Stuart F. Allen, Robert L. Constable, Douglas J. Howe, and William Aitken. The Semantics of Re ected Proof. In Proceedings of the 5th Symposium on Logic in Computer Science, pages 95-197, Philadelphia, Pennsylvania, June 1990. IEEE, IEEE Computer Society Press.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....has 1) an operator name (like sum ) which is a unique name indicating the logic and component of a term; 2) a list of parameters representing constant values; and 3) a set of subterms with possible variable bindings. We use the following syntax to describe terms, based on the NuPRL de nition [2]: opname operator name [p 1 ; pn ] parameters fv 1 :t 1 ; vm :t m g subterms Here are a few examples: Displayed form Term 1 natural number[ 1 ]fg x:b lambda[ fx. bg f(a) apply[ ff; ag v variable[ v ]fg x y sum[ fx; yg Variables are terms with a string ....

Stuart F. Allen, Robert L. Constable, Douglas J. Howe, and William Aitken. The semantics of re ected proof. In Proceedings of the Fifth Symposium on Logic in Computer Science, pages 95-197. IEEE, June 1990.

....has 1) an operator name (like sum ) which is a unique name indicating the logic and component of a term; 2) a list of parameters representing constant values; and 3) a set of subterms with possible variable bindings. We use the following syntax to describe terms, based on the NuPRL de nition [2]: opname operator name [p 1 ; pn ] parameters fv 1 :t 1 ; vm :t m g subterms Displayed form Term 1 number[1]fg x:b lambda[ fx. bg f(a) apply[ ff; ag v variable[ v ]fg x y sum[ fx; yg A few examples are shown at the right. Variables are terms with a string ....

Stuart F. Allen, Robert L. Constable, Douglas J. Howe, and William Aitken. The semantics of re ected proof. In Proceedings of the Fifth Symposium on Logic in Computer Science, pages 95-197. IEEE, June 1990.

....has 1) an operator name (like sum ) which is a unique name indicating the logic and component of a term; 2) a list of parameters representing constant values; and 3) a list of subterms with possible variable bindings. We use the following syntax to describe terms, based on the NuPRL de nition [2]: opname operator name [p 1 ; pn ] parameters fv 1 :t 1 ; vm :t m g subterms Displayed form Term 1 number[1]fg x:b lambda[ fx. bg f(a) apply[ ff; ag v variable[ v ]fg x y sum[ fx; yg A few examples are shown at the right. Variables are terms with a string ....

Stuart F. Allen, Robert L. Constable, Douglas J. Howe, and William Aitken. The semantics of re ected proof. In Proc. of Fifth Symp. on Logic in Comp. Sci., pages 95-197. IEEE, June 1990.

....a placeholder for the extract term which is instantiated after a proof has been completed. This brings us back to the issue of hidden hypotheses. Hidden hypotheses are a technical aspect of Nuprl s type theory, they provide the mechanism for implementing the so called non propositional types [1], which include the quotient type, comprehension subtypes, and the intersection type. Essentially, a nonpropositional type is one whose inhabitants do not carry enough information to prove their own well formedness. It is fair to think of hidden hypotheses as true, but lacking computational ....

S. Allen, R. Constable, D. Howe, and W. Aitken. The semantics of re ected proof. Proc. of Fifth Symp. on Logic in Comp. Sci., IEEE, June 1990.

....side, the paper gives speci c recommendations concerning the veri cation of inference rules and building a veri able re ection mechanism for a theorem proving system. 1 Introduction There is a large variety of theorem provers and proof checkers which can be used for veri cation (cf. 8] [1], 11] The mathematical counterparts of those systems range from rst order logic (e.g. in FOL) and certain fragments of rst order arithmetic to higher order logic (HOL) the systems with powerful principles sucient to accommodate most of the classical mathematics (Mizar) and most of the ....

....concludes that F itself holds requires re ection. 2. The traditional re ection based on the implicit provability predicate does not provide a satisfactory justi cation of formal veri cation. It is well known that the implicit re ection in a given system V cannot be veri ed in V (cf. 8] 12] [1], 11] In particular, this means that implicit re ection cannot justify even the basic proof checking by means of V without imposing additional unveri able assumptions on V . The present paper demonstrates that an iterative use of re ection leads to the re ection tower of implicit re ection ....

[Article contains additional citation context not shown here]

Allen, S., Constable R., Howe D., Aitken W.: The Semantics of Re ected Proofs. In: Proceedings of the Fifth Annual Symposium on Logic in Computer Science, Los Alamitos, CA, USA, IEEE Computer Society Press (1990) 95-107.

No context found.

Stuart F. Allen, Robert L. Constable, Douglas J. Howe, and William Aitken. The semantics of re ected proof. In Proceedings of the Fifth Symposium on Logic in Computer Science, pages 95-197. IEEE, June 1990.

No context found.

Stuart F. Allen, Robert L. Constable, Douglas J. Howe, and William Aitken. The Semantics of Re ected Proof. In Proceedings of the 5th Symposium on Logic in Computer Science, pages 95-197, Philadelphia, Pennsylvania, June 1990. IEEE, IEEE Computer Society Press.

No context found.

Stuart F. Allen, Robert L. Constable, Douglas J. Howe, and William Aitken. The Semantics of Re ected Proof. In Proceedings of the 5th Symposium on Logic in Computer Science, pages 95-197, Philadelphia, Pennsylvania, June 1990. IEEE, IEEE Computer Society Press.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC