Strahm, T. Partial applicative theories and explicit substitutions. Journal of Logic and Computation 6, 1 (1996). Home/Search Document Details and Download
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Call-By-Value, Call-By-Name and the Logic of Values - Stärk (Correct)
....#[t x] 4. If x # FV # (#) then LV # #[t x] # t # # #x#. The last two properties are used to show that the translation of the quantifier axioms of CL p are derivable in LV. This is part of the next theorem. Theorem 2. If CL p # # then LV # # # . 9 4. 4 Explicit substitutions In [12], Thomas Strahm, introduces the system # p # for the partial # calculus. In order to avoid the problem with the commutation of # abstraction and substitution he uses explicit substitutions. This means that he extends the language of terms by the following term formation rule: If s, t 1 , ....
T. Strahm. Partial applicative theories and explicit substitutions. J. of Logic and Computation, 6(1):55--77, 1996.
A Semantics for ...: A Calculus With Overloading and Late-Binding - Studer (1999) (Correct)
....of # abstraction is compatible with substitution, but the totality of the application is needed to make it work. In a partial setting a more complex definition of # abstraction would be required and it would behave very badly as far as substitution in # expressions is concerned (cf. Strahm [23]) Theorem 2 (Recursion theorem) There is a closed term rec of L t such that: #f.recf = f(recf) II. Explicit representation and extensionality. The relation # acts as a naming relation between objects and types, i.e. #(s, A) says that s is a name of the type A. While the representation ....
Thomas Strahm. Partial applicative theories and explicit substitutions. Journal of Logic and Computation, 6(1):55--77, 1996. 24
A Semantics for ...: A Calculus With Overloading and Late-Binding - Studer (1999) (Correct)
....nition of abstraction is compatible with substitution, but the totality of the application is needed to make it work. In a partial setting a more complex de nition of abstraction would be required and it would behave very badly as far as substitution in expressions is concerned (cf. Strahm [23]) Theorem 2 (Recursion theorem) There is a closed term rec of L t such that: 8f:recf = f(recf) II. Explicit representation and extensionality. The relation acts as a naming relation between objects and types, i.e. s; A) says that s is a name of the type A. While the representation of ....
Thomas Strahm. Partial applicative theories and explicit substitutions. Journal of Logic and Computation, 6(1):55-77, 1996. 24
On the Proof Theory of Applicative Theories - Strahm (1996) Self-citation (Strahm) (Correct)
....a detailed plan of our work at this point and refer the reader to the introductions of the individual chapters and sections as well as the table of contents. Finally, let us mention that throughout these investigations we have made free use of the papers Jager and Strahm [52, 50] and Strahm [68, 66]. 5 Acknowledgments I am deeply grateful to Prof. Gerhard Jager for introducing me to mathematical logic and proof theory and for his steady encouragement during the past years. He has not only been an excellent guide, but also a friend. I am indebted to Prof. Solomon Feferman for many ....
....for total models of BON, thus generalizing the Scott Curry undecidability theorem of the untyped calculus. Section 5 contains a very short discussion on finitary inductive data types as an alternative to the type of the natural numbers in BON. In Section 6, finally, we give a review of our paper [68] on partial applicative theories and explicit substitutions, thereby shedding some more light on crucial differences between partial and total applicative theories. For more comprehensive introductions to applicative theories the reader is referred to Beeson [3] Cantini [9] Feferman [18, 20] ....
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Strahm, T. Partial applicative theories and explicit substitutions. Journal of Logic and Computation 6, 1 (1996).
Totality in Applicative Theories - Jäger, Strahm (1995) (1 citation) Self-citation (Strahm) (Correct)
....recursion theoretic models are no longer permitted. Furthermore, theories with a total application operation have some important advantages compared to their partial analogues, e.g. as far as the role of substitutions is concerned. Questions concerning substitutions are discussed in Strahm [15]. Research supported by the Swiss National Science Foundation. The natural and interesting models for total applicative theories are term models with suitable forms of term reduction and Church Rosser properties. As the recursion theoretic models in a partial setting, term models are very ....
Strahm, T. Partial applicative theories and explicit substitutions. Journal of Logic and Computation. To appear.
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