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\DOC combine
\TYPE {combine : ('a -> 'a -> 'a) -> ('a -> bool) -> ('b, 'a) func -> ('b, 'a) func -> ('b, 'a) func}
\SYNOPSIS
Combine together two finite partial functions using pointwise operation.
\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} and {g} are finite partial functions, then {combine op z f g} will
combine them together in the following somewhat complicated way. If just one of
the functions {f} and {g} is defined at point {x}, that will give the value of
the combined function. If both {f} and {g} are defined at {x} with values {y1}
and {y2}, the value of the combined function will be {op y1 y2}. However, if
the resulting value {y} satisfies the predicate {z}, the new function will be
undefined at that point; the intuition is that the two values {y1} and {y2}
cancel each other out.
\FAILURE
Can only fail if the given operation fails.
\EXAMPLE
{
# let f = itlist I [1 |-> 2; 2 |-> 3; 3 |-> 6] undefined
and g = itlist I [1 |-> 5; 2 |-> -3] undefined;;
val f : (int, int) func = <func>
val g : (int, int) func = <func>
# graph(combine (+) (fun x -> x = 0) f g);;
val it : (int * int) list = [(1, 7); (3, 6)]
}
\USES
When finite partial functions are used to represent values with a numeric
domain (e.g. matrices or polynomials), this can be used to perform addition
pointwise by using addition for the {op} argument. Using a zero test as the
predicate {z} will ensure that no zero values are included in the result,
giving a canonical representation.
\SEEALSO
|->, |=>, apply, applyd, choose, defined, dom, foldl, foldr,
graph, is_undefined, mapf, ran, tryapplyd, undefine, undefined.
\ENDDOC
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