Map the arguments and return value of functions.

General use:

• f $* g1 $$ g2 … $$ gn *$ h = \x1 … xn -> h (f (g1 x1) (g2 x2) … (gn xn))

Examples:

• on f g = f $* g $$ g *$ id
• comparing f = compare $* f $$ f *$ id
• f . g = f $* g *$ id

Related work:

• Semantic Editor Combinators (Conal Elliott, 2008/11/24). Introduces composable editors for function arguments and return values.
• Pointless Fun (Matt Hellige, 2008/12/03). Derives a similar operator named ~>. This operator composes an editor which can then be applied to the subject to edit. This better agrees with Conal's concept of Semantic Editor Combinators. In contrast, $* includes the subject as part of the editor, though you can write ($* g1 $$ g2 … $$ gn *$ h) for an editor independent of the subject. Also, ~> is right-associative whereas $* and $$ are left-associative.
• TypeCompose version 0.9.11 (Conal Elliott, 2016/01/15). Package including an implementation of ~>.