D.R. Smith. Derived preconditions and their use in program synthesis. In D.W. Loveland, editor, Proc. CADE'82 , pages 172--193.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of a considerable set of theorems of the axiomatic theory in a framework, which theorems state the combined effects of the functions and relations of the framework. Such theorems could be either hand crafted (and mechanically verified) or generated by forward reasoning. The work of Smith [29, 30] shows that deriving an antecedent A of a formula F (i.e. such that A F is valid) is a generalization both of formula simplification (find a weakest antecedent of optimal syntactic complexity ) and of conventional theorem proving (find true as antecedent) In between these (known) extremes ....

D.R. Smith. Derived preconditions and their use in program synthesis. In D.W. Loveland, editor, Proc. CADE'82 , pages 172--193.

....program synthesis) is not on program analysis (deriving program properties) but on expressing program properties and inferring other properties from them. Thus, generators and transformation systems often offer powerful inference capabilities, in the form of specialized theorem provers (e.g. [43]) 4. Degree of structure in the transformation process: The spectrum of translation engines found in generators is very wide. A good heuristic rule for classifying generators is to compute the average number of transformations that are potentially applicable at every step in the transformation ....

....is: KIDS gets additional input interactively from a human user. The user can make strategic decisions like design a divide andconquer algorithm for this specification or simplify this algorithm by applying finite differencing on this value . The system contains a powerful inference engine [43] that applies pattern based transformations derived from theorems of firstorder logic. To schedule these transformations, the engine uses a combination of heuristic measures, such as the number of logical weakening rules that it has applied. KIDS encodes knowledge of a few general algorithmic ....

D.R. Smith, Derived preconditions and their use in program synthesis, 6th Conf. Automated Deduction, Lecture Notes in Computer Science 138, D.W. Loveland, Ed. : 172-193, Springer-Verlag, Berlin, 1982.

....following section. Note that the Boolean sort comes with a natural partial order and equality (see paragraph 3.1) The MS ETR notation provides the necessary support for applying a unifying form of Polarity Analysis for both formulae (Boolean expressions) and terms. The Rainbow inference system [Smi82, Smi85, Smi90] in KIDS allows inference within the terms of a many sorted specifications with partially ordered sorts ( e.g. sufficient, necessary, equivalent conditions in Boolean, upper, lower bounds and simplified expressions in Integers e.t.c) In order to gain the most out of Polarity Analysis, though, we ....

D. R. Smith. Derived preconditions and their use in program synthesis. In D. W. Loveland, editor, Sixth Conference on Automated Deduction, pages 172--193. Springer-Verlag, 1982.

....and derive those su#cient conditions that will allow a proof to go through. #Unlike some method such as that in Katz Manna #1975#, a correct clause would never be #debugged ; only a clause found faultyby testing is subjected to formal veri#cation. # This approach is inspired by the work of Smith #1982# in which a deductive theorem prover was used to derive a su#cient precondition such that a goal can be shown to logically follow from the conjunction of the precondition and a hypothesis. In other words, the precondition provides any additional conditions under which a goal can be proved from ....

Smith, D. R. #1982#. Derived preconditions and their use in program synthesis. In Proceedings of the Sixth ConferenceonAutomatedDeduction, pages 172#193, New York, NY.

....algorithmic transformations, program optimization techniques and data structures refinement. 6 kids uses a form of deductive inference called directed inference to reason about the problem specification in order to automatically apply tactics, derive filters and perform constraint propagation[Smith 82, Smith Parra 93] Directed inference allows the derivation of sufficient conditions (antecedents) as well as the derivation of necessary conditions (consequents) In directed inference a source formula (S) is transformed into a target formula (T) bearing a specified relationship (inference ....

Douglas R. Smith. Derived Preconditions and Their Use in Program Synthesis. In D. W. Loveland, editor, Sixth Conference on Automated Deduction. Lecture Notes in Computer Science, volume 138. Berlin: Spring-Verlag, 1982.

....research [15] 2 KIDS was developed by Kestrel Institute under Rome Laboratory s Knowledge Based Software Assistant (KBSA) Project managed by Mr. Douglas White. 4 directed inference to reason about the problem specification in order to automatically apply the various transformations [16]. In terms of design knowledge, this technology uses a rich representation for the state of the world at any time (as in planning approaches) which allows efficient constraint reasoning, temporal reasoning in particular (as in scheduling) The planning and scheduling problems are modeled as ....

Douglas R. Smith. Derived Preconditions and Their Use in Program Synthesis. In D.W. Loveland, editor, Sixth Conference on Automated Deduction. Lecture Notes in Computer Science, Volume 138. Berlin: Springer-Verlag, 1982.

....[3] The algorithmic transformations allow the user to add search and control mechanisms to a given problem specification. KIDS uses a form of deductive inference called directed inference to reason about the problem specification in order to automatically apply the various transformations [5]. KIDS has been successfully used in the derivation of high performance transportation schedulers [6,7,11] These applications have shown that advanced planning and scheduling technology is beneficial in complex and realistic problem domains. However, the development of a KIDS domain theory, the ....

Smith, Douglas R. Derived Preconditions and Their Use in Program Synthesis. in D.W. Loveland, editor, Sixth Conference on Automated Deduction. Lecture Notes in Computer Science, Volume 138. Berlin: SpringerVerlag, 1982.

.... transformations are applied in order to improve the efficiency of the code 2 compilation of the code kids uses a form of deductive inference called directed inference to reason about the problem specification in order to otpoimize the code, automatically apply tactics, and derive filters [Smith 82, Smith 87] Directed inference allows the derivation of sufficient conditions (antecedents) as well as the derivation of necessary conditions (consequents) In directed inference a source formula (S) is transformed into a target formula (T) bearing a specified relationship (inference direction ....

Douglas R. Smith. Derived Preconditions and Their Use in Program Synthesis. In D. W. Loveland, editor, Sixth Conference on Automated Deduction. Lecture Notes in Computer Science, volume 138. Berlin: Spring-Verlag, 1982.

....of a considerable set of theorems of the axiomatic theory in a framework, which theorems state the combined effects of the functions and relations of the framework. Such theorems could be either hand crafted (and mechanically verified) or generated by forward reasoning. The work of Smith [15, 16] shows that deriving an antecedent A of a formula F (i.e. such that A F is valid) is a generalisation both of formula simplification (find a weakest antecedent of minimal syntactic complexity ) and of conventional theorem proving (find true as antecedent) In between these (known) extremes ....

D.R. Smith. Derived preconditions and their use in program synthesis. In D.W. Loveland, editor, Proc. CADE'82, pages 172--193.

....and derive those sufficient conditions that will allow a proof to go through. Unlike some method such as that in Katz Manna (1975) a correct clause would never be debugged ; only a clause found faulty by testing is subjected to formal verification. This approach is inspired by the work of Smith (1982) in which a deductive theorem prover was used to derive a sufficient precondition such that a goal can be shown to logically follow from the conjunction of the precondition and a hypothesis. In other words, the precondition provides any additional conditions under which a goal can be proved from a ....

Smith, D. R. (1982). Derived preconditions and their use in program synthesis. In Proceedings of the Sixth Conference on Automated Deduction, pages 172--193, New York, NY.

....a formal definition of reusability, specification matching can be used to evaluate the reusability of a component with respect to a requirements specification. In addition, automated reasoning can be used to determine what changes are necessary to reuse a component and guide component adaptation [29, 39]. To illustrate the potential of using formal methods to assist software reuse, we present a sample scenario of a designer interacting with a specification based retrieval system. First the designer must develop a specification for the desired component that will be used as a query to the library. ....

Douglas R. Smith. Derived preconditions and their use in program synthesis. In Proceedings of the Sixth conference on Automated Deduction, volume 138 of Lecture Notes in Computer Science, pages 172--193. Springer-Verlag, 1982.

....implication specification. A logic specification trivially reduces to another one iff it reduces to it under some substitution and the true condition. This approach is taken in Smith s CYPRESS synthesizer [62] see Example 42) The derivation of weakest possible conditions is shown in [24] 27] [60]. This is akin to abduction [40] Example 39: The logic specification of insert 3 reduces to the logic specification of efface 3 (see the previous example) under substitution F E, M R, S L and condition ordered(L) ordered(R) The condition is the weakest and actually establishes an ....

.... F(Y,D) 29) The contrapositive indicates that descriptors that don t pass the filter cannot contain any solutions. Finding good necessary filters is a problem specific task (because filters are not components of global search theories) and can be done by a generalized theorem prover [60]. Example 49: The derivation of a necessary filter from formula (29) for the concrete algorithm theory obtained in Example 48, namely (after some rewriting) V,W,A,N,K,I [ integer(V) integer(W) 1 V W N array(A,1,N,integer) ordered(A) integer(N) integer(K) integer(I) A[I] K ....

Douglas R. Smith. Derived preconditions and their use in program synthesis. In D.W. Loveland (ed), Proc. of CADE'82, pp. 172--193.

....Waldinger (1986) use polarity analysis to enrich the resolution format with special inference rules for various relations. Our extension of polarity analysis to operators in arbitrary (partially ordered) sorts and the (partially ordered) set of sorts seems to be new. The RAINBOW inference system (Smith (1982), Smith (1985) Smith (1990) in KIDS allows inference within the (terms of the) partially ordered sorts of a po specification. In particular, in boolean it allows the derivation of sufficient conditions, necessary conditions, or equivalent conditions; in integer it allows the derivation of lower ....

Smith, D. R. (1982). Derived preconditions and their use in program synthesis, LNCS 138. In Loveland, D. W., editor, Sixth Conference on Automated Deduction, pages 172--193, Berlin. Springer-Verlag.

....applying general knowledge to particular problems. We have built a system called RAINBOW II that performs a form of deduction called directed inference. In directed inference, a source term (or formula) is transformed into a target term (or formula) bearing a specified relationship to the first [34]. As special cases it can perform first order theorem proving and formula simplification. It also allows the inference of sufficient conditions (antecedents) or necessary conditions (consequents) of a formula. This flexibility allows us to formulate a variety of design and optimization problems as ....

Smith, D. R. Derived preconditions and their use in program synthesis, LNCS 138. In Sixth Conference on Automated Deduction (Berlin, 1982), D. W. Loveland, Ed., Springer-Verlag, pp. 172--193.

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D. Smith. Derived preconditions and their use in program synthesis. In D. Loveland, editor, Proceedings of the Sixth Conference on Automated Deduction, pages 172--193. Springer-Verlag, New York, 1982. Lecture Notes in Computer Science 138.

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