Incremental computations can improve the performance of interactive programs such as spreadsheet programs, program development environments, text editors, etc. Incremental algorithms describe how to compute a required value depending on the input, after the input has been edited. By considering the possible different edit actions on the data type lists, the basic data type used in spreadsheet programs and text editors, we define incremental algorithms on lists. Some theory for the construction of incremental algorithms is developed, and we give an incremental algorithm for a more involved example: formatting a text. CR categories and descriptors: D11 [Software]: Programming Techniques --- Applicative Programming, D43 [Software]: Programming Languages --- Language constructs, I22 [Artificial Intelligence]: Automatic Programming --- Program transformation. General terms: algorithm, design, theory. Additional keywords and phrases: Bird-Meertens calculus for program construction, incremen...

This paper derives a hierarchy of algorithms for pattern matching on arrays in the Bird-Meertens calculus for program transformation. In this calculus, both specifications and algorithms are functions, and a few high-level theorems are used as transformation rules. An algorithm is derived from its specification by means of a calculation which typically consists of a sequence of equalities, each an instantiation of a high-level theorem or a definition. Aspects of the Bird-Meertens calculus can be found in [4], [5], [9], [14], [15], and [13]. The laws we use in the derivation are derived from the definition of the data type

this paper can be used in the construction of an algorithm for coding a tree with respect to a dictionary of trees. This paper is organised as follows. Section 2 describes the edit model and the induced form of incremental algorithms. Section 3 specifies the problem of coding a text with respect to a dictionary, and Section 4 sketches a derivation of an incremental algorithm for this problem. 2 Incremental algorithms and the edit model