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## 11.8 Conditionals

When packages have parameters, you can say that an operation is or is not conditional exported depending on the values of those parameters. When the domain of objects S has an < operation, we can supply one-argument versions of bubbleSort and insertionSort which use this operation for sorting. The presence of the operation < is guaranteed when S is an ordered set.

Exports == with
bubbleSort!: (A,(S,S) -> Boolean) -> A
insertionSort!: (A, (S,S) -> Boolean) -> A
if S has OrderedSet then
bubbleSort!: A -> A
insertionSort!: A -> A

In addition to exporting the one-argument sort operations sort:bubble conditionally, we must provide conditional definitions for the sort:insertion operations in the Implementation part. This is easy: just have the one-argument functions call the corresponding two-argument functions with the operation < from S.

Implementation == add
...
if S has OrderedSet then
bubbleSort!(m) == bubbleSort!(m,< $S)
insertionSort!(m) == insertionSort!(m,< $S)

In ugUserBlocks , we give an alternative definition of bubbleSort using first first List and rest rest List that is more efficient for a list (for which access to any element requires traversing the list from its first node). To implement a more efficient algorithm for lists, we need the operation setelt which allows us to destructively change the first and rest of a list. Using Browse, you find that these operations come from category UnaryRecursiveAggregate. Several aggregate types are unary recursive aggregates including those of List and AssociationList. We provide two different implementations for bubbleSort! and insertionSort!: one for list-like structures, another for array-like structures.

Implementation == add
...
if A has UnaryRecursiveAggregate(S) then
bubbleSort!(m,fn) ==
empty? m => m
l := m
while not empty? (r := l.rest) repeat
r := bubbleSort! r
x := l.first
if fn(r.first,x) then
l.first := r.first
r.first := x
l.rest := r
l := l.rest
m
insertionSort!(m,fn) ==
...

The ordering of definitions is important. The standard definitions come first and then the predicate

A has UnaryRecursiveAggregate(S)

is evaluated. If true, the special definitions cover up the standard ones.

Another equivalent way to write the capsule is to use an if-then-else expression: if

if A has UnaryRecursiveAggregate(S) then
...
else
...
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