11.10 How Packages Work

Recall that packages as abstract datatypes are compiled independently and put into the library. The curious reader may ask: How is the interpreter able to find an operation such as bubbleSort!? Also, how is a single compiled function such as bubbleSort! able to sort data of different types?

After the interpreter loads the package SortPackage, the four operations from the package become known to the interpreter. Each of these operations is expressed as a modemap in which the type modemap of the operation is written in terms of symbolic domains.

See the modemaps for bubbleSort!.

)display op bubbleSort!

There are 2 exposed functions called bubbleSort! :
   [1] D1 -> D1 from SortPackage(D2,D1)
         if D2 has ORDSET and D2 has OBJECT and D1 has
         IndexedAggregate(Integer, D2) with
   [2] (D1,((D3,D3) -> Boolean)) -> D1 from SortPackage(D3,D1)
         if D3 has OBJECT and D1 has
         IndexedAggregate(Integer,D3) with

What happens if you ask for bubbleSort!([1,-5,3])? There is a unique modemap for an operation named bubbleSort! with one argument. Since [1,-5,3] is a list of integers, the symbolic domain D1 is defined as List(Integer). For some operation to apply, it must satisfy the predicate for some D2. What D2? The third expression of the and requires D1 has IndexedAggregate(Integer, D2) with two attributes. So the interpreter searches for an IndexedAggregate among the ancestors of List (Integer) (see ugCategoriesHier ). It finds one: IndexedAggregate(Integer, Integer). The interpreter tries defining D2 as Integer. After substituting for D1 and D2, the predicate evaluates to true. An applicable operation has been found!

Now FriCAS builds the package SortPackage(List(Integer), Integer). According to its definition, this package exports the required operation: bubbleSort!: List Integer->List Integer. The interpreter then asks the package for a function implementing this operation. The package gets all the functions it needs (for example, rest and swap) from the appropriate domains and then it returns a bubbleSort! to the interpreter together with the local environment for bubbleSort!. The interpreter applies the function to the argument [1,-5,3]. The bubbleSort! function is executed in its local environment and produces the result.