Gordon D. Plotkin

Call-by-Name, Call-by-Value and the λ-Calculus

Abstract This paper examines the old question of the relationship between ISWIM and the λ-calculus, using the distinction between call-by-value and call-by-name. It is held that the relationship should be mediated by a standardisation theorem. Since this leads to difficulties, a new λ-calculus is introduced whose standardisation theorem gives a good correspondence with ISWIM as given by the SECD machine, but without the letrec feature. Next a call-by-name variant of ISWIM is introduced which is in an analogous correspondence withthe usual λ-calculus. The relation between call-by-value and call-by-name is then studied by giving simulations of each language by the other and interpretations of each calculus in the other. These are obtained as another application of the continuation technique. Some emphasis is placed throughout on the notion of operational equality (or contextual equality). If terms can be proved equal in a calculus they are operationally equal in the corresponding language. Unfortunately, operational equality is not preserved by either of the simulations.

A framework for defining logics

The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed λ-calculus with dependent types. Syntax is treated in a style similar to, but more general than, Martin-Lo¨fs system of arities. The treatment of rules and proofs focuses on his notion of a judgment. Logics are represented in LF via a new principle, the judgments as types principle, whereby each judgment is identified with the type of its proofs. This allows for a smooth treatment of discharge and variable occurence conditions and leads to a uniform treatment of rules and proofs whereby rules are viewed as proofs of higher-order judgments and proof checking is reduced to type checking. The practical benefit of our treatment of formal systems is that logic-independent tools, such as proof editors and proof checkers, can be constructed.

LCF considered as a programming language

Abstract The paper studies connections between denotational and operational semantics for a simple programming language based on LCF. It begins with the connection between the behaviour of a program and its denotation. It turns out that a program denotes ⊥ in any of several possible semantics if it does not terminate. From this it follows that if two terms have the same denotation in one of these semantics, they have the same behaviour in all contexts. The converse fails for all the semantics. If, however, the language is extended to allow certain parallel facilities behavioural equivalence does coincide with denotational equivalence in one of the semantics considered, which may therefore be called “fully abstract”. Next a connection is given which actually determines the semantics up to isomorphism from the behaviour alone. Conversely, by allowing further parallel facilities, every r.e. element of the fully abstract semantics becomes definable, thus characterising the programming language, up to interdefinability, from the set of r.e. elements of the domains of the semantics.

Petri nets, event structures and domains, part I

Abstract The general aim of this paper is to find a theory of concurrency combining the approaches of Petri and Scott (and others). In part I we introduce our formalisms. To connect the abstract ideas of events and domains of information, we show how casual nets induce certain kinds of domains where the information points are certain sets of events. This allows translations between the languages of net theory and domain theory. Following the idea that events of causal nets are occurrences, we generalise causal nets to occurrence nets, by adding forwards conflict. Just as infinite flow charts unfold finite ones, so transition nets can be unfolded into occurrence nets. Next we extend the above connections between nets and domains to these new nets. Event structures which are intermediate between nets and domains play an important part in all our work. Finally, as an example of how concepts translate from one formalism to the other, we show how Petris notion of confusion ties up with Kahn and Plotkins concrete domains. In part II we shall continue the job of connecting up notions within net theory and the theory of domains. In particular, we shall examine the idea of states of computations.

A calculus for access control in distributed systems

We study some of the concepts, protocols, and algorithms for access control in distributed systems, from a logical perspective. We account for how a principal may come to believe that another principal is making a request, either on his own or on someone elses behalf. We also provide a logical language for accesss control lists and theories for deciding whether requests should be granted.

A Powerdomain Construction

We develop a powerdomain construction,

The Category-Theoretic Solution of Recursive Domain Equations

\mathcal{P}[ \cdot ]

Abstract types have existential type

, which is analogous to the powerset construction and also fits in with the usual sum, product and exponentiation constructions on domains. The desire for such a construction arises when considering programming languages with nondeterministic features or parallel features treated in a nondeterministic way. We hope to achieve a natural, fully abstract semantics in which such equivalences as

Petri Nets, Event Structures and Domains

(p\textit{ par } p) = (q\textit{ par }p)

Abstract syntax and variable binding

hold. The domain (