Introduction to Cost Models

Programming language constructs might have particular asymptotic complexities, which programmers should know, to produce efficient algorithms. In other words, even though an algorithm has some specific, well-known, computational cost, its implementation can have higher complexity, due to an implicit cost model that is part of that languages runtime environment. Furthermore, some programming languages miss features that might complicate the implementation of efficient algorithms. For instance, it will be hard to implement Bucket Sort without random access data structures. These minutia concern an aspect of programming languages' implementation that we call cost models.

In this chapter we will look into four cost models. The first concerns the use of lists in programming languages that follow the Lisp model. The second cost model concerns the invocation of functions in languages that support recursion. After that, we look into Prolog's unification model, trying to reason about the factors that cause unification to be more or less efficient. Finally, we discuss languages that support arrays, which are random access data structures.