Abstract

this paper we introduce a variable typed logic of effects (i.e. a logic of effects where classes can be defined and quantified over) inspired by the variable type systems of Feferman [3, 4] for purely functional languages. A similar extension incorporating non-local control operations was introduced in [27]. The logic we present provides an expressive language for defining specifications and constraints and for studying properties and program equivalences, in a uniform framework. Thus it has an advantage over a plethora of systems in the literature that aim to capture solitary aspects of computation. The theory also allows for the construction of inductively defined sets and derivation of the corresponding induction principles. Classes can be used to express, inter alia, the non-expansiveness of terms [29]. Other effects can also be represented within the system. These include read/write effects and various forms of interference [24]. The first order fragment is described in [16] where it is used to resolve the denotationally problematic examples of [17]. In our language atoms, references and lambda abstractions are all first class values and as such are storable. This has several consequences. Firstly, mutation and variable binding are separate and so we avoid the problems that typically arise (e.g. in Hoare's and dynamic logic) from the conflation of program variables and logical variables. Secondly, the equality and sharing of references (aliasing) is easily expressed and reasoned about. Thirdly, the combination of mutable references and lambda abstractions allows us to study object based programming within our framework. Our atomic formulas express the (operational or observational) equivalence of programs `a la Plotkin [23]. Neither Hoare's logic nor Dynamic logi...

Citations