CRSX - Combinatory Reduction Systems with Extensions

Combinatory Reduction Systems with Extensions (CRSX) is a system available from http://crsx.sourceforge.net and characterized by the following properties: - Higher-order rewriting engine based on pure Combinatory Reduction Systems with full strong reduction (but no specified reduction strategy). - Rule and term syntax based on lambda-calculus and term rewriting conventions including Unicode support. - Strict checking and declaration requirements to avoid idiosyncratic errors in rewrite rules. - Interpreter is implemented in Java 5 and usable stand-alone as well as from an Eclipse plugin (under development). - Includes a custom parser generator (front-end to JavaCC parser generator) designed to ease parsing directly into higher-order abstract syntax (as well as permitting the use of custom syntax in rules files). - Experimental (and evolving) sort system to help rule management. - Compiler from (well-sorted deterministic subset of) CRSX to stand-alone C code

Higher-order Rewriting for Executable Compiler Specifications

In this paper we outline how a simple compiler can be completely specified using higher order rewriting in all stages: parsing, analysis/optimization, and code emission, specifically using the crsx.sf.net system for a small declarative language called "X" inspired by XQuery (for which we are building a production quality compiler in the same way)

The New Rewriting Engine of Dedukti

International audienceDedukti is a type-checker for the λΠ-calculus modulo rewriting, an extension of Edinburgh’s logicalframework LF where functions and type symbols can be defined by rewrite rules. It thereforecontains an engine for rewriting LF terms and types according to the rewrite rules given by the user.A key component of this engine is the matching algorithm to find which rules can be fired. In thispaper, we describe the class of rewrite rules supported by Dedukti and the new implementation ofthe matching algorithm. Dedukti supports non-linear rewrite rules on terms with binders usinghigher-order pattern-matching as in Combinatory Reduction Systems (CRS). The new matchingalgorithm extends the technique of decision trees introduced by Luc Maranget in the OCamlcompiler to this more general context

A journey through resource control lambda calculi and explicit substitution using intersection types (an account)

In this paper we invite the reader to a journey through three lambda calculi with resource control: the lambda calculus, the sequent lambda calculus, and the lambda calculus with explicit substitution. All three calculi enable explicit control of resources due to the presence of weakening and contraction operators. Along this journey, we propose intersection type assignment systems for all three resource control calculi. We recognise the need for three kinds of variables all requiring different kinds of intersection types. Our main contribution is the characterisation of strong normalisation of reductions in all three calculi, using the techniques of reducibility, head subject expansion, a combination of well-orders and suitable embeddings of terms

Resource control and intersection types: an intrinsic connection

In this paper we investigate the $\lambda$ -calculus, a $\lambda$-calculus enriched with resource control. Explicit control of resources is enabled by the presence of erasure and duplication operators, which correspond to thinning and con-traction rules in the type assignment system. We introduce directly the class of $\lambda$ -terms and we provide a new treatment of substitution by its decompo-sition into atomic steps. We propose an intersection type assignment system for $\lambda$ -calculus which makes a clear correspondence between three roles of variables and three kinds of intersection types. Finally, we provide the characterisation of strong normalisation in $\lambda$ -calculus by means of an in-tersection type assignment system. This process uses typeability of normal forms, redex subject expansion and reducibility method.Comment: arXiv admin note: substantial text overlap with arXiv:1306.228