J. Goguen. Types as theories. In G.M. Reed, A.W. Roscoe, and R.F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357--390. Oxford, 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... account of coinduction, a proof technique commonly used in hidden algebra and coalgebra [9, 22, 14] 2 Hidden Algebra In order to motivate the constructions of Section 3, we give a brief introduction to behavioural equality in the context of hidden algebra, which was introduced by Goguen [6] as a foundation for a semantics of the object paradigm. Hidden algebra is based on many sorted equational logic, but has a weaker notion of satisfaction of equations: equations are behaviourally satis ed if no experiment can distinguish between the left and right hand sides of an equation. As a ....

Joseph A. Goguen. Types as theories. In George Michael Reed, Andrew William Roscoe, and Ralph F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357-390. Oxford University Press, 1991.

....Much interest has been shown in the study of institutions since they first appeared in 1986. Institutions have been given for lambda calculus, higher order logic with polymorphic types, second order and modal logics. Mosses [Mos89] shows that (his) unified algebras form an institution, Goguen [Gog91] shows that (his) hidden sorted equational logic is an institution, Mossakowski [Mos96] gives hierarchies of institutions for total, partial and order sorted logics, Rosu [Ros94] gives an institution for order sorted equational logic. Diaconescu, Goguen and Stefaneas [DGS93] and Rosu [Ros99] use ....

Joseph Goguen. Types as theories. In George Michael Reed, Andrew William Roscoe, and Ralph F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357--390. Oxford,

....to handle states in a natural way, using behavioral equivalence and satisfaction. Systems need only satisfy their requirements behaviorally, in the sense of appearing to satisfy them under all possible experiments or tests that can or are intended to be performed. Hidden algebra was introduced in [11] to give algebraic semantics to the object paradigm, and developed further in [13, 3, 18, 19, 31, 32, 10, 7, 6, 17, 21, 26, 15, 14, 30] among other places. Two systems, CafeOBJ [9] and BOBJ [15, 30] supporting hidden algebra and behavioral speci cation and reasoning have been implemented, both ....

J. Goguen. Types as theories. In G. Reed, A. W. Roscoe, and R. Wachter, editors, Topology and Category Theory in Computer Science, pages 357-390. Oxford, 1991.

....on module algebra by Bergstra, Heering and Klint [1] also investigates information hiding formally. Behavioral abstraction is another development in algebraic speci cation which appears under various names in the literature such as hidden algebra in works by Goguen, Diaconescu and many others [17, 19, 23, 22, 42, 26], observational logic in works by Hennicker, Bidoit and many others [29, 7, 4, 3] coherent hidden algebra in Diaconescu [13] hidden logic in Ro su [39] and so on. Most of these approaches appeared as a need to extend algebraic speci cations to ease the process of specifying and verifying ....

....Abstraction Hidden algebra extends algebraic speci cation to handle states in a natural way, using behavioral equivalence. Systems need only satisfy their requirements behaviorally, in the sense of appearing to satisfy them under all possible experiments. Hidden algebra was introduced in [17] and developed further in [19, 8, 23, 24, 38, 40, 42, 13, 10, 22, 26, 31, 20, 21, 39] among other places. Two systems, CafeOBJ [12] and BOBJ [20, 21, 39] supporting behavioral speci cation and reasoning have been implemented, both extending OBJ [27] A comprehensive presentation of hidden algebra ....

J. Goguen. Types as theories. In Topology and Category Theory in Computer Science, pages 357-390. Oxford, 1991.

....be satis ed by the actual parameter modules used in an instantiation. Nevertheless, it has for long been understood that the full generality and power of a module algebra based on the primitives of the Clear OBJ tradition requires parameterized theories and views, not just parameterized modules [34,32]. In this way, a considerably greater degree of genericity, modularity, and reusability can be achieved for speci cations and proofs. However, at present none of the implementations of the algebraic languages we are aware of, except perhaps for some partial prototype e ort, supports parameterized ....

J. Goguen. Types as theories. In G. Reed, A. Roscoe, and R. Wachter, editors, Topology and Category Theory in Computer Science, pages 357-390. Oxford University Press, 1991.

....of specifications in the language COLD are explained: first there is a specification of one s application domain using algebraic data types, and then there is the system description in terms of state machines . This second step corresponds to our coalgebraic (behavioural) specification. In [13, 6] the object paradigm is explained within the algebraic world using signatures with hidden sorts. The hidden part is given a terminal interpretation in [6] In this algebraic approach the output types of methods are unstructured, unlike in the coalgebraic approach below. This paper elaborates ....

J.A. Goguen. Types as theories. In G.M. Reed, A.W. Roscoe, and R.F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357--390. Oxford Univ. Press, 1991.

....graph transformation systems for studying horizontal and vertical structuring techniques as well as their compatibility with each other and with the semantics. Colimits, in particular pushouts and coproducts, are used as the composition mechanism of graph transformation systems, in the spirit of (Goguen, 1991). Colimits as a model for the gluing of systems with shared subsystems are very common, for example, in the area of algebraic specification (see (Ehrig and Mahr, 1985; Ehrig and Mahr, 1990) They have the immediate advantage that they are preserved by free functors. Thus, once we are able to show ....

....as a derived production. This observation leads to the definition of extended GTS morphisms that allow us to map productions to derivations (see Definition 4. 1) 4 The use of colimits to model the gluing of systems with shared subsystems is very common (and it is well motivated, for example, in (Goguen, 1991)) and has the immediate advantage that the semantic functor will be compositional with respect to such operations, because the semantics functor is a free functor which preserves colimits. The existence of colimits for arbitrary (finite) diagrams in GraSys provides the technical basis for this ....

Goguen, J. A. (1991). Types as theories. In Reed, G. M., Roscoe, A. W., and Wachter, R. F., editors, Topology and Category Theory in Computer Science, chapter 14, pages 357--390. Clarendon Press, Oxford.

No context found.

J. Goguen. Types as theories. In G.M. Reed, A.W. Roscoe, and R.F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357--390. Oxford, 1991.

No context found.

Joseph Goguen. Types as theories. In George Michael Reed, Andrew William Roscoe, and Ralph F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357--390. Oxford, 1991.

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Joseph Goguen. Types as theories. In George Michael Reed, Andrew William Roscoe, and Ralph F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357#390. Oxford, 1991. Proceedings of a Conference held at Oxford, June 1989.

....It follows that we should use equational logic wherever possible. Of course, it is not always possible; but this paper will show that many aspects of the object paradigm can be treated with equational reasoning. This paper continues the programme initially sketched in [11] formally begun in [15], and further elaborated in [19] This programme aims to generalise and integrate the classical initial algebraic semantics for Abstract Data Types (ADTs) with relevant aspects of process algebra, such as concurrency, hiding, non determinism, complex data structures, complex objects, and sharing ....

....7 also uses universal constructions. A general discussion of category theory for Computing Science is given in [14] 3 Hidden Sorted Algebra This section gives a brief summary of basic concepts from (overloaded many sorted) hidden sorted algebra, with some motivation, following the lines of [15]. The basic intuition is that an object has a state, which is hidden, i.e. only observed through the e ect of methods on attributes. This approach is a variant of algebra that: 0. xes an algebra D of data values; in typical applications, D might include natural numbers, booleans, character ....

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Joseph Goguen. Types as theories. In George Michael Reed, Andrew William Roscoe, and Ralph F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357-390. Oxford, 1991.

....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] Proofs by coinduction are dual to proofs by induction, in that the former are based on a largest congruence, and the latter on a smallest subalgebra (e.g. see [12] ....

Joseph Goguen. Types as theories. In George Michael Reed, Andrew William Roscoe, and Ralph F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357-- 390. Oxford, 1991.

....to the already present (P3) built in data types, P4) nondeterminism, P5) concurrency, and (P6) non congruent 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 non congruent operations in [5] all this was previously integrated in [21] but this paper gives new examples, institutions, and results ....

....sorted Sigma algebra A such that Aj Psi = D. 2 An adequate discussion of the complex historical and technical relations among the many approaches to behavioral specification is not possible in this short paper, but we do our best to be accurate, if not comprehensive. We drop the restriction of [9, 12] to operations with at most one hidden argument. Operations with hidden arguments may be called attributes if the result is visible, On leave from Fundamentals of Computer Science, Faculty of Mathematics, University of Bucharest, Romania. and methods if it is hidden; those with visible ....

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Joseph Goguen. Types as theories. In George Michael Reed, Andrew William Roscoe, and Ralph F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357--390. Oxford, 1991. Proceedings of a Conference held at Oxford, June 1989.

....specification for communication protocols [127, 128] Recent developments within the OBJ community include CafeOBJ, Maude, and CASL. CafeOBJ [26, 27] is being built at the Japan Institute of Science and Technology under the direction of Prof. Kokichi Futatsugi; it extends OBJ3 with hidden algebra [55, 80, 68, 67] for behavioral specification, and with rewriting logic [113, 114] for applications programming. Maude [112, 16] is being built at SRI International under the direction of Dr. Jos e Meseguer; it extends OBJ with rewriting logic, and has been successfully used for metaprogramming, reflection, and ....

....errors in some older specifications. 4 Parameterized Programming Both the costs and the demands for software are enormous, and are growing rapidly. One way to diminish these effects is to maximize the reuse of software, through the systematic use of what we call parameterized programming (see [85, 47, 52, 49, 36, 37, 55, 77]) Successful software reuse depends upon the following tasks being sufficiently easy: 1. finding old parts that are close enough to what you need; 2. understanding those parts; 3. getting them to do what you need now; and 4. putting them all together correctly. Under these conditions, the ....

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Joseph Goguen. Types as theories. In George Michael Reed, Andrew William Roscoe, and Ralph F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357--390. Oxford, 1991.

....examples. 1 Introduction A natural extension of algebraic speci cation distinguishes visible sorts for data from hidden sorts for states, with states behaviorally equivalent i they are indistinguishable under a given set of experiments; we have formalized this as hidden algebra, originating in [9] and further developed in [11, 20, 18, 19] and other papers. While standard equational proof techniques like induction are suitable for data, coinduction or context induction is generally needed for non trivial behavioral properties, typically requiring extensive human intervention. This is not ....

....variables replaced by the values given by . If one variable of t, say , is of special importance, then we may view the evaluation of t in two steps, as A t : A (A (var(t)f g) A) with the obvious meaning. 2. 2 Behavioral Speci cation and Satisfaction We generalize the hidden algebra of [9, 11, 19] to include variants such as observational logic [1, 3, 14] and coherent hidden algebra [6, 7] See [19] for a detailed presentation of variants, history, many other concepts, and proofs for some results mentioned here. Two important variants of behavioral logic are the xed data and the loose ....

J. Goguen. Types as theories. In G.M. Reed, A.W. Roscoe, and R.F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357-390. Oxford, 1991.

....abstract protocol is parameterized by dependencies among messages, including even non monotonic dependencies; for the concrete tatami protocol, the use of fuzzy truth values for boolean formulae is interesting, in addition to the way that it handles dependencies. 2 Hidden Algebra Hidden algebra [8,9] gives a general semantics for distributed concurrent systems; see [13] for a recent survey of the case where all operations are behavioral and have at most one argument hidden. The goal of hidden algebra is to significantly decrease the difficulty of proving properties of distributed concurrent ....

....E) where Sigma is a hidden signature, Gamma is a hidden subsignature of Sigma, and E is a set of Sigma equations. The operations in Gamma Gamma Psi are called behavioral. A hidden Sigma algebra is a many sorted Sigma algebra A such that Aj Psi = D. This drops the restriction of [8,13] to operations with at most one hidden argument. Operations in Sigma with one hidden argument and visible result may be called attributes, those with one hidden argument and hidden result methods, and those with visible arguments and hidden result (generalized) hidden constants. The data algebra ....

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Joseph Goguen. Types as theories. In George Michael Reed, Andrew William Roscoe, and Ralph F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357--390. Oxford, 1991.

.... that every computable algebra has a nite equational speci cation with some hidden operations, and examples show that the hidden operations are sometimes necessary (see [21] for a survey of this area) Third, 15] shows that every [ nite] behavioral (also called hidden) algebraic speci cation [12, 14, 26, 15, 24] has an equivalent [ nite] information hiding speci cation with the same models, but using ordinary satisfaction. Category theory and institutions are heavily used in this paper. Institutions formalize the informal notion of logical system, with a balanced interplay of syntax and semantics, to ....

Joseph Goguen. Types as theories. In George Michael Reed, Andrew William Roscoe, and Ralph F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357-390. Oxford, 1991. Proceedings of a Conference held at Oxford, June 1989.

....relationships between modules, of which the most basic are those of inheritance, indicated by the edges in the inheritance subgraph. N M means that M inherits from N . This relation is transitive because the composition of two paths is another path. The idea of module graphs originates in [Gog91]. Assumption 2 There are a fixed module graph G and inheritance subgraph H. 2 Another kind of relationship between modules is a view, which asserts that the target module satisfies the axioms given in the source module. The module graph G describes the resources available at a given moment for ....

....of Vth(M) see Figure 1. 3) However, this equation does have many visible consequences, which are equations of visible type, that would be part of Vth(M ) such as top(pop(push(I; S) top(S) top(pop(pop(push(I; S) top(pop(S) Such themes are much further developed in hidden algebra [GM97, Gog91]. Lemma 19 Given sets A and A of Sigma sentences and a subsignature Psi of Sigma, then A A implies Th Psi (A) Th Psi (A ) moreover, Th Psi (Th Psi (A) Th Psi (A) However, it is not true that A Th Psi (A) because Th Psi (A) only contains Psi axioms. Also, it is not ....

[Article contains additional citation context not shown here]

Goguen, J. Types as theories. In Reed, J.M., Roscoe, A.W., and Wachter, R.F., editors, Topology and Category Theory in Computer Science, pages 357--390. Oxford, 1991. Proceedings of a Conference held at Oxford, June 1989.

....such that r f = s g, there is a unique t : D E such that t q = r and t p = s; D is the pushout object. 2 Intuitively, pushouts combine two objects, identifying parts of one with parts of another; this gives an elegant semantics for instantiating parameterized modules. For more detail, see [12]; all this actually works for any logical system, via the formalism of institutions [13] For example, the institution for Lileanna [23, 15] has Anna for speci cations and Ada programs for models. For the special case of Example 1, the construction is as follows: Given a tting morphism f : TRIV ....

....SET and SETW is more subtle, and cannot be captured by just a view. The intuition is that SETW can be used wherever SET is called for. This more general notion is de ned below. 2 De nition 2 Given rst order parameterized algebraic speci cations (which could be modules over any institution [13, 12]) F : I M and F : I a rst order morphism from F to F is a view (i.e. a ground morphism) d : I I and a view r : M M [d] such that the diagram below commutes, d] I ## M where the left square is the pushout of F and d. 2 This de nition improves on ....

[Article contains additional citation context not shown here]

Joseph Goguen. Types as theories. In George Michael Reed, Andrew William Roscoe, and Ralph F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357-390. Oxford, 1991. Proceedings of a Conference held at Oxford, June 1989.

.... Our effort to design, implement, and evaluate tools for behavioral specification and verification includes the Tatami and BOBJ (for Behavioral OBJ, a member of the OBJ specification and verification language family implemented by Kai Lin) systems [10, 8] which are based on hidden algebra [6, 11]. Here we give the first correctness proof for BOBJ s circular coinduction algorithm [9] 2 Hidden Logic Hidden algebra extends algebraic specification to handle states in a natural way, using behavioral satisfaction, whereby systems need only satisfy their requirements behaviorally, in the sense ....

....Hidden Logic Hidden algebra extends algebraic specification to handle states in a natural way, using behavioral satisfaction, whereby systems need only satisfy their requirements behaviorally, in the sense of appearing to satisfy them under all possible experiments. Hidden algebra was introduced [6] to give algebraic semantics for the object paradigm, and developed further in other places [7, 11] One distinctive feature is to split sorts into visible for data, and hidden for states. A model, or hidden algebra, is an abstract implementation, consisting of the possible states, with functions ....

Joseph Goguen. Types as theories. In George Michael Reed, Andrew William Roscoe, and Ralph F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357--

.... Algebra and BOBJ The Tatami project uses an approach to behavioral specification and verification called hidden algebra, which extends standard many sorted algebra by distinguishing between visible sorts used to model data, and hidden sorts used to model states, as originally proposed in [9] and elaborated in many subsequent publications. This framework provides simple and natural ways to define behavioral equivalence of states, behavioral satisfaction of properties, and behavioral refinement of specifications. Standard equational deduction generalizes with small changes, but more ....

....algebra allows better control over the data involved, and admits equations with operations having multiple visible and hidden parameters, thus greatly extending expressive power. Behavioral logic is a diverse research area containing many approaches, including the original hidden algebra of [9] and subsequent improvements in [14,19,18] the coherent hidden algebra of Diaconescu [6,7] the observational logic of Bidoit and Hennicker [1,2,24] and a new generalization of hidden algebra that tries to treat all these variants in a uniform way [35,21] These approaches fall into two broad ....

Joseph Goguen. Types as theories. In George Michael Reed, Andrew William Roscoe, and Ralph F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357--390. Oxford,

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J. Goguen. Types as theories. In Topology and Category Theory in Computer Science, pages 357--390. Oxford, 1991.

No context found.

J. Goguen. Types as theories. In Topology and Category Theory in Computer Science, pages 357--390. Oxford, 1991.

No context found.

Joseph Goguen. Types as theories. In George Michael Reed, Andrew William Roscoe, and Ralph F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357-390. Oxford, 1991.

No context found.

Joseph Goguen. Types as theories. In George Michael Reed, Andrew William Roscoe, and Ralph F. Wachter, editors, Topology and Category Theory in Computer Science, pages 357--390. Oxford, 1991.

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