Arrays and the array subscript notation (not in ISO)

In B-Prolog, the maximum arity of a structure is 65535. This entails that a structure can be used as a one-dimensional array and a multi-dimensional array can be represented as a structure of structures. To facilitate creating and manipulating arrays, B-Prolog provides the following built-ins.

• new_array(X,Dims): Bind X to a new array of the dimensions as specified by Dims, which is a list of positive integers. An array of n elements is represented as a structure with the functor '[]'/n. All the array elements are initialized to be free variables. For example,

        | ?- new_array(X,[2,3])
        X = []([](_360,_364,_368),[](_370,_374,_378))
  

• a2_new(X,N1,N2): The same as new_array(X,[N1,N2]).

• a3_new(X,N1,N2,N3): The same as new_array(X,[N1,N2,N3]).

• is_array(A): Succeeds if A is a structure whose functor is '[]'/n.

The built-in predicate arg/3 can be used to access array elements, but it requires a temporary variable to store the result, and a chain of calls to access an element of a multi-dimensional array. To facilitate accessing array elements, B-Prolog supports the array subscript notation $X$[$I_1$,...,$I_n$], where $X$ is a structure and each $I_i$ is an integer expression. This common notation for accessing arrays is, however, not part of the standard Prolog syntax. To accommodate this notation, the parser is modified to insert a token $^\wedge$ between a variable token and [. So, the notation $X$[$I_1$,...,$I_n$] is just a shorthand for $X$$^\wedge$[$I_1$,...,$I_n$]. This notation is interpreted as an array access when it occurs in an arithmetic expression, a constraint, or as an argument of a call to @=/2. In any other context, it is treated as the term itself. The array subscript notation can also be used to access elements of lists. For example, the nth/3 and nth0/3 predicates can be defined as follows:

    nth(I,L,E) :- E @= L[I].
    nth0(I,L,E) :- E @= L[I+1].

In arithmetic expressions and arithmetic constraints, the term $X^\wedge$length means the size of the compound term $X$. Examples:

      ?-S=f(1,1), Size is S^length.
      Size=2

      ?-L=[1,1], L^length=:=1+1.
      yes

The term $X^\wedge$length is also interpreted as the size of $X$ when it occurs as one of the arguments of a call to @=/2. Examples:

      ?-S=f(1,1), Size @= S^length.
      Size=2

In any other context, the term $X^\wedge$length is interpreted as it is.

The operator @:= is provided for destructively updating an argument of a structure or an element of a list. For example:

      ?-S=f(1,1), S[1] @:= 2.
      S=f(2,1)

The update is undone upon backtracking.

The following built-ins on arrays have become obsolete since they can be easily implemented using foreach and list comprehension (see Chapter 4).

• X^rows @= Rows: Rows is a list of rows in the array X. The dimension of X must be no less than 2.

• X^columns @= Cols: Cols is a list of columns in the array X. The dimension of X must be no less than 2.

• X^diagonal1 @= Diag: Diag is a list of elements in the left-up-diagonal (elements Xn1,...,X1n) of array X, where the dimension of X must be 2 and the number of rows and the number of columns must be equal.

• X^diagonal2 @= Diag: Diag is a list of elements in the left-down-diagonal (elements X11,...,Xnn) of array X, where the dimension of X must be 2 and the number of rows and the number of columns must be equal.

• a2_get(X,I,J,Xij): The same as X^[I,J] @= Xij. .

• a3_get(X,I,J,K,Xijk): The same as X^[I,J,K] @= Xijk. .

• array_to_list(X,List): The term List is a list of all elements in array X. Suppose X is an n dimensional array and the sizes of the dimensions are N1, N2, ..., and Nn. Then List contains the elements with indexes from [1,...,1], [1,...,2], to [N1,N2,...,Nn].