The result of unapply(expr, x) is a functional operator. Applying this operator to x gives the original expression.

In particular, for a function $f\left(x\right)$,

To construct a multi-argument operator from a multi-variate expression, list all the variables as arguments to unapply or explicitly put all variables in a list and pass it as the second argument to unapply.

Use the unapply command when constructing an operator using contents of variables or evaluated expressions.

The variable names may be simple names of type symbol (e.g., x, y, z), or names with type specifiers using :: (e.g, x::numeric, y::integer, z::float).

The following optional arguments are available.

numeric=variables

For this option variables must be a set or list of variable names, or a single variable name, all of which must correspond to a variable in the input for unapply (that is, in either the list or the specified variable names). With this option, unapply constructs an operator that returns unevaluated whenever the specified variables do not evaluate to numeric values.

Note: This option cannot be used for inputs containing derivatives, such as $\frac{\ⅆ}{\ⅆx}f\left(x\right)$ or $\mathrm{DEsol}$ structures.

numeric

This is simply a shortcut for numeric=variables, which places all the variables in the numeric list.

proc_options=keywords

This option must be a keyword, or list or set of keywords. The unapply command constructs the operator with the specified keywords as options. By default, the options {operator,arrow} are used, but any of arrow, inline, operator, remember, or system are valid keywords.

The unapply command implements the lambda-expressions of lambda calculus.

$p≔x^2+\sin \left(x\right)+1$

$p≔x^2+\sin \left(x\right)+1$

$f≔\mathrm{unapply}\left(p\,x\right)$

$f≔x\mapsto x^2+\sin \left(x\right)+1$

$f\left(\frac{\mathrm{\pi }}{6}\right)$

$\frac{{\mathrm{\pi }}^2}{36}+\frac{3}{2}$

$q≔x^2+y^3+1$

$q≔y^3+x^2+1$

$f≔\mathrm{unapply}\left(q\,x\right)$

$f≔x\mapsto y^3+x^2+1$

$f\left(2\right)$

$y^3+5$

$g≔\mathrm{unapply}\left(q\,x\,y\right)$

$g≔\left(x\,y\right)\mapsto y^3+x^2+1$

$g\left(2\,3\right)$

$32$

$h≔\mathrm{unapply}\left(q\,\left[x\,y\right]\right)$

$h≔\left(x\,y\right)\mapsto y^3+x^2+1$

$h\left(2\,3\right)$

$32$

$\mathrm{f1}≔\mathrm{unapply}\left(x^2+1\,x\,\mathrm{numeric}\right)$

$\mathrm{f1}≔\mathbf{proc}\left(x\right)\mathbf{local}\mathrm{unnamed}\&semi;\mathbf{if}\mathrm{type}\left(\mathrm{evalf}\left(x\right)\&comma;\&apos;\mathrm{numeric}\&apos;\right)\mathbf{then}x\&Hat;2\&plus;1\mathbf{elif}\mathrm{procname}<>\&apos;\mathrm{unknown}\&apos;\mathbf{and}\mathbf{not}\mathrm{member}\left(\mathrm{sprintf}\left(''\%a''\&comma;\mathrm{procname}\right)\&comma;\left\{''\%''\&comma;''\%\%''\&comma;''\%\%\%''\right\}\right)\mathbf{then}\&apos;\mathrm{procname}\&apos;\left(x\right)\mathbf{else}\mathrm{unnamed}≔\mathrm{pointto}\left(\left(\left[\begin{array}{r}36893627890009376740\end{array}\right]\right)\&lsqb;1\&rsqb;\right)\&semi;\&apos;\mathrm{unnamed}\&apos;\left(x\right)\mathbf{end\; if}\mathbf{end\; proc}$

$\mathrm{f1}\left(1\right)$

$2$

$\mathrm{f1}\left(x\right)$

$\mathrm{f1}\left(x\right)$

$\mathrm{f2}≔\mathrm{unapply}\left(x^2+1\&comma;x::\mathrm{numeric}\right)$

$\mathrm{f2}≔x::\mathrm{numeric}\mapsto x^2+1$

$\mathrm{f2}\left(1\right)$

$2$

$\mathrm{f2}\left(x\right)$

Error, invalid input: f2 expects its 1st argument, x, to be of type numeric, but received x

f := proc() lprint(`called`); 0; end proc;

$f≔\mathbf{proc}\left(\right)\mathrm{lprint}\left(\mathrm{called}\right)\&semi;0\mathbf{end\; proc}$

$\mathrm{pol}≔\mathrm{unapply}\left(x^2+3x+1+'f'\left(\right)\&comma;x\&comma;\mathrm{proc\_options}=\left\{\mathrm{arrow}\&comma;\mathrm{operator}\&comma;\mathrm{remember}\right\}\right)$

$\mathrm{pol}≔x\mapsto x^2+3\cdot x+1+f\left(\right)$

$\mathrm{pol}\left(1\right)$

called

$5$

$\mathrm{pol}\left(2\right)$

called

$11$

$\mathrm{pol}\left(1\right)$

$5$

Gonnet, G.H. "An Implementation of Operators for Symbolic Algebra Systems" SYMSAC. July 1986.