H. Ehrig and B. Mahr, : "Fundamentals of algebraic specification 1. equations and initial semantics", EATCS Monograph on Theoteritical Computer Science, 6, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are often based on abstract data types and the most popular approaches are based on algebraic semantics . Algebraic specifications denote indeed a lot of different specification languages (LARCH [GH86] ASL [SW83] Wir86] PLUSS [Gau92] CLEAR [BG80] San84] OBJ [FGJM85] ACT ONE ACT TWO [EM85]: and an incredible number of different specification theories. The paradigm of algebraic specifications is rather a 1 Consistency is not decidable in general but there are usually usable sufficient conditions to ensure consistency. 4 way of thinking semantics, with a common set of ....

....of the proposed specification languages, and with a syntax mainly based on equalities. Algebraic models are usually set of values, in most of the approaches each value has one or several types and there are operations or functions which work on those values according to their type(s) GTW78][EM85]. As we can imagine, in such a context time issues are rarely dealt with. A common opinion is that algebraic specifications should be used to describe functional aspects, in complementarity with other frameworks (such as temporal logics, Petri nets or transition systems) to specify real time ....

Ehrig H., Mahr B. : "Fundamentals of Algebraic Specification 1. Equations and initial semantics." EATCS Monographs on Theoretical Computer Science, Vol.6, SpringerVerlag, 1985.

....in the sense of (Francez and Forman, 1996) We shall now illustrate these points by using a subset of COMMUNITY. The simplification consists in omitting data type declarations and external attributes. More precisely, we shall assume a fixed signature (S,W) in the usual algebraic sense (Ehrig and Mahr, 1985), i.e. S is a set (of sort symbols) and W is an S S indexed family (of function symbols) together with a set DT of (first order) axioms over (S,W) defining the properties of the operations. A COMMUNITY program P in this simplified version has the following structure: P ### V #### I ## ....

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

....a structured operational semantics. It describes 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. ffl An abstract datatype language. ACT ONE [EM85], with an initial semantics. A type is defined by its signature (sorts operation on the sorts) and by equations to give a meaning to the operations. The revision of the LOTOS standard is under study in ISO IEC since 1991. The design of this enhanced version called E LOTOS is based on the ....

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 Theorical Computer Science, Springer-Verlag, 1985.

....: v n ] Definition 10 (State Representation) A problem state s is a conjunction of atoms over relational symbols in RP . That is, s 2 L(C; F ; RP ) We presuppose that terms are always evaluated if they are grounded. Evaluation of terms is defined in the usual way (Field Harrison, 1988; Ehrig Mahr, 1985): Definition 11 (Evaluation of Ground Terms) A term t over L(C; F) is evaluated in the following way: ffl eval(c) c, for c 2 C ffl eval(f(t 1 ; t n ) apply(f(eval(t 1 ) eval(t n ) for f 2 F and t 1 ; t n 2 C[F . Function application returns a unique value for ....

Ehrig, H., & Mahr, B. (1985). Fundamentals of Algebraic Specification 1 - Equations and Initial Semantics. Springer, Berlin.

....in the sense of (Francez and Forman, 1996) We shall now illustrate these points by using a subset of COMMUNITY. The simplification consists in omitting data type declarations and external attributes. More precisely, we shall assume a fixed signature (S,W) in the usual algebraic sense (Ehrig and Mahr, 1985), i.e. S is a set (of sort symbols) and W is an S S indexed family (of function symbols) together with a set DT of (first order) axioms over (S,W) defining the properties of the operations. A COMMUNITY program P in this simplified version has the following structure: P var V init I do ....

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

....has been the basis for the development of high level replacement systems. A simple example is the transformation in Figure 2 where we have omitted the inscriptions. Figure 2. Graph Transformation 2. SPEC; M injective ) where SPEC is the category consisting of algebraic specifications as in (Ehrig and Mahr, 1985) and structure preserving injective morphisms. This instance of high level replacement systems corresponds to algebraic specification grammars as introduced in (Ehrig and Parisi Presicce, 1991b) We give the subsequent transformation taken from (Ehrig and Parisi Presicce, 1991b) as an example. ....

.... places and 50 transitions and is represented using suitable horizontal structuring techniques developed in (Padberg et al. 1995) In our case study the data type of an algebraic high level net is defined by the initial semantics (quotient term algebra) of the algebraic specification as given in (Ehrig and Mahr, 1985). The data type of the actual state description is also very comwww rbr hl main.tex; 24 11 1998; 17:21; p.27 28 plex. Without basic data types, as lists, natural numbers, boolean, the full algebraic specification is presented on about 30 pages in (Ermel, 1996) The structuring of the data type ....

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Ehrig, H. and Mahr, B. (1985). Fundamentals of Algebraic Specification 1: Equations and Initial Semantics, volume 6 of EATCS Monographs on Theoretical Computer Science. Springer, Berlin.

....function of the set of axioms to a linear function. On the other hand, we formally prove that the testing coverage is as good as that proposed by Frankl et al. . 2. A SUMMARY OF FRANKL S FUNCTIONAL TESTING APPROACH In their functional testing approach, Frankl et al. . use algebraic specifications [17, 18, 19] of abstract data types (ADTs) to specify classes in target programs. A series of operations on an ADT is known as a term (or called a word in Frankl et al. . Let u 1 and u 2 be two terms of an ADT. Let s 1 and s 2 be the respective sequences of operations in a given implementation. ....

....sorted and N = N nil . sorting = nil [N] sorting = N] L . sorting = L if L . sorted (L [N] N ] L ) sorting = L [N ] N] L ) sorting if N N end A list of functions on an ADT is called a term if and only if it conforms to the standard syntax requirements of term algebra [17, 18] . A term can be transformed into another using the axioms of the specification as progressive left to right rewriting rules. A term is said to be in normal form if and only if no further axiom is applicable. A system of axioms is said to be canonical if and only if every sequence of rewriting on ....

EHRIG, H. and MAHR, B.: `Fundamentals of Algebraic Specifications 1: Equations and Initial Semantics', EATCS Monographs on Theoretical Computer Science, 1985, Vol. 6, Springer-Verlag, Berlin.

.... 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 that the semantics can be defined in terms of a free functor, it is easy to show that it is compositional w.r.t. the horizontal structuring. This is the first main ....

Ehrig, H. and Mahr, B. (1985). Fundamentals of Algebraic Specification 1: Equations and Initial Semantics, volume 6 of EATCS Monographs on Theoretical Computer Science. Springer, Berlin.

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H. Ehrig and B. Mahr, : "Fundamentals of algebraic specification 1. equations and initial semantics", EATCS Monograph on Theoteritical Computer Science, 6, 1985.

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EHRIG, H. and MAHR, B.: `Fundamentals of Algebraic Specifications 1: Equations and Initial Semantics', EATCS Monographs on Theoretical Computer Science, 1985, Vol. 6, Springer-Verlag, Berlin.

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H.Ehrig, B.Mahr "fundamentals of algebraic specification 1:equations and initial semantics,Springer Verlag 1985."

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Ehrig, H. and Mahr, B. 1985. Fundamentals of Algebraic Specification 1: Equations and Initial Semantics, EATCS Monographs, Springer Verlag.

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H. Ehrig and B. Mahr, "Fundamentals of algebraic specification 1: equations and initial semantics", EATCS Monographs, Springer Verlag, 1985.

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