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\DOC foldr
\TYPE {foldr : ('a -> 'b -> 'c -> 'c) -> ('a, 'b) func -> 'c -> 'c}
\SYNOPSIS
Folds an operation iteratively over the graph of a finite partial function.
\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 a finite partial function {p} has graph {[x1,y1; ...; xn,yn]} then the
application {foldl f p a} returns
{
f x1 y1 (f x2 y2 (f x3 y3 (f ... (f xn yn a) ... )))
}
Note that the order in which the pairs are operated on depends on the internal
structure of the finite partial function, and is often not the most obvious.
\FAILURE
Fails if one of the embedded function applications does.
\EXAMPLE
{
# let f = (1 |-> 2) (2 |=> 3);;
val f : (int, int) func = <func>
# graph f;;
val it : (int * int) list = [(1, 2); (2, 3)]
# foldr (fun x y a -> (x,y)::a) f [];;
val it : (int * int) list = [(2, 3); (1, 2)]
}
Note how the pairs are actually processed in the opposite order to the order in
which they are presented by {graph}. The order will in general not be obvious,
and generally this is applied to operations with appropriate commutativity
properties.
\SEEALSO
|->, |=>, apply, applyd, choose, combine, defined, dom, foldl,
graph, is_undefined, mapf, ran, tryapplyd, undefine, undefined.
\ENDDOC
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