Groe-Rhode, M.: 1997, `Transition Specifications for Dynamic Abstract Data Types'. Applied Categorical Structures 5(3), 265--308.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....mainly developed and successfully applied for the purely functional case. Anyway, since most of existing programming languages are imperative and even functional and logic languages are usually extended by imperative facilities, there seems to be a mismatch between theory and practice (see also [30] for a discussion about that) This mismatch is usually faced in two ways. Sometimes it is assumed that formal techniques in top down development always deal with purely functional descriptions, and the final step of translation in an imperative programming language is either straightforward, or ....

....are constituted by a set of states and a family of dynamic operations which model state transformations; moreover, each possible state of the module is a model in an underlying model part (called static framework) depending on the core language. In other words, we adopt a state as algebra approach [21, 28, 9, 30, 47], considering a state as a structure rather than an individual value. This approach has some useful consequences. First of all, it is possible to give a general theory of modules with state, abstracting from the different concrete notions of state which can arise in practice, in the spirit of the ....

Groe-Rhode, M.: 1997, `Transition Specifications for Dynamic Abstract Data Types'. Applied Categorical Structures 5(3), 265--308.

....abstracting from the specific nature of the type; in some sense a polymorphic clause. The model we have presented here can be considered inside the family of the so called state as algebra or dynamic data type approaches to the description and specification of dynamic systems (see, e.g. [6,4,7,9,20]) In all these approaches, the common idea is to model states of a dynamically evolving system by algebras, or more in general structures of some kind (models in the sense of the theory of institutions [8] and dynamic evolution by transformations of such structures. The framework presented in ....

M. Grosse-Rhode. Transition Specifications for Dynamic Abstract Data Types. Applied Categorical Structures, (5):268--308, 1997.

....to values by a partial function that characterizes the state. State transitions are given by manipulations of this partial function that are induced by the operations of the underlying static data type. Further developments concern the description of object sharing and object communities. In [429, 430, 431] a concrete version of the concept of dynamic abstract data types is worked out, based on partial algebras as static data types and states, and a constructive approach to state transitions specified by conditional parallel assignments. States correspond intuitively to environments, that is partial ....

M. Große-Rhode. Transition Specifications for Dynamic Abstract Data Types. accepted for publication in Applied Categorical Structures, \Phi, 1996.

....to values by a partial function that characterizes the state. State transitions are given by manipulations of this partial function that are induced by the operations of the underlying static data type. Further developments concern the description of object sharing and object communities. In [429, 430, 431] a concrete version of the concept of dynamic abstract data types is worked out, based on partial algebras as static data types and states, and a constructive approach to state transitions specified by conditional parallel assignments. States correspond intuitively to environments, that is partial ....

M. Große-Rhode. Transition Specifications for Dynamic Abstract Data Types. Bulletin of the EATCS, 55:121--127, 1995. \Phi.

.... Output(OK ) Buf Cont(Put(10 10 ; Empty) Buf Cont(Dup(Buf Cont) User State = Read(i) NotEq(i; 0) True ) User State(Terminated) Output(ERROR) Buf Cont(Put(10 10 ; Empty) Buf Cont(Dup(Buf Cont) end cases 13.4. 4 Statealgebras with references In [GR95,GR97] Gro e Rhode presents a state as algebra approach based on a general idea of reference . A statealgebra is a partial algebra which is an extension of a given algebra A, called the base model (static value algebra) More precisely, a state is considered as a static data type where references are ....

M. Große-Rhode. Transition specifications for dynamic abstract data types. Applied Categorical Structures, 5, 1997.

....and enough equations such that A, considered as a partial SPEC(A) algebra, is initial in PAlg(SPEC(A) Then A[E] is again a free construction w.r.t. a specification extension. This shows that for each set E of function entries w.r.t. A there is a free extension A[E] For further details see [Gro96] Definition 2.2 (State Space) Given states S and T w.r.t. A a SPEC homomorphism h : S T is a state morphism if it is compatible with the universal morphisms of S and T , i.e. h ffi j S = j T . States and state morphisms constitute the state space States(A) The state space States(A) is a ....

M. Große--Rhode. Transition specifications for dynamic abstract data types. accepted for publication in Applied Categorical Structures, 1996.

....step by step. It is of course not possible to discuss all of Z or to present the whole theory of transition specifications. However, the simplified versions discussed here should suffice to make the general concepts clear. For more detailed presentations the reader is referred to [9, 10] for Z and [7, 5] for transition specifications. The latter ones also contain the compositionality aspects that are not presented formally in this paper. In [6] further details concerning the relationship between Z and transition specifications are discussed. Acknowledgments: We are very grateful to Uwe Wolter who ....

M. Große--Rhode. Transition specifications for dynamic abstract data types. accepted for publication in Applied Categorical Structures, 1996.

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Groe-Rhode, M.: Transition Specifications for Dynamic Abstract Data Types, APCS5:pp. 265-308, 1997

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