M. Huber and I. Varsek. Extended Prolog for order-sorted resolution. In Proceedings of the 4th IEEE Symposium on Logic Programming, pages 34--45, San Francisco, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....with types on logics that account for sorts. Consequently, the computational mechanisms may change, which typically shows up in the unification procedure. One direction, which appeared with Eqlog [GM86] takes order sorted logic as base and employs order sorted unification [Gog78, GM87b, HV87, MGS89, SNGM89, SS85, SS89, Wal83, Wal85, Wal87, Wal88] This thesis generalizes this line of research by incorporating parametric polymorphism. The distinctive difference between order sorted types [Gog78, GM87a, SNGM89] and POStypes is that POS types can come with sort functions such as list or ....

M. Huber and I. Varsek. Extended Prolog for order-sorted resolution. In Proceedings of the 4th IEEE Symposium on Logic Programming, pages 34--45, San Francisco, 1987.

....the well known results concerning paramodulation and its special forms (see [19] Following this hints and applying the strong completeness of paramodulation and its special forms [20] yields the independence of a selection function for ordersorted logic languages. Though languages like Epos [22] or Tel [43] make deliberate use of this result, it has not been proved rigorously. But to repeat it, the operational semantics given herein is above all for demonstration purposes. It can also be regarded as an exercise in understanding order sorted unification towards the much more ambitious ....

....For example, the third equation is interpreted as the set of ostriches is a subset of the set of birds . Sorts are also interpreted as sets and subsorts are usually interpreted as subsets. It is this resemblance that has forced many researches to encode taxonomic information into sorts (e.g. [22]) In the example, the first three sentences can immediately be expressed as the sort pelicans with elements louie, dewey , and hewey, the sort ostriches with element franz , and the sort trouts with element wanda. 19 ae oe ae ae oe ae ostriches ae Franz Louie Dewey Hewey ....

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M. Huber and I. Varsek. Extended Prolog for order-sorted resolution. In Proceedings of the Symposium on Logic Programming, pages 34 -- 45, 1987.

.... and Lindstrom, 1986] An integration of parametric polymorphism as in ML [Harper et al. 1986] with Prolog was suggested in [Mycroft and O Keefe, 1984] Ordersorted type concepts were developed by Goguen et al. and are present in OBJ [Futatsugi et al. 1985] and Eqlog [Goguen and Meseguer, 1986] [Huber and Varsek, 1987] extends Prolog by order sorted unification [Walther, 1988] Polymorphism and order sortedness are provided in the approach of [Dietrich and Hagl, 1988] by using modes to restrict the input output data flow in certain cases. No such mode restrictions are required in the work of [Smolka, 1988a] ....

M. Huber and I. Varsek. Extended Prolog for order-sorted resolution. In Proceedings of the 4th IEEE Symposium on Logic Programming, pages 34--45, San Francisco, 1987.

....a counterpart for subtype supertype (i.e. isa) relation, ordersorted logics have been developed (for overview, see [Obe89] In those, a partial ordering on sorts is assumed which basically is a subsort supersort relation. A good example of an order sorted logic programming language is EPOS [HV87]. The LOGIN [AN86] language (which served as a starting point for the ALF [Mel88] merger of OO and logic) can also be regarded as relying on a variant of order sorted logic (feature types) its peculiarity being that there are no sorts there, and individuals are ordered instead. The ordering ....

M. Huber and I. Varsek. Extended Prolog for order-sorted resolution. In Proc. 1987 Symp. on Logic Programming, San Fransisco, Aug/Sept 1987, pp 34-43. Washington, DC: IEEE Comp. Soc. Press, 1987.

.... ] It has also been argued that deduction with sorts can be implemented more efficiently by specialized procedures [ Cohn, 1989 ] For example, for order sorted logics, there are efficient methods to find the greatest lower bound (glb) of two sorts in a sort hierarchy [ Ait Kaci et al. 1989, Huber and Varsek, 1987 ] Our contribution is an efficient unification method for a very general class of polymorphism. Sorted logics only constrain variables to be of a certain sort which means that a most general unifier often cannot be expressed by the logic. Instead, we attach constraints on terms in order to ....

....fails, we use intelligent backtracking and these additional constraints to effectively reduce the search space. 6 Conclusions Most other implementation oriented approaches to order sorted resolution often avoid polymorphism or impose strong restrictions on it, e.g. Beierle et al. 1991, Huber and Varsek, 1987, Smolka, 1989 ] The approaches by Beierle and Smolka are based on parametric polymorphism (see also [ Hanus, 1989, Mycroft and O Keefe, 1984 ] and allow for sort constructors, which are not supported here. Apart from this, our approach is much more general, since the sortal behavior of ....

H. Huber and L. Varsek. Extended Prolog for order-sorted resolution. In Proceedings of the 4th IEEE Symposium on Logic Programming, pages 34--45, 1987.

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Huber, M. and Varsek I. (1987), `Extended Prolog for Order-Sorted Resolution', In: Proceedings of Symposium on Logic Programming, IEEE, San Francisco, Sept. 1987.

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