The Fortress Language Specification - CiteSeerX

Each element of the left-hand-side of unpasting includes an optional extent specification. An extent specification
low #num describes the indexing and the size of the given part of the matrix. The lower extent must be bound, either
before the unpasting, or earlier (left-or-above) in the unpasting. For example, suppose that an algorithm chooses to
break a matrix into 4 pieces, but retain the original indices for each piece:
barnat p,nat q(X : R r 0#p×c 0 #q ) :() = do
[ A r0 #m ×c 0 #n B r 0 #m ×c 0 +n#q−n
C r0 +m#p−m×c 0 #n D r 0 +m#p−m×c 0 +n#q−n ] = X
. . .
end
Unpasting does not directly support non-uniform decomposition, and does not provide any sort of constraint satisfaction
between the extents of the parts. For example, the following decomposition is not legal because it constrains the
split sizes to be equal with respect to unbound nat parameters:
(∗ Not allowed! ∗)
fubarnat m,nat n(X : R m×n ) :() = do
(∗ p and q unbound ∗)
[ A p×q B p×q
C p×q D p×q ] = X
. . .
end
To get this effect, the programmer should compute the constrained values:
fubarnat m,nat n(X : R 2m×2n ) :() = do
[ A m×n B m×n
C m×n D m×n ] = X
. . .
end
Some non-uniform unpastings can be obtained with composition, which can be expressed either by repeated unpasting:
unequalRowsnat m,nat n(X :R 4m×2n ) = do
[ c1 4m×n c2 4m×n ] = X
[ A m×n
C 3m×n ] = c1
[ B 3m×n
D m×n ] = c2
. . .
end
or simply by nesting matrices in the unpasting:
unequalRowsnat m,nat n(X :R 2m×4n ) = do
[ [ A m×n B m×3n ]
[ C m×3n D m×n ] ] = X
. . .
end
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