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 with more accuracy, thus capturing more program invariants. In this paper, we study some practical aspects of dependent datatypes that affect both type-checking and compiling pattern matching. 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.

In ML style pattern matching, pattern size is not constrained and ambiguous patterns are allowed. This generality leads to a clear and concise programming style but is challenging in the context of lazy evaluation. A first challenge concerns language designers: in lazy ML, the evaluation order of expressions follows actual data dependencies. That is, only the computations that are needed to produce the final result are performed. Once given a proper (that is, non-ambiguous) semantics, pattern matching should be compiled in a similar spirit: any value matching a given pattern should be recognized by performing only the minimal number of elementary tests needed to do so. This challenge was first met by A. Laville. A second challenge concerns compiler designers. As it stands, Laville's compilation algorithm cannot be incorporated in an actual lazy ML compiler for efficiency and completeness reasons. As a matter of fact, Laville's original algorithm did not fully treat the case of intege...

Tools reading binary code, like analysers, debuggers, disassemblers, etc., need to decode the target's machine code. A decision tree is often used to represent the decoding function. Manually writing a decoder is a lengthy and error-prone task. It is desirable to be able to use the vendor's instruction code manual and to easily transform the documentation into a specification that a tool can use to generate a decoder. This paper

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

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.

: 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 ...

We study the semantics of term rewriting systems with rule priorities (PRS), as introduced in [1]. Three open problems posed in that paper are solved, by giving counter examples. Moreover, a class of executable PRSs is identified. A translation of PRSs into transition system specifications (TSS) is given. This translation introduces negative premises. We prove that the translation preserves the operational semantics. Contents 1 Introduction 2 2 Term rewriting with rule priorities 3 2.1 Definition and semantics . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Fixed points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 An executable class of PRSs . . . . . . . . . . . . . . . . . . . . 8 2.4 Counter examples to open questions . . . . . . . . . . . . . . . . 11 3 Transition system specifications 14 3.1 Universal negative premises in TSSs . . . . . . . . . . . . . . . . 15 3.2 Translation of PRSs into TSSs . . . . . . . . . . . . . . . . . . . 18 4 Operational semant...

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We study the semantics of term rewriting systems with rule priorities (PRS), as introduced in [1]. Three open problems posed in that paper are solved, by giving counter examples. Moreover, a class of executable PRSs is identified. A translation of PRSs into transition system specifications (TSS) is given. This translation introduces negative premises. We prove that the translation preserves the operational semantics. Key words: term rewriting systems, rule priorities, structural operational semantics, transition system specification, negative premises. 1 Introduction Motivation. In [1], term rewriting with rule priorities has been introduced. A priority rewrite system (PRS) extends an ordinary term rewriting system (TRS) with a partial order on the rules. The main idea is to resolve a conflict between two rules by giving priority to the largest rule. One may hope that by ordering the rules of a non-confluent TRS, a confluent PRS can be obtained (i.e. a system in which each reduction ev...

We study the semantics of term rewriting systems with rule priorities (PRS), as introduced in Baeten et al. (1989). Three open problems posed in that paper are solved, by giving counter examples. Moreover, a class of executable PRSs is identified. A translation of PRSs into transition system specifications (TSS) is given. This translation introduces negative premises. We prove that the translation preserves the operational semantics. @ 1998-Elsevier Science B.V. All