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Equational Calculi and Constant Depth Propositional Proofs
, 1998
"... . We define equational calculi for proving equations between functions in the complexity classes ACC(2) and TC 0 , and we show that proofs in these calculi can be simulated by polynomial size, constant depth proofs in Frege systems with counting modulo 2 and threshold connectives respectively. Int ..."
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Cited by 5 (1 self)
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. We define equational calculi for proving equations between functions in the complexity classes ACC(2) and TC 0 , and we show that proofs in these calculi can be simulated by polynomial size, constant depth proofs in Frege systems with counting modulo 2 and threshold connectives respectively
A Framework for Defining Logics
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1993
"... The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of ariti ..."
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Cited by 807 (45 self)
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The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system
A Syntactic Approach to Type Soundness
 INFORMATION AND COMPUTATION
, 1992
"... We present a new approach to proving type soundness for Hindley/Milnerstyle polymorphic type systems. The keys to our approach are (1) an adaptation of subject reduction theorems from combinatory logic to programming languages, and (2) the use of rewriting techniques for the specification of the la ..."
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Cited by 634 (25 self)
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soundness proof for polymorphic exceptions and continuations.
Nonmonotonic Reasoning, Preferential Models and Cumulative Logics
, 1990
"... Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of ..."
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Cited by 624 (14 self)
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of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties. We concentrate on a number of families of nonmonotonic consequence relations, defined in the style of Gentzen [13]. Both prooftheoretic and semantic points
Computational LambdaCalculus and Monads
, 1988
"... The calculus is considered an useful mathematical tool in the study of programming languages, since programs can be identified with terms. However, if one goes further and uses fijconversion to prove equivalence of programs, then a gross simplification 1 is introduced, that may jeopardise the ..."
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Cited by 505 (7 self)
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is about logics for reasoning about programs, in particular for proving equivalence of programs. Following a consolidated tradition in theoretical computer science we identify programs with the closed terms, possibly containing extra constants, corresponding to some features of the programming language
Symbolic Model Checking for Realtime Systems
 INFORMATION AND COMPUTATION
, 1992
"... We describe finitestate programs over realnumbered time in a guardedcommand language with realvalued clocks or, equivalently, as finite automata with realvalued clocks. Model checking answers the question which states of a realtime program satisfy a branchingtime specification (given in an ..."
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Cited by 574 (50 self)
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We describe finitestate programs over realnumbered time in a guardedcommand language with realvalued clocks or, equivalently, as finite automata with realvalued clocks. Model checking answers the question which states of a realtime program satisfy a branchingtime specification (given in an extension of CTL with clock variables). We develop an algorithm that computes this set of states symbolically as a fixpoint of a functional on state predicates, without constructing the state space. For this purpose, we introduce a calculus on computation trees over realnumbered time. Unfortunately, many standard program properties, such as response for all nonzeno execution sequences (during which time diverges), cannot be characterized by fixpoints: we show that the expressiveness of the timed calculus is incomparable to the expressiveness of timed CTL. Fortunately, this result does not impair the symbolic verification of "implementable" realtime programsthose whose safety...
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 546 (25 self)
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Least fixpoints as meanings of recursive definitions.
A Compositional Approach to Performance Modelling
, 1996
"... Performance modelling is concerned with the capture and analysis of the dynamic behaviour of computer and communication systems. The size and complexity of many modern systems result in large, complex models. A compositional approach decomposes the system into subsystems that are smaller and more ea ..."
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Cited by 746 (102 self)
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Performance modelling is concerned with the capture and analysis of the dynamic behaviour of computer and communication systems. The size and complexity of many modern systems result in large, complex models. A compositional approach decomposes the system into subsystems that are smaller and more easily modelled. In this thesis a novel compositional approach to performance modelling is presented. This approach is based on a suitably enhanced process algebra, PEPA (Performance Evaluation Process Algebra). The compositional nature of the language provides benefits for model solution as well as model construction. An operational semantics is provided for PEPA and its use to generate an underlying Markov process for any PEPA model is explained and demonstrated. Model simplification and state space aggregation have been proposed as means to tackle the problems of large performance models. These techniques are presented in terms of notions of equivalence between modelling entities. A framewo...
Theory and Practice of Constraint Handling Rules
, 1998
"... Constraint Handling Rules (CHR) are our proposal to allow more flexibility and applicationoriented customization of constraint systems. CHR are a declarative language extension especially designed for writing userdefined constraints. CHR are essentially a committedchoice language consisting of mu ..."
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Cited by 459 (36 self)
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Constraint Handling Rules (CHR) are our proposal to allow more flexibility and applicationoriented customization of constraint systems. CHR are a declarative language extension especially designed for writing userdefined constraints. CHR are essentially a committedchoice language consisting of multiheaded guarded rules that rewrite constraints into simpler ones until they are solved. In this broad survey we aim at covering all aspects of CHR as they currently present themselves. Going from theory to practice, we will define syntax and semantics for CHR, introduce an important decidable property, confluence, of CHR programs and define a tight integration of CHR with constraint logic programming languages. This survey then describes implementations of the language before we review several constraint solvers  both traditional and non standard ones  written in the CHR language. Finally we introduce two innovative applications that benefited from using CHR.
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