To: J3                                                     J3/20-115r1
From: Tom Clune and Van Snyder
Subject: Syntax for rank-independent bounds
Date: 2020-February-26

Reference: 18-007r1, 19-202r2


Introduction:

Paper 19-202r2 proposed requirements and specs for BOUNDS and RANK
attributes that expand the ability to declare arrays in a
rank-agnostic context.   This paper proposes syntax for these features.



Proposed syntax:

- The keyword to specify bounds using arrays shall be BOUNDS.  It
  would be technically unambiguous to use DIMENSION instead, but the
  the new keyword is clearer for users.

- The bounds specification shall be enclosed in parentheses after the
  keyword.

- The keyword to specify rank using an integer shall be RANK.

- The rank shall be specified by a constant non-negative integer
  expression enclosed in parentheses after the keyword.

- There is no BOUNDS statement nor RANK statement.  These keywords
  only appear inside type declaration statements.


Examples:

(1)
    INTEGER, RANK(3), ALLOCATABLE :: X1

is equivalent to

    INTEGER, ALLOCATABLE :: X1(:,:,:)

(2)
    REAL, RANK(0) :: X2 ! scalar dummy

is equivalent to

    REAL :: X2

where X2 is a scalar dummy data object

(3)
     CHARACTER, BOUNDS([80,24]) :: X3 ! lower bounds are default (=1)

is equivalent to

     CHARACTER, DIMENSION(80,24) :: X3

(4)

     INTEGER, PARAMETER(*) :: UPPER = [10,10,10]
     INTEGER, BOUNDS (0:UPPER) :: X4 ! implicit broadcast of lower

is equivalent to

     INTEGER :: X4(0:10,0:10,0:10)

(5)
     REAL, BOUNDS([1,2,3]:10) :: X5 ! implicit broadcast of upper

is equivalent to

     REAL :: X5(1:10,2:10,3:10)

(6)
     INTEGER :: LB(2)
     INTEGER :: UB(2)
     INTEGER, BOUNDS(LB:UB) :: X6A, X6B ! multiple declarations

is equivalent to

     INTEGER, DIMENSION(LB(1):UB(1),LB(2):UB(2)) :: X6A, X6B

(7)

     REAL, BOUNDS([1,1,1]:) :: X7 ! assumed shape dummy

declares an assumed shape dummy argument and is equivalent to

     REAL :: X7(:,:,:)

(8)

    INTEGER, BOUNDS([7,7,7]) :: X8A, X9B(10) ! array spec overrides bounds

declares one array of rank 3 and another array of rank 1.  It is
equivalent to

    INTEGER :: X8A(7,7,7), X9B(10)


Rules and constraints:

<rank-attr-spec> <<is>>  RANK ( <scalar-int-constant-expr> )

Constraint: The value of <scalar-int-constant-expr> in a
     <rank-attr-spec> shall be nonnegative.

Constraint: If <rank-attr-spec> appears, then each declared entity
     shall be a scalar dummy data object or have have the ALLOCATABLE
     or POINTER attribute.

<bounds-attr-spec> <<is>> <explicit-shape-bounds-spec>
                   <<or>> <assumed-shape-bounds-spec>

<explicit-shape-bounds-spec> <<is>> BOUNDS ( <explicit-shape-bounds> )

<explicit-shape-bounds> <<is>> <explicit-bounds-expr>
                        <<or>> :<explicit-bounds-expr>
                        <<or>> <explicit-bounds-expr>:
			                      <explicit-bounds-expr>
                        <<or>> <scalar-int-expr>:<explicit-bounds-expr>
                        <<or>> <explicit-bounds-expr>:<scalar-int-expr>

<explicit-bounds-expr> <<is>> is <restricted-expr>

Constraint: If both specifiers in <explicit-shape-bounds> are
     <explicit-bounds-expr>, they shall have the same size.

<assumed-shape-bounds-spec> <<is>> BOUNDS ( <explicit-bounds-expr>: )

Constraint: <explicit-bounds-expr> shall be an constant size, rank 1,
     integer array.

Constraint: If the specifier is <assumed-shape-bounds-spec>, then
     every declared object shall be a dummy data object.

If only one expression appears in <explicit-shape-bounds>, it
specifies the rank and upper bounds of the array.  The rank is the size
of the <explicit-bounds-expr>.

If an expression appears before a colon in <explicit-shape-bounds> it
specifies the lower bounds of the array.  Otherwise, the lower bounds
are implicitly 1 in each dimension.

If two expressions appear in <explicit-shape-bounds> and one is a
scalar, it is broadcast to the shape of the other.

If the size of an <explicit-shape-bounds> specifier is zero, then it
declares a scalar.


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