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Predicate between/3
Availability:built-in
between(+Low, +High, ?Value)
Low and High are integers, High ≥Low. If Value is an integer, Low ≤Value ≤High. When Value is a variable it is successively bound to all integers between Low and High. If High is inf or infinite121We prefer infinite, but some other Prolog systems already use inf for infinity; we accept both for the time being. between/3 is true iff Value ≥Low, a feature that is particularly interesting for generating integers from a certain value.

Examples

Generate solutions

Generate solutions

?- length(L, 3), maplist(between(0, 1), L).
L = [0, 0, 0] ;
L = [0, 0, 1] ;
L = [0, 1, 0] ;
L = [0, 1, 1] ;
L = [1, 0, 0] ;
L = [1, 0, 1] ;
L = [1, 1, 0] ;
L = [1, 1, 1].
Test for integers in a range

Test for integers in a range

?- maplist(between(1, 3), [1, 2, 3]).
true.

?- maplist(between(1, 3), [1, 2, 99]).
false.
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LogicalCaptain said (2020-05-16T17:05:03):0 upvotes 0 0 downvotes
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Doc needs help

a feature that is particularly interesting for generating integers from a certain value.

... in failure-driven loops.

But failure-driven loops are not particularly interesting (in fact, they are dangerous in practice as they can quickly morph into infinite loops amazingly easily).

Some potentially useful notes

About `between∕3`

Extension of between∕3: a "between" which also takes a negative or positive "step" value

Values are no pre-generated with between/3 and then linearly transformed, but properly generated "on need".

These are defined:

  • `between(+Start,+End,+Step,?Value)`
  • `between(+Start,+End,+Step,?Value,?OptionList)`

Examples:

?-
between(10,20,3,L).

L = 10 ;
L = 13 ;
L = 16 ;
L = 19.
?-
between(10,-10,-3,L).

L = 10 ;
L = 7 ;
L = 4 ;
L = 1 ;
L = -2 ;
L = -5 ;
L = -8.

Extension of between∕3: a "between" which which is able to propose valid intervals

The standard between/3 dataflow allows only to flow from a known (LowerLimit,UpperLimit) to a sequence of Value. Why not allow alternative directions:

  • (LowerLimit,Value) to a sequence of UpperLimit
  • (UpperLimit,Value) to a sequence of LowerLimit
  • Value to a sequence of (LowerLimit,UpperLimit)

These are defined:

  • `between_x(?Low, ?High, ?Value)`

For example, define:

intervalsize(_,inf,inf)        :- !.
intervalsize(Lower,Upper,Size) :- Size is Upper-Lower+1.

Then generate intervals around 0 (below, the printout has been rearranged by hand):

?-
between_x(Lower,Upper,0), intervalsize(Lower,Upper,Size), format("~q:[~q,~q]\n",[Size,Lower,Upper]).

1:[0,0]
2:[-1,0]  2:[0,1]
3:[-2,0]  3:[-1,1]  3:[0,2]
4:[-3,0]  4:[-2,1]  4:[-1,2]  4:[0,3]
5:[-4,0]  5:[-3,1]  5:[-2,2]  5:[-1,3]  5:[0,4]
...

Why doesn't this exist

Instead of trying puzzling code to obtain a list of integers:

% ============================================================================
% Create a list of integers, monotonically increasing by 1.
%
% TODO: Make it work in "reverse direction", too.
% TODO: A lazy list using freeze/2 that generates the next integer on need
%
% create_list_of_integers_between(+Low,+High,?List)
%
% create_list_of_integers_between(+HighInclusive:['high_yes','high_no'],+Low,+High,?List)
% ============================================================================

list_of_integers_between(Low,High,List) :-
   list_of_integers_between(high_yes,Low,High,List).

list_of_integers_between(high_yes,Low,High,List) :-
   !,
   bagof(X,between(Low,High,X),List).
   
list_of_integers_between(high_no,Low,High,List) :-
   !,
   ActualHigh is High-1,
   bagof(X,between(Low,ActualHigh,X),List).
   
list_of_integers_between(HighInclusive,_,_,_) :-
   domain_error([high_yes,high_no],HighInclusive).
?- list_of_integers_between(0,4,L).
L = [0,1,2,3,4].

?- list_of_integers_between(false,0,4,L).
L = [0,1,2,3].

?- list_of_integers_between(true,0,4,L).
L = [0,1,2,3,4].

What would also be nice

A between/5 for which one can specify whether the interval limit is inclusive or exclusive, because performing +1 / -1 operations is a bit annoying.

between(LowLimit,Low,High,HighLimit,Value)

Then one could do

between('[',0,10,'[',Value).

to get the behaviour of between(0,9,Value).

A weird predicate that I don't know what it would be useful for

repeated_success(X) :-
   between(0,10,X),
   between(X,10,_).
?- repeated_success(8).
true ;
true ;
true.

?- repeated_success(9).
true ;
true.

?- repeated_success(10).
true.

?- repeated_success(11).
false.