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Admissible Graph Rewriting and Narrowing
 IN PROCEEDINGS OF THE JOINT INTERNATIONAL CONFERENCE AND SYMPOSIUM ON LOGIC PROGRAMMING
, 1998
"... We address the problem of graph rewriting and narrowing as the underlying operational semantics of rulebased programming languages. We propose new optimal graph rewriting and narrowing strategies in the setting of orthogonal constructorbased graph rewriting systems. For this purpose, we first char ..."
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Cited by 29 (6 self)
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We address the problem of graph rewriting and narrowing as the underlying operational semantics of rulebased programming languages. We propose new optimal graph rewriting and narrowing strategies in the setting of orthogonal constructorbased graph rewriting systems. For this purpose, we first characterize a subset of graphs, called admissible graphs. A graph is admissible if none of its defined operations belongs to a cycle. We then prove the confluence, as well as the confluence modulo bisimilarity (unraveling), of the admissible graph rewriting relation. Afterwards, we define a sequential graph rewriting strategy by using Antoy’s definitional trees. We show that the resulting strategy computes only needed redexes and develops optimal derivations w.r.t. the number of steps. Finally, we tackle the graph narrowing relation over admissible graphs and propose a sequential narrowing strategy which computes independent solutions and develops shorter derivations than most general graph narrowing.
Normalization Results for Typeable Rewrite Systems
, 1997
"... In this paper we introduce Curryfied Term Rewriting Systems, and a notion of partial type assignment on terms and rewrite rules that uses intersection types with sorts and !. Three operations on types  substitution, expansion, and lifting  are used to define type assignment, and are proved to be ..."
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Cited by 24 (23 self)
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In this paper we introduce Curryfied Term Rewriting Systems, and a notion of partial type assignment on terms and rewrite rules that uses intersection types with sorts and !. Three operations on types  substitution, expansion, and lifting  are used to define type assignment, and are proved to be sound. With this result the system is proved closed for reduction. Using a more liberal approach to recursion, we define a general scheme for recursive definitions and prove that, for all systems that satisfy this scheme, every term typeable without using the typeconstant ! is strongly normalizable. We also show that, under certain restrictions, all typeable terms have a (weak) headnormal form, and that terms whose type does not contain ! are normalizable.
Rank 2 Intersection Type Assignment in Term Rewriting Systems
, 1996
"... A notion of type assignment on Curryfied Term Rewriting Systems is introduced that uses Intersection Types of Rank 2, and in which all function symbols are assumed to have a type. Type assignment will consist of specifying derivation rules that describe how types can be assigned to terms, using the ..."
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Cited by 23 (15 self)
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A notion of type assignment on Curryfied Term Rewriting Systems is introduced that uses Intersection Types of Rank 2, and in which all function symbols are assumed to have a type. Type assignment will consist of specifying derivation rules that describe how types can be assigned to terms, using the types of function symbols. Using a modified unification procedure, for each term the principal pair (of basis and type) will be defined in the following sense: from these all admissible pairs can be generated by chains of operations on pairs, consisting of the operations substitution, copying, and weakening. In general, given an arbitrary typeable CuTRS, the subject reduction property does not hold. Using the principal type for the lefthand side of a rewrite rule, a sufficient and decidable condition will be formulated that typeable rewrite rules should satisfy in order to obtain this property. Introduction In the recent years, several paradigms have been investigated for the implementatio...
Lazy rewriting on eager machinery
 ACM Transactions on Programming Languages and Systems
, 2000
"... The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behaviour of a term rewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives a ..."
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Cited by 23 (1 self)
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The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behaviour of a term rewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives as an implementation of eager rewriting. 1
A Complete Transformational Toolkit for Compilers
 ACM Transactions on Programming Languages and Systems
, 1996
"... . In an earlier paper, one of the present authors presented a preliminary account of an equational logic called PIM. PIM is intended to function as a "transformational toolkit" to be used by compilers and analysis tools for imperative languages, and has been applied to such problems as program sl ..."
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Cited by 23 (9 self)
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. In an earlier paper, one of the present authors presented a preliminary account of an equational logic called PIM. PIM is intended to function as a "transformational toolkit" to be used by compilers and analysis tools for imperative languages, and has been applied to such problems as program slicing, symbolic evaluation, conditional constant propagation, and dependence analysis. PIM consists of the untyped lambda calculus extended with an algebraic rewriting system that characterizes the behavior of lazy stores and generalized conditionals. A major question left open in the earlier paper was whether there existed a complete equational axiomatization of PIM's semantics. In this paper, we answer this question in the affirmative for PIM's core algebraic component, PIM t , under the assumption of certain reasonable restrictions on term formation. We systematically derive the complete PIM logic as the culmination of a sequence of increasingly powerful equational systems starti...
Properties of a Firstorder Functional Language with Sharing
 Theoretical Computer Science
, 1994
"... A calculus and a model for a firstorder functional language with sharing is presented. In most implementations of... ..."
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Cited by 22 (4 self)
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A calculus and a model for a firstorder functional language with sharing is presented. In most implementations of...
A rewriting calculus for cyclic higherorder term graphs
 in "2nd International Workshop on Term Graph Rewriting  TERMGRAPH’2004
, 2004
"... graphs ..."
Partial Intersection Type Assignment in Applicative Term Rewriting Systems
 Proceedings of TLCA '93. International Conference on Typed Lambda Calculi and Applications, Utrecht, The Netherlands, volume 664 of Lecture Notes in Computer Science
, 1993
"... This paper introduces a notion of partial type assignment on applicative term rewriting systems that is based on a combination of an essential intersection type assignment system, and the type assignment system as defined for ML [16], both extensions of Curry's type assignment system [11]. Terms a ..."
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Cited by 17 (14 self)
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This paper introduces a notion of partial type assignment on applicative term rewriting systems that is based on a combination of an essential intersection type assignment system, and the type assignment system as defined for ML [16], both extensions of Curry's type assignment system [11]. Terms and rewrite rules will be written as trees, and type assignment will consists of assigning intersection types function symbols, and specifying the way in which types can be assigned to nodes and edges between nodes. The only constraints on this system are local: they are imposed by the relation between the type assigned to a node and those assigned to its incoming and outgoing edges. In general, given an arbitrary typeable applicative term rewriting system, the subject reduction property does not hold. We will formulate a sufficient but undecidable condition typeable rewrite rules should satisfy in order to obtain this property. Introduction In the recent years several paradigms hav...
A Syntactic Approach to Program Transformations
, 1991
"... Kid, a language for expressing compiler optimizations for functional languages is introduced. The language is λcalculus based but treats letblocks as first class objects. Letblocks and associated rewrite rules provide the basis to capture the sharing of subexpressions precisely. The langua ..."
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Cited by 16 (6 self)
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Kid, a language for expressing compiler optimizations for functional languages is introduced. The language is λcalculus based but treats letblocks as first class objects. Letblocks and associated rewrite rules provide the basis to capture the sharing of subexpressions precisely. The language goes beyond λcalculus by including Istructures which are essential to express efficient translations of list and array comprehensions. A calculus and a parallel interpreter for Kid are developed. Many commonly known program transformations are also presented. A partial evaluator for Kid is developed and a notion of correctness of Kid transformations based on the syntactic structure of terms and printable answers is presented.
Using Projection Analysis in Compiling Lazy Functional Programs
 In Proceedings of the 1990 ACM Conference on Lisp and Functional Programming
, 1990
"... Projection analysis is a technique for finding out information about lazy functional programs. We show how the information obtained from this analysis can be used to speed up sequential implementations, and introduce parallelism into parallel implementations. The underlying evaluation model is evalu ..."
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Cited by 15 (6 self)
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Projection analysis is a technique for finding out information about lazy functional programs. We show how the information obtained from this analysis can be used to speed up sequential implementations, and introduce parallelism into parallel implementations. The underlying evaluation model is evaluation transformers, where the amount of evaluation that is allowed of an argument in a function application depends on the amount of evaluation allowed of the application. We prove that the transformed programs preserve the semantics of the original programs. Compilation rules, which encode the information from the analysis, are given for sequential and parallel machines. 1 Introduction A number of analyses have been developed which find out information about programs. The methods that have been developed fall broadly into two classes, forwards analyses such as those based on the ideas of abstract interpretation (e.g. [9, 18, 19, 7, 17, 12, 4, 20]), and backward analyses such as those based...