this paper we take a more direct approach: we compile pattern matching on overlapping patterns. We first recall the semantics of lazy pattern matching, as given by A. Laville [5]. Then, we explain our compilation technique as a source to source transformation. Given a set of patterns, several compilations are possible, we prove that they all satisfy a partial correctness

We present improvements to the backtracking technique of pattern-matching compilation. Several optimizations are introduced, such as commutation of patterns, use of exhaustiveness information, and control ow optimization through the use of labeled static exceptions and context information. These optimizations have been integrated in the ObjectiveCaml compiler. They have shown good results in increasing the speed of pattern-matching intensive programs, without increasing nal code size.

Modern, statically typed, functional languages define functions by pattern matching. Although pattern matching is defined in terms of sequential checking of a value against one pattern after another, real implementations translate patterns into automata that can test a value against many patterns at once. Decision trees are popular automata.

The mechanism for declaring datatypes to model data structures in functional programming languages such as Standard ML and Haskell can offer both convenience in programming and clarity in code. With the introduction of dependent datatypes in DML, the programmer can model data structures more accurately, capturing more program invariants. In this paper, we study some practical aspects of dependent datatypes that affect both type-checking and compiling pattern matching as well as datatype representation. The results, which have already been tested, demonstrate that dependent datatype can not only offer various programming benefits but also lead to performance gains, yielding a concrete case where safer programs run faster.

: Coq is a proof assistant based on a higher-order logic allowing powerful definitions of functions. Coq V6.1 is available by anonymous ftp at ftp.inria.fr:/INRIA/Projects/coq/V6.1 and ftp.ens-lyon.fr:/pub/LIP/COQ/V6.1 Key-words: Coq, Proof Assistant, Formal Proofs, Calculus of Inductives Constructions (R'esum'e : tsvp) This research was partly supported by ESPRIT Basic Research Action "Types" and by the GDR "Programmation " co-financed by MRE-PRC and CNRS. Unit'e de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) T'el'ephone : (33 1) 39 63 55 11 -- T'el'ecopie : (33 1) 39 63 53 30 Manuel de r'ef'erence du syst`eme Coq version V6.1 R'esum'e : Coq est un syst`eme permettant le d'eveloppement et la v'erification de preuves formelles dans une logique d'ordre sup'erieure incluant un riche langage de d'efinitions de fonctions. Ce document constitue le manuel de r'ef'erence de la version V6.1 qui est distribu 'ee par ftp ...

Interpretation versus Demand Propagation Wadler [1987] uses abstract interpretation over a four-point domain for reasoning about strictness on lists. The four points correspond to undefined list (represented by value 0), infinite lists and lists with some tail undefined (value 1), lists with at least one head undefined (value 2), and all lists (value 3). Burn's work [Burn 1987] on evaluation transformers also uses abstract interpretation on the above-mentioned domain for strictness analysis. He defines four evaluators that correspond to the four points mentioned above in the sense that the ith evaluator will fail to produce an answer when given a list with the abstract value i \Gamma 1.

We introduce the notions of sequentiality and strong sequentiality in ordersorted rewriting systems, both closely related to the subsort order and to the form of declarations of the signature. We define free sequentiality for the class of orthogonal systems with constructors, a notion which does not impose conditions over the signature. We provide an effective decision procedure for free sequentiality that gives at the same time a simple construction of a nondeterministic pattern matching tree. These trees describe how the refinement of sorts and structures has to be done along the reduction sequence in such a way that wasteful computations are avoided.

This report details the design and implementation of the ZINC system. This is an implementation of the ML language, intended to serve as a test field for various extensions of the language, and for new implementation techniques as well. This system is strongly oriented toward separate compilation and the production of small, standalone programs

Strongly sequential systems, developed by Huet and Levy [HL79], has formed the basis of equational programming languages. Experience with such languages so far suggests that even complex equational programs are based only on strongly sequential systems with constructors.