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Datatypes in Memory
"... Abstract. Besides functional correctness, specifications must describe other properties of permissible implementations. We want to use simple algebraic techniques to specify resource usage alongside functional behaviour. In this paper we examine the space behaviour of datatypes, which depends on the ..."
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Abstract. Besides functional correctness, specifications must describe other properties of permissible implementations. We want to use simple algebraic techniques to specify resource usage alongside functional behaviour. In this paper we examine the space behaviour of datatypes, which depends on the representation of values in memory. In particular, it varies according to how much values are allowed to overlap, and how much they must be kept apart to ensure correctness for destructive spacereusing operations. We introduce a mechanism for specifying datatypes represented in a memory, with operations that may be destructive to varying degrees. We start from an abstract model notion for datainmemory and then show how to specify the observable behaviour of models. The method is demonstrated by specifications of listsinmemory and pointers; with a suitable definition of implementation, we show that listsinmemory may be implemented by pointers. We then present a method for proving implementations correct and show that it is sound and, under certain assumptions, complete. 1
Dynamic Coalgebraic Modalities
"... With this work we aim to place dynamic modal logics such as Propositional Dynamic Logic (PDL) [1] and Game Logic (GL) [4] in a uniform coalgebraic framework. In our view, a dynamic system S consists of the following ingredients: 1. A set S which represents the global states of S. 2. An algebra L of ..."
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With this work we aim to place dynamic modal logics such as Propositional Dynamic Logic (PDL) [1] and Game Logic (GL) [4] in a uniform coalgebraic framework. In our view, a dynamic system S consists of the following ingredients: 1. A set S which represents the global states of S. 2. An algebra L of labels (denoting actions, programs, games,...). 3. An interpretation of labels as Gcoalgebras on the state space S. 4. A collection of labelled modalities [α], for α ∈ L, where intuitively [α]ϕ reads: “after α, ϕ holds”. Formally, the interpretation of labels is a map σ: L → (GS) S which describes how actions change the global system state. The algebraic structure on L describes how one can compose actions into more complex ones. The same type of algebraic structure should be carried by (GS) S, and we say that σ is standard, if σ is an algebra homomorphism, which means that the semantics of actions is compositional. By considering the exponential adjoint ̂σ: S → (GS) L we obtain a behavioural description of the system in the form of a G Lcoalgebra. These two (equivalent) views of a dynamic system form the basis of our modelling. In short, σ describes structure and dynamics, and ̂σ describes behaviour and induces modalities. σ: L → (GS) S (algebraic view: structure, dynamics)