P. Johann and M. Kohlhase. Unification in an extensional lambda calculus with ordered function sorts and constant overloading. In Proc. of the 12th Int. Conference on Automated Deduction, CADE'94, volume 814 of LNAI, pages 620--634, Nancy, France, 1994. Springer.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....we present a corrected system and complete the enterprise of building order sorted higher order deduction systems by presenting a resolution calculus for SigmaT that uses the unification and pre unification algorithms from [14] as a basis. For details and proofs we refer the reader to [15] and [10], where we treat a subsystem. In the following we will shortly motivate the primary features of SigmaT . In unsorted logics the only way to express the knowledge that an object is a member of a certain 1 However Huet only allows order sorting the universe of individuals 2 2 ORDER SORTED TYPE ....

Patricia Johann and Michael Kohlhase. Unification in an extensional lambda calculus with ordered function sorts and constant overloading. SEKI-Report SR-93-14, Universitat des Saarlandes, 1993. submitted to CADE'94.

....2. 10, there) The notion of partial binding developed here paves the way for remedying both the ill defined unification transformations and the flawed completeness proof of [Koh92] For a detailed treatment of our results and the issues surrounding them, the reader is referred to the full paper [JK93]. 2 The Calculus The set of types T is obtained by inductively closing a set of base types T 0 under the operation ff fi; assuming right associativity of , the length of a type ff j ff 1 ff 2 : ff n , denoted length(ff) is n Gamma 1. Types are denoted by lower case Greek letters. ....

P. Johann and M. Kohlhase. Unification in an Extensional Lambda Calculus with Ordered Function Sorts and Constant Overloading. Technical Report SR-93-14, Universitat des Saarlandes, 1993.

....is not covariant in the domain sort (this principle semantically corresponds to implicit function restriction) Furthermore the term declaration mechanism is much more powerful than the declaration schemas proposed in those logical systems. This paper is an extension of the results presented in [8, 9]. This subsystem of SigmaT only allows signatures consisting of constant declarations and thus treats the interaction of functional base sorts and extensionality in isolation. In contrast to this subsystem the powerful mechanism of term declarations in SigmaT allows a straightforward ....

..... This set of rules is used with the convention that all formulae are eagerly reduced to fi normal form. Since we have captured the relevant features of SigmaT in the structure and general binding theorems (both of which are nearly trivial in ) we can now use the standard techniques (cf. [20, 9]) to soundness and completeness. Theorem 4.5 (Completeness Theorem for SigmaU T ) For any well sorted unification problem E and any 2 wsU( Sigma; E) there is a sequence of transformations in SigmaU T , such that E SigmaU T E 0 , where E 0 is in Sigma solved form and oe E 0 fij ....

Patricia Johann and Michael Kohlhase. Unification in an extensional lambda calculus with ordered function sorts and constant overloading. In Proc. CADE'94, LNCS,Springer Verlag, 1994.

....is not covariant in the domain sort (this principle semantically corresponds to implicit function restriction) Furthermore the term declaration mechanism is much more powerful than the declaration schemas proposed in those logical systems. This paper is an extension of the results presented in [8, 9]. This subsystem of SigmaT only allows signatures consisting of constant declarations and thus treats the interaction of functional base sorts and extensionality in isolation. In contrast to this subsystem the powerful mechanism of term declarations in SigmaT allows a straightforward ....

Patricia Johann and Michael Kohlhase. Unification in an extensional lambda calculus with ordered function sorts and constant overloading. SEKI-Report SR-93-14, Universitat des Saarlandes, 1993.

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P. Johann and M. Kohlhase. Unification in an extensional lambda calculus with ordered function sorts and constant overloading. In Proc. of the 12th Int. Conference on Automated Deduction, CADE'94, volume 814 of LNAI, pages 620--634, Nancy, France, 1994. Springer.

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