Weidong Chen and Michael Kifer. Polymorphic types in higher-order logic programming. Technical Report 93/20, Department of Computer Science, SUNY at Stony Brook, Stony Brook, NY, USA, December 1993. 165  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Several explicitly typed semantics for logic programming have been presented [30, 34, 50] The semantics of Lakshman and Reddy [50] was also used to prove soundness of the Mycroft O Keefe type system. Several type systems have been de ned for higher order programming with parametric polymorphism [9, 10, 28, 35, 73]. Extending parametric polymorphism with subtyping in the context of logic programming was considered in [23, 65, 89, 94, 95, 110] Soft type systems for logic programming have been investigated in [15] Recent work on types for logic programming have concentrated on implementation techniques for ....

Weidong Chen and Michael Kifer. Polymorphic types in higher-order logic programming. Technical Report 93/20, Department of Computer Science, SUNY at Stony Brook, Stony Brook, NY, USA, December 1993. 165

....sometimes have to cope with severe undecidability problems, or they restrict the language or impose a run time overhead that is not accepted by most programmers. Closer to our type system are proposals using so called implication types [Red88, PR89] or type dependencies ( KW90] see also [CK93]) An example for a type dependency is appendhlist(T ) list(T ) list(T ) 1; 2 3; 3 1; 2i. Its meaning is: For all , if the first two arguments of append have the type list( then so does the third argument, and vice versa. This type dependency has a similar effect for append as our ....

Weidong Chen and Michael Kifer. Polymorphic types in higher-order logic programming. TR 93/20, SUNY, December 1993.

....data atoms comply with all relevant signatures, i.e. with all signatures that cover them. Therefore, saying that all canonic F models of a program must be typed is tantamount to saying that the program does not imply data atoms that do not comply with the signatures implied by that program. In [33], this property is called semantic adequacy. 19 Such a class, called employmentGroup, was introduced towards the end of Section 3. 20 As determined by the chosen theory of canonic models, such as the theory of perfect F models described in Appendix A. 13 WELL TYPED PROGRAMS AND TYPE ERRORS ....

....of a correct logic program. However, another source of type errors comes from rules that never fire (because some body literal is false) and that have signature incompatible literals in the body. Unfortunately, this latter kind of errors is not captured by Definition 13.5. In the terminology of [33], this means that the above notion of type correctness is syntactically inadequate. A detailed discussion of these issues and some solutions can be found in [108, 33] Because the above notion of well typing is so general, it comes as no surprise that it is undecidable to check if an arbitrary ....

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W. Chen and M. Kifer. Polymorphic types in higher-order logic programming. Technical Report 93/20, Department of Computer Science, SUNY at Stony Brook, December 1993.

....execution. Finally, sorts lead to more natural and concise programs. In accordance with this philosophy, the sort structure of HiLog does not support such essential elements of a viable type system as parametric and inclusion polymorphism. This is relegated to a richer, meta level type system [4]. However, our sort system is arity polymorphic and recursive, and despite its sophistication, well formedness of HiLog formulas with respect to this sort system can be checked using a linear number of elementary operations such as retrieving the sort declaration of a variable. It should be noted, ....

....and functions may occur in predicate calculus. As a result, higher order predicates and functions can be defined with ease and, furthermore, higher order constructs can be parameterized. This, for example, 2 Problems also arise from the interaction of parametric sorts and subsorts. See [12, 4] for some work related to these issues. allows the programmer to define generic predicates that accept other predicates as parameters and whose contents depend on these parameters. Despite the fact that HiLog treats predicates and functions as first class entities, it maintains the semantic ....

W. Chen and M. Kifer. Polymorphic types in higher-order logic programming. Technical Report 93/20, Department of Computer Science, SUNY at Stony Brook, December 1993.

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