Carlos Alberto Lor'ia-S'aenz. A Theoretical Framework for Reasoning about Program Construction Based on Extensions of Rewrite Systems. PhD thesis, Universitat Kaiserslautern, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....2 This theorem has two obvious corollaries: ffl s R s 0 implies s R s 0 and ffl R 0 implies s R 0 s. However, the above proof fails if one reduces the statement of the theorem to one of the corollaries. A slightly different version of Thm. 3. 8 is also shown by Lor ia [15]: he uses conditional rewrite rules whose left hand sides are patterns; his proof relies more on considerations about term positions. Finally we lift Thm. 3.8 from to , at least for a special case: Corollary 3.9 Let R be a GHRS. If s R s 0 and t R t 0 then fx 7 t gs R fx 7 t 0 ....

Carlos Alberto Lor'ia-S'aenz. A Theoretical Framework for Reasoning about Program Construction Based on Extensions of Rewrite Systems. PhD thesis, Universitat Kaiserslautern, 1993.

....rule applications The theory of first order term rewriting offers different alternatives to solve this problem, i.e. to guarantee termination (see, for example, Der87] For introductions to TRSs see, for example, DJ90, AM90] See also [DO90] for a survey on conditional rewriting systems. In [Lor93], criteria for testing confluence and termination of some classes of higher order conditional TRSs (HCTRSs) have been developed (see also [AL94] HCTRSs naturally extend (unconditional) HTRSs as defined in [Nip91] Lor93] follows the approach of [Nip91] by combining term rewriting and the ....

....AM90] See also [DO90] for a survey on conditional rewriting systems. In [Lor93] criteria for testing confluence and termination of some classes of higher order conditional TRSs (HCTRSs) have been developed (see also [AL94] HCTRSs naturally extend (unconditional) HTRSs as defined in [Nip91] [Lor93] follows the approach of [Nip91] by combining term rewriting and the calculus. For the calculus the reader is referred to [HS86] Example 1. In order to illustrate how both computational paradigms calculus and TRSs interact, let us consider an algebraic specification of the addition ( ....

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Carlos Lor'ia-S'aenz. A theoretical framework for reasoning about program construction based on extensions of rewrite systems. PhD Thesis, Fachbereich Informatik, Universitat Kaiserslautern (Germany), December 1993.

....maximal basic type. Several examples are carried out. This idea of extending a recursive path ordering to higher order terms in j long fi normal form was first explored in [9] The authors restricted their study to patterns in the sense of Miller, and this restriction survived in subsequent work [8, 10]. We were able to get rid of this superflous assumption by proving the properties of our ordering for ground terms. For instance, we prove that (a first approximation of) our ordering enjoys the subterm property for ground terms. This does not contradict the fact that a term X(a) is not greater ....

....Our ordering is no panacea, unfortunately. There are many important examples such as the apply function or Godels recursors that cannot be oriented with our current definition. A careful analysis points at a potential remedy, an original, powerful notion of higher order subterm discussed in [8]. We believe that its use in our definition would overcome the limitations of our current proposal. Our framework is described in section 2 and the ordering in section 3. Section 4 is devoted to compatible orderings on types and examples of application. A comparison with previous work is given in ....

[Article contains additional citation context not shown here]

Carlos Lor'ia-S'aenz. A Theoretical Framework for Reasoning about Program Construction based on Extensions of Rewrite Systems. PhD thesis, Fachbereich Informatik der Universitat Kaiserslautern, 1993.

....theorem has two obvious corollaries: ffl s s 0 implies s s 0 and ffl 0 implies s 0 s. However, the above proof fails if one reduces the statement of the theorem to one of the corollaries. A slightly different version of Theorem 3. 9 is also shown by Lor ia [20]: he uses conditional rewrite rules whose left hand sides are patterns; his proof relies more on considerations about term positions. Finally we lift Theorem 3.9 from to , at least for a special case: Corollary 3.10 Let R be an HRS. If s s 0 and t t 0 then fx 7 tgs fx ....

Carlos Alberto Lor'ia-S'aenz. A Theoretical Framework for Reasoning about Program Construction Based on Extensions of Rewrite Systems. PhD thesis, Universitat Kaiserslautern, 1993.

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