1:- module(reif_utils,
    2  [ (#<)/3
    3  , (#>)/3
    4  , (#=<)/3
    5  , (#>=)/3
    6  , (==)/3
    7  , (\==)/3
    8  , (@<)/3
    9  , (@=<)/3
   10  , (@>)/3
   11  , (@>=)/3
   12  , ($<)/3
   13  , ($=<)/3
   14  , ($>)/3
   15  , ($>=)/3
   16  , op(700, xfx, #>)
   17  , op(700, xfx, #<)
   18  , op(700, xfx, #>=)
   19  , op(700, xfx, #=<)
   20  , op(700, xfx, ==)
   21  , op(700, xfx, \==)
   22  , op(700, xfx, @<)
   23  , op(700, xfx, @=<)
   24  , op(700, xfx, @>)
   25  , op(700, xfx, @>=)
   26  , op(700, xfx, $<)
   27  , op(700, xfx, $=<)
   28  , op(700, xfx, $>)
   29  , op(700, xfx, $>=)
   30  ]).   31
   32:- use_module(library(clpfd)).   33
   34% Integer representations for booleans
   35bool_rep(true, 1).
   36bool_rep(false, 0).
   37
   38%! #<(+X:integer, +Y:integer, +Cond:boolean) is semidet.
   39%! #<(+X:integer, +Y:integer, -Cond:boolean) is det.
   40%! #<(+X:integer, -Y:integer, +Cond:boolean) is det.
   41%! #<(+X:integer, -Y:integer, -Cond:boolean) is multi.
   42%! #<(-X:integer, +Y:integer, +Cond:boolean) is det.
   43%! #<(-X:integer, +Y:integer, -Cond:boolean) is multi.
   44%! #<(-X:integer, -Y:integer, +Cond:boolean) is det.
   45%! #<(-X:integer, -Y:integer, -Cond:boolean) is multi.
   46%
   47% True whenever 1) X is strictly less than Y and Cond is true, or 2) whenever
   48% X is greater than or equal to Y and Cond is false. Intended to have zero unnecessary
   49% choice points.
   50#<(X, Y, Cond) :-
   51  (X #< Y #<==> B), bool_rep(Cond, B).
   52
   53%! #>(+X:integer, +Y:integer, +Cond:boolean) is semidet.
   54%! #>(+X:integer, +Y:integer, -Cond:boolean) is det.
   55%! #>(+X:integer, -Y:integer, +Cond:boolean) is det.
   56%! #>(+X:integer, -Y:integer, -Cond:boolean) is multi.
   57%! #>(-X:integer, +Y:integer, +Cond:boolean) is det.
   58%! #>(-X:integer, +Y:integer, -Cond:boolean) is multi.
   59%! #>(-X:integer, -Y:integer, +Cond:boolean) is det.
   60%! #>(-X:integer, -Y:integer, -Cond:boolean) is multi.
   61%
   62% True whenever 1) X is strictly greater than Y and Cond is true, or 2) whenever
   63% X is less than or equal to Y and Cond is false. Intended to have zero unnecessary
   64% choice points.
   65#>(X, Y, Cond) :-
   66  (X #> Y #<==> B), bool_rep(Cond, B).
   67
   68%! #=<(+X:integer, +Y:integer, +Cond:boolean) is semidet.
   69%! #=<(+X:integer, +Y:integer, -Cond:boolean) is det.
   70%! #=<(+X:integer, -Y:integer, +Cond:boolean) is det.
   71%! #=<(+X:integer, -Y:integer, -Cond:boolean) is multi.
   72%! #=<(-X:integer, +Y:integer, +Cond:boolean) is det.
   73%! #=<(-X:integer, +Y:integer, -Cond:boolean) is multi.
   74%! #=<(-X:integer, -Y:integer, +Cond:boolean) is det.
   75%! #=<(-X:integer, -Y:integer, -Cond:boolean) is multi.
   76%
   77% True whenever 1) X is less than or equal to Y and Cond is true, or 2) whenever
   78% X is strictly greater than Y and Cond is false. Intended to have zero unnecessary
   79% choice points.
   80#=<(X, Y, Cond) :-
   81  (X #=< Y #<==> B), bool_rep(Cond, B).
   82
   83%! #>=(+X:integer, +Y:integer, +Cond:boolean) is semidet.
   84%! #>=(+X:integer, +Y:integer, -Cond:boolean) is det.
   85%! #>=(+X:integer, -Y:integer, +Cond:boolean) is det.
   86%! #>=(+X:integer, -Y:integer, -Cond:boolean) is multi.
   87%! #>=(-X:integer, +Y:integer, +Cond:boolean) is det.
   88%! #>=(-X:integer, +Y:integer, -Cond:boolean) is multi.
   89%! #>=(-X:integer, -Y:integer, +Cond:boolean) is det.
   90%! #>=(-X:integer, -Y:integer, -Cond:boolean) is multi.
   91%
   92% True whenever 1) X is greater than or equal to Y and Cond is true, or 2) whenever
   93% X is strictly less than Y and Cond is false. Intended to have zero unnecessary
   94% choice points.
   95#>=(X, Y, Cond) :-
   96  (X #>= Y #<==> B), bool_rep(Cond, B).

 ==(+X, +Y, +Cond:boolean) is semidet

==(+X, +Y, -Cond:boolean) is det

==(+X, -Y, +Cond:boolean) is semidet

==(+X, -Y, -Cond:boolean) is det

==(-X, +Y, +Cond:boolean) is semidet

==(-X, +Y, -Cond:boolean) is det

==(-X, -Y, +Cond:boolean) is semidet

==(-X, -Y, -Cond:boolean) is det

Impure reified term (dis)equivalence: this predicate is true whenever 1) X == Y and Cond is true or 2) X \== Y and Cond is false. All modes are supported; intended to have zero unnecessary choice points. This predicate is not steadfast: ==(X, Y, false), X = a, Y = a is true with solution X = a, Y = a but ==(a, a, false) is false.

  111==(X, Y, Cond) :-
  112  (  var(Cond)
  113  -> ( X == Y -> Cond = true ; Cond = false )
  114  ;  ground(Cond)
  115  -> ( Cond = true -> X == Y ; Cond = false -> X \== Y)
  116  ).

 \==(+X, +Y, +Cond:boolean) is semidet

\==(+X, +Y, -Cond:boolean) is det

\==(+X, -Y, +Cond:boolean) is semidet

\==(+X, -Y, -Cond:boolean) is det

\==(-X, +Y, +Cond:boolean) is semidet

\==(-X, +Y, -Cond:boolean) is det

\==(-X, -Y, +Cond:boolean) is semidet

\==(-X, -Y, -Cond:boolean) is det

Impure reified term (dis)equivalence: this predicate is true whenever 1) X \== Y and Cond is true or 2) X == Y and Cond is false. All modes are supported; intended to have zero unnecessary choice points. This predicate is not steadfast: \==(X, Y, true), X = a, Y = a is true with solution X = a, Y = a but \==(a, a, true) is false.

  131\==(X, Y, Cond) :-
  132  (  var(Cond)
  133  -> ( X \== Y -> Cond = true ; Cond = false )
  134  ;  ground(Cond)
  135  -> ( Cond = true -> X \== Y ; Cond = false -> X == Y)
  136  ).

 @<(+X, +Y, +Cond:boolean) is semidet

@<(+X, +Y, -Cond:boolean) is det

@<(+X, -Y, +Cond:boolean) is semidet

@<(+X, -Y, -Cond:boolean) is det

@<(-X, +Y, +Cond:boolean) is semidet

@<(-X, +Y, -Cond:boolean) is det

@<(-X, -Y, +Cond:boolean) is semidet

@<(-X, -Y, -Cond:boolean) is det

Impure reified term comparison: this predicate is true whenever 1) X @< Y and Cond is true or 2) X @>= Y and Cond is false. All modes are supported; intended to have zero unnecessary choice points. This predicate is not steadfast: @<(X, Y, true), X = b, Y = a is true with solution X = b, Y = a but @<(b, a, true) is false.

  151@<(X, Y, Cond) :-
  152  (  var(Cond)
  153  -> ( X @< Y -> Cond = true ; Cond = false )
  154  ;  ground(Cond)
  155  -> ( Cond = true -> X @< Y ; Cond = false -> X @>= Y )
  156  ).

 @=<(+X, +Y, +Cond:boolean) is semidet

@=<(+X, +Y, -Cond:boolean) is det

@=<(+X, -Y, +Cond:boolean) is semidet

@=<(+X, -Y, -Cond:boolean) is det

@=<(-X, +Y, +Cond:boolean) is semidet

@=<(-X, +Y, -Cond:boolean) is det

@=<(-X, -Y, +Cond:boolean) is semidet

@=<(-X, -Y, -Cond:boolean) is det

Impure reified term comparison: this predicate is true whenever 1) X @=< Y and Cond is true or 2) X @> Y and Cond is false. All modes are supported; intended to have zero unnecessary choice points. This predicate is not steadfast: @=<(X, Y, true), X = b, Y = a is true with solution X = b, Y = a but @=<(b, a, true) is false.

  171@=<(X, Y, Cond) :-
  172  (  var(Cond)
  173  -> ( X @=< Y -> Cond = true ; Cond = false )
  174  ;  ground(Cond)
  175  -> ( Cond = true -> X @=< Y ; Cond = false -> X @> Y )
  176  ).

 @>(+X, +Y, +Cond:boolean) is semidet

@>(+X, +Y, -Cond:boolean) is det

@>(+X, -Y, +Cond:boolean) is semidet

@>(+X, -Y, -Cond:boolean) is det

@>(-X, +Y, +Cond:boolean) is semidet

@>(-X, +Y, -Cond:boolean) is det

@>(-X, -Y, +Cond:boolean) is semidet

@>(-X, -Y, -Cond:boolean) is det

Impure reified term comparison: this predicate is true whenever 1) X @> Y and Cond is true or 2) X @=< Y and Cond is false. All modes are supported; intended to have zero unnecessary choice points. This predicate is not steadfast: @>(X, Y, false), X = b, Y = a is true with solution X = b, Y = a but @>(b, a, false) is false.

  191@>(X, Y, Cond) :-
  192  (  var(Cond)
  193  -> ( X @> Y -> Cond = true ; Cond = false )
  194  ;  ground(Cond)
  195  -> ( Cond = true -> X @> Y ; Cond = false -> X @=< Y )
  196  ).

 @>=(+X, +Y, +Cond:boolean) is semidet

@>=(+X, +Y, -Cond:boolean) is det

@>=(+X, -Y, +Cond:boolean) is semidet

@>=(+X, -Y, -Cond:boolean) is det

@>=(-X, +Y, +Cond:boolean) is semidet

@>=(-X, +Y, -Cond:boolean) is det

@>=(-X, -Y, +Cond:boolean) is semidet

@>=(-X, -Y, -Cond:boolean) is det

Impure reified term comparison: this predicate is true whenever 1) X @>= Y and Cond is true or 2) X @< Y and Cond is false. All modes are supported; intended to have zero unnecessary choice points. This predicate is not steadfast: @>=(X, Y, false), X = b, Y = a is true with solution X = b, Y = a but @>=(b, a, false) is false.

  211@>=(X, Y, Cond) :-
  212  (  var(Cond)
  213  -> ( X @>= Y -> Cond = true ; Cond = false )
  214  ;  ground(Cond)
  215  -> ( Cond = true -> X @>= Y ; Cond = false -> X @< Y )
  216  ).

 $<(+X, +Y, +Cond:boolean) is semidet

$<(+X, +Y, -Cond:boolean) is det

$<(+X, -Y, +Cond:boolean) is det

$<(+X, -Y, -Cond:boolean) is det

$<(-X, +Y, +Cond:boolean) is det

$<(-X, +Y, -Cond:boolean) is det

$<(-X, -Y, +Cond:boolean) is det

$<(-X, -Y, -Cond:boolean) is det

Pure reified term comparison: this predicate is true whenever 1) X @< Y upon sufficient instantiation of both variables and Cond is true or 2) X @>= Y upon sufficient instantiation of both variables and Cond is false. All modes are supported; intended to have zero unnecessary choice points. This predicate guarantees referential transparency by delaying evaluation where necessary.

  232$<(X, Y, Cond) :-
  233  (  var(Cond)
  234  -> when(?=(X, Y), ( X @< Y -> Cond = true ; Cond = false ) )
  235  ;  ground(Cond)
  236  -> ( Cond = true -> when(?=(X, Y), X @< Y) ; Cond = false -> when(?=(X, Y), X @>= Y) )
  237  ).

 $=<(+X, +Y, +Cond:boolean) is semidet

$=<(+X, +Y, -Cond:boolean) is det

$=<(+X, -Y, +Cond:boolean) is det

$=<(+X, -Y, -Cond:boolean) is det

$=<(-X, +Y, +Cond:boolean) is det

$=<(-X, +Y, -Cond:boolean) is det

$=<(-X, -Y, +Cond:boolean) is det

$=<(-X, -Y, -Cond:boolean) is det

Pure reified term comparison: this predicate is true whenever 1) X @=< Y upon sufficient instantiation of both variables and Cond is true or 2) X @> Y upon sufficient instantiation of both variables and Cond is false. All modes are supported; intended to have zero unnecessary choice points. This predicate guarantees referential transparency by delaying evaluation where necessary.

  253$=<(X, Y, Cond) :-
  254  (  var(Cond)
  255  -> when(?=(X, Y), ( X @=< Y -> Cond = true ; Cond = false ) )
  256  ;  ground(Cond)
  257  -> ( Cond = true -> when(?=(X, Y), X @=< Y) ; Cond = false -> when(?=(X, Y), X @> Y) )
  258  ).

 $>(+X, +Y, +Cond:boolean) is semidet

$>(+X, +Y, -Cond:boolean) is det

$>(+X, -Y, +Cond:boolean) is det

$>(+X, -Y, -Cond:boolean) is det

$>(-X, +Y, +Cond:boolean) is det

$>(-X, +Y, -Cond:boolean) is det

$>(-X, -Y, +Cond:boolean) is det

$>(-X, -Y, -Cond:boolean) is det

Pure reified term comparison: this predicate is true whenever 1) X @> Y upon sufficient instantiation of both variables and Cond is true or 2) X @=< Y upon sufficient instantiation of both variables and Cond is false. All modes are supported; intended to have zero unnecessary choice points. This predicate guarantees referential transparency by delaying evaluation where necessary.

  274$>(X, Y, Cond) :-
  275  (  var(Cond)
  276  -> when(?=(X, Y), ( X @> Y -> Cond = true ; Cond = false ) )
  277  ;  ground(Cond)
  278  -> ( Cond = true -> when(?=(X, Y), X @> Y) ; Cond = false -> when(?=(X, Y), X @=< Y) )
  279  ).

 $>=(+X, +Y, +Cond:boolean) is semidet

$>=(+X, +Y, -Cond:boolean) is det

$>=(+X, -Y, +Cond:boolean) is det

$>=(+X, -Y, -Cond:boolean) is det

$>=(-X, +Y, +Cond:boolean) is det

$>=(-X, +Y, -Cond:boolean) is det

$>=(-X, -Y, +Cond:boolean) is det

$>=(-X, -Y, -Cond:boolean) is det

Pure reified term comparison: this predicate is true whenever 1) X @>= Y upon sufficient instantiation of both variables and Cond is true or 2) X @< Y upon sufficient instantiation of both variables and Cond is false. All modes are supported; intended to have zero unnecessary choice points. This predicate guarantees referential transparency by delaying evaluation where necessary.

  295$>=(X, Y, Cond) :-
  296  (  var(Cond)
  297  -> when(?=(X, Y), ( X @>= Y -> Cond = true ; Cond = false ) )
  298  ;  ground(Cond)
  299  -> ( Cond = true -> when(?=(X, Y), X @>= Y) ; Cond = false -> when(?=(X, Y), X @< Y) )
  300  )