Robert L. Constable. Using reflection to explain and enhance type theory. In Helmut Schwichtenberg, editor, Proof and Computation, volume 139 of NATO Advanced Study Institute, International Summer School held in Marktoberdorf, Germany, July 20-August 1, NATO Series F, pages 65--100. Springer, Berlin, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....whose strategy language was initially defined as an external language. However, in ELAN reflection and strategies have not yet been fully integrated. In the context of typed lambda calculi, the important advantages of having an internal strategy language have also been stressed by several authors [1, 9, 25]. 1.2 Rewriting Logic and Maude A rewrite theory T consists of a signature Sigma of operators, a set E of equations, and a set of labeled rewrite rules. The deductions of T are rewrites modulo E using such rules. Such rewriting deductions are formalized as proofs using four simple inference ....

R. L. Constable. Using reflection to explain and enhance type theory. In H. Schwichtenberg, editor, Proof and Computation, volume 139 of Computer and System Sciences, pages 109--144. Springer, 1995.

.... or it may be necessary to consider eval functions with a bound on the number of rewrites to remain within the language (see, for example, 47, 31] for a careful treatment of this problem for the calculus of constructions, 45] for a study of reflection in the polymorphic lambda calculus, and [20, 2, 10] for the treatment of reflection in Nuprl s constructive type theory a la Martin Lof) Yet another promising recent development in this general area is the use of lambda calculi and monads a la Moggi [39] to give semantics to reflective languages [11, 33] 3.1.2 Equational Languages There is ....

....context of typed lambda calculi, the important advantages of having an internal strategy language has been stressed by several authors. Thus, using reflective capabilities both tactics and decision pocedures can be specified, reasoned about, and executed inside the Nuprl constructive type theory [2, 10]. Similarly, Rue [32] discusses in detail an elegant 1 For the definition of a transformation M of this kind in which the strategy expressions actually coincide with multisets of proof expressions see [27] details for other strategy languages M will appear elsewhere. approach for endowing the ....

Robert L. Constable. Using reflection to explain and enhance type theory. In Proof and Computation, pages 109--144, 1995.

....encodings is generally too low to allow complex developments we must look for ways to incorporate equational theories directly into the underlying meta logic or type theory without sacrificing decidability and other desirable properties. Some promising work in this direction includes reflection [Con94] and dependently typed rewriting [Vir95] 4 Search and Meta Programming The representation of a deductive system in a logical framework may be used for a variety of purposes. The obvious application is to construct derivations within a deductive system, with the support of the framework ....

Robert L. Constable. Using reflection to explain and enhance type theory. In Proof and Computation, NATO ASI Series. Springer-Verlag, 1994.

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Robert L. Constable. Using reflection to explain and enhance type theory. In Helmut Schwichtenberg, editor, Proof and Computation, volume 139 of NATO Advanced Study Institute, International Summer School held in Marktoberdorf, Germany, July 20-August 1, NATO Series F, pages 65-- 100. Springer, Berlin, 1994.

....to accompany the actual on line theorems. Various references are made to Nuprl libraries in the text. In the html version these were hot references (one could click on them to open the referenced files) 2 Type Theory Preliminaries Accounts of Nuprl s type theory can be found in several sources [8, 35, 20, 1, 6]. 2.1 Basic Types The integers Z= f0; Sigma1; Sigma2; g are a primitive type of Nuprl with primitive operations of ; Gamma ; Delta ; Xi ; rem (for remainder) Equality, x = y in Z, and order, x y , are also primitive. The natural numbers N are defined as fi : Zj 0 ig, and the ....

Robert L. Constable. Using reflection to explain and enhance type theory. In Helmut Schwichtenberg, editor, Proof and Computation, volume 139 of NATO Advanced Study Institute, International Summer School held in Marktoberdorf, Germany, July 20-August 1, NATO Series F, pages 65--100. Springer, Berlin, 1994.

No context found.

Robert L. Constable. Using reflection to explain and enhance type theory. In Helmut Schwichtenberg, editor, Proof and Computation, volume 139 of NATO Advanced Study Institute, International Summer School held in Marktoberdorf, Germany, July 20-August 1, NATO Series F, pages 65--100. Springer, Berlin, 1994.

No context found.

Robert L. Constable. Using reflection to explain and enhance type theory. In Helmut Schwichtenberg, editor, Proof and Computation, volume 139 of NATO Advanced Study Institute, International Summer School held in Marktoberdorf, Germany, July 20-August 1, NATO Series F, pages 65--100. Springer, Berlin, 1994.

No context found.

Robert L. Constable. Using reflection to explain and enhance type theory. In Helmut Schwichtenberg, editor, Proof and Computation, volume 139 of Computer and System Sciences, pages 109--144. Springer, 1995.

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