formal/hol/Help/.valmod.doc

\DOC |->

\TYPE {(|->) : 'a -> 'b -> ('a, 'b) func -> ('a, 'b) func}

\SYNOPSIS
Modify a finite partial function at one point.

\DESCRIBE
This is one of a suite of operations on finite partial functions, type
{('a,'b)func}. These may sometimes be preferable to ordinary functions since
they permit more operations such as equality comparison, extraction of domain
etc.  If {f} is a finite partial function then {(x |-> y) f} gives a modified
version that maps {x} to {y} (whether or not {f} was defined on {x} before and
regardless of the old value) but is otherwise the same.

\FAILURE
Never fails.

\EXAMPLE
{
  # let f = (1 |-> 2) undefined;;
  val f : (int, int) func = <func>
  # let g = (1 |-> 3) f;;
  val g : (int, int) func = <func>
  # apply f 1;;
  val it : int = 2
  # apply g 1;;
  val it : int = 3
}

\SEEALSO
|=>, apply, applyd, choose, combine, defined, dom, foldl, foldr,
graph, is_undefined, mapf, ran, tryapplyd, undefine, undefined.

\ENDDOC