34.9.2 Range Expressions

A range expression has one of the following forms, where R_i denote range expressions, T_i denote integer valued term expressions, S(T_i) denotes the integer value of T_i in S, X denotes a variable, I denotes an integer, and S denotes the current store.

dom(X)

evaluates to D(X,S)

{T_1,\ldots,T_n}

evaluates to \S(T_1),\ldots,S(T_n)\. Any T_i containing a variable that is not “quantified” by unionof/3 will cause the indexical to suspend until this variable has been assigned.

T_1..T_2

evaluates to the interval between S(T_1) and S(T_2).

R_1/\R_2

evaluates to the intersection of S(R_1) and S(R_2)

R_1\/R_2

evaluates to the union of S(R_1) and S(R_2)

\R_2

evaluates to the complement of S(R_2)

R_1+R_2

R_1+T_2

evaluates to S(R_2) or S(T_2) added pointwise to S(R_1)

-R_2

evaluates to S(R_2) negated pointwise

R_1-R_2

R_1-T_2

T_1-R_2

evaluates to S(R_2) or S(T_2) subtracted pointwise from S(R_1) or S(T_1)

R_1 mod R_2

R_1 mod T_2

evaluates to S(R_1) pointwise modulo S(R_2) or S(T_2)

R_1 ? R_2

evaluates to S(R_2) if S(R_1) is a non-empty set; otherwise, evaluates to the empty set. This expression is commonly used in the context (R_1 ? (inf..sup) \/ R_3), which evaluates to S(R_3) if S(R_1) is an empty set; otherwise, evaluates to inf..sup. As an optimization, R_3 is not evaluated while the value of R_1 is a non-empty set.

unionof(X,R_1,R_2)

evaluates to the union of S(E_1),\ldots,S(E_N), where each E_I has been formed by substituting K for X in R_2, where K is the I:th element of S(R_1). See N Queens, for an example of usage.

Please note: if S(R_1) is infinite, the evaluation of the indexical will be abandoned, and the indexical will simply suspend.

switch(T,MapList)

evaluates to S(E) if S(T_1) equals K and MapList contains a pair K-E. Otherwise, evaluates to the empty set. If T contains a variable that is not “quantified” by unionof/3, the indexical will suspend until this variable has been assigned.

When used in the body of an FD predicate (see Goal Expanded Constraints), a relation/3 expression expands to two indexicals, each consisting of a switch/2 expression nested inside a unionof/3 expression. Thus, the following constraints are equivalent:

     p(X, Y) +: relation(X, [1-{1},2-{1,2},3-{1,2,3}], Y).
     
     q(X, Y) +:
             X in unionof(B,dom(Y),switch(B,[1-{1,2,3},2-{2,3},3-{3}])),
             Y in unionof(B,dom(X),switch(B,[1-{1},2-{1,2},3-{1,2,3}])).