J. Martin, A. King, and P. Soper. Typed norms for typed logic programs. In J. Gallagher, editor, LNCS, volume 1207, pages 224-238. Springer-Verlag, 1996. Proc. of LOPSTR'96.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Automatic derivation of typed norms is considered in [11] in which typed norms are automatically derived from type graphs. These type graphs are constructed by a separate type graph analysis since the subject programs are untyped. Our work, on the other hand, is similar to the analysis of [19] in that it assumes that type information is present and that norms are derived from the readily available type de nitions in the program. Polymorphism is dealt with in [19] by imposing a constraint that states that the size of a polymorphic term must be equal to the size of each of its ....

....type graph analysis since the subject programs are untyped. Our work, on the other hand, is similar to the analysis of [19] in that it assumes that type information is present and that norms are derived from the readily available type de nitions in the program. Polymorphism is dealt with in [19] by imposing a constraint that states that the size of a polymorphic term must be equal to the size of each of its instances. This contrasts with our work, in which no such constraints are imposed. We do introduce a similar condition, however, in order to distinguish whether the results of a ....

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Jonathan Martin, Andy King, and Paul Soper. Typed norms for typed logic programs. In John P. Gallagher, editor, Logic Programming Synthesis and Transformation, LOPSTR'96, Proceedings, volume 864 of LNCS, pages 224 - 238. SpringerVerlag, 1996.

.... context can be completed by processing the results of the polymorphic analysis in the interface of the module de ning the imported predicates (at least when there are no circular dependencies) It has been recognised before that types provides a useful insight to the problem of guessing a norm [4, 11, 21, 12, 10] as recursive types represent recursive data structures and thus identify potential sources of in nite recursion. The idea of combining norms has been suggested before by King et al. 16] in the context of lower bound time complexity analysis. For what concerns the problem of norm selection, 9] ....

....of its polymorphic typing. Re analysing the program for the type based constituents of the context in which it appears is pointless. 5 Related Work The idea of using type information to de ne norms for termination analysis has previously been studied by Bossi et al. 4] Martin et al. [21], and by Decorte et al. 11, 12, 10] In this approach attention is focused on the class of programs, termination for which depends on disciplined manipulation of recursive data structures. Our approach to basing termination analysis on type information builds primarily on the technique of Decorte ....

J. Martin and A. King. Typed norms for typed logic programs. In Logic Program Synthesis and Transformation. Springer-Verlag, August 1996. Available at http://www.cs.ukc.ac.uk/pubs/1996/511.

.... [13] Guessing a suitable norm reduces the level of intervention by the user and is often considered the main missing link in automatic termination analysis [10] It Combining Norms to Prove Termination 3 has been recognized that type information provides a useful insight to this problem [3, 10, 20, 11, 12, 23] as recursive types represent recursive data structures and thus identify potential sources of in nite recursion. We infer one norm per recursive data type in the program. Intuitively, for each type a corresponding norm k k counts the number of subterms of type in (typed) terms. This idea ....

....main di erences between our approach and the one described in [23] 4 Norms from Types In this section we reconsider how norms can be de ned based on type information which may be inferred or provided. We refer (as do others) to such norms as typed norms. This has been considered previously in [3, 10, 20, 11, 12, 23]. Inferring norms from type information makes sense as recursive types represent recursive data structures and thus identify some potential sources of in nite recursion. Moreover, typed norms are more re ned than semi linear norms because whereas semi linear norms measure the size of a term T ....

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Jon Martin and Andy King. Typed norms for typed logic programs. In Logic Program Synthesis and Transformation. Springer-Verlag, August

....the solutions proposed for all these components in the initial termination analysis approaches and to improve on them, at least in terms of precision. This line of research includes work on inferring norms and level mappings from mode and type information ( Verschaetse 1992; Decorte et al. 1993; Martin et al. 1996]) automatic inference of interargument and size relations ( De Schreye and Verschaetse 1995; Brodsky and Sagiv 1991; Lindenstrauss and Sagiv 1997] automatic veri cation of the well founded constraints (for instance through CLP techniques) De Schreye et al. 1992; Mesnard 1996] At least on ....

Martin, J. C., King, A., and Soper, P. 1996. Typed norms for typed logic programs. In Proceedings of LOPSTR'96: Logic Program Synthesis and Transformation, J. Gallagher, Ed. Number 1207 in LNCS. Springer-Verlag, Stockholm, 143-153.

....A (g, sg) Ap A (sl, 1 sg, s) Note that Godel notation is used throughout: variables are denoted by identifiers beginning with a lower case letter and constants by identifiers beginning with an upper case letter. Once an appropriate measure of term size (norm) like list length, is deduced [12, 23], the problem of inferring argument relationships is essentially reduced to that of inferring invariants of a CLP(R) program [14] Qs A 2 for example, an abstraction of Qs 2, is a form of abstract program [14] that is obtained by a syntactic transformation in which each term in the first ....

J. Martin, A. King, and P. Soper. Typed Norms for Typed Logic Programs. In LOPSTR'96. Springer-Verlag, 1996.

....The n tuple represents the sizes of the n arguments of the corresponding (concrete) predicate. Time complexity analysis is performed by inferring relationships between the time argument and the size arguments of the n tuple. Other measures of term size, for instance, term depth, can also be used [10, 19] to generate the abstract program. Qs(d, l, s) d 16, d = 1 d 1 , Qs(d 1 , l, s, 0) Qs(d, 0, l, l) d 16, d = 1. Qs(d, 1 xs, h, t) d 16, d = 1 d 1 d 2 d 3 , Pt(d 1 , xs, l, g) Qs(d 2 , l, h, 1 m) Qs(d 3 , g, m, t) Pt(d, 0, 0, 0) d 16, d = 1. Pt(d, 1 xs, ....

....= P i=1 d i . 4 Abstract compilation By applying program transformation (abstract compilation [13, 14] the problem of inferring how time complexity depends on argument size is recast as the problem of inferring the invariants of a CLP(R) program. Our transformation is dubbed ff. Size, as usual [10, 19], is expressed in terms of norms that map terms to (possibly non ground) constraint in Lin. In the case of the list length norm [22, 19] for example, jj[ jj leng = 0, jj[x]jj leng = 1 and jj[xjy]jj leng = 1 y. In addition, to ensure that the norm is always defined, if t cannot be ....

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J. Martin, A. King, and P. Soper. Typed Norms for Typed Logic Programs. In LOPSTR'96. Springer-Verlag, 1996.

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J. Martin, A. King, and P. Soper. Typed norms for typed logic programs. In J. Gallagher, editor, LNCS, volume 1207, pages 224-238. Springer-Verlag, 1996. Proc. of LOPSTR'96.

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J. Martin, A. King, and P. Soper. Typed norms for typed logic programs. LOPSTR, LNCS 1207:224--238, 1996.

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