Pure patterns type systems

Barthe, Gilles; Cirstea, Horatiu; Kirchner, Claude; Liquori, Luigi

doi:10.1145/604131.604152

Cited by 43 publications

(50 citation statements)

References 19 publications

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“…Observe that compared with 'non-strategic' implementations of the Rewriting Calculus (Cirstea et al 2001a;Cirstea et al 2001b;Cirstea et al 2002;Barthe et al 2003), the delayed matching constraint [P ∆ A].B, now just becomes syntactic sugar for (P ∆ A) B (which is omitted from the source language but will still be present in the set of output values).…”

Section: Functional Syntaxmentioning

confidence: 99%

“…The type system can probably be extended with a subtyping relation, or with bounded polymorphism, to capture the behaviour of structuresas-objects, and object-oriented features. Compared with previous type systems for the (functional) Rho (Cirstea et al 2001b;Cirstea et al 2002;Barthe et al 2003;Cirstea et al 2004), structures can now have different types, that is, thanks to the following typing rule, which is new compared with the previous typed formulations of the Rewriting Calculus:…”

Section: The Type Systemmentioning

confidence: 99%

“…This modification greatly improves the expressiveness compared with previous typing disciplines on the Rewriting Calculus (Cirstea et al 2004) in the sense that it gives a type to terms that will not be stuck at run time, but it does complicate the metatheory and mechanical proof development. The main enhancement compared with previous versions of the Rewriting Calculus (Barthe et al 2003) is that here the elements of the structure are not forced to have the same type. The type system A is algorithmic: the type rules are deterministic and suggest two decision procedures for type reconstruction and type checking.…”

Section: The Type Systemmentioning

confidence: 99%

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iRho: an imperative rewriting calculus

Liquori¹,

Serpette²

2008

Math. Struct. Comp. Sci.

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We propose an imperative version of the Rewriting Calculus, a calculus based on pattern matching, pattern abstraction and side effects, which we call iRho. We formulate both a static and big-step call-by-value operational semantics of iRho. The operational semantics is deterministic, and immediately suggests how an interpreter for the calculus may be built. The static semantics is given using a first-order type system based on a form of product types, which can be assigned to term-like structures (that is, records). The calculus isà la Church, that is, pattern abstractions are decorated with the types of the free variables of the pattern. iRho is a good candidate for the core of a pattern-matching imperative language, where a (monomorphic) typed store can be safely manipulated and where fixed points are built into the language itself. Properties such as determinism of the interpreter and subject-reduction have been completely checked using a machine-assisted approach with the Coq proof assistant. Progress and decidability of type checking are proved using pen and paper. IntroductionThe study of rewriting-based languages (such as Elan Although rewriting-based languages are less popular than object-oriented languages such as Java (Sun 2005) and C# (Microsoft 2005) for ordinary programming, they can serve as common typed intermediate languages for implementing compilers for rewritingbased, functional, object-oriented, logic, and other high-level modern languages (Cirstea et al. 2001a;Cirstea et al. 2002;Cirstea et al. 2004).Pattern matching has been used widely in functional and logic programming (for example, in ML (Milner et al. 1997;Cristal Team 2005), Haskell (Jones 2003), Scheme (R. Kelsey 1998), Curry (Hanus 1997) and Prolog (Kowalski 1979)), but it has generally been considered to be a convenient mechanism for expressing complex requirements about the function's argument, rather than as a basis for an ad hoc paradigm of computation.One of the main advantages of rewriting-based languages is pattern matching, which allows one to discriminate between alternatives. These languages permit non-determinism in the sense that they can represent a collection of results. That is, pattern matching need not be exclusive, multiple branches can be 'fired' simultaneously. An empty collection of L. Liquori and B. P. Serpette 2 results represents an application failure, a singleton represents a deterministic result, and a collection with more than one element represents a non-deterministic choice between the elements of the collection.This feature highlights a difference compared with those functional languages featuring pattern matching, such as ML, Haskell and Scheme. It shares some similarities with backtracking and exhaustive proof search in logic languages like Prolog. It is possible to make a pair of two functions having the same pattern, and when the pair is applied to an argument, both functions will be fired. Optimistic and pessimistic operational semantics † , with a fixed strategy, can then be imposed on the langua...

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Section: Functional Syntaxmentioning

confidence: 99%

Section: The Type Systemmentioning

confidence: 99%

Section: The Type Systemmentioning

confidence: 99%

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iRho: an imperative rewriting calculus

Liquori¹,

Serpette²

2008

Math. Struct. Comp. Sci.

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“…Internalisation of general, non-deterministic term rewriting has been studied by H. Cirstea, C. Kirchner and others as the rewriting calculus, also called ρ-calculus [4,5], and, most recently, in typed variants as "pure pattern type systems" [2]. The ρ-calculus is parameterised by a theory modulo which matching is performed; this can be used to deal with views [23].…”

Section: Related Workmentioning

confidence: 99%

Basic Pattern Matching Calculi: a Fresh View on Matching Failure

Kahl

2004

Functional and Logic Programming

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Abstract. We propose pattern matching calculi as a refinement of λ-calculus that integrates mechanisms appropriate for fine-grained modelling of non-strict pattern matching. Compared with the functional rewriting strategy usually employed to define the operational semantics of pattern matching in non-strict functional programming languages like Haskell or Clean, our pattern matching calculi achieve the same effects using simpler and more local rules. The main device is to embed into expressions the separate syntactic category of matchings; the resulting language naturally encompasses pattern guards and Boolean guards as special cases. By allowing a confluent reduction system and a normalising strategy, these pattern matching calculi provide a new basis for operational semantics of non-strict programming languages and also for implementations.

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“…The evaluation mechanism, generalizing beta-reduction, strongly relies on term matching in various theories. Several variants of the calculus have been already studied, such as typed versions [5], extensions with explicit substitutions [8] or with imperative features [15].…”

Section: Introductionmentioning

confidence: 99%

The Graph Rewriting Calculus: Confluence and Expressiveness

Bertolissi

2005

Lecture Notes in Computer Science

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Abstract. Introduced at the end of the nineties, the Rewriting Calculus (ρ-calculus, for short) is a simple calculus that uniformly integrates termrewriting and λ-calculus. The ρg-calculus has been recently introduced as an extension of the ρ-calculus, handling structures with cycles and sharing. The calculus over terms is naturally generalized by using unification constraints in addition to the standard ρ-calculus matching constraints. This leads to a term-graph representation in an equational style where terms consist of unordered lists of equations. In this paper we show that the (linear) ρg-calculus is confluent. The proof of this result is quite elaborated, due to the non-termination of the system and to the fact that we work on equivalence classes of terms. We also show that the ρg-calculus can be seen as a generalization of first-order term-graph rewriting, in the sense that for any term-graph rewrite step a corresponding sequence of rewritings can be found in the ρg-calculus.

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Pure patterns type systems

Cited by 43 publications

References 19 publications

iRho: an imperative rewriting calculus

iRho: an imperative rewriting calculus

Basic Pattern Matching Calculi: a Fresh View on Matching Failure

The Graph Rewriting Calculus: Confluence and Expressiveness

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