Combining a monad and a comonad

We give a systematic treatment of distributivity for a monad and a comonad as arises in giving category theoretic accounts of operational and denotational semantics, and in giving an intensional denotational semantics. We do this axiomatically, in terms of a monad and a comonad in a 2-category, giving accounts of the Eilenberg–Moore and Kleisli constructions. We analyse the eight possible relationships, deducing that two pairs are isomorphic, but that the other pairs are all distinct. We develop those 2-categorical definitions necessary to support this analysis.     

Distributivity for a monad and a comonad

We give a systematic treatment of distributivity for a monad and a comonad as arises in incorporating category theoretic accounts of operational and denotational semantics, and in giving an intensional denotational semantics. We do this axiomatically, in terms of a monad and a comonad in a 2-category, giving accounts of the Eilenberg-Moore and Kleisli constructions. We analyse the eight possible relationships, deducing that two pairs are isomorphic, but that the other pairs are all distinct. We develop those 2-categorical definitions necessary to support this analysis.     

An initial algebra approach to term rewriting systems with variable binders

We present an extension of first-order term rewriting systems. It involves variable binding in the term language. We develop systems called binding term rewriting systems (BTRSs) in a stepwise manner. First we present the term language, then formulate equational logic. Finally, we define rewriting systems. This development is novel because we follow the initial algebra approach in an extended notion of Σ-algebras in various functor categories. These are based on Fiore-Plotkin-Turi’s presheaf semantics of variable binding and Lüth-Ghani’s monadic semantics of term rewriting systems. We characterise the terms, equational logic and rewrite systems for BTRSs as initial algebras in suitable categories. Then, we show an important rewriting property of BTRSs: orthogonal BTRSs are confluent. Moreover, by using the initial algebra semantics, we give a complete characterisation of termination of BTRSs. Finally, we discuss our design choice of BTRSs from a semantic perspective. An erlier version appeared in Proc. Fifth ACM-SIGPLAN International Conference on Principles and Practice of Declarative Programming (PPDP2003).     

Semantics of plan revision in intelligent agents

In this paper, we give an operational and denotational semantics for a meta-language of the 3APL agent programming language. With this meta-language, various 3APL interpreters can be programmed. We prove equivalence of the operational and denotational semantics. Furthermore, we give an operational semantics for object-level 3APL. Using this semantics, we relate the 3APL meta-language to object-level 3APL by providing a specific interpreter, the semantics of which will prove to be equivalent to object-level 3APL.     

A formal framework for software product lines

ContextA Software Product Line is a set of software systems that are built from a common set of features. These systems are developed in a prescribed way and they can be adapted to fit the needs of customers. Feature models specify the properties of the systems that are meaningful to customers. A semantics that models the feature level has the potential to support the automatic analysis of entire software product lines.ObjectiveThe objective of this paper is to define a formal framework for Software Product Lines. This framework needs to be general enough to provide a formal semantics for existing frameworks like FODA (Feature Oriented Domain Analysis), but also to be easily adaptable to new problems.MethodWe define an algebraic language, called SPLA, to describe Software Product Lines. We provide the semantics for the algebra in three different ways. The approach followed to give the semantics is inspired by the semantics of process algebras. First we define an operational semantics, next a denotational semantics, and finally an axiomatic semantics. We also have defined a representation of the algebra into propositional logic.ResultsWe prove that the three semantics are equivalent. We also show how FODA diagrams can be automatically translated into SPLA. Furthermore, we have developed our tool, called AT, that implements the formal framework presented in this paper. This tool uses a SAT-solver to check the satisfiability of an SPL.ConclusionThis paper defines a general formal framework for software product lines. We have defined three different semantics that are equivalent; this means that depending on the context we can choose the most convenient approach: operational, denotational or axiomatic. The framework is flexible enough because it is closely related to process algebras. Process algebras are a well-known paradigm for which many extensions have been defined.     

Two-level languages for program optimization

Two-level languages incorporate binding time information inside types, that is, whether a piece of code is completely known at compile-time, or needs some more inputs and can be evaluated only at run-time. We consider the use of 2-level languages in the framework of partial evaluation, and use a 2-level version of the simply typed lambda calculus with recursion. We give an operational semantics, an equational theory and a denotational semantics, that give an account of the distinction between compilation and execution phases. An adequacy theorem is given to relate the two semantics, showing in particular how they agree on non-termination at compile time. We finally give a more refined model using functor categories.     

Compositional specification of commercial contracts

We present a declarative language for compositional specification of contracts governing the exchange of resources. It extends Eber and Peyton Jones’s declarative language for specifying financial contracts (Jones et al. in The Fun of Programming. 2003) to the exchange of money, goods and services amongst multiple parties and complements McCarthy’s Resources, Events and Agents (REA) accounting model (McCarthy in Account Rev. LVII(3), 554–578, 1982) with a view- independent formal contract model that supports definition of user-defined contracts, automatic monitoring under execution and user-definable analysis of their state before, during and after execution. We provide several realistic examples of commercial contracts and their analyses. A variety of (real) contracts can be expressed in such a fashion as to support their integration, management and analysis in an operational environment that registers events. The language design is driven by both domain considerations and semantic language design methods: a contract denotes a set of traces of events, each of which is an alternative way of concluding the contract successfully, which gives rise to a CSP-style (Brooker et al. in J.ACM 31(3), 560–599, 1984; Hoare in Communicating Sequential Processes, 1985) denotational semantics. The denotational semantics drives the development of a sound and complete small-step operational semantics, where a partially executed contract is represented as a (full) contract that represents the remaining contractual commitments. This operational semantics is then systematically refined in two stages to an instrumented operational semantics that reflects the bookkeeping practice of identifying the specific contractual commitment a particular event matches at the time the event occurs, as opposed to delaying this matching until the contract is concluded.     

Semantic theories of programs with nested interrupts

In the design of dependable software for embedded and real-time operating systems, time analysis is a crucial but extremely difficult issue, the challenge of which is exacerbated due to the randomness and nondeterminism of interrupt handling behaviors. Thus research into a theory that integrates interrupt behaviors and time analysis seems to be important and challenging. In this paper, we present a programming language to describe programs with interrupts that is comprised of two essential parts: main program and interrupt handling programs. We also explore a timed operational semantics and a denotational semantics to specify the meanings of our language. Furthermore, a strategy of deriving denotational semantics from the timed operational semantics is provided to demonstrate the soundness of our operational semantics by showing the consistency between the derived denotational semantics and the original denotational semantics.     

A mathematical semantics for a nondeterministic typed λ-calculus

This paper is concerned with the problems encountered in defining the semantics of nondeterministic algorithms. A nondeterministic control structure is added to a typed λ-calculus and the usual operational semantics for the deterministic language is generalized to take into account the more complex behaviour of nondeterministic algorithms. A mathematical model is then given for the language and the relationship between the denotational and operational semantics is explored.     

A Provably Correct Translation of the λ-Calculus into a Mathematical Model of C++

We introduce a translation of the simply typed λ-calculus into C++, and give a mathematical proof of the correctness of this translation. For this purpose we develop a suitable fragment of C++ together with a denotational semantics. We introduce a formal translation of the λ-calculus into this fragment, and show that this translation is correct with respect to the denotational semantics. We show as well a completeness result, namely that by translating λ-terms we obtain essentially all C++ terms in this fragment. We introduce a mathematical model for the evaluation of programs of this fragment, and show that the evaluation computes the correct result with respect to this semantics.     

CPO Models for Compact GSOS Languages

In this paper, we present a general way of giving denotational semantics to a class of languages equipped with an operational semantics that fits the GSOS format of Bloom, Istrail, and Meyer. The canonical model used for this purpose will be Abramsky's domain of synchronization trees, and the denotational semantics automatically generated by our methods will be guaranteed to be fully abstract with respect to the finitely observable part of the bisimulation preorder. In the process of establishing the full abstraction result, we also obtain several general results on the bisimulation preorder (including a complete axiomatization for it), and give a novel operational interpretation of GSOS languages.     

A denotational semantics for Handel-C

We present a denotational semantics for a fully functional subset of the Handel-C hardware compilation language (Celoxica Ltd., Handel-C Language Reference Manual, v3.0, 2002, ), based on the concept of typed assertion traces. We motivate the choice of semantic domains by illustrating the complexities of the behaviour of the language, paying particular attention to the prialt (priority-alternation) construct of Handel-C. We then define the typed assertion traces over an abstract notion of actions, and demonstrate key properties of the key semantic operations on these. The denotational semantics is then given using traces with actions instantiated as state-transformers.     

The semantics of the combination of atomized statements and parallel choice

In this paper we define a uniform language that is an extension of the language underlying the process algebraPA. One of the main extensions of this language overPA is given by so-called atomizing brackets. If we place these brackets around a statement then we treat this statement as an atomic action. Put differently, these brackets remove all interleaving points. We present a transition system for the language and derive its operational semantics. We show that there are several options for defining a transition system such that the resulting operational semantics is a conservative extension of the semantics forPA. We define a semantic domain and a denotational model for the language. Next we define a closure operator on the semantic domain and show how to use this closure operator to derive a fully abstract denotational semantics. Then the algebraic theory of the language is considered. We define a collection of axioms and a term rewrite system based on these axioms. Using this term rewrite system we are able to identify normal forms for the language. It is shown that these axioms capture the denotational equality. It follows that if two terms are provably equal then they have the same operational semantics. Finally, we show how to extend the axiomatization in order to axiomatize its operational equivalence.     

From algebraic semantics to denotational semantics for Verilog

This paper considers how the algebraic semantics for Verilog relates with its denotational semantics. Our approach is to derive the denotational semantics from the algebraic semantics. We first present the algebraic laws for Verilog. Every program can be expressed as a guarded choice that can model the execution of a program. In order to investigate the parallel expansion laws, a sequence is introduced, indicating which instantaneous action is due to which exact parallel component. A head normal form is defined for each program by using a locality sequence. We provide a strategy for deriving the denotational semantics based on head normal form. Using this strategy, the denotational semantics for every program can be calculated. Program equivalence can also be explored by using the derived denotational semantics. A short version of this paper appeared in Proc. ICECCS 2006: 11th IEEE International Conference on Engineering of Complex Computer Systems [48]. This work is partially supported by the National Basic Research Program of China (No. 2005CB321904), the National High Technology Research and Development Program of China (No. 2007AA010302) and the National Natural Science Foundation of China (No. 90718004). Jonathan Bowen is a visiting professor at King’s College London and an emeritus professor at London South Bank University.     

Coalgebraic semantics for timed processes

We give a coalgebraic formulation of timed processes and their operational semantics. We model time by a monoid called a “time domain”, and we model processes by “timed transition systems”, which amount to partial monoid actions of the time domain or, equivalently, coalgebras for an “evolution comonad” generated by the time domain. All our examples of time domains satisfy a partial closure property, yielding a distributive law of a monad for total monoid actions over the evolution comonad, and hence a distributive law of the evolution comonad over a dual comonad for total monoid actions. We show that the induced coalgebras are exactly timed transition systems with delay operators. We then integrate our coalgebraic formulation of time qua timed transition systems into Turi and Plotkin’s formulation of structural operational semantics in terms of distributive laws. We combine timing with action via the more general study of the combination of two arbitrary sorts of behaviour whose operational semantics may interact. We give a modular account of the operational semantics for a combination induced by that of each of its components. Our study necessitates the investigation of products of comonads. In particular, we characterise when a monad lifts to the category of coalgebras for a product comonad, providing constructions with which one can readily calculate.     

A unifying approach to goal-directed evaluation

Goal-directed evaluation, as embodied in Icon and Snobol, is built on the notions of backtracking and of generating successive results, and therefore it has always been something of a challenge to specify and implement. In this article, we address this challenge using computational monads and partial evaluation. We consider a subset of Icon and we specify it with a monadic semantics and a list monad. We then consider a spectrum of monads that also fit the bill, and we relate them to each other. For example, we derive a continuation monad as a Church encoding of the list monad. The resulting semantics coincides with Gudeman’s continuation semantics of Icon. We then compile Icon programs by specializing their interpreter (i.e., by using the first Futamura projection), using type-directed partial evaluation. Through various back ends, including a run-time code generator, we generate ML code, C code, and OCaml byte code. Binding-time analysis and partial evaluation of the continuation-based interpreter automatically give rise to C programs that coincide with the result of Proebsting’s optimized compiler. Basic Research in Computer Science (www.brics. dk), funded by the Danish National Research Foundation. Olivier Danvy, Ph.D., Habilitation: He is an Associate Professor at the Department of Computer Science at the University of Aarhus, in Denmark. He obtained his Ph.D. degree in 1986 and his Habilitation in 1993 from the Université Pierre et Marie Curie (Paris VI), France. His research interests are in Programming Languages in general and in Partial Evaluation and Continuations in particular. He has published over 75 refereed research papers and edited several proceedings. He has both served on and chaired program committees of scientific meetings in the area of Programming Languages. He is presently chairing the PEPM steering committee at ACM SIGPLAN and serving as external reviewer in computer science for the Danish Universities, as board member in the BRICS PhD School, and as co-Editor-in-Chief of the journal Higher-Order and Symbolic Computation (http://www.wkap.nl/journals/hosc). Bernd Grobauer, M.Sc.: He is a Ph.D. student at the BRICS International Ph.D. school, University of Aarhus, Denmark, and will graduate in the summer of 2001. He obtained his Masters degree from the Munich University of Technology (TUM), Germany. His research interests are in formal methods (especially theorem proving) and programming languages (semantics of programming languages, program analysis, program transformation, types). He serves as editorial assistant for the journal Higher-Order and Symbolic Computation and as chairman of the BRICS Juniorklubben. Morten Rhiger, M.Sc.: He is a Ph.D. student at the BRICS International Ph.D. school, University of Aarhus, Denmark, and will graduate in the summer of 2001. He obtained his Masters degree from the University of Aarhus in 1998. His research interests are in the semantics and implementation of programming languages.     

一种基于模块单子语义的动态程序切片方法

提出一种基于程序模块单子语义的新动态切片方法--模块单子动态切片.首先通过单子转换器,将切片这一类计算抽象成独立于具体语言的实体：切片单子转换器.然后,将该切片转换器作为模块加载到实际程序中,并给出相应的模块单子动态切片算法.据此,可直接在抽象语法结构上计算动态切片,不必记录程序执行历史;相应单子切片器也无需显式地构造诸如依赖图的中间结构.这种模块化抽象机制使得文中的动态切片算法具有很强的可扩展性和重用性.