By Barry Jay

Over time, uncomplicated examine has a tendency to guide to specialization – more and more slender t- ics are addressed by way of more and more focussed groups, publishing in more and more con ned workshops and meetings, discussing more and more incremental contri- tions. Already the group of programming languages is divided into quite a few s- groups addressing assorted facets and paradigms (functional, vital, relational, and object-oriented). just a couple of humans be capable to retain a broader view, or even fewer step again to be able to achieve an figuring out concerning the simple rules, 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 technique, bridging the gaps among diverse programming kinds and paradigms in keeping with a brand new slogan – compu- tion is development matching. it's the contribution of this e-book to systematically and assuredly current and assessment the facility of trend matching because the guiding paradigm of programming. styles are dynamically generated, stumbled on, handed, utilized, and instantly tailored, in keeping with development matching and rewriting know-how, which permits one to elegantly relate issues as disparate as services and knowledge buildings. after all, development matching isn't new. It underlies time period rewriting – it's, for instance, inc- porated in, more often than not practical, programming languages, like general 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

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The difficulty is that while group and x are both symbols, group is to be a variable while x is to be a matchable. In the static calculus, all symbols in a pattern are matchable but now both kinds of symbols are terms in their own right (patterns are terms) and so must be clearly distinguished. The solution adopted is to allow each symbol x to appear as either a variable x or as a matchable x. ˆ For example, the dynamic pattern for a group is now group xˆ in which group is free and x will be bound.

T then cdr t else error. Of course, this approach quickly becomes cumbersome. For example, to safely obtain the head of a list (built using Cons) requires λ x. if pair? x then if pair? (car x) then if Cons eqa (car (car x)) then cdr x else error else error else error. In the next chapter, the compound calculus will be shown to be equivalent to the static pattern calculus, in which the head of a list can be written as the case Cons x y → x . Given the dramatic simplification of terms that this entails, all further examples will be postponed until Sect.

Does one choice preclude the other? Can a single term have two normal forms? 4 Confluence Without knowing if a term has any normal forms, the question of their uniqueness must be generalised to arbitrary terms. A reduction relation −→ is confluent if for any term t and pair of reductions t −→∗ t1 and t −→∗ t2 there is a term t3 and a pair of reductions t1 −→∗ t3 and t2 −→∗ t3 . It follows that if t1 and t2 are both irreducible then they must both be t3 . That is, if reduction produces a normal form then it is unique.

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