D. Smith. Constructing specification morphisms. Journal of Symbolic Computation, 16:571--606, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of (the composition of) refinements between logical algebraic specifications, as well as the construction of such refinements. Other applications include modularity in deductive databases [25] and support for a joint extension of systems development environments [37] and algorithmic design tools [35, 36, 31] so that more advanced and general refinements are supported. e.g. SpecWare[37] supports only refinements ff=hi ff ; e ff i such that e ff is extension by definitions, and KIDS [35, 36] is based on (first order) Unskolemization [7, 21, 6, 36, 31] which can be easily extended, within a Development ....

....[25] and support for a joint extension of systems development environments [37] and algorithmic design tools [35, 36, 31] so that more advanced and general refinements are supported. e.g. SpecWare[37] supports only refinements ff=hi ff ; e ff i such that e ff is extension by definitions, and KIDS [35, 36] is based on (first order) Unskolemization [7, 21, 6, 36, 31] which can be easily extended, within a Development Workspace, so that non skolem E Spec functions and E Spec predicates, are also abstracted. Depending on the status of E Spec , this expansion may allow the extraction of ....

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D. R. Smith. Constructing specification morphisms. Symbolic Computation, 15(5-6):571--606, May-June 1993.

....We call this specification formalism MS ETR representation. Other advantages of this formalism include a better diagrammatic representation, a unifying framework for the application of various known extension methods ( Dim95, Dim96a] and support for a global Polarity Analysis in the fashion of [Smi93b]. In Section 4, we outline a top down approach to Polarity Analysis that respects [Smi93b] extends [MW86] and exploits the extensibility of theories in a dual manner to the classical approach of [Lyn59] Polarity Analysis gives rise to some useful derived inference rules and an abstract ....

.... include a better diagrammatic representation, a unifying framework for the application of various known extension methods ( Dim95, Dim96a] and support for a global Polarity Analysis in the fashion of [Smi93b] In Section 4, we outline a top down approach to Polarity Analysis that respects [Smi93b], extends [MW86] and exploits the extensibility of theories in a dual manner to the classical approach of [Lyn59] Polarity Analysis gives rise to some useful derived inference rules and an abstract interpretation of the term algebra. It is a fundamental pre process in the construction of several ....

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D. R. Smith. Constructing specification morphisms. Symbolic Computation, 15(5-6):571--606, May-June 1993.

....of data that could be hidden, i.e. properties or derivations that are valid in any context that includes the accessible data as a module. Potential practical applications in Computer Science include the joint extension of systems development environments [45] and algorithmic design tools [41, 44, 43] so that modularity is improved and more advanced and general refinements are supported. Reasoning by means of (E Dev encapsulations of) uniform schemata may also assist in specifying and developing formal presentations of algorithmic structure via algorithm theories [44] In fact similar methods ....

D. R. Smith. Constructing specification morphisms. Symbolic Computation, 15(56) :571--606, May-June 1993.

....dev on the basis of the proof calculus for E spec ) But this is out of the scope of this paper and it is in fact a subject of on going research. The pursued practical applications in Computer Science include the joint extension of systems development environments [35] and algorithmic design tools [32, 34, 33] so that more advanced and general manipulations of specification modules are supported. As is explained in Chapters 5 and 6 of [10] and in [11, 13] a Development Workspace can be used as the means of generating a back end development formalism E dev for a given front end specification ....

D. R. Smith. Constructing specification morphisms. Symbolic Computation, 15(5-6):571--606, May-June 1993.

.... syntax: One can derive an 8 , 9 free witness : from the deductive proof of a 9 bound formula. The practical applications in Computer Science we intend to pursue, include the joint extension of application software and systems development environments [35] and algorithmic design tools [32, 34, 33] so that more advanced manipulations of specification modules are supported. ....

D. R. Smith. Constructing specification morphisms. Symbolic Computation, 15(56) :571--606, May-June 1993.

....uniform interpolants have the same implicit (meta)form. It should be noted that, in our case, this common form is revealed in the formal syntax. Potential practical applications in Computer Science include the joint extension of systems development environments [39] and algorithmic design tools [35, 37, 36] so that more advanced and general refinements are supported. For example, SPECWARE[39] is based on logical theory manipulations, but supports only refinements ff=hi ff ; e ff i such that e ff is an extension by definitions and (first order) Unskolemization [6, 25, 5, 36] underlies basic ....

....algorithmic design tools [35, 37, 36] so that more advanced and general refinements are supported. For example, SPECWARE[39] is based on logical theory manipulations, but supports only refinements ff=hi ff ; e ff i such that e ff is an extension by definitions and (first order) Unskolemization [6, 25, 5, 36] underlies basic operations in KIDS [35, 36] Within a Development Workspace, the uniformity of interpolants gives rise to proof obligations that guard the correct composition of sequential or parallel refinements ( 11] Moreover, non skolem E Spec functions and ESpec predicates can be ....

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D. R. Smith. Constructing specification morphisms. Symbolic Computation, 15(5-6):571--606, May-June 1993.

....with deductive synthesis, but to go beyond horn logic to first order logic with equality. Another possibility would be to utilize a higher order logic. Finally, entirely different approaches to program synthesis may be considered, for example, a methodology based on specification morphisms [ Smith, 1993 ] or constructive type theory [ Constable, 1986 ] In any case, a more complete diagnosis of the difficulty awaits further investigation. 4 Related Work Our research was originally motivated by difficulties encountered in attempting to apply the SIGMA scientific modeling system [ Keller et al. ....

D. Smith. Constructing specification morphisms. Journal of Symbolic Computation, 16, 1993.

....express requirements that have to hold in every state of the component. Note that synthesising morphisms has already attracted some attention in the literature in the context of the KIDS system where the focus is on transforming (first order) specifications into efficient algorithms (Smith, 1990, 1993). See also (Dimitrakos, 1996) for further development of these ideas. synthesising programs from specifications. In particular, given a specification diagram #: #####, the functor ### generates (synthesises) by composition, a program diagram #######:#####. Because nothing can be assumed about ....

Smith, D. (1993) Constructing Specification Morphisms. Journal of Symbolic Computation 15 (5-6), 571-606.

....techniques studied in [1] 11] and [2] the programs that are automatically extracted are close to those a human developer would have written and the structure of the specification is mirrored in the dependencies of the module extracted. The only similar approach we know of is that of Smith [16] in the SpecWare system. He uses similar techniques to construct specification morphisms. Our technique differs from his in the specification building operations and in the program extraction technique. The paper is organized as follows: In x 2, we introduce the specification language and ....

Smith, D.R. Constructing Specification Morphisms, J. Symbolic Computation (1993), 15, 571-606.

.... Smith s one in the way to: ffl characterize the class of Greedy Algorithms as Smith already did for Divide and Conquer [Smi85a, Smi85b, Smi87a] Problem Reduction Generators [Smi91] Global Search [Smi87b] and with Lowry for Local Search (see Appendix) ffl formalize the synthesis process [SL90, Smi92, Smi93] Two interesting consequences of this study would be: 1. to create a framework which could help in synthesizing greedy algorithms; 2. to improve Smith s hierarchy of classes [Smi93] by inserting the Greedy Algorithms class and comparing it to some others (see Appendix) A ....

....purpose of this section is to show how it is possible to use the algorithm theory developped in the previous section in order to help the synthesis of greedy programs from formal specifications of problems underlain by the structure of a matroid. Smith explained how this purpose can be achieved [Smi92, Smi93] We shall shortly explain his method and we recommend the interested reader to refer to [Smi93] for further details. The method is based on category theory [BW90, Poi92] Its basic idea is represented in Figure 6. In that graph, the nodes and the arcs represent respectively theories and ....

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D.R. Smith. Constructing specifications morphisms. Technical Report KES.U.92.1, Kestrel Institute, 1992.

....techniques studied by one of the authors in [1] the programs that are automatically extracted are in readable form and are close to those a human developer would have written out by hand. The only similar approach we know of is the technique used by Smith in the SpecWave system (see [15]) There Smith uses similar techniques to construct specification morphisms. Our technique differs from Smith s in the specificationbuilding operations and in the program extraction technique. The paper is organized as follows: In section 2, we introduce the specification language and show how ....

....axioms 8l : Seq:8x : Elem:x in l x bound Seq (l) endaxioms Then we get the specification of sequences, SEQ. SEQ = enriches ELEM; Delta Seq ; Delta BdSeq Later in the paper we shall show how we get a program BdSeq for the bound of a sequence. We shall use unSkolemization (cf. Smith [15]) and program extraction. First we unSkolemize the axiom for bound: 8l : Seq:9y : Elem:8x : Elem:x in l x y: 1) We shall then show how we extract a program from the proof of this formula. This will involve using the other axioms and various components of the specification, see section 5. 3 ....

Smith, D.R. Constructing Specification Morphisms, J. Symbolic Computation (1993), 15, 571-606.

....an incremental development process. That is to say, given a configuration diagram Note that synthesising morphisms has already attracted some attention in the literature in the context of the KIDS system where the focus is on transforming (first order) specifications into efficient algorithms (Smith, 1990, 1993). See also (Dimitrakos, 1996) for further development of these ideas. S C Spec(P) s where P represents the existing system (e.g. the program vending machine) and S the specification of the component that is to be added (e.g. the regulator) we should be able to synthesise an interconnection ....

Smith, D. (1993) Constructing Specification Morphisms. Journal of Symbolic Computation 15 (5-6), 571-606.

....as schemas which are then reused in later synthesis problems. We believe that the benefits of integration will only be realized if concrete algorithm re use is also enabled. KIDS has a facility for reusing concrete components via a process for deriving specification morphisms using unskolemization [21]. These morphisms can be applied to existing components to produce new operators (e.g. to derive a composition operator from a decomposition operator) However, the choice of source component must be done manually, i.e. the retrieval problem emerges in the same way as in the ....

D. R. Smith. "Constructing specification morphisms", JSC, 15:571--606, 1993.

....and parallelization schemes operating mostly on arrays. The concept of shapes resembles our data distribution (algebras) It must be noted, however, that the mechanisms implemented in this extension to Fortran only yields a small subset of the mechanism provided by skeletons. The KIDS system [15,16] designed by Douglas R. Smith et al. also aims at deriving efficient programs from abstract formal specifications. While this system works on imperative programming languages for sequential computers, it has much in common with our approach in that transformations are perceived as being guided by ....

Douglas R. Smith. Constructing specification morphisms. Journal of Symbolic Computation, 15(5/6):571--606, May/June 1993.

....1. If we want to find a function which satisfies this relation, we have to further refine the enclosing specification. This refinement can be guided by a hierarchy of algorithm theories which are used to impose additional structure on the specification. Details of this process can be found in [Smith 93, Smith and Lowry 90] Algorithm synthesis is one of the creative parts of software development and can be used to construct basic interpretations which can then be composed. Specware aids this by providing a scaffolding which takes care of the mundane details, thus letting the developer identify ....

Smith, D. R. Constructing specification morphisms. Journal of Symbolic Computation, Special Issue on Automatic Programming 15, 5-6 (May-June 1993), 571--606.

....they are highly syntactic in nature. Much of the semantic content which forms the basis of program synthesis resides implicitly, e.g. as part of interpretations, connections, homomorphisms, etc. Structured sorts are part of a larger effort to introduce some semantic content into morphisms [14,10]. 10.1. Related Work There has been little work on adding object oriented features to algebraic specification; see, for example, 15,16] Goguen and Meseguer consider objects with state, with each object being an algebra; this needs reflective semantics. Specialization by adding structure is not ....

Douglas R. Smith. Constructing specification morphisms. Journal of Symbolic Computation, Special Issue on Automatic Programming, 15(5-6):571--606, May-June 1993.

....is reformulated as descriptors of promising operators. We will now present this method in detail. 4.3. 1 Polarity analysis Polarity analysis is a technique for tracing qualitative changes in function values (e.g. increase or decrease) back to qualitative changes in the function s arguments (see [80, 126]) In this research, we have adopted polarity analysis as a method by which to extract promising patching operators (i.e. parameter value changes) from RAPevaluation functions. 114 Polarity analysis rules Polarity analysis is a rule based process; rules associated with functions capture ....

Douglas R. Smith. Constructing specification morphisms. Journal of Symbolic Computation, Special Issue on Automatic Programming, 15(5-6):571--606, MayJune 1993.

....of operators. By virtue of our abductive polarity analysis, this subset is a priori known to contain the overall best operator) The method of abductive polarity analysis has been developed as part of this dissertation research. It is modeled after a known technique called polarity analysis [78, 124]) over which is has the advantage of handling functions that are nonmonotonic (details in Chapter 4) 20 1.2.2 The key ideas of this dissertation The work of this dissertation is based on roughly four ideas and insights. We briefly summarize each one. Problem classes RAP. A variety of ....

....4 kB is the Boltzmann constant. 232 are already provided by the current version of MENDER. 7.5 Other Related Research 7.5.1 Polarity Analysis Polarity analysis as a reasoning technique is not new. In fact, it has been used for purposes as varied as the construction of specification morphisms [124], speed up of search in resolution theorem proving [80] and qualitative algebraic reasoning for the design and verification of physical systems [152] Smith employs polarity analysis in the automated design of algorithms. Algorithm design is viewed as the construction of a specification morphism, ....

D. R. Smith. Constructing Specification Morphisms. Technical Report KES.U.92.1, Kestrel Institute, April 1992.

....a classification arrow from A to S 0 which classifies S 0 as having A structure bymaking explicit how S 0 has at least the structure of A. Finally the refinement is applied by computing the pushout in the category of diagrams. The creativework lies in constructing the classification arrow [5,6]. 4 Scaling up The process of refining specification S 0 described above has three basic steps: 1) select a refinement A = B from a library, 2) construct a classification arrow A = S 0 ,and (3) compute the pushout S 1 of B ( A = S 0 . The resulting refinement is the cocone arrow S 0 = ....

....from the top down. The initial interpretation from A 0 to Spec 0 is often simple to construct. The rungs of the ladder are constructed by a constraint solving process that involves user choices, the propagation of consistency constraints, calculation of colimits, and constructive theorem proving [5,6]. Generally, the rung construction is stronger than a colimit even though a cocone is being constructed. The intentincontructing I i : A i Spec i is that Spec i has sufficient defined symbols to serve as the codomain. In other words, the implicitly defined symbols in A i are translated to ....

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Smith, D. R. Constructing specification morphisms. Journal of Symbolic Computation, Special Issue on Automatic Programming 15, 5-6 (May-June 1993), 571--606.

....a classification arrow from A to S 0 which classifies S 0 as having A structure by making explicit how S 0 has at least the structure of A. Finally the refinement is applied by computing the pushout in the category of diagrams. The creative work lies in constructing the classification arrow [7, 9]. 3.3. Development of Sorting Algorithms Our goal in this section is to show a simple example that refines a requirement spec to code by applying (1) an algorithm design refinement, 2) a datatype refinement, and (3) an expression optimization refinement. We step through the refinement of a ....

....(x 0 ; x 1 ; x 2 ) O(x 1 ; z 1 ) O(x 2 ; z 2 ) OCompose2 (z 0 ; z 1 ; z 2 ) O(x 0 ; z 0 ) cannot be translated into Sorting because OCompose2 has no translation yet. However, a technique called unskolemization allows us to use inference tools to deduce a suitable translation for OCompose2 [7]. Unskolemizing operator symbol OCompose2 replaces the occurrence of OCompose2 by a fresh existentially quantified variable in the scope of the quantifiers for z 0 ; z 1 ; z 2 : 8(z 0 ; z 1 ; z 2 : R) 9(y : Boolean) 8(x 0 ; x 1 ; x 2 : D) ODecompose2 (x 0 ; x 1 ; x 2 ) O(x 1 ; z 1 ) O(x 2 ; z ....

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Smith, D. R. Constructing specification morphisms. Journal of Symbolic Computation, Special Issue on Automatic Programming 15, 5-6 (May-June 1993), 571--606.

....support for this approach. Although the classification approach applies to the incremental application of any kind of knowledge formally represented 7 in a hierarchy of theories, our work mainly focused on a hierarchy of algorithm design theories and its applications to logistical applications [39, 38]. This technique enable us to integrate at a deep semantic level problem solving methods from Computer Science (e.g. divide and conquer, global search) Artificial Intelligence (e.g. heuristic search, constraint propagation, neural nets) and Operations Research (e.g. Simplex, integer programming, ....

....in any order the above sequence is typical of our experiments in algorithm design. A new system, called Specware, is currently under construction at Kestrel as a successor to KIDS. Specware is based on concepts of higher order algebraic specifications, morphisms, and categorical constructions [20, 38, 39, 50]. 4 Specifying a Scheduler 4.1 What is Scheduling The essential notion of scheduling is that certain activities are assigned to resources over certain time intervals. Various constraints on the assignments must be satisfied and certain measures of the cost or goodness of the assignment are ....

[Article contains additional citation context not shown here]

Smith, D. R. Constructing specification morphisms. Journal of Symbolic Computation, Special Issue on Automatic Programming 15, 5-6 (May-June 1993), 571--606.

....a classification arrow from A to S 0 which classifies S 0 as having A structure by making explicit how S 0 has at least the structure of A. Finally the refinement is applied by computing the pushout in the category of diagrams. The creative work lies in constructing the classification arrow [7, 9]. 3.3. Development of Sorting Algorithms Our goal in this section is to show a simple example that refines a requirement spec to code by applying (1) an algorithm design refinement, 2) a datatype refinement, and (3) an expression optimization refinement. We step through the refinement of a ....

....(x 0 ; x 1 ; x 2 ) O(x 1 ; z 1 ) O(x 2 ; z 2 ) OCompose2 (z 0 ; z 1 ; z 2 ) O(x 0 ; z 0 ) cannot be translated into Sorting because OCompose2 has no translation yet. However, a technique called unskolemization allows us to use inference tools to deduce a suitable translation for OCompose2 [7]. Unskolemizing operator symbol OCompose2 replaces the occurrence of OCompose2 by a fresh existentially quantified variable in the scope of the quantifiers for z 0 ; z 1 ; z 2 : 8(z 0 ; z 1 ; z 2 : R) 9(y : Boolean) 8(x 0 ; x 1 ; x 2 : D) ODecompose2 (x 0 ; x 1 ; x 2 ) O(x 1 ; z 1 ) O(x 2 ; z ....

[Article contains additional citation context not shown here]

Smith, D. R. Constructing specification morphisms. Journal of Symbolic Computation, Special Issue on Automatic Programming 15, 5-6 (May-June 1993), 571--606.

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D. Smith. Constructing specification morphisms. Journal of Symbolic Computation, 16:571--606, 1993.

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. D.Smith, "Constructing Specification Morphisms", Journal of Symbolic Computation 15 (5-6), 571-606, 1993.

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Douglas R. Smith. Constructing specification morphisms. Journal of Symbolic Computation, Special Issue on Automatic Programming, 16(56) :571--606, 1993.

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