Compilation of Non-Linear, Second Order Patterns on S-Expressions

Pattern matching is a key concept for rule-based expert systems. Simple pattern interpreters appear in nearly every book on Lisp. Pattern matching is also a useful tool for case analyses as provided by functional languages such as ML or Miranda TM. These two uses are somewhat diierent since functional languages emphasize a discrimination based on types while Lisp, or Plasma, make use of S-expressions or segments of S-expressions within patterns. The paper presents an intermediate language for patterns and its denotational semantics. This reduced language is powerful enough to express boolean composition of patterns as well as segment handling and unbounded pattern repetition. A compiler is then deened which translates patterns into functional code. We discuss some compilation variant as well as the integration of the pattern sub-language into Lisp. These capabilities make pattern matching an useful and eecient tool for a wide class of applicative languages and allow to incorporate into patterns more knowledge about the form or gestalt of the data to be matched. Pattern matching is gaining more and more audience within functional languages. Pattern matching is used to deene functions, or just expressions, that perform case analyses. First introduced in NPL Burstall 69] and SASL Turner 76], then in ML Weis 89] or Haskell Hudak & Wadler 90] case construct is an archetypic example of the use of pattern matching within functional languages. Pattern matching is also a key concept in rule-based expert systems and has long been known in the Lisp community. Most textbooks on Lisp Abelson & Sussman 85, Kessler 88, Queinnec 84, Winston 88] contain the description of simple pattern interpreters. The rst pattern compiler was written by Masinter Teitelman 78] and ooered since 1972 as part of the InterLisp programming environment. Pattern matching compares a datum and a pattern. Two eeects are simultaneously involved: check the aspect of the datum, destructure this very datum and extract some of its components. The rst eeect yields a boolean result indicating if the datum matches the pattern i.e.there exists an environment binding pattern variables to data that makes the pattern, with pattern variables substituted by their value in this very environment, equal to the original datum. The second eeect may be considered as a by-product since the destructuration is in fact the precise environment binding pattern variables to parts of the original datum and constructed as part of the matching process. The omnipresent list structure …