Wadge, W. W., Ashcroft, E. A. Lucid, the Dataflow Programming Language. Academic Press 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....3.3. Let P be a Disjunctive Chronolog program and C 2 TDHBP . Then the following are equivalent: 1. C is true in all minimal temporal Herbrand models of P . 2. C is in MTMSP . 3. C is in exp(lfp(T P ) 4. C is a logical consequence of P . 4 Conclusions Temporal programming, either functional[WA85, RW96] or logic [OM94, Org91, PG95] have been widely used as a means for describing systems that are inherently dynamic. On the other hand the need to express uncertainty has led researchers in introducing disjunctive logic programming[LMR92] We have developed the syntax and declarative semantics of ....

W. W. Wadge and E. A. Ashcroft. Lucid, the dataflow Programming Language. Academic Press, 1985.

....by enumerating and evaluating (one by one) the set of all canonical instances of the goal clause. The above enumeration strategy is the standard technique which has been adopted for the Chronolog family of languages. The origins of this approach date back to the functional dataflow language Lucid [27], in which the basic data structures are streams. The Chronolog language, designed by the same research group, inherited the operators, the stream oriented nature, and some of the implementation decisions of Lucid. A similar idea as the enumeration strategy described above, has been used in Lucid ....

....branching time logic programming paradigm. Finally, an interesting direction for future work is the addition of negation in Cactus. Promising results in this direction (for the linear logic language Chronolog) are reported in [32] 7 Conclusions Temporal programming languages, either functional [27] or logic [1, 3, 33] have been widely used as a means for describing dynamic systems. However, most temporal languages use a linear notion of time a fact that makes them unsuitable for certain types of applications. In this paper we have introduced the branching time logic programming language ....

W. W. Wadge and E. A. Ashcroft. Lucid, the dataflow programming language. Academic Press, 1985. 21

....design called ActiveVRML [7] DirectX Animation is used from more mainstream imperative languages, and so mixes the functional and imperative approaches. There are also several languages designed around a synchronous data flow notion of computation. The generalpurpose functional language Lucid [21] is an example of this style of language, but more importantly are the languages Signal [11] and Lustre [4] which were specifically designed for control of real time systems. In Signal, the most fundamental idea is that of a signal, a time ordered sequence of values. Unlike Fran, however, time ....

W.W. Wadge and E.A. Ashcroft. Lucid, the Dataflow Programming Language. Academic Press U.K., 1985.

.... space time continuum becomes the different dimensions of the context of evaluation, and the laws are expressed naturally using intensional definitions [7] Lucid is a multidimensional intensional programming language whose semantics is based on the possible world semantics of intensional logic [1, 10]. It is a functional language in which expressions and their valuations are allowed to vary in an arbitrary number of dimensions. Intensional programming (in the sense of Lucid) has been successfully applied to resolve problems with a new perspective that enables a more natural understanding of ....

W. W. Wadge and E. A. Ashcroft. Lucid, the Dataflow Programming Language. Academic

....description to the various intermediate steps can be carried out with tools of guaranteed performance. Such an approach is standard in certain communities, where languages with strong formal properties are used to ensure robust design. Examples include ML [2] dataflow languages (e.g. Lucid [3], Haskell [4] and synchronous languages (e.g. Lustre, Signal, Esterel [5] There is a broad range of potential formalizations of a design, but most tools and designers describe the behavior of a design as a relation between a set of inputs and a set of outputs. This relation may be informal, ....

W. Wadge and E.A. Ashcroft, Lucid, the dataflow programming language, Academic Press, 1985.

....would have to be rejected. In other words, an effective stratification test for temporal logic programming should also examine for temporal circularities in the program. In [Wad81] W. Wadge developed the cycle sum test which ensures that a given temporal functional program of the language Lucid [WA85], is deadlock free. The test was later extended by S. Matthews [Mat95] to a wider context (but still in the area of functional programming) We show that the test is also applicable in the area of temporal logic programming with negation, and we demonstrate that programs that pass the test have a ....

W. W. Wadge and E. A. Ashcroft. Lucid, the Dataflow Programming Language. Academic Press, 1985.

....Lustre [46] and Silage [50] languages all have a visual and a textual syntax, the latter available in the commercial Mentor Graphics DSP Station as DFL. Other languages with related semantics, such as Sisal [73] are used primarily or exclusively with textual syntax. The language Lucid [92][96], while primarily used with textual syntax, has experimental visual forms [10] Hierarchy in graphical program structure can be viewed as an alternative to the more usual abstraction of subprograms via procedures, functions, or objects. It is better suited than any of these to a visual syntax, and ....

W. W. Wadge and E. A. Ashcroft, Lucid, the dataflow programming language, London Academic Press, 1985.

....determined, then the appropriate versions of each component are determined, and so on. In order for automatic software configuration to take place, a process called eduction must be used. Eduction, a form of demand driven lazy evaluation, was first proposed for the execution of dataflow languages (Wadge and Ashcroft 1985). Since then, it has been generalized for many other computer problems (Orgun and Ashcroft 1996) The eductive process for software configuration is as follows (Plaice and Wadge 1993) A version of a system is requested from a warehouse, in this case a software repository. To build that version, ....

Wadge, W.W. and Ashcroft, E.A. 1985. Lucid, the Dataflow Programming Language. Academic Press.

....DSP Station) allows an arbitrary mixture of visual and textual specification, both based on the applicative language Silage [35] Several other languages with related semantics, such as SIGNAL [9] 52] and Sisal [57] are used primarily or exclusively with textual syntax. The language LUCID [75][77], while primarily used with textual syntax, has experimental visual forms [7] Hierarchy in graphical program structure can be viewed as an alternative to the more usual abstraction of subprograms via procedures, functions, or objects. It is better suited than any of these to a visual syntax, and ....

W. W. Wadge and E. A. Ashcroft, Lucid, the dataflow programming language, London Academic Press, 1985.

....specific models and subsystems that relate only to time. The other possibility is that time is just another axis in a coordinate system, i.e. a t axis in a coordinate system already containing an x , y , and perhaps a z axis. This approach was used in an early spreadsheet language based on Lucid [23] known as Plane Lucid [6] which gave 2 D operators such as hsby and vsby for horizontally vertically spatially by (to the right below) to reference elements along the x and y axis of a spreadsheet grid and analogous operators such as fby meaning followed by (temporally next) to reference ....

W. Wadge and E. Ashcroft, Lucid, the Dataflow Programming Language, Academic Press, London, 1985.

....if a cell named foo had the formula earlier (foo 1) initially 1 until (foo 5) foo s temporal vector would be (1, t 1 ) 2, t 2 ) 3, t 3 ) 4, t 4 ) 5, t 5 ) 6, t 6 ) and its vt tuple at time t 6 would never expire. Fby is a syntactic alternative to earlier inspired by Lucid [Wadge and Ashcroft 1985], and in fact is internally implemented using earlier. It simply allows the initial value to precede the operator without a keyword, thus specifying an initial value for time t 1 and a sequence beginning at time t 2 . For example, 1 fby earlier (foo 1) until (foo 5) specifies the same ....

....time. Thus, any cell referencing the result cell on an animation form, or in fact referencing any other time varying cell, will also vary over time. This transitivity is also present in other time varying languages such as those termed synchronous or reactive languages, such as Lucid [Wadge and Ashcroft 1985; Du and Wadge 1990] and related languages such as Chronolog, Esterel and LUSTRE [Orgun and Wadge 1992; Liu and Orgun 1996; Halbwachs 1993] however, these languages did not extend support to the realm of graphics and animations. Fran [Elliott and Hudak 1997] is a recent Haskell based system that ....

W. Wadge and E. Ashcroft, Lucid, the Dataflow Programming Language, Academic Press, London, 1985.

....and Wise [78a] is implicit in the application of a list (See Figure 2.2) It is a generalization of Map1. The data recursion above is equivalent to rec: Z 1 [inc ] Z] Z] inc ] evaluates to a non terminating list of incrementation operations. A style of expression reminiscent of Lucid [WaAs86] is prevalent among Daisy programers. Iterations are embedded in recursively defined structure. For instance, one is more likely to see the fibonacci function defined as an indexing operation on a sequence, FIB = N. rec: U V] 1 V 1 [add ] U V] N:F ] than its function ....

Wadge and Aschroft. Lucid, the Data Flow Programming Language. 1986.

....equations It appears clearly that a system of boolean equations lies under each SIGNAL process. We hinted that during the presentation of the kernel of SIGNAL. We recapitulate these equations in Table 1. At this stage, the main difference between SIGNAL and the classical data flow languages [16] [25] is that in SIGNAL we manipulate synchronized data flow by means of clocks. The main purpose of synchronized data flow is that all the synchronizations (expressed in terms of equations over clocks) should be completely handled at compile time. For more details, see [17] 3 signal process clock ....

W. W. Wadge and E. A. Ashcroft. LUCID, the Dataflow Programming Language. Academic Press, 1985. 11

....all. As a consequence, we use the general algorithm whatever the rank of the reference. 4 Applications 4.1 Conversion to Single Assignment Form Single assignment programs have been proposed by several authors[27, 25] as a mean of specifying algorithms for highly parallel systems. Another point[6, 7] is that since a memory cell in such a program is defined only once, its contents may be considered as a variable in the mathematical sense and subjected to the familiar algebraic and analytic manipulations. The following algorithm may be used to convert a static control program to single ....

E. A. Ashcroft and W. W. Wadge. Lucid, the Data-flow Programming Language. Academic Press, 1985.

....and once by filter evens. In the general case the switch function would be applied to each input token n times. This could be serious if the test were expensive. The second method takes care of this problem by synchronizing all output streams using special padding symbols called hiatons [14]. Typical code looks like this: define filter odd even (lambda (int stream) let ( v (car int stream) if (even v) cons (cons v #) filter odd even (cdr int stream) cons (cons # v) filter odd even (cdr int stream) define filter odds (lambda (pair stream) let ( v (cdr ....

W. W. Wadge, and E. A. Ashcroft, Lucid, the Dataflow Programming Language, Academic Press (1985). 21 APPENDIX A The code for implementing imperative streams (define create-channel (lambda () (let ([channel (cons '() (cons '!no-consumer-cell? '!null?))])

....framework for abstract programs is provided by the applicative language AL. The language is derived from Ampl ( applicative multiprogramming language ) developed in [Bro86] Conceptually it can be compared to functional languages like Haskell [HJW 91] or dataflow languages like Lucid [WA85] AL contains means for the definition of stream processing functions, and moreover admits the definition of mutually recursive stream equations. Here is a simple numerical AL program: 1 In fact, there exists an implementation of Ampl, a predecessor of AL, on the SUN SPARCstation (see [Nue88] ....

W. Wadge and E. Ashcroft. Lucid, the dataflow programming language. Academic Press, 1985.

....of recurrence equations (SRE) as a mean of specifying parallel processes results from the convergence of several trends of research. A pioneer paper by Karp et.al. 17] was motivated by the study of explicit difference schemes for the solution of systems of differential equations. Other authors [18, 19] were interested in the mathematical simplicity of SRE and their use for proving program correctness. The last motivation [20] was the fact that in SRE parallelism detection (if not parallelism exploitation) is obvious. Hence, it is felt that SRE are well adapted to the specification of massively ....

E. A. Ashcroft and W. W. Wadge. Lucid, the Data-flow Programming Language. Academic Press, 1985.

....description to the various intermediate steps can be carried out with tools of guaranteed performance. Such an approach is standard in certain communities, where languages with strong formal properties are used to ensure robust design. Examples include ML [MTH90] dataflow languages (e.g. Lucid [WA85] Haskell [Dav92] and synchronous languages (e.g. Lustre, Signal, Esterel [Hal93] There is a broad range of potential formalizations of a design, but most tools and designers describe the behavior of a design as a relation between a set of inputs and a set of outputs. This relation may be ....

W. Wadge and E.A. Ashcroft. Lucid, the dataflow programming language. Academic Press, 1985.

....any top level expression (the expression that represents the whole program) is implicitly associated with a single port. 4. Programming in Pscheme 4.1. An application of multi ports A typical use of multi ports is stream based programming, as is often seen in data flow languages like Lucid [WA85]. For example, to calculate Fibonacci numbers, we observe that the infinite Fibonacci stream f satisfies f = 1 : 1 : add list f (cdr f) The stream f can be generated by an adding cell with feedback wires to its two inputs as shown in Figure 4. The input arcs are captured by multi ports in ....

W. Wadge and E. A. Ashcroft. Lucid, the Dataflow Programming Language, Academic Press, 1985. 9

....LACS does not impose such an interpretation) 1. A broadcast of X[N,N] to X at all points (size of X is N) can be written as an ACE: X[N,N] i,j 0 i,j =N: Y[i,j] 2. A reduction (with addition as the operator) of X on the first row, whose result overwrites the value that used to be in X[1,1] may be described by the ACE: i 0 i =N: X[1,i] X[1,1] 3. The same reduction, but the result is now broadcast back along the row: i 0 i =N: X[1,i] i 0 i =N: X[1,i] 4. A scatter of N different X values (stored along a third dimension) from point [1,N] to all points ....

....of X[N,N] to X at all points (size of X is N) can be written as an ACE: X[N,N] i,j 0 i,j =N: Y[i,j] 2. A reduction (with addition as the operator) of X on the first row, whose result overwrites the value that used to be in X[1,1] may be described by the ACE: i 0 i =N: X[1,i] X[1,1] 3. The same reduction, but the result is now broadcast back along the row: i 0 i =N: X[1,i] i 0 i =N: X[1,i] 4. A scatter of N different X values (stored along a third dimension) from point [1,N] to all points along the same column (this is a PAS, like all subsequent ....

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E. A. Ashcroft and W. W. Wadge. Lucid, the Data-Flow Programming Language. Academic Press, 1985.

....the data flow approach from the theoretical point of view. As we have widely discussed, the data flow paradigm provides a natural framework for control and signal processing, and more generally, for engineering people. Many attempts have been made to use a data flow approach in Computer Science [20, 1, 13], yet not successfully 5 , for two major reasons : the composition of bounded memory data flow systems may not be bounded memory, see [11] the composition of equivalent non deterministic data flow systems may not yield equivalent systems, see [10] 6 . So far, several solutions have ....

E. A. Ashcroft and W. W. Wadge , Lucid, the data-flow programming language , Academic Press, 1985

....in a variety of high level languages. Examples of languages that elegantly support computations over streams include modern lazy functional languages such as Haskell [18] hardware description languages such as MHDL [6] an extension of Haskell) data flow programming languages such as Lucid [4, 5], and synchronous programming languages such as Esterel [8, 9] Lustre [11] and Signal [7] These languages have been remarkably successful in supporting the rapid development of reliable systems. First, streams are the fundamental and most widely supported data structure in most of these ....

Ashcroft, E. A., and Wadge, W. W. Lucid, the Data-Flow Programming Language. Academic Press, 1985.

....they cannot have changed as a result of the Color button being pressed. Thus, LM fails the responsiveness requirement because it may examine variables whose values have not changed. LM s temporal aspects draw from earlier research related to temporal aspects of the lazy dataflow language Lucid [2]. Typical of this work were the optimizations done by Ostrum [17] Faustini [11] and Denbaum [9] Most of these approaches include memoization, some using EM and some using the notion of expiration times (which is an important aspect of LM) but this work has not been extended to meet the ....

Ashcroft, E. and Wadge, W. Lucid, the Dataflow Programming Language, Academic Press, London, England, (1985).

....in the derivation of sequential, process control software was discussed in [16] The constraint net model is more closely related to dataflow like models and languages, such as the operator net model, LUSTRE, SIGNAL and temporal automata. The operator net model [2] abstracted from Lucid [28] is defined on continuous algebras using fixpoint theory. The most attractive feature of this model is its independence of any particular algebra. Given a continuous algebra which specifies data types and basic operations, a sequence (continuous) algebra is obtained on which an operator net can ....

W. W. Wadge and E. A. Ashcroft. Lucid, the dataflow programming language. Academic Press, 1985.

....the multiplicity of a in m. For any two multisets m 1 and m 2 we say that m 1 is included in m 2 if m 1 (a) m 2 (a) for any a 2 Delta. The multiset domain consists of all multisets ordered by inclusion. It is easy to check that the multiset domain is F domain. Streams with holes : Sometimes [25] in dataflow theory the domain of stream with holes is considered. This domain consists of all infinite sequence over Delta [ and is partially ordered by pointwise ordering. It is isomorphic to the set of all partial functions from the natural numbers into Delta. It is easy to check that the ....

Wadge, W. Ashcroft, E., LUCID, the Data Flow Programming Language, Academic Press, 1985

....for protocol implementation, including the object based abstraction provided in [14] Currently, the Cicero library is designed for implementing protocols above the transport layer, such as RPC. ffl Restricted Dataflow Execution Model: The dataflow model [21] is well known, and many languages [1, 26] and machines [27, 28] have been designed based on it. Instead of describing data dependency or data access disciplines, Cicero uses the dataflow model to describe event driven execution, allowing programmers to explore parallelism in different granularities by changing the amount of computation ....

W. W. Wadge and E. A. Ashcroft. Lucid, the Dataflow Programming Language. Academic Press U.K., 1985.

....a good opportunity to discuss temporally dependent iterations, where the outcome of a cycle depends on one or more of the previous cycles [2] Typical solutions to this problem in data flow languages assume some means to refer to the values produced on the previous iteration of the loop. LUCID [16] considers variable names as placeholders for the temporal streams of values and provides powerful means to manipulate streams. Val [1] and Id [3] data flow languages provide determinant determinant e: I: e D ( 1) I 1) S1: S2: S1 S2 R 0 C 0 D: SIZE:R: C: R = 0 C = 0 1 1 . ....

W.Wadge, E.Ashcroft, LUCID, the dataflow programming language, Academic Press, 1985.

....As concluding remarks, we will compare the Lustre approach with some alternative approaches, from both programming language and verification points of view. 6.1 Related programming languages 6.1. 1 Dataflow The dataflow model has been a basis of several programming languages, for instance [AW85, Gra82, BFM84, Bro89], and it has been given a nice formal definition by Kahn in [Kah74] When trying to locate Lustre within the dataflow world, it looks very close to Lucid from a syntactical point of view. This similarity is not casual since Lucid was the first main reference in the design of Lustre. However, the ....

E. A. Ashcroft and W. W. Wadge. Lucid, the data-flow programming language. Academic Press, 1985.

....P r 1 ; P r 2 the process P r 1 kP r 2 is fat and implements the connected relation value(P r 1 ) value(P r 2 ) Proof. Similary to the proof of calim 3. 8 Processes with Message Passing We describe two different extensions of the notion linear process which are used in models of dataflow [WA, PA]. We show that (up to isomorphism) both are instances of the general notion process over F domain . It follows in particular, that claims 1 000 ; 3 0 hold in both cases. 8.1 Example 1. Stream Processing Often one has to be more specific about the action alphabet of the linear processes. ....

....is isomorphic to that of the abstract processes over the F domains STREAM ( Delta) Namely, isomorphism is provided just by the mapping OE which transforms a run s of the process into the corresponding strict chain. 8.2 Example 2. Processing Streams with Holes Sometimes in dataflow theory [PA, WA] are used also processes related to the domain of streams with holes over a set Delta. This domain consists of all infinite sequences over Delta [ and is partially ordered by pointwise ordering. It is isomorphic to the domain of functions from natural numbers to Delta [ and also to the ....

Wadge, W. Ashcroft, E., LUCID, the Data Flow Programming Language, Academic Press, 1985

....time with its usual ordering relation . There are two temporal operators in TL, namely first and next, which are applied to formulas. The temporal operators refer to the initial moment and the next moment in time respectively. Note that these operators are inspired by those of the Lucid language [32]. The values of formulas of TL vary with the moments in time in . TL extends a first order language without any function symbols with two new formation rules: if A is a formula, so are firstA and nextA. The informal semantics of temporal operators are given as follows: A formula of the form ....

W. W. Wadge and E. A. Ashcroft. Lucid, the Dataflow Programming Language. Academic Press, 1985.

....partial failures, and the resilience of failure can vary greatly across protocols. Also, this separation allows Cicero to adopt additional programming abstractions for protocol implementation, including the object based abstraction provided in [20] ffl Dataflow Execution Model : Many languages [1, 21] and machines [22, 23] have been designed based on this model. Cicero uses this model differently, and primarily to describe event driven execution at different granularities, and as formalism to allow Cicero to be translated to from other protocol specification models (e.g. Petri nets [19] ffl ....

W. W. Wadge and E. A. Ashcroft. Lucid, the Dataflow Programming Language. Academic Press U.K., 1985.

....description to the various intermediate steps can be carried out with tools of guaranteed performance. Such an approach is standard in certain communities, where languages with strong formal properties are used to ensure robust design. Examples include ML [2] dataflow languages (e.g. Lucid [3], Haskell [4] and synchronous languages (e.g. Lustre, Signal, Esterel [5] There is a broad range of potential formalizations of a design, but most tools and designers describe the behavior of a design as a relation between a set of inputs and a set of outputs. This relation may be informal, ....

W. Wadge and E.A. Ashcroft, Lucid, the dataflow programming language, Academic Press, 1985.

....0 (x 1) computes the stream of positive integers. Here, the x 1 expression stands for extend (extend (const )x)y using the classical addition between scalars. 1 stands for a stream of 1 (thus, const 1) We have : x [x0 ] Gamma x 0 x [x0 ] Gamma x 0 x [x0 ] Gamma x 0 1 [1] Gamma 1 x [x0 ] Gamma x 0 x 1 [x0 1] Gamma x 0 1 x [x0 ] Gamma x 0 pre 0(x 1) 0] Gamma pre (x 0 1) x 0 1) rec x:pre 0(x 1) rec [x0 ] 0] Gamma rec x 0 :pre (x 0 1) x 0 1) rec [x 0 ] 0] x 0 ] which reduces to : rec x:pre 0(x ....

E. A. Ashcroft and W. W. Wadge. Lucid, the data-flow programming language. Academic Press, 1985.

.... dataflow , as early as the late 1960s (see for example [157] and [5] The term dataflow originates from the term data flow analysis (see [3] used to evaluate potential concurrency in computations. 2. 2 The 1970s The first dataflow language, and probably still the most famous, is Lucid (see [223]) that was conceived in 1974. Lucid is based in part on the language POP 2 (see [51] that allowed a limited use of streams. Other relevant dataflow references from the 1970s are [6] 135] 68] 226] and [10] In 1974 G Kahn published his well known work (see [121] outlining a simple ....

....enables us to show how mutual recursion is expressed; how vector valued components are specified; and how each language deals with explicit synchronization. The interested reader can find studies of the Flip Flop at various levels of abstraction in [114] 208] 200] and [134] 9. 4 Lucid Lucid ([223]) is perhaps the best known of all the dataflow languages that have been developed. A Lucid programme is essentially a system of recursion equations, although Lucid is described by its authors as a functional dataflow programming language . The term dataflow is chosen because each Lucid ....

W W Wadge and E A Ashcroft. Lucid, the Dataflow Programming Language. Academic Press, 1985.

....as simulation, dataflow computation, mesh oriented computation, and spreadsheets. InTense [24] is based on a multi dimensional logic which is very much like ML( However, InTense also includes a large repertoire of Lucid like intensional operators such as asa (as soon as) and wvr (whenever) [38]. It is not clear how such operators can be given an operational semantics and whether proof rules can be defined for them, and yet they are implemented. The correctness of the implementation is not addressed, nor the declarative semantics of the language. In contrast to InTense, our work starts ....

....implemented in Prolog. In our approach, there is a natural correspondence between the multidimensional interface and MLP(n) Also, the interface can be naturally used as a programming tool. Du and Wadge [12] proposed a 3D spreadsheet based on intensional logic and the functional language Lucid [38]. 6 Concluding Remarks We have established a theoretical foundation of logic programming based on multi dimensional logics, and outlined its features and use. We have in particular discussed the declarative and operational semantics of MLP. Orgun and Wadge [29] provided a language independent ....

W. W. Wadge and E. A. Ashcroft. Lucid, the Dataflow Programming Language. Academic Press, 1985.

....partage avec ses restrictions r eactives les memes propri et es de compilation efficace. Mots cl es : Flots de donn ees synchrones, evaluation sans listes, r ecursivit e, r ecursivit e terminale. 1. Introduction 1.1. Flots de donn ees Dans les ann ees 70, le langage Lucid a et e propos e [2, 1], pour pallier l inefficacit e des langages fonctionnels, en introduisant un style d it eration fond e sur les suites de valeurs. A peu pr es a la meme epoque, Gilles Kahn montrait [13] que la s emantique de r eseaux de processus asynchrones et d eterministes, communiquant par des files ....

E. A. Ashcroft and W. W.Wadge. Lucid, the data-flow programming language. Academic Press, 1985.

....primitives on a distributed memory architecture. II.b. The concept of stream LUCID [WAD 76] is one of the first programming languages defining equations between infinite sequences of values. This approach has the advantage of representing iterations in a mathematically respectable way [WAD 85] and to quote [WAT 91] series expressions are to loops as structured control constructs are to gotos . Streams can be manipulated as a whole, using filters, transducers. ARV 83] and so can be visualised as collections. Nevertheless we carefully make a distinction between stream and ....

W. W. Wadge and E.A. Ashcroft, Lucid, the Data flow Programming Language , Academic Press U.K., 1985.

....Intensional Programming, pp. 26 32, Sidney, B.C. Canada, Apr. 7 8 1988. Wadge [1985] proposed a tensed extension of Horn logic programming (called THLP) which was later developed into Chronolog (see below) The design of THLP was influenced by the dataflow language Lucid of Wadge and Ashcroft [14], and its original target application was modelling nonterminating dataflow computations. THLP has two temporal operators (borrowed from Lucid) first refers to the initial moment in time, and next to the next moment in time. Like Templog, it uses the set of natural numbers as the collection of ....

W. W. Wadge and E. A. Ashcroft. Lucid, the Dataflow Programming Language. Academic Press, 1985.

....of large dynamical systems. II. The parallel language 81 2 The simulation of a system consists in computing the trajectories of the variables describing the system. By variable trajectory, we mean the successive values in time of a variable. This notion fits well with the concept of stream [9]. The 81 2 language focuses on models described by a set of functional relationships between stream variables, i.e. an 81 2 program takes the following form: 1) x = f 1 (x, y, y = f 2 (x, y, where x, y, denotes streams. Because relations like (1) often apply ....

....in 81 2. II.1. The concept of synchronous stream [11] have considered, to simplify the formal treatment of a program, that a variable denotes an infinite sequence of values rather than a single value. This approach takes advantage of representing iterations in a mathematically respectable way [9] and to quote [12] series expressions are to loops as structured control constructs are to gotos . Such infinite sequences are called streams and are manipulated as a whole, using filters, transductors, etc. Consider the following nested C loops: for (i = 0; i 3; i ) i 0; 1; 2 for (j = ....

W. W. Wadge and E.A. Ashcroft, Lucid, the Data flow Programming Language , Academic Press U.K., 1985.

....that make the definitions true (there may be more than one) we select the one that is least in the domain theoretic sense. Roughly speaking, this is the solution that can be calculated by using the definitions as computation rules. This least fixpoint semantics is described in more detail in [1]) For least fixpoints to be defined, the original algebra A has to be a continuous algebra, which implies that its universe must be a complete partial order with a least element ( bottom ) The original (temporal) Lucid extends ISWIM by adding the temporal operators first, next and fby and by ....

W.W. Wadge and E.A. Ashcroft. Lucid, the Dataflow Programming Language. Academic Press, U.K., 1985.

....nat 0 = 0 nat t 1 = nat t 1 The intensional program avoids the explicit use of the time index. The sequence of natural numbers is defined using the temporal operator fby rather than using subscripts (i.e. indices) The example given above is actually a program of the intensional language Lucid [WA85] (which was probably the first such language) The value of a Lucid expression depends on a hidden time parameter. In other words, the meanings of entities in Lucid programs are not ordinary data values but infinite sequences of ordinary values. The statements of a Lucid program are equations ....

....to be able to compute larger and larger parts of the desired output of the program. An implementation can start by computing the first value of the output sequence, then the second, and so on. The traditional implementation of Lucid programs is based on a computational model known as eduction [WA85]. We illustrate the main idea of eduction using an example. Suppose we want to calculate the first three Fibonacci numbers. Moreover, assume that we have implemented a simple interpreter EV AL which computes the output of Lucid programs at successive time points. The interpreter uses the ....

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W. W. Wadge and E. A. Ashcroft. Lucid, the Dataflow Programming Language. Academic Press, 1985.

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Wadge, W. W., Ashcroft, E. A. Lucid, the Dataflow Programming Language. Academic Press 1985.

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W. W. Wadge and E. A. Ashcroft. Lucid, the Dataflow Programming Language. Academic Press, Orlando, Florida, 1985. 98

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W. W. Wadge and E. A. Ashcroft. Lucid, the Dataflow Programming Language. Academic Press, 1985.

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W. W. Wadge and E. A. Ashcroft. Lucid, the dataflow programming language. Academic Press U.K., 1985.

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W. W. Wadge and E. A. Ashcroft, Lucid, the Dataflow Programming Language. London, U.K.: Academic, 1985.

No context found.

William W. Wadge. Lucid, the Dataflow Programming Language. Academic Press, 1985.

No context found.

William W. Wadge and Edward A. Ashcroft, Lucid, the Dataflow Programming Language, Academic Press, Inc. (London), 1985.

No context found.

W. W. Wadge and E. A. Ashcroft. Lucid, the Dataflow Programming Language. Academic Press, 1985.

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