## Diagrammatic Representations in Domain-Specific Languages (2000)

Citations: | 1 - 1 self |

### BibTeX

@TECHREPORT{Tourlas00diagrammaticrepresentations,

author = {Konstantinos Tourlas},

title = {Diagrammatic Representations in Domain-Specific Languages},

institution = {},

year = {2000}

}

### OpenURL

### Abstract

One emerging approach to reducing the labour and costs of software development favours the specialisation of techniques to particular application domains. The rationale is that programs within a given domain often share enough common features and assumptions to enable the incorporation of substantial support mechanisms into domain-specific programming languages and associated tools. Instead of being machine-oriented, algorithmic implementations, programs in many domain-specific languages (DSLs) are rather user-level, problem-oriented specifications of solutions. Taken further, this view suggests that the most appropriate representation of programs in many domains is diagrammatic, in a way which derives from existing design notations in the domain. This thesis conducts an investigation, using mathematical techniques and supported by case studies, of issues arising from the use of diagrammatic representations in DSLs. Its structure is conceptually divided into two parts: the first is co...

### Citations

1994 | A theory of timed automata
- Alur, Dill
- 1994
(Show Context)
Citation Context ...ds (minimal and maximal delays) on transitions to obtain timed transition systems [66, 67], and the introduction of 18 "clocks" (i.e. variables recording the passage of time) to obtain timed=-= automata [1, 2]-=-. In spite of recent progress, the current mathematical theory of real-time software is in many ways unsatisfactory and remains the subject of much ongoing research. Hoogeboom and Halang [69] discuss ... |

674 | G.: The esterel synchronous programming language: Design, semantics, implementation
- Berry, Gonthier
- 1992
(Show Context)
Citation Context ...is [10, 89], that each reaction of the system is instantaneous. Any reference to "real time" within synchronous programs may then be eliminated, resulting in the development of simple semant=-=ic models [12, 15, 92, 21]-=-. 19 bin_empty (sensor) truck_on_ramp (sensor) bin_valve TRUCK BIN BELT CONTROL PANEL sw load run Figure 2.1: A gravel dump site. Labels having arrows pointing towards them represent inputs to the PLC... |

494 | The synchronous dataflow programming language LUSTRE
- Halbwachs, Caspi, et al.
- 1991
(Show Context)
Citation Context ... hard to predict. In reaction to this unsatisfactory situation, a number of so-called synchronous languages were developed in the 1980's, the most prominent among which being Esterel [16, 14], Lustre =-=[57, 20]-=-, Signal [38], Statecharts [62] and Argos [91]. The design of synchronous languages rests on the idealisation, called the synchrony hypothesis [10, 89], that each reaction of the system is instantaneo... |

407 |
Automata for modeling real-time systems
- Alur, Dill
- 1990
(Show Context)
Citation Context ...ds (minimal and maximal delays) on transitions to obtain timed transition systems [66, 67], and the introduction of 18 "clocks" (i.e. variables recording the passage of time) to obtain timed=-= automata [1, 2]-=-. In spite of recent progress, the current mathematical theory of real-time software is in many ways unsatisfactory and remains the subject of much ongoing research. Hoogeboom and Halang [69] discuss ... |

395 |
Category theory for computing science
- Barr, Wells
- 1990
(Show Context)
Citation Context ... introduction being comprehensive for any purpose other than understanding the material in this thesis. For thorough introductions to the subject the reader is referred to the books by Barr and Wells =-=[8]-=-, and Pierce [114] which are targeted specifically for audiences in computer science. Shorter introductions, together with further pointers to the numerous applications of categories in computing, are... |

381 | Usability analysis of visual programming environments: a â€™cognitive dimensionsâ€™ framework
- Green, Petre
- 1996
(Show Context)
Citation Context ...er computational benefits of diagrams through analysis of inherent constraints [9, 60, 123, 124, 125]; or (from an HCI perspective) features and properties which impact upon the cognition of the user =-=[39, 43, 85, 109, 129]-=-. Studies such as [41, 130, 148] have indicated that the most e#ective representations are those which are well matched to what they represent, in the context of particular reasoning tasks. Furthermor... |

370 | The Synchronous Approach to Reactive and Real-Time Systems
- Benveniste, Berry
- 1991
(Show Context)
Citation Context ...inent among which being Esterel [16, 14], Lustre [57, 20], Signal [38], Statecharts [62] and Argos [91]. The design of synchronous languages rests on the idealisation, called the synchrony hypothesis =-=[10, 89], that eac-=-h reaction of the system is instantaneous. Any reference to "real time" within synchronous programs may then be eliminated, resulting in the development of simple semantic models [12, 15, 92... |

307 |
A.: On the development of reactive systems
- Harel, Pnueli
- 1989
(Show Context)
Citation Context ...l representations of programs in order to cater for the needs of human users and system tools alike. 2.1 Reactive, embedded and Real-Time systems Following a tradition established by Harel and Pnueli =-=[61]-=- (also [90], pages 3--5), the universe of computer programs is conceptually partitioned into those which are transformational and those which are reactive. The purpose of a transformational program is... |

249 | Lustre / A declarative language for programming synchronous systems
- Halbwachs, Caspi, et al.
- 1967
(Show Context)
Citation Context ... hard to predict. In reaction to this unsatisfactory situation, a number of so-called synchronous languages were developed in the 1980's, the most prominent among which being Esterel [16, 14], Lustre =-=[57, 20]-=-, Signal [38], Statecharts [62] and Argos [91]. The design of synchronous languages rests on the idealisation, called the synchrony hypothesis [10, 89], that each reaction of the system is instantaneo... |

241 |
Graph rewriting: An algebraic and logic approach
- Courcelle
- 1990
(Show Context)
Citation Context ...isation of graphs generally do not capture such pragmatic considerations in a manner which would be su#cient to account for this kind of support for reasoning. Graph grammars for example (surveyed in =-=[25]), general-=-ly treat spatial relations as uninterpreted, and thus in some sense as "meaningless". By contrast theories based upon spatial logics (see [95] for a survey of both these and grammatical appr... |

206 | Composing reactive animations
- Elliott
- 1998
(Show Context)
Citation Context ...f user-defined semantic e#ects via monad transformations [87].) When an adequate semantic match exists, the results can be highly satisfactory as demonstrated by case studies in 3D graphics animation =-=[29, 30], picture--=-drawing [78] and "geometric region servers" [19]. More recently, variants of the approach employ the host language to construct standalone, modular interpreters for DSLs. There appears to be... |

201 | The foundations of Esterel
- Berry
- 2000
(Show Context)
Citation Context ... became extremely hard to predict. In reaction to this unsatisfactory situation, a number of so-called synchronous languages were developed in the 1980's, the most prominent among which being Esterel =-=[16, 14]-=-, Lustre [57, 20], Signal [38], Statecharts [62] and Argos [91]. The design of synchronous languages rests on the idealisation, called the synchrony hypothesis [10, 89], that each reaction of the syst... |

197 |
The Situation in Logic
- Barwise
- 1989
(Show Context)
Citation Context ... representation and system/task. Previous studies of diagrammatic representations have typically sought to explicate either computational benefits of diagrams through analysis of inherent constraints =-=[9, 60, 123, 124, 125]-=-; or (from an HCI perspective) features and properties which impact upon the cognition of the user [39, 43, 85, 109, 129]. Studies such as [41, 130, 148] have indicated that the most e#ective represen... |

175 |
Introduction to the Algebraic Theory of Graph Grammars (A Survey), in: Graph Grammars and their Application to
- Ehrig
- 1979
(Show Context)
Citation Context ...g some of their objects and arrows. In particular, variants of pushout constructions have been used extensively as algebraic tools in the theory of graph transformations and graph grammars (see, e.g. =-=[28, 24]-=-). Here we present the details of the pushout construction in Graph, which is induced by amalgams of sets. Definition 5.7. Let G = (O, A, # 0 , # 1 ), G # = (O # , A # , # # 0 , # # 1 ) be graphs and ... |

165 |
Traced monoidal categories
- Joyal, Street, et al.
- 1996
(Show Context)
Citation Context ...x - n) = (p ## p)(x - n) = (# n,m ; (p ## p))(x). 5.6.2 Traces on tensor categories Another common feature of many symmetric tensor categories is what Joyal, Street and Verity have called a "tra=-=ce" [75]; categori-=-es equipped with a trace being called "traced (tensor) categories". The application of traced categories in computing is growing rapidly as many examples of iteration, feedback and general r... |

153 | Cognitive Dimensions of Notations, In
- Green
- 1989
(Show Context)
Citation Context ..., in the context of particular reasoning tasks. Furthermore, it has been demonstrated in [43, 110, 112] that pragmatic features of diagrammatic representations (termed "secondary notations "=-= by Green [42]-=-) play a significant role in achieving such matching. Earlier work at Edinburgh [47], informed by these previous analyses and the results of psychological studies of individual di#erences in users res... |

151 |
Statecharts: A Visual Approach to Complex Systems
- Harel
- 1987
(Show Context)
Citation Context ...is unsatisfactory situation, a number of so-called synchronous languages were developed in the 1980's, the most prominent among which being Esterel [16, 14], Lustre [57, 20], Signal [38], Statecharts =-=[62] and -=-Argos [91]. The design of synchronous languages rests on the idealisation, called the synchrony hypothesis [10, 89], that each reaction of the system is instantaneous. Any reference to "real time... |

145 |
The Geometry of tensor calculus I
- Joyal, Street
- 1991
(Show Context)
Citation Context ...e specifications will be expressions denoting arrows in a (suitably chosen) tensor category. 6.3.1 Diagrams of arrows in tensor categories A remarkable recent development has been the introduction in =-=[74]-=- (and also [75]) of an intuitive diagrammatic representation for expressions denoting arrows in a variety of tensor categories. The resulting diagrams are modelled in terms of topological graphs, that... |

142 |
The Esterel language
- Boussinot, Simone
- 1991
(Show Context)
Citation Context ... became extremely hard to predict. In reaction to this unsatisfactory situation, a number of so-called synchronous languages were developed in the 1980's, the most prominent among which being Esterel =-=[16, 14]-=-, Lustre [57, 20], Signal [38], Statecharts [62] and Argos [91]. The design of synchronous languages rests on the idealisation, called the synchrony hypothesis [10, 89], that each reaction of the syst... |

140 | Building Domain-Specific Embedded Languages
- Hudak
(Show Context)
Citation Context ...f DSLs into general-purpose languages and the domain-specific compiler or program specialisation. The use of general-purpose languages as hosts for DSLs is advocated mainly by the groups led by Hudak =-=[70]-=- and Kamin [77]. In their approach, a newly devised DSL inherits the infrastructure of a high-level, strongly-typed functional language such as ML or Haskel. In addition to drastically cutting down im... |

125 | Modular Domain-Specific Languages and Tools
- Hudak
- 1998
(Show Context)
Citation Context ...ts of the approach employ the host language to construct standalone, modular interpreters for DSLs. There appears to be some friction between the objectives of interpreter modularity and optimisation =-=[71]-=- and a variety of technologies (including staging, monads [122] and partial evaluation [71]) are currently being evaluated. The other popular approach regards programs in a DSL as a family, i.e. a cla... |

113 |
ALogical Approach to Discrete Math
- Gries, Schneider
- 1994
(Show Context)
Citation Context ...so be useful, so we provide a brief and simplified review of the basic concepts. 1 Three texts which the author recommends as particularly gentle, pleasing-to-read introductions to sets and logic are =-=[44, 133, 59]-=- 14 1.5.1 Algebras, signatures and terms A multi-sorted algebra is a collection A of sets, called the carriers, together with functions of the form f : A 1 . . . A n # Am (where A k # A), called opera... |

110 | Verification of realtime systems using linear relation analysis
- Halbwachs, Proy, et al.
- 1997
(Show Context)
Citation Context ...g over R seriously impedes the practical application of the theory to the verification of real-life systems. In response, techniques based on Q (the set of rational numbers) as an approximation (e.g. =-=[58]-=-) have been developed. 2.1.2 The synchronous approach to embedded control In contrast to the general situation, the theory of embedded control software exhibits remarkable simplicity and has achieved ... |

108 |
Coherence for compact closed categories
- Kelly, Laplaza
- 1980
(Show Context)
Citation Context ...its "dual" A # . Thus, what we have called "unitcounit pairs" correspond to the components of the unit and counit (di)natural transformations ([88], page 214) of a self-dual, compa=-=ct-closed structure [81]-=- on a symmetric monoidal category. Self-duality in this context means A # = A for all objects A in the category. There is a standard way in which unit-counit pairs equip a symmetric tensor category wi... |

101 | A categorical manifesto
- Goguen
- 1991
(Show Context)
Citation Context ...[114] which are targeted specifically for audiences in computer science. Shorter introductions, together with further pointers to the numerous applications of categories in computing, are provided in =-=[115, 40, 119, 26]-=-. The definitive text on category theory is MacLane's book [88]. 5.1 Graphs A graph consists of a set of objects O (vertices), a set of arrows A (edges) and a pair of functions # 0 , # 1 : A # O, call... |

80 |
Categories for Types
- Crole
- 1993
(Show Context)
Citation Context ...[114] which are targeted specifically for audiences in computer science. Shorter introductions, together with further pointers to the numerous applications of categories in computing, are provided in =-=[115, 40, 119, 26]-=-. The definitive text on category theory is MacLane's book [88]. 5.1 Graphs A graph consists of a set of objects O (vertices), a set of arrows A (edges) and a pair of functions # 0 , # 1 : A # O, call... |

78 | Timed transition systems
- Henzinger, Manna, et al.
- 1992
(Show Context)
Citation Context ...tems have been extended in various ways. The two most popular approaches consist in the specification of temporal bounds (minimal and maximal delays) on transitions to obtain timed transition systems =-=[66, 67], and the -=-introduction of 18 "clocks" (i.e. variables recording the passage of time) to obtain timed automata [1, 2]. In spite of recent progress, the current mathematical theory of real-time software... |

73 | Service combinators for web computing
- Cardelli, Davies
(Show Context)
Citation Context ... to semantics. 1.3.3 Summary On the whole, recent research on domain-specific languages has focused almost exclusively on textual languages and domains within mainstream computing (e.g. web computing =-=[18] and netwo-=-rking [137]). In such domains, language specificity manifests itself primarily as "special [textual] syntax, operations and types" [77]. We wish to argue that, in general, the understanding ... |

60 | Models of Sharing Graphs: A Categorical Semantics of let and letrec. Distinguished Dissertation Series
- Hasegawa
- 1999
(Show Context)
Citation Context ...f : X# A -# B ## X and g : B # -# B 6. Sliding: Tr X A,B (f ; (1 B# g)) = Tr Y A,B ((1 A# g); f) where f : X# A -# Y# B and g : Y -# X. Remark. The above axiomatisation of traces in due to Hasegawa [=-=63, 64]-=- and is a specialised application of the general definition in [75] which applies to a wide class of tortile tensor categories [126]. 93 5.6.3 Units and counits Beyond symmetries, symmetric tensor cat... |

50 |
F.: Algebraic Approaches to Graph Transformation I : Basic Concepts and Double Pushout Approach, in: Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations
- Corradini, Ehrig, et al.
- 1997
(Show Context)
Citation Context ...g some of their objects and arrows. In particular, variants of pushout constructions have been used extensively as algebraic tools in the theory of graph transformations and graph grammars (see, e.g. =-=[28, 24]-=-). Here we present the details of the pushout construction in Graph, which is induced by amalgams of sets. Definition 5.7. Let G = (O, A, # 0 , # 1 ), G # = (O # , A # , # # 0 , # # 1 ) be graphs and ... |

45 | Recursion from cyclic sharing: traced monoidal categories and models of cyclic lambda-calculi
- Hasegawa
- 1997
(Show Context)
Citation Context ... been shown to be instances of traces. These include feedback in the calculus of "flownomials" [127], feedback in asynchronous data-flow networks [68] and circuits [80], recursion from cycli=-=c sharing [64], and-=- reflection in action calculi [101] among many others. Our interest in traces stems from the fact that their axioms neatly capture a particular notion of equivalence between diagrams containing "... |

44 |
Signal, a declarative language for synchronous programming of real-time systems
- Gautier, Guernic, et al.
- 1990
(Show Context)
Citation Context ... In reaction to this unsatisfactory situation, a number of so-called synchronous languages were developed in the 1980's, the most prominent among which being Esterel [16, 14], Lustre [57, 20], Signal =-=[38]-=-, Statecharts [62] and Argos [91]. The design of synchronous languages rests on the idealisation, called the synchrony hypothesis [10, 89], that each reaction of the system is instantaneous. Any refer... |

44 | Temporal proof methodologies for timed transitions systems
- Henzinger, Manna, et al.
(Show Context)
Citation Context ...tems have been extended in various ways. The two most popular approaches consist in the specification of temporal bounds (minimal and maximal delays) on transitions to obtain timed transition systems =-=[66, 67], and the -=-introduction of 18 "clocks" (i.e. variables recording the passage of time) to obtain timed automata [1, 2]. In spite of recent progress, the current mathematical theory of real-time software... |

42 | Bicategories of processes
- Katis, Sabadini, et al.
- 1997
(Show Context)
Citation Context ...and general recursion operators have been shown to be instances of traces. These include feedback in the calculus of "flownomials" [127], feedback in asynchronous data-flow networks [68] and=-= circuits [80]-=-, recursion from cyclic sharing [64], and reflection in action calculi [101] among many others. Our interest in traces stems from the fact that their axioms neatly capture a particular notion of equiv... |

40 | Incorporating application semantics and control into compilation
- Engler
- 1997
(Show Context)
Citation Context ...roach regards programs in a DSL as a family, i.e. a class of programs characterised by a large number of common features. The idea is to incorporate application semantics into the compilation process =-=[32]-=- by applying a range commonality analysis techniques. Due to the costs associated with 11 compiler design and implementation, which are often disproportionally high to the size of typical DSLs, interp... |

39 |
Axiomatizing the algebra of net computations and processes
- Degano, Meseguer, et al.
- 1996
(Show Context)
Citation Context ...rovide a syntactic description of nets which gives places and transitions equal status (as in Definition 7.1). 137 Nevertheless, the idea of concatenable metagraphs owes its very existence to work in =-=[27, 120] extending-=- the basic theory of net computations. There, a notion of "concatenable process" was introduced for nets. Suitably adapted, this inspired our Definition 7.5 of concatenable metagraphs. Anoth... |

38 |
Real time programming: Special purpose or general purpose languages
- Berry
- 1989
(Show Context)
Citation Context ...n for our interest in embedded control is twofold: . One of the first, principled and highly convincing arguments for the need to design and employ domain-specific languages originated in this domain =-=[13]-=-. . Most languages specific to the domain are naturally diagrammatic or admit both diagrammatic and textual representations of programs in order to cater for the needs of human users and system tools ... |

37 |
Domain Analysis Concepts and Research Directions
- Arango, Prieto-Diaz
- 1991
(Show Context)
Citation Context ...f domain engineering address the issue of identifying or creating reusable assets within a problem domain following thorough analysis of commonalities and variability among specific problem instances =-=[7]-=-. In this respect, requirements for a domain-specific language may be seen as a possible product of domain engineering. The SDA (standing for Software Design Automation) methodology, proposed by Hook ... |

34 | Modeling interactive 3d and multimedia animation with an embedded language
- Elliott
- 1997
(Show Context)
Citation Context ...f user-defined semantic e#ects via monad transformations [87].) When an adequate semantic match exists, the results can be highly satisfactory as demonstrated by case studies in 3D graphics animation =-=[29, 30], picture--=-drawing [78] and "geometric region servers" [19]. More recently, variants of the approach employ the host language to construct standalone, modular interpreters for DSLs. There appears to be... |

31 |
Clocks in dataflow languages
- Caspi
- 1992
(Show Context)
Citation Context ...is [10, 89], that each reaction of the system is instantaneous. Any reference to "real time" within synchronous programs may then be eliminated, resulting in the development of simple semant=-=ic models [12, 15, 92, 21]-=-. 19 bin_empty (sensor) truck_on_ramp (sensor) bin_valve TRUCK BIN BELT CONTROL PANEL sw load run Figure 2.1: A gravel dump site. Labels having arrows pointing towards them represent inputs to the PLC... |

28 |
Logic for mathematicians
- Hamilton
- 1987
(Show Context)
Citation Context ...so be useful, so we provide a brief and simplified review of the basic concepts. 1 Three texts which the author recommends as particularly gentle, pleasing-to-read introductions to sets and logic are =-=[44, 133, 59]-=- 14 1.5.1 Algebras, signatures and terms A multi-sorted algebra is a collection A of sets, called the carriers, together with functions of the form f : A 1 . . . A n # Am (where A k # A), called opera... |

27 | A relational model of non-deterministic dataflow
- Hildebrandt, Panangaden, et al.
- 2004
(Show Context)
Citation Context ...eration, feedback and general recursion operators have been shown to be instances of traces. These include feedback in the calculus of "flownomials" [127], feedback in asynchronous data-flow=-= networks [68]-=- and circuits [80], recursion from cyclic sharing [64], and reflection in action calculi [101] among many others. Our interest in traces stems from the fact that their axioms neatly capture a particul... |

23 | Effective diagrammatic communication: syntactic, semantic and pragmatic issues
- Gurr
- 1999
(Show Context)
Citation Context ... this is the potential to directly capture pertinent aspects of the represented artifact (whether this be a concrete artifact or some abstract concept). To clarify this argument, which is explored in =-=[50, 47], we must explain wh-=-at is meant here by the terms "direct" and "pertinent". Firstly, diagrammatic relations can often be directly semantically interpreted. This is to say that certain diagrammatic rel... |

22 | Data-flow Synchronous Languages
- Benveniste, Caspi, et al.
- 1994
(Show Context)
Citation Context ...of assignments to the output labels with references to the input labels and the outputs of block instances (in the form INSTANCE.OUTPUT). In essence, function blocks are simple, synchronous data-flow =-=[11]-=- programs specifying the outputs as functions of the inputs. In general, the function computed may be dependent on the history of its own computation. History dependencies are introduced by means of f... |

16 |
General topology, volume 6 of Sigma Series in Pure Mathematics
- Engelking
- 1989
(Show Context)
Citation Context ...ith this particular class of diagrams. Example 6.2. From left to right, the diagrams in Figure 6.4 correspond to the expressions: 1. f ; (1# h) ; (g# 1) ; k 2. f ; (g# h) ; k and 2 A homeomorphic map =-=[134, 31]-=- is an isomorphism of topological spaces. 104 . . . . . . . . . . . . . . . . . . . . . . . . . # # # # # # f g h k # # # # # # # # f g h k . . . . . . . . . . . . . . . . . . . . . . . . . # # # # # ... |

15 | What makes a good Domain-Specific Language? APOSTLE, and its Approach to Parallel Discrete Event Simulation
- Bruce
- 1997
(Show Context)
Citation Context ...ruction of interpreters using techniques borrowed from general-purpose languages). Whereas it is widely agreed that a good DSL must capture the native notation and semantics of its application domain =-=[17, 70], the range of langu-=-ages studied thus far has led to a particularly narrow perception of both "notation" and "semantics". By emphasising industrial (engineering) domains and diagrammatic representatio... |

14 |
A denotational theory of synchronous reactive systems
- Benveniste, Guernic, et al.
- 1992
(Show Context)
Citation Context ...is [10, 89], that each reaction of the system is instantaneous. Any reference to "real time" within synchronous programs may then be eliminated, resulting in the development of simple semant=-=ic models [12, 15, 92, 21]-=-. 19 bin_empty (sensor) truck_on_ramp (sensor) bin_valve TRUCK BIN BELT CONTROL PANEL sw load run Figure 2.1: A gravel dump site. Labels having arrows pointing towards them represent inputs to the PLC... |

14 | Towards the principled design of software engineering diagrams
- Gurr, Tourlas
- 2000
(Show Context)
Citation Context ...th the exception of the material in Chapter 6 which is the product of joint work with Dr Corin A. Gurr 1 . Early versions of parts of this thesis have already been published elsewhere: . Chapter 3 as =-=[49]-=- (sections 3.4 and 3.5) and [5, 6] (rest of chapter) . Chapter 4 as [4]; and . Chapter 6 as [48]. Konstantinos Tourlas 1 Corin Gurr is a member of the Human Communication Research Centre (HCRC) at the... |

13 |
Semantic frameworks for complexity
- Gurr
- 1991
(Show Context)
Citation Context ...nly when issues of termination or complexity are discussed. Even then, either a qualitative account of time passage su#ces [65], or the semantic model is explicitly augmented with complexity measures =-=[53]-=-. On the other hand, the modelling of reactive programs is typically operational in style, relying on transition systems to provide a mathematical abstraction of their behaviour [90]. A transition sys... |

12 |
Abstractions of Time
- Hehner
- 1994
(Show Context)
Citation Context ...l programming languages [121]. In this framework, reference to time is made only when issues of termination or complexity are discussed. Even then, either a qualitative account of time passage su#ces =-=[65]-=-, or the semantic model is explicitly augmented with complexity measures [53]. On the other hand, the modelling of reactive programs is typically operational in style, relying on transition systems to... |