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.

DESCRIPTION

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 CONDITIONS

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 = 
  val g : (int, int) 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.