Theory and Practice of Action Semantics

Action Semantics is a framework for the formal descriptionof programming languages. Its main advantage over other frameworksis pragmatic: action-semantic descriptions (ASDs) scale up smoothly torealistic programming languages. This is due to the inherent extensibilityand modifiability of ASDs, ensuring that extensions and changes tothe described language require only proportionate changes in its description.(In denotational or operational semantics, adding an unforeseenconstruct to a language may require a reformulation of the entire description.)After sketching the background for the development of action semantics,we summarize the main ideas of the framework, and provide a simpleillustrative example of an ASD. We identify which features of ASDsare crucial for good pragmatics. Then we explain the foundations ofaction semantics, and survey recent advances in its theory and practicalapplications. Finally, we assess the prospects for further developmentand use of action semantics.The action semantics framework was initially developed at the Universityof Aarhus by the present author, in collaboration with David Watt(University of Glasgow). Groups and individuals scattered around fivecontinents have since contributed to its theory and practice

Type inference for action semantics

Action semantics, developed by Mosses and Watt, is a metalanguage for denotational semantics in which program denotations are actions. We study actions as polymorphic combinators that operate on collections of types. Our work includes a category-sorted algebra-based model for action semantics; a unification-based type inference algorithm for action expressions similar to that used for ML, extended with subtypes and records; proofs of its soundness and completeness with respect to the model; and an algorithm for simplifying inheritance subtyping constraints on records to constraints on non-record primitives. Our work extends other research on type inference with subtypes and records, primarily because our results are based on a semantic model: we avoid the large constraint sets encountered by previous researchers because coercions are not needed in our model. Our system provides record concatenation and union operations, without the need for complex constraints on record types

Semantic Domains and Denotational Semantics

The theory of domains was established in order to have appropriate spaces on which to define semantic functions for the denotational approach to programming-language semantics. There were two needs: first, there had to be spaces of several different types available to mirror both the type distinctions in the languages and also to allow for different kinds of semantical constructs - especially in dealing with languages with side effects; and second, the theory had to account for computability properties of functions - if the theory was going to be realistic. The first need is complicated by the fact that types can be both compound (or made up from other types) and recursive (or self-referential), and that a high-level language of types and a suitable semantics of types is required to explain what is going on. The second need is complicated by these complications of the semantical definitions and the fact that it has to be checked that the level of abstraction reached still allows a precise definition of computability

The action semantics of object-oriented languages

Action Semantics is a framework for defining the semantics of languages. It is intended to be accessible to a wider audience of Computer Scientists than traditional semantics frameworks (such as Denotational Semantics). There has been little work carried out to date on the techniques required to define object-oriented languages with Action Semantics. The work presented in this thesis examines four potential approaches to defining the Action Semantics of object-oriented languages. In order to illustrate the four approaches a simple language EIL (Example Inheritance Language) is given, and described using these four approaches. The language Smalltalk-80 has been selected for a case study of a practical application of one of the techniques described above. It is important to be able to relate Action Semantics definitions of object-oriented languages to similar definitions given in other frameworks. It is described how this can be achieved. An example is given for the Action Semantics and Denotational Semantics of Smalltalk. This thesis concludes that it is feasible to produce Action Semantics definitions of object-oriented languages

Action semantics of unified modeling language

The Uni ed Modeling Language or UML, as a visual and general purpose modeling language, has been around for more than a decade, gaining increasingly wide application and becoming the de-facto industrial standard for modeling software systems. However, the dynamic semantics of UML behaviours are only described in natural languages. Speci cation in natural languages inevitably involves vagueness, lacks reasonability and discourages mechanical language implementation. Such semi-formality of UML causes wide concern for researchers, including us. The formal semantics of UML demands more readability and extensibility due to its fast evolution and a wider range of users. Therefore we adopt Action Semantics (AS), mainly created by Peter Mosses, to formalize the dynamic semantics of UML, because AS can satisfy these needs advantageously compared to other frameworks. Instead of de ning UML directly, we design an action language, called ALx, and use it as the intermediary between a typical executable UML and its action semantics. ALx is highly heterogeneous, combining the features of Object Oriented Programming Languages, Object Query Languages, Model Description Languages and more complex behaviours like state machines. Adopting AS to formalize such a heterogeneous language is in turn of signi cance in exploring the adequacy and applicability of AS. In order to give assurance of the validity of the action semantics of ALx, a prototype ALx-to-Java translator is implemented, underpinned by our formal semantic description of the action language and using the Model Driven Approach (MDA). We argue that MDA is a feasible way of implementing this source-to-source language translator because the cornerstone of MDA, UML, is adequate to specify the static aspect of programming languages, and MDA provides executable transformation languages to model mapping rules between languages. We also construct a translator using a commonly-used conventional approach, in i which a tool is employed to generate the lexical scanner and the parser, and then other components including the type checker, symbol table constructor, intermediate representation producer and code generator, are coded manually. Then we compare the conventional approach with the MDA. The result shows that MDA has advantages over the conventional method in the aspect of code quality but is inferior to the latter in terms of system performance

Time and space complexity of rule-based graph programs

This thesis concerns the time and space efficiency of programs in GP 2, a rule-based graph transformation language that facilitates formal program analysis. Such programs are a sequence of control structures in which rules are called. A rule describes how part of a host graph is changed to another by specifying a subgraph that is to be replaced. We call the process of finding the specified subgraph in the host graph matching, which takes polynomial time in general. In practise however, we often want rule application to take constant time since it likely corresponds to a single step in a classical algorithm. Several case studies show that the time complexity of GP 2 programs can be on the same level as that of their imperative counterparts. We give linear-time programs for connectedness checking, DAG recognition, and topological sorting, as well as an efficient implementation of Boruvka’s algorithm for finding minimum spanning trees. This efficiency is achieved via roots, which are special nodes in rules and graphs that can be accessed in constant time and allow matching to happen locally around them. The given programs also use depth-first search to traverse graphs in linear time instead of iterating over nodes because GP 2 abstracts away from internal graph data structures. In the spirit of formal program analysis, we give a framework in which to describe the time complexity of these efficient programs. This framework is underpinned by a formal semantics that describes program execution in a sequence of steps that do not cover more than one rule application. On the topic of space efficiency, we give a theoretical result that shows GP 2, like some graph-based machine models, can simulate Turing machines using less space and only quadratic time overhead

The Theory of Interacting Deductions and its Application to Operational Semantics

This thesis concerns the problem of complexity in operational semantics definitions. The appeal of modern operational semantics is the simplicity of their metatheories, which can be regarded as theories of deduction about certain shapes of operational judgments. However, when applied to real programming languages they produce bulky definitions that are cumbersome to reason about. The theory of interacting deductions is a richer metatheory which simplifies operational judgments and admits new proof techniques. An interacting deduction is a pair (F, I), where F is a forest of inference trees and I is a set of interaction links (a symmetric set of pairs of formula occurrences of F), which has been built from interacting inference rules (sequences of standard inference rules, or rule atoms). This setting allows one to decompose operational judgments. For instance, for a simple imperative language, one rule atom might concern a program transition, and another a store transition. Program judgments only interact with store judgments when necessary: so stores do not have to be propagated by every inference rule. A deduction in such a semantics would have two inference trees: one for programs and one for stores. This introduces a natural notion of modularity in proofs about semantics. The proof fragmentation theorem shows that one need only consider the rule atoms relevant to the property being proved. To illustrate, I give the semantics for a simple process calculus, compare it with standard semantics and prove three simple properties: nondivergence, store correctness and an equivalence between the two semantics. Typically evaluation semantics provide simpler definitions and proofs than transition semantics. However, it turns out that evaluation semantics cannot be easily expressed using interacting deductions: they require a notion of sequentiality. The sequential deductions contain this extra structure. I compare the utility of evaluation and transition semantics in the interacting case by proving a simple translation correctness example. This proof in turn depends on proof-theoretic concerns which can be abstracted using dangling interactions. This gives rise to the techniques of breaking and assembling interaction links. Again I get the proof fragmentation theorem, and also the proof assembly theorem, which allow respectively both the isolation and composition of modules in proofs about semantics. For illustration, I prove a simple type-checking result (in evaluation semantics) and another nondivergence result (in transition semantics). I apply these results to a bigger language, CSP, to show how the results scale up. Introducing a special scoping side-condition permits a number of linguistic extensions including nested parallelism, mutual exclusion, dynamic process creation and recursive procedures. Then, as an experiment I apply the theory of interacting deductions to present and prove sound a compositional proof system for the partial correctness of CSP programs. Finally, I show that a deduction corresponds to CCS-like process evaluation, justifying philosophically my use of the theory to give operational semantics. A simple corollary is the undecidability of interacting-deducibility. Practically, the result also indicates how one can build prototype interpreters for definitions