Jackson, P. Enhancing the NUPRL Proof Development System and Applying it to Computational Abstract Algebra. PhD thesis, Department of Computer Science, Cornell University, Ithaca, New York, Apr. 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....But as long as the Vicious Circle Principle is to be applied, syntactical criteria are appropriate: what a correct de nition is should be a matter of syntax. Though the basic ideas for this were already present in the works of Frege. See for instance Uber Sinn und Bedeutung [28] See [41], where many algebraic notions are developed within the Nuprl Proof Development System, a proof checker based on the hierarchy of types and orders of RTT without the Axiom of Reducibility. 4.3 Derami cation The rst impulse to such a solution was given by Ramsey in 1926 [60] He recalls that ....

P.B. Jackson. Enhancing the Nuprl Proof Development System and Applying it to Computational Abstract Algebra. PhD thesis, Cornell University, Ithaca, New York, 1995.

....hierarchies are similar to ours. However they often have not been used in a large proof development. Our framework has been written and optimized for real life use (to prove the fundamental theorem of algebra) and not as a toy exercise in abstract mathematics. Paul Jackson, in his Ph.D. thesis [10], presents a constructive development of algebra in Nuprl and uses it to prove some results in abstract algebra. Nuprl, like Coq, is based on type theory, but it uses an extensional equality. This makes several constructions easier (e.g. quotienting) but renders type checking undecidable. As ....

P. Jackson. Enhancing the Nuprl proof-development system and applying it to computational abstract algebra. Ph.D. thesis, Cornell University, 1995.

....untyped # calculus. This possibility for the Nuprl type system was first noted by Allen in 1984 who realized that applications of Y could be assigned a type. Based on Allen s proof, Howe [6, 7] developed the current methodology for defining and using general recursive functions in Nuprl. Jackson [8, 9] incorporated Howe s methodology into his tactics for Nuprl 4. We will only present details of Nuprl s type theory here as necessary. A hypertext account of the type theory is available online [2] and the reader is urged to examine this document. Most of the notation used here will be familiar. ....

Paul B. Jackson. Enhancing the Nuprl proof development system and applying it to computational abstract algebra. PhD thesis, Cornell University, 1995.

....an untyped calculus. This possibility for the Nuprl type system was rst noted by Allen in 1984 who realized that applications of Y could be assigned a type. Based on Allen s proof, Howe [6, 7] developed the current methodology for de ning and using general recursive functions in Nuprl. Jackson [8, 9] incorporated Howe s methodology into his tactics for Nuprl 4. We will only present details of Nuprl s type theory here as necessary. A hypertext account of the type theory is available online [2] and the reader is urged to examine this document. Most of the notation used here will be familiar. ....

Paul B. Jackson. Enhancing the Nuprl proof development system and applying it to computational abstract algebra. PhD thesis, Cornell University, 1995.

.... (tan x) is continuous on (0; is clearly false and this can be easily seen from the graph of tan x over the speci ed interval (0; However, attempting to show that this is false within a theorem prover is very dicult, requiring a model of the real numbers which is a topic of active research [17, 18]. Proof attempts which fail to show whether a VC is valid or invalid may indicate that the program annotations and or the background theory needs to be extended. VC s which are found to be invalid mean that there is a mistake, probably in the program or the annotations but possibly in the theory ....

Jackson, P. Enhancing the NUPRL Proof Development System and Applying it to Computational Abstract Algebra. PhD thesis, Department of Computer Science, Cornell University, Ithaca, New York, Apr. 1995.

....with the following type. proof proof list (proof list proof) Goals are represented as incomplete proofs with only one node. To evaluate the application of tactics to goals, the refiner is implemented as an interactive read eval loop for Nuprl ML. Users often build tactics modularly [10]. First, simple tactics are created that only perform one primitive refinement. These tactics use very simple heuristics or none at all. They can be described as follows. 1. Perform some heuristic. 2. Choose a primitive refinement rule based on the result of the heuristic. 3. Refine the goal ....

....concurrent tactics using the concurrent tacticals PTHEN and PORELSEL. PTHEN is constructed from the function PThenOnEach (see Line 19 in Figure 3) PTHENOnEach is derived from THENOnEach for creating the various forms of THEN in the standard tactic collection of Nuprl 4. 1 created by Paul Jackson [10]. We provide the code of PThenOnEach in Figure 3. The else portion of the if ( some helper functions ) 1. fun applyTac (t,g) t(g) 2. val reqHandler = requestHandler applyTac ( 3. fun PTHENOnEach tac extTac goal = 4. let 5. val (subgoals,validation) tac goal 6. val tactics = ....

[Article contains additional citation context not shown here]

Paul Jackson. Enhancing the Nuprl Proof Development System and Applying it to Computational Abstract Algebra. PhD thesis, Cornell University, 1995.

....implemented by Bailey [Bai97] and Saibi [Sai97] for defining coercions between types or classes of types developed for the proof assistants LEGO [Pol94a] and Coq [Bar97] respectively. They have also formalized corresponding large scale case studies on Galois theory and Category theory. 17 In [Jac95] algebraic structures are formalized in Nuprl s version of type theory [Con86] using sets of unlabeled dependent pairs and subsets. No general solution is given in this work to the problem of representing the inclusion of types of structures that we have been considering. In [Luo96] a calculus ....

P. Jackson. Enhancing the Nuprl Proof Development System and Applying it to Computational Abstract Algebra. PhD thesis, Cornell University, 1995.

.... as use of theorem provers in hardware and software verification creates a large body of formal mathematics (O Leary et al. 1994; Rushby 1997; Gordon Melham 1993) There is also independent interest in the subject of formalized mathematics for its own sake (Cederquist, Coquand, Negri 1997; Jackson 1995). Some automated reasoning groups are putting their formal mathematics on the web but it cannot be searched in its current form by standard web tools. This kind of material may also play a role in mathematics education. In each case, there is interest in making the formal mathematics produced ....

....the same size as a human reasoning step; the proof already resembles the assertion level proof that Huang claims is necessary for generating a good text version of a proof. The Nuprl Theorem Prover Since 1983, the Nuprl proof development system (Constable et al. 1986; Constable 1997; Jackson 1995) has been used to help people interactively create formal proofs in a theory considered adequate as a foundation for all mathematics, including computational mathematics and programming. The system has been used to produce thousands of proofs. Most of these have been by products of verifying that ....

Jackson, P. B. 1995. Enhancing the Nuprl Proof Development System and Applying it to Computational Abstract Algebra. Ph.D. Dissertation, Cornell University, Ithaca, NY.

....be) far from proving what any mathematician can easily prove. Nevertheless, there have been attempts to develop large fragments of mathematics within theorem provers. One of the rst attempt has been the Automath project [16] Some recent eoeorts include Jackson s work on computational algebra [13], Harrison s work on real analysis [11] and Shankar s work on G#del s theorems [22] Finally the largest current attempt is, without any doubt, the Mizar project [20] There would be obvious benets in having a framework where both proving and computing are possible: Algorithms in computer ....

Paul B. Jackson. Enhancing the Nuprl proof development system and applying it to computational abstract algebra. Technical Report TR95-1509, Cornell University, 1995.

....this development would benefit from efficient multi relations rewriting tactics. These tactics ought to be extensible enough to allow the user specification of rewriting strategies, and generic enough to be usable in other developments. Such tactics have already been written for LCF [11] and NuPRL [9]. Their adaptation to Coq is currently under study. This logical reconstruction of the basics of category theory follows initial attempts by R. Dyckhoff[5] in Martin Lof type theory. It shows that intentional type theory is sufficient for developing this kind of mathematics, and we may thus hope ....

P. B. Jackson. "Enhancing the NuPRL proof development system and applying it to computational abstract algebra." Ph.D. dissertation, Cornell University, Ithaca, NY, 1995.

.... of Divisibility Theory in Nuprl Paul B. Jackson Laboratory for Foundations of Computer Science, University of Edinburgh, King s Buildings, Edinburgh EH9 3JZ, United Kingdom Abstract. The formalization of divisibility theory over cancellation monoids in Nuprl is described. The main theorems presented concern the existence and uniqueness of ....

....Theory 19 6.1 Basic Definitions 19 6.2 Greatest Common Divisors 21 6.3 Existence Theorem 23 6.4 Uniqueness Theorem 24 6.5 Unique Factorization Monoid Existence 27 6.6 The Fundamental Theorem of Arithmetic 28 7 Discussion of Development Style 28 7. 1 Style of Definitions and Theorems 28 2 Paul B. Jackson 7.2 Style of Proofs 29 8 Automation 31 8.1 Type Checking 31 8.2 Rewriting 32 8.3 Relational Reasoning 34 9 Related Work 35 10 Adequacy of Constructive Type Theory 36 11 Conclusions 37 A Divisibility Theory 40 A.1 Existence Theorem 40 A.2 Uniqueness Theorem 42 1. Introduction The aim of this ....

[Article contains additional citation context not shown here]

Paul B. Jackson. Enhancing the Nuprl Proof Development System and Applying it to Computational Abstract Algebra. PhD thesis, Cornell University, January 1995. Available as Cornell Department of Computer Science Technical Report TR95-1509, April 1995.

....Jackson pbj dcs.ed.ac.uk October 12th, 1995 1 Introduction Constructive type theories (CTTs) are advocated as a foundation for mathematics which replaces classical logic and set theory. Significant work has gone into building interactive theorem proving systems based on CTTs [dB80, C 86, Jac95, AGNvS94, LP92, CCF 95] and it seems desirable to involve the projects currently around such systems in any future QED venture. However, mathematics based on CTTs is rather di#erent from the usual classical mathematics taught in schools and universities. QED must support this classical ....

....usually not extensional and a principle of comprehension is usually lacking. Also, many CTTs are regarded as being too complex to be acceptable as foundational theories. Examples of formalization of mathematics in CTTs include the intermediate value theorem and some basic abstract algebra [For93, Jac95] For the above reasons, formalizing Bishop style mathematics in CTTs seems to be a significantly slower and more uncertain process than formalizing classical mathematics. 3 Opportunities for Cooperation 3.1 Libraries Sharing of libraries on elementary concrete topics such as integers and ....

Paul B. Jackson. Enhancing the Nuprl Proof Development System and Applying it to Computational Abstract Algebra. PhD thesis, Cornell University, January 1995. Available as 5 Cornell Computer Science Technical Report TR95-1509 from http://cs-tr.cs.cornell.edu.

No context found.

Jackson, P. Enhancing the NUPRL Proof Development System and Applying it to Computational Abstract Algebra. PhD thesis, Department of Computer Science, Cornell University, Ithaca, New York, Apr. 1995.

No context found.

Jackson, P.B., 1995. Enhancing the nuprl proof developmentsystem and applying it to computational abstract algebra. Ph.D. Thesis, Department of Computer Science, Cornell University, Ithaca, New York.

No context found.

Paul B. Jackson. Enhancing the NuPRL Proof Development System and Applying it to Computational Abstract Algebra. PhD thesis, Cornell University, Ithaca, NY, January 1995.

No context found.

Paul B. Jackson. Enhancing the NuPRL Proof Development System and Applying it to Computational Abstract Algebra. PhD thesis, Cornell University, Ithaca, NY, January 1995.

No context found.

Paul B. Jackson. Enhancing the nuprl proof development system and applying it to computational abstract algebra. Technical Report TR951509, Computer Science Department, Cornell University, Ithaca, NY, 18, 1995.

No context found.

P. Jackson. Enhancing the Nuprl proof-development system and applying it to computational abstract algebra. Ph.D. thesis, Cornell University, 1995.

No context found.

P. B. Jackson, Enhancing the nuprl proof development system and applying it to computational abstract algebra, Ph.D. thesis, Cornell University, Ithaca, New York, 1995.

No context found.

Paul Bernard Jackson. Enhancing the NuPRL Proof Development System and Applying it to Computational Abstract Algebra. PhD thesis, Cornell University, January 1995.

No context found.

Paul B. Jackson. Enhancing the Nuprl proof development system and applying it to computational abstract algebra. PhD thesis, Cornell University, 1995.

No context found.

Paul B. Jackson. Enhancing the Nuprl proof development system and applying it to computational abstract algebra. PhD thesis, Cornell University, 1995.

No context found.

P. B. Jackson. "Enhancing the NuPRL proof development system and applying it to computational abstract algebra." Ph.D. dissertation, Cornell University, Ithaca, NY, 1995.

No context found.

P. B. Jackson. "Enhancing the NuPRL proof development system and applying it to computational abstract algebra." Ph.D. dissertation, Cornell University, Ithaca, NY, 1995.

No context found.

Paul B. Jackson. Enhancing the Nuprl Proof Development System and Applying it to Computational Abstract Algebra. PhD thesis, Cornell University, Ithaca, NY, 1995. TR95-1509.

First 50 documents

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