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A Structural Approach to Operational Semantics
, 1981
"... Syntax of a very simple programming language called L. What is abstract about it will be discussed a little here and later at greater length. For us syntax is a collection of syntactic sets of phrases; each set corresponds to a different type of phrase. Some of these sets are very simple and can be ..."
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Cited by 1541 (3 self)
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be taken as given: Truthvalues This is the set T = ftt; ffg and is ranged over by (the metavariable) t (and we also happily employ for this (and any other) metavariable sub and superscripts to generate other metavariables: t ; t 0 ; t 1k ).
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 of arities. The treatment of rules and proofs focuses on his notion of a judgement. Logics are represented in LF via a new principle, the judgements as types principle, whereby each judgement is identified with the type of its proofs. This allows for a smooth treatment of discharge and variable occurrence conditions and leads to a uniform treatment of rules and proofs whereby rules are viewed as proofs of higherorder judgements and proof checking is reduced to type checking. The practical benefit of our treatment of formal systems is that logicindependent tools such as proof editors and proof checkers can be constructed.
LSCs: Breathing Life into Message Sequence Charts
, 2001
"... While message sequence charts (MSCs) are widely used in industry to document the interworking of processes or objects, they are expressively weak, being based on the modest semantic notion of a partial ordering of events as defined, e.g., in the ITU standard. A highly expressive and rigorously defin ..."
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Cited by 438 (71 self)
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While message sequence charts (MSCs) are widely used in industry to document the interworking of processes or objects, they are expressively weak, being based on the modest semantic notion of a partial ordering of events as defined, e.g., in the ITU standard. A highly expressive and rigorously defined MSC language is a must for serious, semantically meaningful tool support for usecases and scenarios. It is also a prerequisite to addressing what we regard as one of the central problems in behavioral specification of systems: relating scenariobased interobject specification to statemachine intraobject specification. This paper proposes an extension of MSCs, which we call live sequence charts (or LSCs), since our main extension deals with specifying "liveness", i.e., things that must occur. In fact, LSCs allow the distinction between possible and necessary behavior both globally, on the level of an entire chart and locally, when specifying events, conditions and progress over time within a chart. This makes it possible to specify forbidden scenarios, for example, and enables naturally specified structuring constructs such as subcharts, branching and iteration.
Tactic Theorem Proving with RefinementTree Proofs and Metavariables
 Proceedings, 12th International Conference on Automated Deduction
, 1994
"... . This paper describes a prototype of a programmable interactive theoremproving system. The main new feature of this system is that it supports the construction and manipulation of treestructured proofs that can contain both metavariables and derived rules that are computed by tactic programs. The ..."
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Cited by 7 (1 self)
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. This paper describes a prototype of a programmable interactive theoremproving system. The main new feature of this system is that it supports the construction and manipulation of treestructured proofs that can contain both metavariables and derived rules that are computed by tactic programs
The Use of Explicit Plans to Guide Inductive Proofs
 9TH CONFERENCE ON AUTOMATED DEDUCTION
, 1988
"... We propose the use of explicit proof plans to guide the search for a proof in automatic theorem proving. By representing proof plans as the specifications of LCFlike tactics, [Gordon et al 79], and by recording these specifications in a sorted metalogic, we are able to reason about the conjectures ..."
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Cited by 296 (40 self)
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We propose the use of explicit proof plans to guide the search for a proof in automatic theorem proving. By representing proof plans as the specifications of LCFlike tactics, [Gordon et al 79], and by recording these specifications in a sorted metalogic, we are able to reason about the conjectures to be proved and the methods available to prove them. In this way we can build proof plans of wide generality, formally account for and predict their successes and failures, apply them flexibly, recover from their failures, and learn them from example proofs. We illustrate this technique by building a proof plan based on a simple subset of the implicit proof plan embedded in the BoyerMoore theorem prover, [Boyer & Moore 79].
The Revised Report on the Syntactic Theories of Sequential Control and State
 THEORETICAL COMPUTER SCIENCE
, 1992
"... The syntactic theories of control and state are conservative extensions of the v calculus for equational reasoning about imperative programming facilities in higherorder languages. Unlike the simple v calculus, the extended theories are mixtures of equivalence relations and compatible congruen ..."
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Cited by 292 (37 self)
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The syntactic theories of control and state are conservative extensions of the v calculus for equational reasoning about imperative programming facilities in higherorder languages. Unlike the simple v calculus, the extended theories are mixtures of equivalence relations and compatible congruence relations on the term language, which significantly complicates the reasoning process. In this paper we develop fully compatible equational theories of the same imperative higherorder programming languages. The new theories subsume the original calculi of control and state and satisfy the usual ChurchRosser and Standardization Theorems. With the new calculi, equational reasoning about imperative programs becomes as simple as reasoning about functional programs.
A new approach to abstract syntax with variable binding
 Formal Aspects of Computing
, 2002
"... Abstract. The permutation model of set theory with atoms (FMsets), devised by Fraenkel and Mostowski in the 1930s, supports notions of ‘nameabstraction ’ and ‘fresh name ’ that provide a new way to represent, compute with, and reason about the syntax of formal systems involving variablebinding op ..."
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Cited by 286 (64 self)
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Abstract. The permutation model of set theory with atoms (FMsets), devised by Fraenkel and Mostowski in the 1930s, supports notions of ‘nameabstraction ’ and ‘fresh name ’ that provide a new way to represent, compute with, and reason about the syntax of formal systems involving variablebinding operations. Inductively defined FMsets involving the nameabstraction set former (together with Cartesian product and disjoint union) can correctly encode syntax modulo renaming of bound variables. In this way, the standard theory of algebraic data types can be extended to encompass signatures involving binding operators. In particular, there is an associated notion of structural recursion for defining syntaxmanipulating functions (such as capture avoiding substitution, set of free variables, etc.) and a notion of proof by structural induction, both of which remain pleasingly close to informal practice in computer science. 1.
Classes and Mixins
 In Principles of Programming Languages (POPL
, 1998
"... While classbased objectoriented programming languages provide a flexible mechanism for reusing and managing related pieces of code, they typically lack linguistic facilities for specifying a uniform extension of many classes with one set of fields and methods. As a result, programmers are unable ..."
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Cited by 284 (27 self)
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While classbased objectoriented programming languages provide a flexible mechanism for reusing and managing related pieces of code, they typically lack linguistic facilities for specifying a uniform extension of many classes with one set of fields and methods. As a result, programmers are unable to express certain abstractions over classes. In this paper we develop a model of classtoclass functions that we refer to as mixins. A mixin function maps a class to an extended class by adding or overriding fields and methods. Programming with mixins is similar to programming with single inheritance classes, but mixins more directly encourage programming to interfaces. The paper develops these ideas within the context of Java. The results are 1. an intuitive model of an essential Java subset; 2. an extension that explains and models mixins; and 3. type soundness theorems for these languages.
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