Y. Bertot. Une Automatisation du Calcul des R'esidus en S'emantique Naturelle. PhD thesis, INRIA, Sophia-Antipolis, 1991. In French.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... does not literally recur in the initial term, is it possible to identify a set of subterms in the initial term which in some sense were responsible for its creation Trying to capture how intermediate and final terms originate from the initial term is formalized in a notion called origin tracking [4, 5, 10]. Origin tracking is based on so called residuals . Residuals have been used successfully in more theoretical work [15, 21, 23] for reasoning about optimal reduction strategies in TRSs. Figure 1: Example of a generated environment using origin tracking. 1.1 Applications Our motivation for ....

....[ ffl u ffl u Delta v 0 ffl u Delta v 0 Delta w v OE u v j u v j u Delta v 0 Delta w Figure 2: Relative positions of v with respect to contractum position u 1. 3 Definition of the Origin Function We give the definition of origins as described in [10] following the presentation of [4]. Let t u;oe Gamma r t 0 , where r is a rule p q, be an elementary reduction step. With each step we associate a function org : O(t 0 ) P(O(t) mapping occurrences in t 0 to sets of occurrences in t. Let v 2 O(t 0 ) We define org by distinguishing the following cases (see Figure ....

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Y. Bertot. Une Automatisation du Calcul des R'esidus en S'emantique Naturelle. PhD thesis, INRIA, Sophia-Antipolis, 1991. In French.

....class of TRSs, since we do not restrict ourselves to orthogonal TRSs, but allow ambiguous, not left linear, conditional TRSs. Residuals are typically used to study concepts like confluence, termination, or reduction strategy, rather than for the practical purposes we have in mind. Bertot [Ber91a, Ber91b] also studies residuals in TRSs and in the calculus with the aim of applying them to debuggers or automatic error handling. How his work and that of others relates to ours is discussed in Section 6. The idea to study these topics came to mind while working on the ASF SDF metaenvironment [Hen91, ....

....TRSs without conditions. The reason for introducing descendants is of a theoretical nature; they are used to study properties like confluence or normalization, and to find optimal orders for contracting redexes [HL79] Current research concerning this topic can be found in [Mar92] Bertot [Ber91b, Ber91a] studies residuals in Term Rewriting Systems and calculus, and introduces marking functions to represent the residual relation. He provides a formal language to describe computations on these marking functions, and shows how the marking functions can be integrated in formalisms for the ....

Y. Bertot. Une Automatisation du Calcul des R'esidus en S'emantique Naturelle. PhD thesis, INRIA, Sophia-Antipolis, 1991. In French.

....with higher order specifications, since these allow one to avoid deterministic behavior, which adversely affects slice accuracy. However, this would require extension of the dependence tracking notion of [17, 18] to higher order rewriting systems. Fraer [20] uses a variation on origin tracking [7, 6, 8] to trace the origins of assertions in a program verification system. In cases where an assertion cannot be proved, origin tracking enables one to determine the assertions and program components that contributed to the failure of the verification condition. Flanagan et al. 19] have developed ....

....In this model, a type check function rewrites a program s abstract syntax tree to a list of type errors. Dynamic dependence tracking [17, 18] is used to associate a slice [37, 31] of the program with each error message. Unlike previous approaches for automatic determination of error locations [12, 10, 11, 33, 32, 7, 6, 8], ours does not rely on a specific specification style, nor does it require additional specification level information for tracking locations. The computed slices have an interesting semantic property: The slice P e associated with error message e is a projection of the original program P that, ....

Bertot, Y. Une Automatisation du Calcul des R'esidus en S'emantique Naturelle. PhD thesis, INRIA, Sophia-Antipolis, 1991. In French.

....interpreters, compilers, and so on. A Typol specification consists of a set of axioms and inference rules which are compiled to Prolog. A key property of Typol specifications is that the meaning of a language construct is expressed in terms of the meanings of its sub constructs. Bertot [Ber91c, Ber91b] presents a formal framework for residuals and origin functions in left linear unconditional term rewriting systems and the calculus. He contributes a technique called subject tracking to Typol, for relating execution to locations in a program. 16 To this end, a special variable, ....

Y. Bertot. Une Automatisation du Calcul des R'esidus en S'emantique Naturelle. PhD thesis, INRIA, Sophia-Antipolis, 1991. In French. 18

....common variables are established (Bergstra and Klop [BK86] also use quasidescendants linking the redex and contractum as well) Moreover, descendants are defined for a smaller class of TRSs; only orthogonal (left linear and non overlapping) TRSs without conditional equations are allowed. Bertot [Ber91c, Ber91b] studies residuals in TRSs and calculus, and introduces marking functions to represent the residual relation. He provides a formal language to describe computations on these marking functions, and shows how the marking functions can be integrated in formalisms for the specification of programming ....

Y. Bertot. Une Automatisation du Calcul des R'esidus en S'emantique Naturelle. PhD thesis, INRIA, Sophia-Antipolis, 1991. In French.

.... literally recur in the initial term, can it be possible to identify a set of subterms in the initial term which in some sense were responsible for its the creation Trying to capture how intermediate and final terms originate from the initial term is formalized in a notion called origin tracking [Ber91, Ber92, DKT93] Origin tracking is based on so called residuals, which have been used successfully in more theoretically oriented papers [HL91, Mar91] for reasoning about optimal reduction strategies in TRSs. 1.1 Applications Our motivation to work on origin tracking was that we needed it for ....

....we will write t u;oe Gamma r t 0 for the one step rewrite relation, indicating that rule r is applied at occurrence u in term t under substitution oe. 1. 3 Definition of the Origin Function We give the definition of origins as described in [DKT93] following the presentation of [Ber91] Let t u;oe Gamma r t 0 , where r is a rule p q, be an elementary reduction step. With each step we associate a function org : O(t 0 ) P(O(t) mapping occurrences in t 0 to sets of occurrences in t. Let v 2 O(t 0 ) We define org by distinguishing three cases (see Figure 2) ffl ....

[Article contains additional citation context not shown here]

Y. Bertot. Une Automatisation du Calcul des R'esidus en S'emantique Naturelle. PhD thesis, INRIA, Sophia-Antipolis, 1991. In French.

.... This manipulation of the rules for substitution goes along with a manipulation of the rule fi that yields the following rule: M [xnN ] M 0 ; w (x:M)N M 0 ; w ffi c( s 2 ffi s 1 ; s 1 ffi s 1 ; s 2 ] nil) All these rule manipulations can actually be automatized, as is shown in [2]. 6 Conclusion. In this paper, we have presented a new method for studying descendance and residuals. The original aspects of this method are that it does not use labels, it uses the similarity between concatenation of occurrences and composition of functions, and it uses a canonical rewriting ....

Y. Bertot, Une automatisation du Calculs des R'esidus en S'emantique Naturelle, Ph.D Thesis, University of Nice, France, 1991.

.... Compiling the dynamic semantics specification into a Prolog program yields an interpreter that can be used to run programs [Des84] If the programming environment generator also provides subject tracking and breakpointing facilities, a complete debugger can also be derived from this specification [Ber91] Static Semantics In the same way that we specified the execution of programs, we can express the property that programs respect a type discipline. We will consider a program to be well typed if every variable used in the program is declared in the initial list of declarations and if all ....

Y. Bertot. Une Automatisation du Calcul des R'esidus en S'emantique Naturelle. PhD thesis, Universit'e de Nice-Sophia Antipolis, 1991.

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