Filters








5,431 Hits in 4.3 sec

Generating Mutually Inductive Theorems from Concise Descriptions

Sol Swords
2020 Electronic Proceedings in Theoretical Computer Science  
We describe defret-mutual-generate, a utility for proving ACL2 theorems about large mutually recursive cliques of functions.  ...  One application of defret-mutual-generate has been to support proofs about the FGL rewriter, which consists of a mutually recursive clique of 49 functions.  ...  Intuitively we might expect to prove these using the induction scheme of a flag function generated from the clique.  ... 
doi:10.4204/eptcs.327.10 fatcat:iqubseeonjfxznjjdbfvlnt2pa

Invisible Invariants in the Spotlight

Christoph Welzel, Mikhail Raskin, Javier Esparza
2020 Zenodo  
We show that this technique is able to automatically produce modular proofs of mutual exclusion for basic algorithms from the literature.  ...  Formulating generalizations of these invariants in first-order logic allows us to use the mature tooling of automated theorem proving to discharge required proof obligations.  ...  computed from the syntactic description of the algorithm, without state-space exploration [22, 21] .  ... 
doi:10.5281/zenodo.4091560 fatcat:nwt4uh4z4ffnneaq73z57kjdfa

Invisible Invariants in the Spotlight

Christoph Welzel, Mikhail Raskin, Javier Esparza
2020 Zenodo  
We show that this technique is able to automatically produce modular proofs of mutual exclusion for basic algorithms from the literature.  ...  Formulating generalizations of these invariants in first-order logic allows us to use the mature tooling of automated theorem proving to discharge required proof obligations.  ...  computed from the syntactic description of the algorithm, without state-space exploration [22, 21] .  ... 
doi:10.5281/zenodo.4094708 fatcat:pdzvwxzaabbfjdnslwqmuprhkq

On Hierarchical Compression and Power Laws in Nature [chapter]

Arthur Franz
2017 Lecture Notes in Computer Science  
as a means for solving induction problems for generally intelligent systems.  ...  Even though assuming the compositionality of data generation and the locality of information may result in a loss of the universality of induction, it has still the potential to be general in the sense  ...  Theorem 3 (Bound on the length of descriptive map). Let f be the shortest descriptive map of a finite string x.  ... 
doi:10.1007/978-3-319-63703-7_8 fatcat:irminnmlaffajmi5di3filu2n4

Studying the ML module system in HOL

E. Gunter
1995 Computer journal  
This command defines a relation from a family of rules giving an inductive description of the relation.  ...  support for generating definitions for functions from primitive mutually recursive specifications over those types.  ... 
doi:10.1093/comjnl/38.2.142 fatcat:lq4nbgznc5detnhneadpa4nz3q

Studying the ML module system in HOL [chapter]

Savi Maharaj, Elsa Gunter
1994 Lecture Notes in Computer Science  
This command defines a relation from a family of rules giving an inductive description of the relation.  ...  support for generating definitions for functions from primitive mutually recursive specifications over those types.  ... 
doi:10.1007/3-540-58450-1_53 fatcat:ivu3xgb46rgazakwzypyhyg4iy

Towards an Algorithmic Statistics [chapter]

Peter Gács, John Tromp, Paul Vitányi
2000 Lecture Notes in Computer Science  
absolute notion is needed for the relation between an individual data sample and an individual model summarizing the information in the data, for example, a nite set where the data sample typically came from  ...  The optimal models make the two-part description as concise as the shortest one-part description of the data.  ...  In general S denotes the shortest binary program from which S can be computed and whether this is an implicit or explicit description will be clear from the context.  ... 
doi:10.1007/3-540-40992-0_4 fatcat:673bcuz4vvcrliz73oqnt3h2mq

Formal Grammars as Models of Logic Derivations

Sharon Sickel
1977 International Joint Conference on Artificial Intelligence  
A description of that language is a description of the set of objects we desire. We describe a concise, closed form and discuss how to derive it.  ...  In the ground case, all substitutions are empty and are therefore all mutually compatible. Ignoring substitutions simplifies the problem so we Theorem Proving-3: Sikel Thm 1.  ... 
dblp:conf/ijcai/Sickel77 fatcat:4gek4zhb6jcdhptiqhitexiaq4

Verifying a Self-Stabilizing Mutual Exclusion Algorithm [chapter]

S. Qadeer, N. Shankar
1998 Programming Concepts and Methods PROCOMET '98  
We present a detailed description of a machine-assisted verification of an algorithm for self-stabilizing mutual exclusion that is due to Dijkstra [Dij74].  ...  This comparison yields several observations regarding the challenges of formalizing and mechanically verifying distributed algorithms in general.  ...  A detailed description of the mechanized proof is as follows. First, there exists an injection f from S(v) to the segment below N-1.  ... 
doi:10.1007/978-0-387-35358-6_27 fatcat:7gs3mtx7drbhtjccdknrazteri

Automation of Mathematical Induction as part of the History of Logic [article]

J Strother Moore, Claus-Peter Wirth
2014 arXiv   pre-print
We review the history of the automation of mathematical induction  ...  In general, these approaches are not disjoint from explicit induction.  ...  According to Aristotle, induction means to go from the special to the general, and to realize the general from the memorized perception of particular cases.  ... 
arXiv:1309.6226v5 fatcat:i7nzngq47zfd7its4kfynlfpti

Page 1211 of Mathematical Reviews Vol. , Issue 93c [page]

1993 Mathematical Reviews  
{Reviewer’s remark: This paper seems worth studying quite apart from the interest of its specific results, as an example of how to organize a fairly substantial bit of mathematics concisely, without sacrificing  ...  A significant number of theorems of classical descriptive set theory (e.g., Luzin’s separation theorem and the perfect set theorem for analytic sets) are already known to be equivalent to ATRo over a weaker  ... 

Algorithms in Philosophy, Informatics and Logic. A Position Manifesto 2017

Dov M. Gabbay, Jörg H. Siekmann
2017 IfColog journal of logics and their applications (FLAP)  
In general, these approaches are not disjoint from explicit induction.  ...  According to Aristotle, induction means to go from the special to the general, and to realize the general from the memorized perception of particular cases.  ...  hypotheses in a possibly mutual induction proof has its own tree [Kühler, 2000] .  ... 
dblp:journals/flap/GabbayS17 fatcat:wvtsqquk3vhm3ohgsxn6lzc22u

Parallelization in calculational forms

Zhenjiang Hu, Masato Takeichi, Wei-Ngan Chin
1998 Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '98  
but powerful parallelization theorem is developed. l We make the first attempt to construct a calculational algorithm for parallelization, deriving associative operators from data type definition and  ...  Being more constructive, our method is not only helpful in the design of efficient parallel programs in general but also promising in the construction of parallelizing compiler.  ...  Its success owes much to its concise description of transformation algorithms and its strong thcoretical foundation based on category theory.  ... 
doi:10.1145/268946.268972 dblp:conf/popl/HuTC98 fatcat:5tvnkc2aunbchdt3n2vr4f4mmi

Set Theory for Verification: II. Induction and Recursion [article]

Lawrence C. Paulson
2000 arXiv   pre-print
Inductively defined sets are expressed as least fixedpoints, applying the Knaster-Tarski Theorem over a suitable set.  ...  Worked examples include the transitive closure of a relation, lists, variable-branching trees and mutually recursive trees and forests.  ...  Cantor's Theorem implies that there is no set D such that ℘(D) ⊆ D. A General Induction Rule Because lfp(D, h) is a least fixedpoint, it enjoys an induction rule.  ... 
arXiv:cs/9511102v1 fatcat:ci7pogpbavbw5jp4jkeukd6pvm

Set theory for verification. II: Induction and recursion

Lawrence C. Paulson
1995 Journal of automated reasoning  
Inductively defined sets are expressed as least fixedpoints, applying the Knaster-Tarski Theorem over a suitable set.  ...  Worked examples include the transitive closure of a relation, lists, variable-branching trees and mutually recursive trees and forests.  ...  Cantor's Theorem implies that there is no set D such that ℘(D) ⊆ D. A General Induction Rule Because lfp(D, h) is a least fixedpoint, it enjoys an induction rule.  ... 
doi:10.1007/bf00881916 fatcat:jtuvs7ssd5behor724fmlmwwgq
« Previous Showing results 1 — 15 out of 5,431 results