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\DOC foldl
\TYPE {foldl : ('a -> 'b -> 'c -> 'a) -> 'a -> ('b, 'c) func -> 'a}
\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 a p} returns
{
f (f ... (f (f a x1 y1) x2 y2) ...) xn yn
}
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
The {graph} function is implemented based on the following invocation of
{foldl}, with an additional sorting phase afterwards:
{
# let f = (1 |-> 2) (2 |=> 3);;
val f : (int, int) func = <func>
# graph f;;
val it : (int * int) list = [(1, 2); (2, 3)]
# foldl (fun a x y -> (x,y)::a) [] f;;
val it : (int * int) list = [(1, 2); (2, 3)]
}
Note that in this case the order happened to be the same, but this is an
accident.
\SEEALSO
|->, |=>, apply, applyd, choose, combine, defined, dom, foldr,
graph, is_undefined, mapf, ran, tryapplyd, undefine, undefined.
\ENDDOC
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