Towards a Uniform Theory of Effectful State Machines

Using recent developments in coalgebraic and monad-based semantics, we present a uniform study of various notions of machines, e.g. finite state machines, multi-stack machines, Turing machines, valence automata, and weighted automata. They are instances of Jacobs' notion of a T-automaton, where T is a monad. We show that the generic language semantics for T-automata correctly instantiates the usual language semantics for a number of known classes of machines/languages, including regular, context-free, recursively-enumerable and various subclasses of context free languages (e.g. deterministic and real-time ones). Moreover, our approach provides new generic techniques for studying the expressivity power of various machine-based models.Comment: final version accepted by TOC

A comparative study of formalisms for programming language definition : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Computer Science at Massey University

This study looks at a number of methods for defining the full syntax and semantics of computer programming languages. The syntax, especially the nature of context-dependent conditions in it, is first examined, then some extensions of context-free grammars are compared to see to what extent they can encompass the full context-conditions of typical programming languages. It is found that several syntax extensions are inadequate in this regard, and that the ability to calculate complicated functions and conditions, and to eventually delete the values of such functions, is needed. This ability may be obtained either by allowing unrestricted rules and meta-variables in the phrase-structure, or by associating mathematical functions either with individual production rules or with the whole context-free structure, to transform it into an 'abstract syntax'. Since the form of a definition of a programming language semantics depends critically on how one conceives "meaning", five main types of semantics are considered: these are called 'natural', 'prepositional', 'functional', and 'structural' semantics, as well as a semantics based on string rewriting rules. The five types are compared for their success in defining the semantics of computing languages, of the example Algol-like language ALEX in particular. Among other conclusions, it is found that the semantics of structures and computations on structures is the only type sufficiently comprehensive, precise, and readable

Left Recursion in Parsing Expression Grammars

Parsing Expression Grammars (PEGs) are a formalism that can describe all deterministic context-free languages through a set of rules that specify a top-down parser for some language. PEGs are easy to use, and there are efficient implementations of PEG libraries in several programming languages. A frequently missed feature of PEGs is left recursion, which is commonly used in Context-Free Grammars (CFGs) to encode left-associative operations. We present a simple conservative extension to the semantics of PEGs that gives useful meaning to direct and indirect left-recursive rules, and show that our extensions make it easy to express left-recursive idioms from CFGs in PEGs, with similar results. We prove the conservativeness of these extensions, and also prove that they work with any left-recursive PEG. PEGs can also be compiled to programs in a low-level parsing machine. We present an extension to the semantics of the operations of this parsing machine that let it interpret left-recursive PEGs, and prove that this extension is correct with regards to our semantics for left-recursive PEGs.Comment: Extended version of the paper "Left Recursion in Parsing Expression Grammars", that was published on 2012 Brazilian Symposium on Programming Language

On the formalization of some results of context-free language theory

This work describes a formalization effort, using the Coq proof assistant, of fundamental results related to the classical theory of context-free grammars and languages. These include closure properties (union, concatenation and Kleene star), grammar simplification (elimination of useless symbols, inaccessible symbols, empty rules and unit rules), the existence of a Chomsky Normal Form for context-free grammars and the Pumping Lemma for context-free languages. The result is an important set of libraries covering the main results of context-free language theory, with more than 500 lemmas and theorems fully proved and checked. This is probably the most comprehensive formalization of the classical context-free language theory in the Coq proof assistant done to the present date, and includes the important result that is the formalization of the Pumping Lemma for context-free languages.info:eu-repo/semantics/publishedVersio

Presenting Distributive Laws

Distributive laws of a monad T over a functor F are categorical tools for specifying algebra-coalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of well-behaved structural operational semantics and, more recently, also for enhancements of the bisimulation proof method. If T is a free monad, then such distributive laws correspond to simple natural transformations. However, when T is not free it can be rather difficult to prove the defining axioms of a distributive law. In this paper we describe how to obtain a distributive law for a monad with an equational presentation from a distributive law for the underlying free monad. We apply this result to show the equivalence between two different representations of context-free languages

Context-free languages, coalgebraically

We give a coalgebraic account of context-free languages using the functor ${\cal D}(X) = 2 \times X^A$ for deterministic automata over an alphabet $A$, in three different but equivalent ways: (i) by viewing context-free grammars as ${\cal D}$-coalgebras; (ii) by defining a format for behavioural differential equations (w.r.t. ${\cal D}$) for which the unique solutions are precisely the context-free languages; and (iii) as the ${\cal D}$-coalgebra of generalized regular expressions in which the Kleene star is replaced by a unique fixed point operator. In all cases, semantics is defined by the unique homomorphism into the final coalgebra of all languages, thus paving the way for coinductive proofs of context-free language equivalence. Furthermore, the three characterizations are elementary to the extent that they can serve as the basis for the definition of a general coalgebraic notion of context-freeness, which we see as the ultimate long-term goal of the present study

Local constraints in programming languages part I: syntax

AbstractThe method of local constraints attempts to describe context-free languages in an apparently context-sensitive form which helps to retain the intuitive insights about the grammatical structure. This form of description, while apparently context-sensitive is, in fact, context-free and allows a program derivation structure to be represented as a tree with additional constraints, thus allowing for the possibility of a correctness proof in the form of Knuthian semantics. These semantic aspects will be discussed in a sequel to this paper (Part II: Semantics). Several detailed examples are given to motivate the use of local constraints grammars including some examples from the syntax of ALGOL 60. A parsing algorithm has been described; its purpose is to show that the computation of local constraints is quite reasonable. Transformation rules for transferring a context-free grammar into a local constraints grammar have been described and some heuristic approaches for the inverse transformation have been presented

A Coalgebraic Semantics for Imperative Programming Languages

In the theory of programming languages, one often takes two complementary perspectives. In operational semantics, one defines and reasons about the behaviour of programs; and in denotational semantics, one abstracts away implementation details, and reasons about programs as mathematical objects or denotations. The denotational semantics should be compositional, meaning that denotations of programs are determined by the denotations of their parts. It should also be adequate with respect to operational equivalence: programs with the same denotation should be behaviourally indistinguishable. One often has to prove adequacy and compositionality independently for different languages, and the proofs are often laborious and repetitive. These proofs were provided systematically in the context of process algebras by the mathematical operational semantics framework of Turi and Plotkin – which represented transition systems as coalgebras, and program syntax by free algebras; operational specifications were given by distributive laws of syntax over behaviour. By framing the semantics on this abstract level, one derives denotational and operational semantics which are guaranteed to be adequate and compositional for a wide variety of examples. However, despite speculation on the possibility, it is hard to apply the framework to programming languages, because one obtains undesirably fine-grained behavioural equivalences, and unconventional notions of operational semantics. Moreover, the behaviour of these languages is often formalised in a different way – such as computational effects, which may be thought of as an interface between programs and external factors such as non-determinism or a variable store; and comodels, or transition systems which implement these effects. This thesis adapts the mathematical operational semantics framework to provide semantics for various classes of programming languages. After identifying the need for such an adaptation, we show how program behaviour may be characterised by final coalgebras in suitably order- enriched Kleisli categories. We define both operational and denotational semantics, first for languages with syntactic effects, and then for languages with effects and/or comodels given by a Lawvere theory. To ensure adequacy and compositionality, we define concrete and abstract operational rule-formats for these languages, based on the idea of evaluation-in-context; we give syntactic and then categorical proofs that those properties are guaranteed by operational specifications in these rule-formats.Open Acces

On the Semantic Approaches to Boolean Grammars

Boolean grammars extend context-free grammars by allowing conjunction and negation in rule bodies. This new formalism appears to be quite expressive and still efficient from a parsing point of view. Therefore, it seems reasonable to hope that boolean grammars can lead to more expressive tools that can facilitate the compilation process of modern programming languages. One important aspect concerning the theory of boolean grammars is their semantics. More specifically, the existence of negation makes it difficult to define a simple derivation-style semantics (such as for example in the case of context-free grammars). There have already been proposed a number of different semantic approaches in the literature. The purpose of this paper is to present the basic ideas behind each method and identify certain interesting problems that can be the object of further study in this area

Software meta-language engineering and CBS

The SLE conference series is devoted to the engineering principles of software languages: their design, their implementation, and their evolution. This paper is about the role of language specification in SLE. A precise specification of a software language needs to be written in a formal meta-language, and it needs to co-evolve with the specified language. Moreover, different software languages often have features in common, which should provide opportunities for reuse of parts of language specifications. Support for co-evolution and reuse in a meta-language requires careful engineering of its design.The author has been involved in the development of several meta-languages for semantic specification, including action semantics and modular variants of structural operational semantics (MSOS, I-MSOS). This led to the PLanCompS project, and to the design of its meta-language, CBS, for component-based semantics. CBS comes together with an extensible library of reusable components called ‘funcons’, corresponding to fundamental programming constructs. The main aim of CBS is to optimise co-evolution and reuse of specifications during language development, and to make specification of language semantics almost as straightforward as context-free syntax specification.The paper discusses the engineering of a selection of previous meta-languages, assessing how well they support co-evolution and reuse. It then gives an introduction to CBS, and illustrates significant features. It also considers whether other current meta-languages might also be used to define an extensible library of funcons for use in component-based semantics