By Barry Jay

Over time, simple examine has a tendency to guide to specialization – more and more slender t- ics are addressed via more and more focussed groups, publishing in more and more con ned workshops and meetings, discussing more and more incremental contri- tions. Already the neighborhood of programming languages is divided into a variety of s- groups addressing various elements and paradigms (functional, important, relational, and object-oriented). just a couple of humans have the capacity to keep a broader view, or even fewer step again with the intention to achieve an realizing concerning the easy ideas, their interrelation, and their influence in a bigger context. The trend calculus is the results of a profound re-evaluation of a 50-year - velopment. It makes an attempt to supply a unifying strategy, bridging the gaps among diversified programming kinds and paradigms in accordance with a brand new slogan – compu- tion is trend matching. it's the contribution of this ebook to systematically and skillfully current and assessment the facility of trend matching because the guiding paradigm of programming. styles are dynamically generated, chanced on, handed, utilized, and immediately tailored, in accordance with development matching and rewriting know-how, which permits one to elegantly relate issues as disparate as features and knowledge buildings. in fact, trend matching isn't really new. It underlies time period rewriting – it really is, for instance, inc- porated in, usually useful, programming languages, like ordinary ML – however it hasn't ever been pursued because the foundation of a unifying framework for programming.

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**Extra resources for Pattern Calculus: Computing with Functions and Structures**

**Sample text**

The generic apply2all is able to act on employees wherever they are found. Now let us add a new twist. Suppose that salary increases are to be limited to employees within groups. If groups are a fixed part of the organisation’s structure, represented by a constructor Group, then it is enough to write patterns of the form Group x just as before. The more interesting possibility is that the concept of group is dynamic. At one time it may be a department, at another time it may be a division, or even a department within a division.

8. Size The simplest measure of a data structure is given by size = x y → plusNat (size x) (size y) | x → 1. As mentioned before, this can be modified so that natural numbers all have size 1 by size = Successor x → 1 | x y → plusNat (size x) (size y) |x→1. 9. Selecting Selecting is achieved by select f x = (if f x then Cons x else (y → y)) (( z y → append (select f x z) (select f x y) | y → Nil) x) . The last two lines perform the path polymorphism. For example, if the argument is a compound then the results of selecting on each component are appended.

3 β -Reduction Now let us consider the semantic equality of terms. s) u = {u/x}s formalises the original description of abstractions as functions. t x if x ∈ fv(t) asserts that every pure λ -term is a function. The β η -equality of terms is the congruence relation s = t generated by these rules. In computation, the η -rule is not so interesting, since it does not hold when data structures are added as primitives. Rather than study full β η -equality, let us focus on β -reduction as the basis of computation.