Interprocedural array analysis must provide precise results in
the presence of array reshapes at procedure boundaries,
as when a slice of
an array is passed into a procedure, and as in linearization,
when a multi-dimensional array in one procedure is treated as a linear
array in another.
In the following example, FOO passes BAR
the Kth column of the array X. This 10000-element vector
from FOO,
is manipulated as a 
array in
BAR.
SUBROUTINE FOO SUBROUTINE BAR(Y)
INTEGER X(10000, 10) INTEGER Y(100, 100)
.... DO 9 I= 1,100
CALL BAR(X(1, K)) DO 9 J= 1,50
Y(I,J) = ...
9 CONTINUE
Mapping an array summary from callee to caller is not a simple rename operation. We perform this mapping by deriving inequalities for the indices of the actual parameter in terms of the indices of the formal parameter and use the projection operation to eliminate the formal parameter's indices.
We formalize the mapping of summary S
for an n-dimensional formal array parameter F,
where 
is passed at the call site and actual
A is an m-dimensional array,
using the mapping function:
Where
are variables representing the indices of
accesses to array F.
are variables representing the indices of
accesses to array A.
is the set of bounds for the array F given by its
type declaration. (Note that the exact bounds of the outermost dimension
are not required.)
is the set of bounds for the array A given by its type
declaration.
describes the conditions under which an access 
in the procedure and
an access 
in the callee refer to the same
location.
This occurs when the memory offset of 
is equal to
the memory offset of 
minus the memory offset of
.
This relationship between memory offsets is represented as an equality
relation; other known facts about variables used in the equality may
be included in the system.
Thus when when using the mapping function on the summary of the array Y at the start of subroutine BAR:
This approach handles precisely cases where complex numbers in one procedure are treated as real numbers in another by modeling a complex number as an array with two elements. Some reshapes are not handled precisely. If array dimensions are unknown, for example, there is no linear relationship between the indices of the actual and formal parameters, and unless the unknown dimensions are identical, we must approximate.