27.12 Comparisons of Lists

list1 = list2
list1 < list2

The equality operator = evaluates to true if the two lists list1 and list2 are equal and false otherwise. The inequality operator < evaluates to true if the two lists are not equal and false otherwise. Two lists list1 and list2 are equal if and only if for every index i, either both entries list1[i] and list2[i] are unbound, or both are bound and are equal, i.e., list1[i] = list2[i] is true.

    gap> [ 1, 2, 3 ] = [ 1, 2, 3 ];
    true
    gap> [ , 2, 3 ] = [ 1, 2, ];
    false
    gap> [ 1, 2, 3 ] = [ 3, 2, 1 ];
    false 

list1 < list2, list1 <= list2 list1 list2, list1 = list2

The operators <, <=, and = evaluate to true if the list list1 is less than, less than or equal to, greater than, or greater than or equal to the list list2 and to false otherwise. Lists are ordered lexicographically, with unbound entries comparing very small. That means the following. Let i be the smallest positive integer i, such that neither both entries list1[i] and list2[i] are unbound, nor both are bound and equal. Then list1 is less than list2 if either list1[i] is unbound (and list2[i] is not) or both are bound and list1[i] < list2[i] is true.

    gap> [ 1, 2, 3, 4 ] < [ 1, 2, 4, 8 ];
    true    # '<list1>[3] \<\ <list2>[3]'
    gap> [ 1, 2, 3 ] < [ 1, 2, 3, 4 ];
    true    # '<list1>[4]' is unbound and therefore very small
    gap> [ 1, , 3, 4 ] < [ 1, 2, 3 ];
    true    # '<list1>[2]' is unbound and therefore very small 

You can also compare objects of other types, for example integers or permutations with lists. Of course those objects are never equal to a list. Records (see Records) are greater than lists, objects of every other type are smaller than lists.

    gap> 123 < [ 1, 2, 3 ];
    true
    gap> [ 1, 2, 3 ] < rec( a := 123 );
    true 

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