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12
Hiding More of Hidden Algebra
 FM'99  Formal Methods
, 1999
"... This paper generalizes the hidden algebra approach to allow: (P1) operations with multiple hidden arguments, and (P2) defining behavioral equivalence with a subset of operations, in addition to the already present (P3) builtin data types, (P4) nondeterminism, (P5) concurrency, and (P6) noncongruen ..."
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Cited by 42 (15 self)
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This paper generalizes the hidden algebra approach to allow: (P1) operations with multiple hidden arguments, and (P2) defining behavioral equivalence with a subset of operations, in addition to the already present (P3) builtin data types, (P4) nondeterminism, (P5) concurrency, and (P6) noncongruent operations. All important results generalize, but more elegant formulations use the new institution in Section 5. Behavioral satisfaction appeared 1981 in [20], hidden algebra 1989 in [9], multiple hidden arguments 1992 in [1], congruent and behavioral operations in [1, 18], behavioral equivalence defined by a subset of operations in [1], and noncongruent operations in [5]; all this was previously integrated in [21], but this paper gives new examples, institutions, and results relating hidden algebra to information hiding. We assume familiarity with basics of algebraic specification, e.g., [11, 13].
Observer Complete Definitions are Behaviourally Coherent
 OBJ/CAFEOBJ/MAUDE AT FORMAL METHODS '99
, 1999
"... We consider observational specifications of statebased systems which incorporate the declaration of a distinguished set of observer operations. These observers determine an indistinguishability relation for states which is called "observational equality". An important requirement for the nono ..."
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Cited by 34 (5 self)
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We consider observational specifications of statebased systems which incorporate the declaration of a distinguished set of observer operations. These observers determine an indistinguishability relation for states which is called "observational equality". An important requirement for the nonobserver operations is the compatibility with the observational equality. In the CafeOBJ language (and in extended hidden algebra) this property is called "behavioural coherence". In this presentation we introduce the notion of an "observer complete definition" and we show that any (nonobserver) operation which is defined using this pattern is behaviourally coherent. We also discuss some consequences of this result for relating observational logic and extended hidden algebra semantics and for proving the correctness of observational implementations.
Hidden Congruent Deduction
 Automated Deduction in Classical and NonClassical Logics
, 1998
"... This paper presents some techniques of this kind in the area called hidden algebra, clustered around the central notion of coinduction. We believe hidden algebra is the natural next step in the evolution of algebraic semantics and its first order proof technology. Hidden algebra originated in [7], a ..."
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Cited by 27 (18 self)
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This paper presents some techniques of this kind in the area called hidden algebra, clustered around the central notion of coinduction. We believe hidden algebra is the natural next step in the evolution of algebraic semantics and its first order proof technology. Hidden algebra originated in [7], and was developed further in [8, 10, 3, 12, 5] among other places; the most comprehensive survey currently available is [12]
Social and Semiotic Analyses for Theorem Prover User Interface Design
 Formal Aspects of Computing
, 1999
"... We describe an approach to user interface design based on ideas from social science, narratology (the theory of stories), cognitive science, and a new area called algebraic semiotics. Social analysis helps to identify certain roles for users with their associated requirements, and suggests ways to m ..."
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Cited by 19 (11 self)
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We describe an approach to user interface design based on ideas from social science, narratology (the theory of stories), cognitive science, and a new area called algebraic semiotics. Social analysis helps to identify certain roles for users with their associated requirements, and suggests ways to make proofs more understandable, while algebraic semiotics, which combines semiotics with algebraic specification, provides rigorous theories for interface functionality and for a certain technical notion of quality. We apply these techniques to designing user interfaces for a distributed cooperative theorem proving system, whose main component is a website generation and proof assistance tool called Kumo. This interface integrates formal proving, proof browsing, animation, informal explanation, and online background tutorials, drawing on a richer than usual notion of proof. Experience with using the interface is reported, and some conclusions are drawn.
Conditional Circular Coinductive Rewriting with Case Analysis
, 2002
"... We argue for an algorithmic approach to behavioral proofs, review the hidden algebra approach, develop circular coinductive rewriting for conditional goals, extend it with case analysis, and give some examples. ..."
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Cited by 18 (1 self)
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We argue for an algorithmic approach to behavioral proofs, review the hidden algebra approach, develop circular coinductive rewriting for conditional goals, extend it with case analysis, and give some examples.
Circular Coinduction
 In International Joint Conference on Automated Reasoning
, 2000
"... Circular coinduction is a technique for behavioral reasoning that extends cobasis coinduction to specifications with circularities. Because behavioral satisfaction is not recursively enumerable, no algorithm can work for every behavioral statement. However, algorithms using circular coinduction can ..."
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Cited by 12 (5 self)
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Circular coinduction is a technique for behavioral reasoning that extends cobasis coinduction to specifications with circularities. Because behavioral satisfaction is not recursively enumerable, no algorithm can work for every behavioral statement. However, algorithms using circular coinduction can prove every practical behavioral result that we know. This paper proves the correctness of circular coinduction and some consequences.
Hidden Algebra for Software Engineering
 Proceedings Combinatorics, Computation and Logic
, 1999
"... : This paper is an introduction to recent research on hidden algebra and its application to software engineering; it is intended to be informal and friendly, but still precise. We first review classical algebraic specification for traditional "Platonic" abstract data types like integers, vectors, ma ..."
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Cited by 10 (0 self)
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: This paper is an introduction to recent research on hidden algebra and its application to software engineering; it is intended to be informal and friendly, but still precise. We first review classical algebraic specification for traditional "Platonic" abstract data types like integers, vectors, matrices, and lists. Software engineering also needs changeable "abstract machines," recently called "objects," that can communicate concurrently with other objects through visible "attributes" and statechanging "methods." Hidden algebra is a new development in algebraic semantics designed to handle such systems. Equational theories are used in both cases, but the notion of satisfaction for hidden algebra is behavioral, in the sense that equations need only appear to be true under all possible experiments; this extra flexibility is needed to accommodate the clever implementations that software engineers often use to conserve space and/or time. The most important results in hidden algebra are ...
Modular Swinging Types
, 1999
"... . Swinging types [18] provide an integrated framework for specifying software on the basis of manysorted logic in terms of "static" functions and relations as well as "dynamic" transition systems. Swinging types combine equational, Horn and modal logic for the purpose of using evaluation and pr ..."
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Cited by 8 (8 self)
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. Swinging types [18] provide an integrated framework for specifying software on the basis of manysorted logic in terms of "static" functions and relations as well as "dynamic" transition systems. Swinging types combine equational, Horn and modal logic for the purpose of using evaluation and proof rules from all three logics for rapid prototyping and verification. A swinging specification separates from each other visible sorts that denote domains of data identified by their structure; hidden sorts that denote domains of data identified by their behavior in response to observers; predicates (least relations) that represent inductive (ly provable) properties; and predicates (greatest relations) that represent complementary "coinductive" properties. The paper at hand deals with structured specifications with swinging components. Vertical structuring is supported by a deductionoriented refinement criterion that admits, for instance, to implement visible sorts by hidden s...
Hidden Congruent Deduction
 Automated Deduction in Classical and NonClassical Logics
, 1998
"... This paper presents some techniques of this kind in the area called hidden algebra, ..."
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Cited by 7 (0 self)
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This paper presents some techniques of this kind in the area called hidden algebra,