K.-K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini (eds), Proc. of LOPSTR'94 and META'94, pp. 104--  Home/Search   Document Details and Download   Summary   Related Articles   Check

....language is gradually introduced as we go along. Whenever types are not so important, we omit them. Our results should be transposed to the more useful general case where an ad hoc language can be dynamically constructed, and even parameterised, such as through the composition of (open) frameworks [14]. As the additional theoretical apparatus might obstruct the ideas we are trying to convey, we shall always stick to minimalism, and view the identified extensions as future work. We also ask the reader to bear with us whenever there are (often deliberate) theoretical imprecisions or vague ....

K.-K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini (eds), Proc. of LOPSTR'94 and META'94, pp. 104--121. LNCS 883. Springer-Verlag, 1994.

....of logic programs. ACM Transactions on Programming Languages and Systems (TOPLAS) 16(3) 607 648, May 1994. 12] B. Martens, D. De Schreye, and T. Horv ath. Sound and complete partial deduction with unfolding based on well founded measures. Theoretical Computer Science, 122(1 2) 97 117, 1994. [13] S. Muggleton and L. De Raedt. Inductive logic programming: Theory and methods. The Journal of Logic Programming, 19 20:629 680, May 1994. 14] A. Mulkers, W. Winsborough, and M. Bruynooghe. Live structure dataflow analysis. ACM Transactions on Programming Languages and Systems (TOPLAS) ....

....for constructive negation. In P. Van Hentenryck, editor, Proceedings of the Eleventh International Conference on Logic Programming, pages 520 534s. The MIT Press, 1994. 12] D. Boulanger and M. Bruynooghe. Using abstract interpretation for goal replacement. In Deville [30] pages 210 228. [13] D. Boulanger and M. Bruynooghe. A systematic construction of abstract domains. In B. Le Charlier, editor, Proceedings of the First International Static Analysis Symposium, Lecture Notes in Computer Science 864, pages 61 77. Springer Verlag, 1994. 14] D. Boulanger, M. Bruynooghe, and M. ....

K.-K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In Logic Program Synthesis and Transformation. Proceedings of LOPSTR'94, Pisa, Italy, 1994. To be published.

....of logic programs. ACM Transactions on Programming Languages and Systems (TOPLAS) 16(3) 607 648, May 1994. 12] B. Martens, D. De Schreye, and T. Horv ath. Sound and complete partial deduction with unfolding based on well founded measures. Theoretical Computer Science, 122(1 2) 97 117, 1994. [13] S. Muggleton and L. De Raedt. Inductive logic programming: Theory and methods. The Journal of Logic Programming, 19 20:629 680, May 1994. 14] A. Mulkers, W. Winsborough, and M. Bruynooghe. Live structure dataflow analysis. ACM Transactions on Programming Languages and Systems (TOPLAS) ....

....for constructive negation. In P. Van Hentenryck, editor, Proceedings of the Eleventh International Conference on Logic Programming, pages 520 534s. The MIT Press, 1994. 12] D. Boulanger and M. Bruynooghe. Using abstract interpretation for goal replacement. In Deville [30] pages 210 228. [13] D. Boulanger and M. Bruynooghe. A systematic construction of abstract domains. In B. Le Charlier, editor, Proceedings of the First International Static Analysis Symposium, Lecture Notes in Computer Science 864, pages 61 77. Springer Verlag, 1994. 14] D. Boulanger, M. Bruynooghe, and M. ....

K.-K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In Logic Program Synthesis and Transformation. Proceedings of LOPSTR'94, Pisa, Italy, 1994. To be published.

....Future Work We have shown how correct and a priori correctly reusable (divide and conquer) programs can be synthesised, in a schema guided way, from formal specifications expressed in the first order language of a framework. Related work at the framework and steadfastness level is described in [20, 23, 24]. It focuses mainly on a model theoretic characterisation of the semantics of frameworks (and specifications) and steadfastness. This provides a sound theoretical basis for modular program development by composing or reusing frameworks as well as steadfast programs. In terms of synthesis, it uses ....

K.-K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR/META'94 , pages 104--121. LNCS 883, Springer-Verlag, 1994.

.... = hae(S) ae(F ) ae(R)i, where ae(S) is the image of S, ae(F ) contains the declarations ae(f) ae(a) ae(s) 4 A proof of Theorem 1 can be found in [1] Isoinitial semantics is closely related to initial semantics used in algebraic ADTs [14] Discussions of these semantics can also be found in [7, 12]. 5 We can also use induction principles in T (P ) such that f : a s 2 F , and ae(R) the declarations ae(r) ae(a) such that r : a 2 R. If ae is a map from the symbols of Sigma to those of another signature Delta, and if ae( Sigma) Delta, then we say that ae is a signature morphism ....

K.K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR 94 and META 94 , Lecture Notes in Computer Science 883, pages 104--121, SpringerVerlag, 1994.

....we must be careful and use only adequate definitions, that is definitions which give rise to expansions of the isoinitial model (of the framework) that are also isoinitial. In this connection, a useful criterion for adequacy is the existence of a totally correct program for the specified relation ([6]) This means that we can actually use formal program derivation, or program synthesis, to enrich the specification language by adequate definitions. The model theoretic relation between an if and only if specification S of a relation r and a program P to compute r is illustrated in Figure 2. ....

K.K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR 94 and META 94 , Lecture Notes in Computer Science 883, pages 104--121, Springer-Verlag, 1994.

.... correctness is based on the comparison between specifications and the intended models of programs (see e.g. 4] for a brief survey) The distinguishing feature of our approach is that specifications, programs and correctness are defined within a framework F (the use of frameworks is discussed in [9, 11]) We shall define F to be a full first order logical theory, S a first order formula in F that defines a (set of) relation(s) r, and P a Horn theory whose language contains the relation(s) r. Both F and P have intended models: the intended model of P is its minimum Herbrand model H, while the ....

....In this connection, a useful criterion for adequacy is the existence of a totally correct program for the specified relation such that its completion can be proved in the framework. This means that we can actually use program synthesis to enrich the specification language by adequate definitions ([9]) To return to the subset example, in SET we can define the subset relation in the usual way: A B 8x: x 2 A x 2 B) Q2) Since we represent sets by lists, and our programs will compute on lists, we specify sublist as follows: sublist(X; Y ) fXg fY g (Q3) Note that (Q3) corresponds ....

K.-K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR 94 and META 94 , Lecture Notes in Computer Science 883, pages 104--121, Springer-Verlag, 1994.

.... of a new function f in F consists of a definition of the form y = f(x) R(x; y) where R(x; y) is a formula of the language of F such that F 8x9 y R(x; y) In this connection, a useful criterion for adequacy is the existence of a totally correct program for the specified relation ([8]) 14 The model theoretic relation between an if and only if specification S of a relation r and a program P to compute r is illustrated in Figure 2. P . r(x) r(x) r(x) R(x) Prog spec S Iff interpretation I in r of unique interpretation H in r of Framework Models Figure 2: ....

....That is Ocomp(P1 ) free(K) which we will also call a Herbrand instance of P1 , has an isoinitial model. It should be obvious, in this simple example, that in every Herbrand instance free(K) SET (Elem) the corresponding (Herbrand) instance of 28 A formal treatment of adequacy can be found in [8]. P1 is semantically correct with respect to (2) Thus we say that P1 is semantically correct in the open framework SET (Elem) Similarly, the open program P2 is also semantically correct (with respect to (2) in SET (Elem) In general, we can informally define semantic correctness of a ....

K.K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR 94 and META 94 , Lecture Notes in Computer Science 883, pages 104--121, Springer-Verlag, 1994.

....our approach is very general, and it should be equally applicable to the synthesis of constraint logic programs [8, 9] In this paper, we propose a formal approach to deductive synthesis of CLP programs, based on our work in standard LP. Our approach to synthesis in standard LP is deductive [10, 12, 11], i.e. it iteratively derives clauses for a program from its specification. The synthesis process starts from a specification that is defined in the context of a (first order) theory 1 The first author was partially supported by the European Union HCM project on Logic Program Synthesis and ....

....(re)used in a class of computation domains. Therefore steadfastness provides a basis for modular programming. Furthermore, specification frameworks (both open and closed) can be constructed, and thus maintained, in an incremental manner by using the result of synthesis itself, as we showed in [11]. Thus, altogether our approach can provide a basis for object oriented LP software engineering. In this paper, we extend our approach to the synthesis of CLP programs. We define specification frameworks so that they can contain constraint domains or constraint theories, and develop an abstract ....

[Article contains additional citation context not shown here]

K.K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR 94 and META 94 , Lecture Notes in Computer Science 883, pages 104-121, Springer-Verlag, 1994.

....expansions, and such definitions are also said to be adequate. So we say a framework is adequate if it is constructed only from adequate expansions. A useful criterion for the adequacy of an expansion is the existence of a steadfast program to compute the relation defined by the expansion (see [5]) Thus program synthesis itself provides a means of adequately expanding a framework. To extend this discussion to open frameworks, we need to address closed instances of an open framework F , i.e. compositions of F with closed frameworks C s that are closed frameworks themselves. So we will now ....

K.K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR 94 and META 94 , LNCS 883:104--121, Springer-Verlag, 1994.

....that if F is a (possibly infinite) recursively enumerable axiomatisation, then there exists an isoinitial model in which relation symbols are interpreted by decidable relations, and function symbols by total computable functions. In practice, we only ever construct and use such frameworks (see [15, 17] for a related discussion) A framework F typically defines a new abstract data type by using pre defined types. Axioms for the old sorts are imported, and new ones are added to define new functions and relations on T . For lack of space, we cannot give the full syntax of frameworks here, but it ....

....A framework F typically defines a new abstract data type by using pre defined types. Axioms for the old sorts are imported, and new ones are added to define new functions and relations on T . For lack of space, we cannot give the full syntax of frameworks here, but it can be found in e.g. [15] along with examples of commonly uses frameworks. 3.1 Closed and Open Frameworks We distinguish between closed and open frameworks, depending on the absence or presence of parameters. Whilst a closed framework has one intended (isoinitial) model, an open framework has a class of intended ....

K.-K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR 94 and META 94, LNCS 883, pages 104--121, SpringerVerlag, 1994.

.... correctness is based on the comparison between specifications and the intended models of programs (see e.g. 4] for a brief survey) The distinguishing feature of our approach is that specifications, programs and correctness are defined within a framework F (the use of frameworks is discussed in [9, 11]) We shall define F to be a full first order logical theory, S a first order formula in F that defines a relation r, 3 and P a Horn theory whose language contains the relation r. Both F and P have intended models: the intended model of F is its isoinitial model I , while that of P is its ....

....that is definitions which give rise to expansions of the isoinitial model (of F) that are also isoinitial. In this connection, a useful 9 criterion for adequacy is the existence of a totally correct program for the specified relation such that its completion can be proved in the framework ([9]) 10 The model theoretic relation between an if and only if specification S of a relation r and a program P to compute r is illustrated in Figure 3.2. P . r(x) r(x) r(x) R(x) Prog spec S Iff interpretation I in r of unique interpretation H in r of Framework Models FIGURE 3.2. ....

[Article contains additional citation context not shown here]

K.K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR 94 and META 94 , Lecture Notes in Computer Science 883, pages 104--121, Springer-Verlag, 1994.

....semantic approach and show that a schema S consists of a syntactic component, viz. a template T , and a semantic component. T is formalised as an open (firstorder) logic program in the context of the problem domain, characterised as a first order axiomatisation called a specification framework F [10, 11]. F endows the schema S with a formal semantics, and enables us to define and reason about its correctness. In particular, we define a special kind of correctness for open programs such as templates, that we call steadfastness. A steadfast (open) program is always correct (wrt its specification) ....

K.-K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR /META'94, pages 104--121. LNCS 883, SpringerVerlag, 1994.

....the form 8(r(x) R(x) where R is any formula of the language, it may happen that the axioms of F are too weak to completely characterise the meaning of the new symbol r. 6 A useful criterion for adequacy is the existence of a totally correct program for computing the specified relation (see [15]) In other words, program synthesis can actually be used to expand F with adequate if and only if specifications. The possibility of adding new closed symbols allows us to build up a specification language for specifying programs on the problem domain in a natural and purely declarative way. ....

K.K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR 94 and META 94 , Lecture Notes in Computer Science 883, pages 104--121, Springer-Verlag, 1994.

....of r expansions of the models of F . A useful criterion for adequacy is the existence of a program P for computing the specified relation, such that P existentially terminates and the completion of P can be proved in the framework F , enriched by the iff specifications of the predicates in P (see [16]) In other words, program synthesis can actually be used to expand F with adequate iff specifications. Expansions of frameworks by new function symbols are equally important: Definition 3. An (adequate) iff specification of a new function f in a framework F consists of a definition of the form ....

K.K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR 94 and META 94 , Lecture Notes in Computer Science 883, pages 104--121, SpringerVerlag, 1994.

....defined thus: s Ijae = ae(s) I f Ijae : a s = ae(f ) I : ae(a) ae(s) r Ijae : a = ae(r) I : ae(a) Ijae will be called the ae reduct of I. 5 [1] gives a proof of Theorem 1. Isoinitial semantics is closely related to initial semantics used in algebraic ADTs [14] see also [7, 12]) 6 We can also use induction principles in T (P ) If ae(oe) oe for every symbol oe, i.e. Sigma Delta, we get the usual notion of reduct to a subsignature (see e.g. 5] In this case, the reduct will also be denoted by Ij Sigma. It is immediate to extend a morphism ae : Sigma ....

K.K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR 94 and META 94 , LNCS 883, pages 104--121, Springer-Verlag, 1994.

....of steadfastness to correctness with respect to parametric specifications in Section 6, and in the previous section we have briefly discussed related pieces of work and their differences with our approach. The idea of steadfastness is primarily motivated by our work in deductive synthesis [24, 17, 18] of logic programs. However, we believe that it is an important concept for formal software development in general. Indeed, steadfastness is a combination of modularity, reusability, and (formal) correctness. As such it provides a basis for hierarchical formal program development that can be used ....

K.-K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR 94 and META 94 , LNCS 883, pages 104-121, Springer-Verlag, 1994.

.... r) formula of the form 8x : r(x) R(x) where the defining formula R(x) is a Sigma formula. An explicit definition of a new function f is a ( Sigma f) formula of the form 8x : F (x; f(x) where the defining formula F (x; y) is a Sigma formula such that Ax 8x9 y : F (x; y) In [17] we have shown how adequate explicit definitions can be established by means of programs synthesis. In [26] it is shown that constructive proof systems can be used to prove adequacy. For this paper, it suffices to know that if the defining formula is quantifier free, then an explicit definition is ....

....we can build many closed expansions, that we call instances . Also, adequate open frameworks can be built incrementally, starting from a small, well understood kernel, and defining new symbols by adequate definitions , namely definitions that are inherited in a sound way (for more details, see [17, 14]) The existence of many instances implies reusability : every theorem, expansion, specification or correct program developed in an open framework are inherited, and can be reused in all its instances. Reusability was an important motivation behind open frameworks and has been used in [22] to ....

K.-K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR 94 and META 94 , Lecture Notes in Computer Science 883, pages 104--121, Springer-Verlag, 1994.

....expansions, and such definitions are also said to be adequate. So we say a framework is adequate if it is constructed only from adequate expansions. A useful criterion for the adequacy of an expansion is the existence of a steadfast program to compute the relation defined by the expansion (see [5]) Thus program synthesis itself provides a means of adequately expanding a framework. To extend this discussion to open frameworks, we need to address closed instances of an open framework F , i.e. compositions of F with closed frameworks C s that are closed frameworks themselves. So we will now ....

K.K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR 94 and META 94, LNCS 883:104--121, Springer-Verlag, 1994.

No context found.

K.K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, LNCS 883, pages 104--121, Springer-Verlag, 1994.

.... the usual ADTs, since it can also contain any relevant axioms for reasoning about ADTs (e.g. induction axioms) as well as other axioms for reasoning about the domain (e.g. stating that in a library each book has a title, a list of authors, and so on) We endow frameworks with isoinitial semantics [1, 8, 14]. It is closely related to initial semantics used in algebraic ADTs [17] In initial semantics the intended models are initial models, whereas in isoinitial semantics they are isoinitial models. We choose isoinitial semantics because the existence of an isoinitial model corresponds to the ....

K.K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR 94 and META 94 , Lecture Notes in Computer Science 883, pages 104--121, SpringerVerlag, 1994.

....models, viz. their minimum Herbrand models, we can define program correctness in a model theoretic manner in a module. Consequently, as we will see in Section 3, we can also use model theoretic semantics to reason about the correctness of modules. A more formal treatment of frameworks is given in [11]. 2.2 Specifications A framework is the context where a specification must be written, where it receives its proper meaning, and where we can reason about it and derive correct programs from it. More formally, a specification S ffi in a framework F = h Sigma; Ax ; Ii is a set of axioms that ....

....expansions, and such definitions are also said to be adequate. So we say a framework is adequate if it is constructed only from adequate expansions. A useful criterion for the adequacy of an expansion is the existence of a steadfast program to compute the relation defined by the expansion (see [11]) Thus program synthesis itself provides a means of adequately expanding a framework. To extend this discussion to open frameworks, we need to address closed instances of an open framework F , i.e. compositions of F with closed frameworks C s that are closed frameworks themselves. So we will ....

K.-K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini, editors, Proc. LOPSTR 94 and META 94 , LNCS 883, pages 104--121, Springer-Verlag, 1994.

No context found.

K.-K. Lau and M. Ornaghi. On specification frameworks and deductive synthesis of logic programs. In L. Fribourg and F. Turini (eds), Proc. of LOPSTR'94 and META'94, pp. 104--

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Lau, K-K. and Ornaghi, M. On Specification Frameworks and Deductive Synthesis of Logic Programs. Proceedings of LOPSTR'94 and META'94. Springer-Verlag, 1994.

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