listable.

  • Protected, Listable. ToExpression[{"1+1", "2+2"}] evaluates to {2, 4}.
  • Returns the symbol $Failed if the parser cannot consume the input.
  • A non-string input or an unsupported form leaves the call unevaluated.

Attributes: Listable, Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References

Notes & additional examples

Worked examples

In[1]:= ToExpression["1 + 2*3"]
Out[1]= 7

In[1]:= ToExpression["D[ArcTan[x], x]"]
Out[1]= 1/(1 + x^2)

In[1]:= ToExpression["Series[Exp[x], {x, 0, 4}]"]
Out[1]= 1 + x + 1/2 x^2 + 1/6 x^3 + 1/24 x^4 + O[x]^5

In[1]:= ToExpression["x^2 + 1", InputForm, Hold]
Out[1]= Hold[x^2 + 1]

In[1]:= ToExpression["bad syntax ]["]
Out[1]= $Failed

Notes

ToExpression[input] parses a string as Mathilda input and evaluates the result — so the full symbolic engine is reachable from text, including D, Series, Solve, and friends. The three-argument form wraps a head around the parsed tree before evaluation; ToExpression[s, InputForm, Hold] is the standard way to get the unevaluated parsed form. A syntax error yields $Failed rather than an abort, making ToExpression safe to use on untrusted input or in Map.