ACL2 A Computational Logic for Applicative Common Lisp is a software system consisting of a programming language , an extensible theory in a first order logic , and a mechanical theorem prover . ACL2 is designed ... and Computer hardware hardware verification. The input language and implementation of ACL2 are built on Common Lisp . ACL2 is free software free , open source GNU General Public License GPL software. The ACL2 programming language is an applicative programming language applicative Side effect computer science side effect free variant of Common Lisp. ACL2 is untyped. All ACL2 Function programming functions are Total function total that is, every function maps each object in the ACL2 Universe mathematics universe to another object in its universe. ACL2 s base theory axiom atizes the semantics ... proof logical consistency . The core of ACL2 s theorem prover is based on term rewriting ... proof techniques for subsequent conjectures . ACL2 is intended to be an industrial strength version of the Boyer Moore theorem prover, Nqthm NQTHM . Toward this goal, ACL2 has many features to support clean engineering of interesting mathematical and computational theories. ACL2 also derives efficiency ... Moore family of provers, which includes ACL2, received the ACM Software System Award for pioneering ... Awards title Software System Award accessdate Start date 2012 1 14 ref Proofs ACL2 has been used on numerous applications. ref http www.cs.utexas.edu users moore publications acl2 papers.html Books and Papers about ACL2 and Its Applications ref ref http www.cs.utexas.edu users moore acl2 workshops.html The ACL2 Workshop Series ref For example, J Strother Moore and Matt Kaufmann used ACL2 to prove ... algorithm ref References reflist External links http www.cs.utexas.edu users moore acl2ACL2 website http www.cs.utexas.edu users moore acl2 current ACL2 TUTORIAL.html A Tutorial Introduction to ACL2 http acl2s.ccs.neu.edu ACL2s ACL2 Sedan An Eclipse based interface developed by Peter Dillinger and Pete ... more details
File J Strother Moore FLoC 2006.jpg thumb J Strother Moore 2006 J Strother Moore his first name is the alphabetic character J &ndash not an abbreviated J. is a computer science computer scientist , and he is a co developer of the Boyer Moore string search algorithm and the Boyer Moore automated theorem prover, Nqthm . An example of the workings of the Boyer Moore string search algorithm is given http www.cs.utexas.edu users moore best ideas string searching fstrpos example.html in Moore s website . Moore received his SB in mathematics at Massachusetts Institute of Technology in 1970 and his Ph.D in Symbolic computation computational logic at University of Edinburgh in Scotland in 1973. ref cite web url http www.cs.utexas.edu users moore education.html title J Moore s Home Page, Education Page accessdate 2009 05 26 ref In addition, Moore is a co author of the ACL2 automated theorem prover. He and others used ACL2 to prove the correctness of the floating point division operations of the AMD K5 microprocessor in the wake of the Pentium FDIV bug . For his contributions to Automated theorem proving automated deduction , Moore received the 1999 Herbrand Award with Robert S. Boyer , and in 2006 he was inducted as a Fellow of the Association for Computing Machinery . He is currently the Bobby Ray Inman Admiral B.R. Inman Centennial Chair in Computing Theory at University of Texas at Austin The University of Texas at Austin . Before joining the Department of Computer Sciences as the chair, he formed a company, http www.computationallogic.com Computational Logic Inc. , along with others including his close friend at the University of Texas at Austin and one of the highly regarded professors in the field of Automated Reasoning, Robert S. Boyer . Moore enjoys rock climbing . ref cite web url http www.cs.utexas.edu users moore personal index.html title J Moore s Home Page, Interests Section accessdate 2008 08 22 ref References reflist External links Commons category http www.cs. ... more details
Infobox software name GNU Common Lisp logo screenshot caption developer GNU The GNU Project latest release version 2.6.7 latest release date release date 2005 08 10 latest preview version latest preview date operating system Unix like , Microsoft Windows programming language genre Interpreter computing Interpreter , compiler license GNU General Public License GPL website http www.gnu.org software gcl www.gnu.org software gcl GNU Common Lisp GCL is the GNU Project s Common Lisp compiler, an evolutionary development of Kyoto Common Lisp . It produces native object code by first generating C programming language C code and then calling a C compiler. Although it does not yet fully comply with the American National Standards Institute ANSI Common Lisp specification, GCL is the implementation of choice for several large projects including the mathematical tools Maxima software Maxima , AXIOM and ACL2 . GCL runs under eleven different architectures on Linux , and under FreeBSD , Solaris operating system Solaris , and Microsoft Windows . GCL has not had a release since 2005, although binaries for Windows were produced in early 2008. Development is still very active on the CVS repository. This Lisp system keeps the memory image as small as possible, so on modern computers it needs tuning the default memory allocation scheme. ref http savannah.nongnu.org forum forum.php?forum id 1610 GNU Common Lisp News 2.5.1 is released. Item posted by Camm Maguire camm on Sun 02 Mar 2003 03 53 24 PM UTC. ref References Reflist Portal Free software GNU Common Lisp DEFAULTSORT Gnu Common Lisp Category Common Lisp implementations Category Common Lisp software Category GNU Project software Common Lisp Category Free compilers and interpreters Category Windows software Category Linux programming tools compu prog stub prog lang stub ca GNU Common Lisp de GNU Common Lisp es GNU Common Lisp ru GNU Common Lisp ... more details
About the professor of computer science the victim of Charles Whitman s 1966 shooting spree Robert Boyer disambiguation Robert Stephen Boyer , aka Bob Boyer , is a retired professor of computer science , mathematics , and philosophy at University of Texas at Austin The University of Texas at Austin . He and J Strother Moore invented the Boyer Moore string search algorithm , a particularly efficient string searching algorithm , in 1977. He and Moore also collaborated on the Boyer Moore automated theorem prover, Nqthm , in 1992. ref name nqthm cite web title Nqthm, the Boyer Moore prover url http www.cs.utexas.edu boyer ftp nqthm accessdate 2006 04 21 ref Following this, he worked with Moore, and Matt Kaufmann on another theorem prover called ACL2 . Publications Boyer has published extensively, including the following books A Computational Logic Handbook , with J S. Moore. Second Edition. Academic Press, London, 1998. Automated Reasoning Essays in Honor of Woody Bledsoe , editor. Kluwer Academic, Dordrecht, The Netherlands, 1991. A Computational Logic Handbook , with J S. Moore. Academic Press, New York, 1988. The Correctness Problem in Computer Science , editor, with J S. Moore. Academic Press, London, 1981. A Computational Logic , with J S. Moore. Academic Press, New York, 1979. See Also QED manifesto References references External links http www.cs.utexas.edu boyer Home page of Robert S. Boyer . Accessed March 21, 2009. http www.utexas.edu cola college news current retiredfaculty08 University of Texas, College of Liberal Arts Honors Retired Faculty 2008 . Accessed March 21, 2009. Persondata Metadata see Wikipedia Persondata . NAME Boyer, Robert S. ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Boyer, Robert S. Category American scientists Category Living people Category Alumni of the University of Edinburgh Boyer, Robert S. Category University of Texas at Austin faculty Category Fellows of the Association f ... more details
primary sources date September 2011 Theorem Proving in Higher Order Logics TPHOLs is an annual international academic conference on the topic of automated reasoning in higher order logic s. The first TPHOLs was held in Cambridge , United Kingdom UK in 1987, but in the early years was an informal gathering of researchers interested in the HOL theorem prover HOL system and had no formal proceedings. Since 1990 TPHOLs has published formal peer reviewed proceedings, published by Springer Science Business Media Springer s Lecture Notes in Computer Science LNCS series. TPHOLs brings together the communities using many systems based on higher order logic such as Coq , Isabelle theorem prover Isabelle , NuPRL , Prototype Verification System PVS , and Twelf . Individual workshops or meetings devoted to individual systems are usually held concurrently with the conference. Together with Conference on Automated Deduction CADE and TABLEAUX , TPHOLs is usually one of the three main conferences of the International Joint Conference on Automated Reasoning IJCAR whenever it convenes, In 2006, TPHOLs was part of the Federated Logic Conference FLoC held in Seattle , United States of America USA . TPHOLs is superseded by the international conference on Interactive Theorem Proving ITP , which combines the old TPHOLs with the ACL2 Workshop series. The first ITP meeting was in 2010, held as part of FLoC in Edinburgh , Scotland . External links http www.cl.cam.ac.uk Research HVG HOL Home page of the HOL group at the University of Cambridge , the traditional home of TPHOLs. DEFAULTSORT Theorem Proving In Higher Order Logics Category Theoretical computer science conferences Category Logic conferences Compu conference stub ... more details
function was total, using the ACL2 theorem prover. References cite journal author Zohar Manna ... of McCarthy s 91 function title Computer Aided reasoning ACL2 case studies publisher Kluwer Academic Publishers year 2000 pages 283 299 url http www.cs.utexas.edu users moore acl2 workshop 1999 Cowles ... more details
Image CoqProofOfDecidablityOfEqualityOnNaturalNumbers.png thumb An interactive proof session in CoqIDE, showing the proof script on the left and the proof state on the right. In computer science and mathematical logic , a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proof s by man machine collaboration. This involves some sort of interactive proof editor, or other User interface interface , with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer . Comparison Need to add at least Automath , PhoX class wikitable rowspan 2 Name rowspan 2 Latest version rowspan 2 Developer s rowspan 2 Implementation language colspan 6 Features Higher order logic Dependent type s de Bruijn criterion Small kernel Proof automation Proof by reflection Program extraction ACL2 4.3 Matt Kaufmann and J Strother Moore Common Lisp no no no partial Unverified no Agda programming language Agda 2.3.0 Ulf Norell Chalmers University of Technology Chalmers Haskell yes yes yes no partial n a Coq 8.3pl2 INRIA OCaml yes yes yes yes yes yes Isabelle theorem prover Isabelle HOL 2011 1 Larry Paulson University of Cambridge Cambridge , Tobias Nipkow Technische Universit t M nchen M nchen and Makarius Wenzel Universit Paris Sud Paris Sud Standard ML yes no yes yes no yes LEGO proof assistant LEGO 1.3.1 Randy Pollack University of Edinburgh Edinburgh Standard ML yes yes NuPRL 5 Cornell University Common Lisp yes yes yes yes unknown yes Prototype Verification System PVS 5.0 SRI International Common Lisp yes partial no partial Unverified no Twelf 1.7.1 Frank Pfenning and Carsten Sch rmann Standard ML yes partial unknown no no see also Dependent type Comparison Automated theorem proving Comparison Other proof assistants ACL2 a programming language, a first order logical theory, and a theorem prover with both interactive and automatic modes in the Boyer Moore tradition. Coq Which allo ... more details
abbr on at 3200 rpm. In following years appeared the type ACL2, BDF1, BDF2 and BDS1, the production ... KZ11 KZ18 KZ24 Second generation ACL1 ACL2 BDF1 BDF2 BDS1 BDS2 Characteristics Speed Convert 120 km ... more details
Prover9 is an Automated theorem proving automated theorem prover for First order logic First order and equational logic developed by William McCune . Prover9 is the successor of the Otter theorem prover . Prover9 is intentionally paired with Mace4 , which searches for finite models and counterexamples. Both can be run simultaneously from the same input, with Prover9 attempting to find a proof, while Mace4 attempts to find a disproving counter example. Prover9, Mace4, and many other tools are built on an underlying library named LADR to simplify implementation. Resulting proofs can be double checked by Ivy, a proof checking tool that has been separately verified using ACL2 . In July 2006 the LADR Prover9 Mace4 input language made a major change which also differentiates it from Otter . The key distinction between clauses and formulas completely disappeared formulas can now have free variables and clauses are now a subset of formulas . Prover9 Mace4 also supports a goal type of formula, which is automatically negated for proof. Prover9 attempts to automatically generate a proof by default in contrast, Otter s automatic mode must be explicitly set. Prover9 was under active development, with new releases every month or every other month, until 2009. Prover9 is free software open source software it is released under GNU General Public License GPL version 2 or later. Examples Socrates The traditional all men are mortal , Socrates is a man , prove Socrates is mortal can be expressed this way in Prover9 formulas assumptions . man x > mortal x . open formula with free variable x man socrates . end of list. formulas goals . mortal socrates . end of list. This will be automatically converted into clausal form which Prover9 also accepts formulas sos . man x mortal x . man socrates . mortal socrates . end of list. Square Root of 2 is irrational A proof that the square root of 2 is irrational can be expressed this way formulas assumptions . 1 x x. identity x y y x. commutativit ... more details
In mathematical logic , a logical theory math T 2 math is a Proof theory proof theoretic conservative extension of a theory math T 1 math if the language of math T 2 math extends the language of math T 1 math every theorem of math T 1 math is a theorem of math T 2 math and any theorem of math T 2 math which is in the language of math T 1 math is already a theorem of math T 1 math . More generally, if is a set of formulas in the common language of math T 1 math and math T 2 math , then math T 2 math is conservative over math T 1 math if every formula from provable in math T 2 math is also provable in math T 1 math . To put it informally, the new theory may possibly be more convenient for proving theorem s, but it proves no new theorems about the language of the old theory. Note that a conservative extension of a consistent theory is consistent. Hence, conservative extensions do not bear the risk of introducing new inconsistencies. This can also be seen as a methodology for writing and structuring large theories start with a theory, math T 0 math , that is known or assumed to be consistent, and successively build conservative extensions math T 1 math , math T 2 math , ... of it. The theorem provers Isabelle theorem prover Isabelle and ACL2 adopt this methodology by providing a language for conservative extensions by definition. Recently, conservative extensions have been used for defining a notion of ontology modularization module for Ontology computer science ontologies if an ontology is formalized as a logical theory, a subtheory is a module if the whole ontology is a conservative extension of the subtheory. An extension which is not conservative may be called a proper extension . Examples ACA sub 0 sub a subsystem of second order arithmetic is a conservative extension of first order Peano arithmetic . Von Neumann Bernays G del set theory is a conservative extension of Zermelo Fraenkel set theory with the axiom of choice ZFC . Internal set theory is a conserva ... more details
Nqthm is a Automated theorem proving theorem prover sometimes referred to as the Boyer Moore theorem prover . It was a precursor to ACL2 . ref cite web url http www.cs.utexas.edu users boyer ftp nqthm title Nqthm, the Boyer Moore prover ref History The system was developed by Robert S. Boyer and J Strother Moore , professors of computer science at the University of Texas at Austin University of Texas, Austin . They began work on the system in 1971 in Edinburgh , Scotland . Their goal was to make a fully automatic, logic based theorem prover. They used a variant of Purely functional Pure Lisp programming language LISP as the working logic. Definitions Definitions are formed as totally Recursion computer science recursive functions , the system makes extensive use of rewriting and an mathematical induction induction heuristic that is used when rewriting and something that they called symbolic evaluation fails. The system was built on top of Lisp and had some very basic knowledge in what was called Ground zero , the state of the machine after Bootstrapping computing bootstrapping it onto a Common Lisp implementation. This is an example of the proof of a simple arithmetic theorem. The function TIMES is part of the BOOT STRAP called a satellite and is defined to be DEFN TIMES X Y IF ZEROP X 0 PLUS Y TIMES SUB1 X Y Theorem formulation The formulation of the theorem is also given in a Lisp like syntax prove lemma commutativity of times rewrite equal times x z times z x Should the theorem prove to be true, it will be added to the knowledge basis of the system and can be used as a rewrite rule for future proofs. The proof itself is given in a quasi natural language manner. The authors randomly choose typical mathematical phrases for embedding the steps in the mathematical proof, which does actually make the proofs quite readable. There are macros for LaTeX that can transform the Lisp structure into more or less readable mathematical language. The proof of the commutativity o ... more details
BLP sources date January 2011 Infobox musical artist See Wikipedia WikiProject Musicians name Susan Voelz image Susan Voelz ACL2 by Ron Baker.jpg caption Voelz performing with Poi Dog Pondering at the 2009 Austin City Limits Music Festival background solo singer birth name Susana Maria Voelz origin Wauwatosa, Wisconsin Wauwatosa , Wisconsin br United States instrument Singing Vocals , violin , guitar genre Alternative rock occupation Musician br Composer br Arrangement Musical Arranger br Writer years active label Texas Hotel Records Columbia Records Columbia Premonition br Plate.tec.tonic associated acts Poi Dog Pondering website http susanvoelz.com Official site notable instruments Susan Voelz born Susana Maria Voelz is an United States American musician. A Grammy Award nominate d vocalist, violin ist, and composer . She is a member of the alternative rock band, Poi Dog Pondering . She has also worked with a long list of famous musicians. ref name Official site bio1 cite web url http susanvoelz.com sv index.php?option com content&view article&id 47&Itemid 54 title Susan Voelz last Voelz first Susan work Official Website biography section accessdate 2 January 2011 ref She has worked on film score s for movie and television soundtracks . She has continued with her own solo career, she has released two albums, which have received positive reviews. As a writer, she has published a book with Billboard Random House in 2007 The Musicians Guide to the Road . ref name Official site bio1 Biography Voelz was born and raised in Wauwatosa, Wisconsin Wauwatosa , Wisconsin in the United States . As a child, she discovered her grandfather s violin in the attic of the family home, and began to learn to play. Nurtured by family members who each played a variety of instruments, she frequently joined in playing in the family concerts in the living room, now saying in retrospect saying We were cheerful and awful. Discovering in secondary school that the violin could be played in rock ... more details
Moore string search algorithm . Co creator of the Nqthm and ACL2 theorem provers. align center ... string search algorithm . Co creator of the Nqthm and ACL2 theorem provers. ACM Fellow . Elected ... more details
string searching, ACL2 theorem prover Julian C. Bradfield logic and concurrency, Expressivity ... Moore string searching, ACL2 theorem prover Hans Moravec robotics Robert Tappan Morris Morris ... more details
for the season. ref name Doty ACL1 ref name Doty ACL2 Regular season The Connecticut ... August 2010 publisher ESPN accessdate 25 February 2011 ref ref name Doty ACL2 cite web url http blogs.courant.com ... more details
More footnotes date May 2011 Infobox programming language name Common Lisp family Lisp programming language Lisp paradigm Multi paradigm programming language Multi paradigm procedural programming procedural , functional programming functional , object oriented programming object oriented , metaprogramming meta , reflective programming reflective , generic programming generic generation 3GL released 1984, 1994 for ANSI Common Lisp designer developer ANSI X3J13 committee standard reference Common Lisp HyperSpec latest release version latest release date typing Type system Dynamic typing dynamic , Strongly typed programming language strong scope lexical, optionally dynamic implementations Allegro Common Lisp Allegro CL , Armed Bear Common Lisp ABCL , CLISP , Clozure CL , CMUCL , Corman Common Lisp , Embeddable Common Lisp ECL , GNU Common Lisp GCL , LispWorks , Movitz , Scieneer Common Lisp Scieneer CL , SBCL , Genera operating system Symbolics Common Lisp dialects CLtL1, CLtL2, ANSI Common Lisp influenced by Lisp programming language Lisp , Lisp Machine Lisp , MacLisp , Scheme programming language Scheme , InterLisp influenced Clojure , Dylan programming language Dylan , Emacs Lisp , EuLisp , Java programming language Java , ISLISP , Le Lisp , Cadence SKILL SKILL , Stella, SubL operating system Cross platform license website URL http common lisp.net Common Lisp CL is a dialect of the Lisp programming language Lisp programming language , published in American National Standards Institute ANSI standard document ANSI INCITS 226 1994 R2004 , formerly X3.226 1994 R1999 . ref http webstore.ansi.org RecordDetail.aspx?sku ANSI INCITS 226 1994 R2004 Document page at ANSI website ref From the ANSI Common Lisp standard the Common Lisp HyperSpec has been derived ref http www.lispworks.com documentation HyperSpec Front Help.htm Authorship Authorship of the Common Lisp HyperSpec ref for use with web browsers. Common Lisp was developed to standardize the divergent variants of Lisp t ... more details
First order logic is a formal system used in mathematics , philosophy , linguistics , and computer science . It is also known as first order predicate calculus , the lower predicate calculus , quantification theory , and predicate logic a less precise term . First order logic is distinguished from propositional logic by its use of Quantifier Logic quantified variables . First order logic with a specified domain of discourse over which the quantified variables range, one or more interpreted predicate letters, and proper axiom s involving the interpreted predicate letters, is a first order theory . The adjective first order distinguishes first order logic from higher order logic in which there are predicates having predicates or functions as arguments, or in which one or both of predicate quantifiers or function quantifiers are permitted. ref cite book last Mendelson first Elliott title Introduction to Mathematical Logic year 1964 publisher Van Nostrand Reinhold pages 56 ref In first order theories, predicates are often associated with sets. In interpreted higher order theories, predicates may be interpreted as sets of sets. There are many deductive system s for first order logic that are Soundness Logical systems sound all provable statements are true and Completeness Logical completeness complete all true statements are provable . Although the logical consequence relation is only semidecidability semidecidable , much progress has been made in automated theorem proving in first order logic. First order logic also satisfies several metalogic al theorems that make it amenable to analysis in proof theory , such as the L wenheim Skolem theorem and the compactness theorem . First order logic is of great importance to the foundations of mathematics , because it is the standard formal logic for axiomatic system s. Many common axiomatic systems, such as first order Peano arithmetic and axiomatic set theory , including the canonical Zermelo Fraenkel set theory ZF , can be for ... more details
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