Can someone help me to understand a couple of things in the mini zinc tutorial:
function set of $T: 'intersect'(set of $T: x, set of $T: y)
This return the intersection of sets x and y . Obviously x and y are sets - but what does $T mean in this context?
function var set of int: 'union'(var set of int: x, var set of int: y)
Return the union of sets x and y. from what I understand x is a set of integers and y is also a set of integers - but what does 'var set of int' mean? what is 'var' ?
function set of $U: array_union(array [$T] of set of $U: x)
Return the union of the sets in array x. Could you explain:
function set of $U
and:
array_union(array [$T] of set of $U: x)
$T or $U means any type. $T can be int, float, etc. If it says int, then you must supply a int, but if it says $T, you can supply any type.
In the expression function set of $U: array_union(array [$T] of set of $U: x), $U and $T can be different types but in function set of $T: 'intersect'(set of $T: x, set of $T: y) all $T have to be the same. Different variables for $ just means that they can be a different type. Same variable $ name and all need to have the same type.
Example: function set of float: array_union(array [int] of set of float: x) and function set of int: 'intersect'(set of int: x, set of int: y).
array [$T] is a bit special and just means that the array can be of any dimension. i.e array [int], array [int,int] or array [int,int,int,int,int] etc. So array [$T] of set of $U means that we have an array of size $T, for example [int,int], a two dimensional array. This array is filled with sets of any type. For example sets of integers, for example {1,4,7,145}.
var int and int are different types. int is just regular numbers. var int is variable integers, i.e those varaibles that MiniZinc are trying to assign a value to and solve the problem.
For example var 1..150: age or
var int: age if we want to solve some age problem.