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Incremental Dynamics
, 1998
"... An incremental semantics for a logic with dynamic binding is developed on the basis of a variable free notation for dynamic logic. The variable free indexing mechanism guarantees that active registers are never overwritten by new quantifier actions. The resulting system has the same expressive power ..."
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Cited by 17 (4 self)
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An incremental semantics for a logic with dynamic binding is developed on the basis of a variable free notation for dynamic logic. The variable free indexing mechanism guarantees that active registers are never overwritten by new quantifier actions. The resulting system has the same expressive power as Dynamic Predicate Logic or Discourse Representation Theory, but comes with a more well behaved consequence relation. A calculus for dynamic reasoning with anaphora is presented and its soundness and completeness are established. Incremental dynamic logic provides an explicit account of anaphoric context and yields new insight into the dynamics of anaphoric linking in reasoning. 1991 Mathematics Subject Classification: 03B65, 68Q55 1991 Computing Reviews Classification System: F.3.1, F.3.2, I.2.4, I.2.7 Keywords and Phrases: dynamic semantics of natural language, complete calculus for dynamic reasoning with anaphora, incremental interpretation, monotonic semantics, anaphora and context ...
Composition and Compilation in Functional Programming Languages
, 1994
"... Functional programming languages, such as Backus' FP, and high level expression oriented languages, such as APL, are examples of programming languages in which the primary method of program construction is the process of composition. In this paper we describe an approach to generating code for ..."
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Cited by 6 (2 self)
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Functional programming languages, such as Backus' FP, and high level expression oriented languages, such as APL, are examples of programming languages in which the primary method of program construction is the process of composition. In this paper we describe an approach to generating code for languages based on compositions. The approach involves finding an intermediate representation which grows in size very slowly as additional terms are composed. In particular, the size of the intermediate representation of a composed object should be considerably smaller, and easier to interpret, than the sum of the sizes of the internal representations of the individual elements. We illustrate this technique by showing how to generate conventional code for Backus' language FP. The general technique, however, is applicable to other languages, as well as other architectures. 1 Introduction The purposes of this paper are twofold. First, we want to describe an approach to compilation and code gener...
On the Formal Semantics of IFlike Logics
, 2009
"... In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Information Friendly (IF) logics. In this paper we argue that this is not an inherent characteristic of the ..."
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In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Information Friendly (IF) logics. In this paper we argue that this is not an inherent characteristic of these logics but a defect in the way in which the compositional semantics given by Hodges for the regular fragment was generalized to arbitrary formulas. We fix this by proposing an alternative formalization, based on a variation of the classical notion of valuation. Basic metatheoretical results are proven. We present these results for Hodges' slash logic (from which these can be easily transferred to other IFlike logics) and we also consider the flattening operator, for which we give novel gametheoretical semantics.
DOI 10.3233/FI2010306 IOS Press Church–Rosser Made Easy
"... Abstract. The Church–Rosser theorem states that the λcalculus is confluent under βreductions. The standard proof of this result is due to Tait and MartinLöf. In this note, we present an alternative proof based on the notion of acceptable orderings. The technique is easily modified to give conflue ..."
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Abstract. The Church–Rosser theorem states that the λcalculus is confluent under βreductions. The standard proof of this result is due to Tait and MartinLöf. In this note, we present an alternative proof based on the notion of acceptable orderings. The technique is easily modified to give confluence of the βηcalculus. Keywords: lambdacalculus, confluence, Church–Rosser theorem
Sharing in the Graph Rewriting Calculus
, 2012
"... The graph rewriting calculus is an extension of the ρcalculus, handling graph like structures, with explicit sharing and cycles, rather than simple terms. We study a reduction strategy for the graph rewriting calculus which is intended to maintain the sharing in the terms as long as possible. We sh ..."
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The graph rewriting calculus is an extension of the ρcalculus, handling graph like structures, with explicit sharing and cycles, rather than simple terms. We study a reduction strategy for the graph rewriting calculus which is intended to maintain the sharing in the terms as long as possible. We show that the corresponding reduction relation is adequate w.r.t. the original semantics of the graph rewriting calculus, formalising the intuition that the strategy avoids useless unsharing.
Completeness of Conversion between Reactive Programs for Ultrametric Models
"... Abstract. In 1970 Friedman proved completeness of beta eta conversion in the simplytyped lambda calculus for the settheoretical model. Recently Krishnaswami and Benton have captured the essence of Hudak’s reactive programs in an extension of simply typed lambda calculus with causal streams and a t ..."
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Abstract. In 1970 Friedman proved completeness of beta eta conversion in the simplytyped lambda calculus for the settheoretical model. Recently Krishnaswami and Benton have captured the essence of Hudak’s reactive programs in an extension of simply typed lambda calculus with causal streams and a temporal modality and provided this typed lambda calculus for reactive programs with a sound ultrametric semantics. We show that beta eta conversion in the typed lambda calculus of reactive programs is complete for the ultrametric model. 1
ABSTRACT Typed Logics With States
, 1997
"... and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of ..."
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and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of
Under consideration for publication in J. Functional Programming 1 The Lambda Calculus is Algebraic
"... This paper serves as a selfcontained, tutorial introduction to combinatory models of the untyped lambda calculus. We focus particularly on the interpretation of free variables. We argue that free variables should not be interpreted as elements in a model, as is usually done, but as indeterminates. ..."
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This paper serves as a selfcontained, tutorial introduction to combinatory models of the untyped lambda calculus. We focus particularly on the interpretation of free variables. We argue that free variables should not be interpreted as elements in a model, as is usually done, but as indeterminates. We claim that the resulting interpretation is more natural and leads to a closer correspondence between models and theories. In particular, it solves the problem of the notorious ξrule, which asserts that equations should be preserved under binders, and which fails to be sound for the usual interpretation.