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410
Combinatory Reduction Systems: introduction and survey
 THEORETICAL COMPUTER SCIENCE
, 1993
"... Combinatory Reduction Systems, or CRSs for short, were designed to combine the usual firstorder format of term rewriting with the presence of bound variables as in pure λcalculus and various typed calculi. Bound variables are also present in many other rewrite systems, such as systems with simpl ..."
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Cited by 88 (9 self)
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Combinatory Reduction Systems, or CRSs for short, were designed to combine the usual firstorder format of term rewriting with the presence of bound variables as in pure λcalculus and various typed calculi. Bound variables are also present in many other rewrite systems, such as systems with simplification rules for proof normalization. The original idea of CRSs is due to Aczel, who introduced a restricted class of CRSs and, under the assumption of orthogonality, proved confluence. Orthogonality means that the rules are nonambiguous (no overlap leading to a critical pair) and leftlinear (no global comparison of terms necessary). We introduce the class of orthogonal CRSs, illustrated with many examples, discuss its expressive power, and give an outline of a short proof of confluence. This proof is a direct generalization of Aczel's original proof, which is close to the wellknown confluence proof for λcalculus by Tait and MartinLof. There is a wellknown connection between the para...
Analysis and Caching of Dependencies
, 1996
"... We address the problem of dependency analysis and caching in the context of the calculus. The dependencies of a  term are (roughly) the parts of the term that contribute to the result of evaluating it. We introduce a mechanism for keeping track of dependencies, and discuss how to use these depend ..."
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Cited by 71 (6 self)
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We address the problem of dependency analysis and caching in the context of the calculus. The dependencies of a  term are (roughly) the parts of the term that contribute to the result of evaluating it. We introduce a mechanism for keeping track of dependencies, and discuss how to use these dependencies in caching.
Inductive Families
 Formal Aspects of Computing
, 1997
"... A general formulation of inductive and recursive definitions in MartinLof's type theory is presented. It extends Backhouse's `DoItYourself Type Theory' to include inductive definitions of families of sets and definitions of functions by recursion on the way elements of such sets ar ..."
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Cited by 70 (13 self)
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A general formulation of inductive and recursive definitions in MartinLof's type theory is presented. It extends Backhouse's `DoItYourself Type Theory' to include inductive definitions of families of sets and definitions of functions by recursion on the way elements of such sets are generated. The formulation is in natural deduction and is intended to be a natural generalization to type theory of MartinLof's theory of iterated inductive definitions in predicate logic. Formal criteria are given for correct formation and introduction rules of a new set former capturing definition by strictly positive, iterated, generalized induction. Moreover, there is an inversion principle for deriving elimination and equality rules from the formation and introduction rules. Finally, there is an alternative schematic presentation of definition by recursion. The resulting theory is a flexible and powerful language for programming and constructive mathematics. We hint at the wealth of possible applic...
Preservation of Strong Normalisation in Named Lambda Calculi with Explicit Substitution and Garbage Collection
 IN CSN95: COMPUTER SCIENCE IN THE NETHERLANDS
, 1995
"... In this paper we introduce and study a new lambdacalculus with explicit substitution, lambdaxgc, which has two distinguishing features: first, it retains the use of traditional variable names, specifying terms modulo renaming; this simplifies the reduction system. Second, it includes reduction rul ..."
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Cited by 69 (7 self)
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In this paper we introduce and study a new lambdacalculus with explicit substitution, lambdaxgc, which has two distinguishing features: first, it retains the use of traditional variable names, specifying terms modulo renaming; this simplifies the reduction system. Second, it includes reduction rules for explicit garbage collection; this simplifies several proofs. We show that lambdaxgc is a conservative extension which preserves strong normalisation (PSN) of the untyped lambdacalculus. The result is obtained in a modular way by first proving it for garbagefree reduction and then extending to `reductions in garbage'. This provides insight into the counterexample to PSN for lambdasigma of Melliès (1995); we exploit the abstract nature of lambdaxgc to show how PSN is in conflict with any reasonable substitution composition rule (except for trivial composition rules of which we mention one). Key words: lambda calculus, explicit substitution, strong normalisation, garbage collection.
Programming with Intersection Types and Bounded Polymorphism
, 1991
"... representing the official policies, either expressed or implied, of the U.S. Government. ..."
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Cited by 68 (4 self)
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representing the official policies, either expressed or implied, of the U.S. Government.
Efficient Representation and Validation of Proofs
, 1998
"... This paper presents a logical framework derived from the Edinburgh Logical Framework (LF) [5] that can be used to obtain compact representations of proofs and efficient proof checkers. These are essential ingredients of any application that manipulates proofs as firstclass objects, such as a Proof ..."
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Cited by 66 (9 self)
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This paper presents a logical framework derived from the Edinburgh Logical Framework (LF) [5] that can be used to obtain compact representations of proofs and efficient proof checkers. These are essential ingredients of any application that manipulates proofs as firstclass objects, such as a ProofCarrying Code [11] system, in which proofs are used to allow the easy validation of properties of safetycritical or untrusted code. Our framework, which we call LF i , inherits from LF the capability to encode various logics in a natural way. In addition, the LF i framework allows proof representations without the high degree of redundancy that is characteristic of LF representations. The missing parts of LF i proof representations can be reconstructed during proof checking by an efficient reconstruction algorithm. We also describe an algorithm that can be used to strip the unnecessary parts of an LF representation of a proof. The experimental data that we gathered in the context of a Proof...
Implementing Typed Intermediate Languages
, 1998
"... Recent advances in compiler technology have demonstrated the benefits of using strongly typed intermediate languages to compile richly typed source languages (e.g., ML). A typepreserving compiler can use types to guide advanced optimizations and to help generate provably secure mobile code. Types, u ..."
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Cited by 64 (16 self)
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Recent advances in compiler technology have demonstrated the benefits of using strongly typed intermediate languages to compile richly typed source languages (e.g., ML). A typepreserving compiler can use types to guide advanced optimizations and to help generate provably secure mobile code. Types, unfortunately, are very hard to represent and manipulate efficiently; a naive implementation can easily add exponential overhead to the compilation and execution of a program. This paper describes our experience with implementing the FLINT typed intermediate language in the SML/NJ production compiler. We observe that a typepreserving compiler will not scale to handle large types unless all of its typepreserving stages preserve the asymptotic time and space usage in representing and manipulating types. We present a series of novel techniques for achieving this property and give empirical evidence of their effectiveness.
Models of Sharing Graphs: A Categorical Semantics of let and letrec
, 1997
"... To my parents A general abstract theory for computation involving shared resources is presented. We develop the models of sharing graphs, also known as term graphs, in terms of both syntax and semantics. According to the complexity of the permitted form of sharing, we consider four situations of sha ..."
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Cited by 63 (9 self)
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To my parents A general abstract theory for computation involving shared resources is presented. We develop the models of sharing graphs, also known as term graphs, in terms of both syntax and semantics. According to the complexity of the permitted form of sharing, we consider four situations of sharing graphs. The simplest is firstorder acyclic sharing graphs represented by letsyntax, and others are extensions with higherorder constructs (lambda calculi) and/or cyclic sharing (recursive letrec binding). For each of four settings, we provide the equational theory for representing the sharing graphs, and identify the class of categorical models which are shown to be sound and complete for the theory. The emphasis is put on the algebraic nature of sharing graphs, which leads us to the semantic account of them. We describe the models in terms of the notions of symmetric monoidal categories and functors, additionally with symmetric monoidal adjunctions and traced
Unification via Explicit Substitutions: The Case of HigherOrder Patterns
 PROCEEDINGS OF JICSLP'96
, 1998
"... In [6] we have proposed a general higherorder unification method using a theory of explicit substitutions and we have proved its completeness. In this paper, we investigate the case of higherorder patterns as introduced by Miller. We show that our general algorithm specializes in a very convenient ..."
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Cited by 56 (14 self)
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In [6] we have proposed a general higherorder unification method using a theory of explicit substitutions and we have proved its completeness. In this paper, we investigate the case of higherorder patterns as introduced by Miller. We show that our general algorithm specializes in a very convenient way to patterns. We also sketch an efficient implementation of the abstract algorithm and its generalization to constraint simplification, which has yielded good experimental results at the core of a higherorder constraint logic programming language.