InputForm is an expression printed as notatio you could have typed. It is what the components put on the clipboard, what the REPL prints, and what the InputForm entry in any Out menu shows.
The name is Wolfram's, and so is the idea. InputForm there is a printer, not a hold: it renders whatever expression it is handed, in a linear syntax you can type back in. Evaluation is a separate question — HoldForm[1 - 2x] prints 1 - 2*x while InputForm[E^(I Pi) + 1] prints 0, because the second one evaluated before InputForm ever saw it. Ours works the same way: hand it what you typed and it prints what you typed; hand it a result and it prints the result.
The rule is the one the components already follow: the syntax is notatio, and LaTeX appears only inside a $…$ island. InputForm never emits an island — a test asserts it — so what comes out is always something the notatio parser reads on its own.
box holds the expression instead of evaluating it, so the Out is the integral itself, spelled as notatio. Switch the Out menu to compare it with MathJSON or TeXForm.
<notatio-cell value="Integrate(x ^ 2, (x, 0, 1))" out-form="input" box />
<notatio-cell value="Sum(n ^ 2, (n, 1, 10))" out-form="input" box />
<notatio-cell value="(x + 1) / (y - 2)" out-form="input" box />
<notatio-cell value="Limit(Sin(x) / x, 0)" out-form="input" box />Drop the box and the same cells evaluate first — which is the Wolfram behaviour above, not a different format. InputForm prints what it is handed.
<notatio-cell value="Integrate(x ^ 2, (x, 0, 1))" out-form="input" />
<notatio-cell value="Sum(n ^ 2, (n, 1, 10))" out-form="input" />
<notatio-cell value="e ^ (i * Pi) + 1" out-form="input" />Both columns below are InputForm. They differ because they are printing two different expressions: the one you typed, and the one compute-engine canonicalized it into.
| Typed | As typed | Canonicalized |
|---|---|---|
\frac{x+1}{y-2} | (x + 1) / (y - 2) | (x + 1) / (y - 2) |
1 - 2x | 1 - 2x | -2 * x + 1 |
a - (b - c) | a - (b - c) | a - b + c |
x \ge 3 | x >= 3 | 3 <= x |
\int_0^1 x^2 dx | Integrate(x ^ 2, (x, 0, 1)) | Integrate(x ^ 2, (x, 0, 1)) |
\lim_{x\to 0}\frac{\sin x}{x} | Limit(Sin(x) / x, 0) | Limit(Sin(x) / x, 0) |
e^{i\pi}+1 | e ^ (i * Pi) + 1 | 1 + ExponentialE ^ (i * Pi) |
\log_2(8) | Lb(8) | Log(8, 2) |
\begin{pmatrix}1&2\\3&4\end{pmatrix} | Matrix([[1, 2], [3, 4]]) | Matrix([[1, 2], [3, 4]]) |
Copying out of a <notatio-in> gives you the first column: the field knows the LaTeX you typed, so it prints from that rather than from a canonicalized rewrite of it. An Out renders whatever the cell computed, which is usually the second.
serializeEpsil alone prints both trees badly, each in its own way, so InputForm rewrites a handful of shapes first. None of them changes what the expression means.
| Shape | Prints as | Why it is there |
|---|---|---|
InvisibleOperator(2, x) | 2x | the as-typed parse of juxtaposition |
Add(x, -2) | x - 2 | canonicalization turns subtraction into a negative addend |
Multiply(-1, x) | -x | and negation into a coefficient |
Function(do {f}, x) in Integrate | Integrate(f, …) | canonicalization wraps a body in a lambda |
Limits(x, 0, 1) | (x, 0, 1) | and its bounds in a head |
Delimiter(e) | e | the as-typed parse keeps the parentheses you wrote |
Complex(0, 1) | i | what a person types |
The point of the format is that what it prints, you can type back in. Every expression in the test corpus is printed from both trees and parsed back, and both must give the same canonical expression the original LaTeX means. A rule that changed the meaning would fail there rather than merely looking prettier.
That is also why the rules stop where they do. Reordering -2 * x + 1 into 1 - 2 * x would read better, but it is the canonical expression saying what it is; InputForm prints expressions, it does not rewrite them.
<notatio-in> yields InputForm rather than LaTeX, for the selected range or the whole field.<notatio-out> offers InputForm alongside StandardForm, MathJSON and the code forms.InputForm is the display form the REPL prints, and notatio -f inputform exports it. notatio, text and the old Notatio still resolve to it.toInputForm(json) and normalizeInputForm(json) from @enumeratio/formats.