Hartmut Ehrig and Bernd Mahr. Fundamentals of Algebraic Specification 2. Springer-Verlag Berlin Heidelberg, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....specification. We will only consider the verification of dynamic behaviour, whereas a complete treatment would require additional reasoning concerning the role of the data types that are used. Standard theory on the verification of abstract data types can be found in, for example, [10, 11]. This limitation means that the specifications presented in Section 3 can be simplified by replacing the events that model the communication of data with 12 events that model merely synchronization (each event consists of only a gate name) Alternatively, one can view the simplification as ....

H. Ehrig and B. Mahr, Fundamentals of Algebraic Specification 1 (Springer-Verlag, 1985).

....HETEROGENEOUS INSTITUTIONAL FRAMEWORK In this section we introduce the syntactic and semantic definition of the notions of module and heterogeneous modular system considered. The notion of module that we consider is inspired in the one defined in [8] and is quite close to the notion studied in [5] (also used in [14] and to other module notions (e.g. 17] The intuition behind this concept is the following one: a module MOD is some kind of specification (or program) unit that not only consists of a specification BOD of the objects specified in the unit, but also includes two additional ....

....representing the relations among these specifications in Spec . We consider that the semantics of a module MOD is just the class U v (Mod(BOD) This may be considered too simple, but it is actually a generalization of the most standard semantics. For instance, the semantics of ACT TWO modules [5] can be seen as a special case of this one, if we 3 assume that BOD includes (as axioms) some free generating constraints [16] Often modules are seen as some kind of functions that, given some kind of realization of the import specification yield a realization of the export specification. In our ....

H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification 2. Springer, 1989.

....p calculus) and logic (universal and existential quantification 8 and 9) Binding signatures generalise signatures in that they allow an operator to bind variables in some of its argument. A binding algebra for a binding signature is then a generalisation of an algebra for a signature (see e.g. [EM85]) providing a suitable interpretation for operations which bind variables. We present the treatment of binding algebras in [FPT99] generalised to multisorted signatures. Binding Signatures and Terms We define binding signatures and algebras in a multi sorted (or typed) setting, as is needed ....

H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification 1. Springer, 1985.

....new specification Stack(Nat) What is reused is the text of the parameterized specification. Except for that, the model classes of Stack(El) and Stack(Nat) are just model classes of two di#erent specifications, related merely by the existence of a reduct functor from the latter to the former, e.g. [2]. Specification of a parameterized data type, PDT [12, 13] on the other hand, is a specification which requires a reusable implementation. e.g. specification of a data type stack parameterized by elements, Stack[El] requires an implementation of a data type with a parameter, i.e. one ....

....the idea of specifying actual architecture of designed software should appeal to one s sense of potential applicability of specifications. We mention a few possible reasons of this negligence which also indicate the approach of this paper. Study of PSPs has long tended in the direction of PDTs [1, 2, 3, 5]. One of the problems is that, while the former continued the tradition of working with classes axiomatized by (possibly conditional) equations, the latter require a precise grasp on individual algebras (which, for modeling purposes, can be identified with programs) a program P taking as a ....

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Hartmut Ehrig and Bernd Mahr. Fundamentals of Algebraic Specification 1. Springer, 1985.

....to summarize here. An overview with an annotated bibliography can be found in [Bidoit, Kreowski, Lescanne, Orejas, Sannella, 1991] First of all, one may ask on which results from the literature our own work is built. In fact, all we use is the theory of initial algebra semantics (as described in [Ehrich, Mahr, 1985]) the theory of term rewriting systems (as described in [Dershowitz, Jouannaud, 1991] and [Klop, 1991] and the theory of path orderings ( Huet, Oppen, 1980] This theory is well known and may be considered background knowledge for people working in the field of algebraic specifications. The ....

....Oppen, 1980] This theory is well known and may be considered background knowledge for people working in the field of algebraic specifications. The notion of persistence is also part of this background knowledge . It is treated extensively in classics like [Goguen, Thatcher, Wagner, 1976] [Ehrich, Mahr, 1985], Padawitz, 1983] and [Broy, Wirsing, 1982] Still, even though the part of the theory that we use is well known, in order to make the presentation of our Perspect language self contained we give an (almost) complete account of it in chapter 2. For definitions and proofs that we copied from the ....

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H. Ehrich, B. Mahr. Fundamentals of Algebraic Specification 1, Equations and Initial Semantics. Springer-Verlag. Berlin, etc., 1985.

....refer to [11] for more details on the composition procedure. 2 Preliminaries: Typed and Parameterized Signatures A signature Sigma = S; OP ) is given by a set S of sort symbols (marked with sorts) including the symbol for the empty type and a set OP of operation symbols (marked with opns) [3]. Operations are defined by name and functionality op : w s, where w = s 1 Theta : Theta s n with s 2 S and n 1 ) s i 6= Operations with empty domain are called constants, operations with empty codomain are called predicates [7] In parameterized signatures we distinguish between the ....

Hartmut Ehrig and Bernd Mahr. Fundamentals of Algebraic Specification 1. SpringerVerlag Berlin Heidelberg, 1985.

....the behaviour of processes and their interactions. LOTOS has a rich set of operators (multiway synchronization and abstraction like in CSP, disabling, and an explicit internal action like in CCS. LOTOS is briefly introduced in the appendix. An algebraic datatype language, ACT ONE [EM85] A type is defined by its signature (sorts operations on the sorts) and by equations to give a meaning to the operations. 3.1. Behaviour The LOTOS specification models both the Equicrypt system and the environment that it interacts with as two processes EquicryptSystem and Environment (fig. ....

H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification 1, Equations and Initial Semantics. In: W. Brauer, B. Rozenberg, A. Salomaa, eds., EATCS , Monographs on Theoretical Computer Science, Springer Verlag, 1985.

....the behaviour of processes and their interactions. LOTOS has a rich set of operators (multiway synchronization and abstraction like in CSP, disabling, and an explicit internal action like in CCS. LOTOS is briefly introduced in the appendix. An algebraic datatype language, ACT ONE [EM85] A type is defined by its signature (sorts operations on the sorts) and by equations to give a meaning to the operations. The LOTOS specification is composed of four processes: two CHAP entities A and B, and two simplex communication media (figure 2) Both entities share a common secret S ab ....

H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification 1, Equations and Initial Semantics. In: W. Brauer, B. Rozenberg, A. Salomaa, eds., EATCS , Monographs on Theoretical Computer Science, Springer Verlag, 1985.

....ODP concepts and is the core of our formalization work. The work may be continued in future with part 3 that presents the constraints to which ODP standards must confirm. Part 4 of RM ODP describes the recommendations for approaching the standard formalization with LOTOS ( 16] 25] ACT ONE [13], SDL 92 [18] Z ( 10] 36] and ESTELLE [15] languages. Unfortunately, these are just recommendations or, in the best cases, small unrelated pieces of formalization presented with different formal techniques for the part 2 concepts. As a matter of fact, while the goal of the part 4 is to present ....

H. Ehrig and B. Mahr. "Fundamentals of algebraic specification". EATCS Monographs on Theoretical Computer Science, vol. 6, Springer-Verlag, 1985.

....aspects are available in the LOTOS language [17, 5, 20] that was developed for the specification of distributed systems. The dynamic part is based on process algebra, like CCS [21] or CSP [15] and the static part is based on abstract data types, as in the algebraic specification language ACT ONE [7]. This work was achieved while this author was at IRIN. Among the few methods related to LOTOS development, the main tendencies are the constraint oriented approach and the state oriented approach. In the constraint oriented approach the overall system is split into concurrent subprocesses. ....

....offer synchronization and it does nothing, it is a blocked process. 2.2 Full LOTOS Full LOTOS copes with data specifications, data transfer during synchronizations and process parameterization over specified data domains. Data structures and values are described algebraically as in ACT ONE [7]. Variables are typed (X:NAT, Y:BOOL, and the language is typed. Types are predefined and imported from a library or defined by a specification: type . endtype. In full LOTOS, communications on gates are enriched by value passing. For example, in the following expression: exchange Put ....

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H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification, volume 1. SpringerVerlag, Berlin, 1985.

.... care attitude as to which among a number of computational paths will actually be utilized in a particular computation (e.g. Dijkstra 1976] or as a means of increasing the level of abstraction [Meldal 1989, Walicki 1994a] The present work proceeds from the theory of algebraic specifications [Ehrig 1985, Wirsing 1990] and generalizes it so that it can be applied to describing nondeterministic operations. Our main concern is to make such an extension non intrusive, i.e. such that it does not change the existing framework, and in particular, reduces to the standard deterministic theory when only ....

....for every sort but other ways of restricting the signatures [Goguen 1981, Huet 1980] or ensuring nonemptiness [Goguen 1981, Goguen 1987] can be used instead. It seems also that the most flexible approach which generalizes calculus by introducing explicit variables [Goguen 1981, Goguen 1982, Ehrig 1985] can be adapted to our framework. An equivalent (and the original) formulation of the syntax and the following results could use sequents A , B, where all atoms in A are equalities (corresponding to ) and all atoms in B equalities or inclusions. Because such a formulation complicates the ....

Ehrig, H., Mahr, B., Fundamentals of Algebraic Specification , vol. 1, Springer, 1985.

....and types definition describes data structure. The data structure is based on the formal theory on abstract data types, in particular the methods of equational specification of data types with initial algebra semantics. Most of the concepts are based on the abstract data type technique ACT ONE [EHR. 85] While, the control structure describes the systems externally observable behaviour by describing the temporal relations among the interactions. The concept for this description technique are based on process algebraic methods or process algebras, specially on Milner s work on CCS [MIL. 80] ....

H. Ehrig and B. Mahr, "Fundamentals of Algebraic Specifications", Springer Verlag, (19985).

....contextsensitive rewriting. term rewriting systems, regularity, functional programming. This work has been partially supported by CICYT under grant TIC 95 0433 C03 03. Salvador Lucas The theory of Term Rewriting Systems (TRSs) has proven useful to mechanize the execution of functional programs [3] by imposing directionality on the use of equations in proofs [1, 2] Directed equations, called rewrite rules , are used to replace equals by equals, but only in the indicated direction. In this scheme, computation consists of rewriting terms to a normal form, i.e. an expression that cannot be ....

H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification. volume 6 of . Springer-Verlag, Berlin, 1985.

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Hartmut Ehrig and Bernd Mahr. Fundamentals of Algebraic Specification 2. Springer-Verlag Berlin Heidelberg, 1990.

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Hartmut Ehrig and Bernd Mahr. Fundamentals of Algebraic Specification 1. Springer-Verlag Berlin Heidelberg, 1985.

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H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification 2. Springer-Verlag, 1989.

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Ehrig, H. and Mahr, B. (1985). Fundamentals of Algebraic Specifications, 1:Equations and Initial Semantics. Springer Verlag, Berlin.

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H. Ehrig, B. Mahr. " Fundamentals of Algebraic Specification". Vol-1 & 2. SpringerVerlag1985.

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H. Ehrig, B. Mahr, Fundamentals of Algebraic Specification 2, Module Specifications Constraints, Springer Verlag, 1990

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H. Ehrig, B. Mahr, Fundamentals of Algebraic Specification 1, Springer Verlag, 1985

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H. Ehrig, B. Mahr, Fundamentals of Algebraic Specification 1, Springer 1985

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H. Ehrig, B. Mahr, Fundamentals of Algebraic Specification 1, Springer 1985

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Hartmut Ehrig and Bernd Mahr. Fundamentals of Algebraic Specification 1. Springer, 1985.

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Hartmut Ehrig and Bernd Mahr. Fundamentals of Algebraic Specification 1. SpringerVerlag Berlin Heidelberg, 1985.

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H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification 1. SpringerVerlag, Berlin 1985

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