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Logic programming language
Twelf is an implementation of the logical framework LF developed by Frank Pfenning and Carsten Schürmann at Carnegie Mellon University. It is used for
Twelf
Play by William Shakespeare
Twelfth Night, or What You Will is a romantic comedy by William Shakespeare, believed to have been written around 1601–1602 as a Twelfth Night entertainment
Twelfth_Night
Software used in mathematical applications
Proving System Twelf Alt-Ergo Automath CARINE CVC E IsaPlanner LCF Mizar NuPRL Paradox Prover9 PVS ResearchCyc SPARK (programming language) Twelf Wolfram Mathematica
Mathematical_software
Natural number
numerals during the 12th-century Renaissance. Derived from Old English, twelf and tuelf are first attested in the 10th-century Lindisfarne Gospels' Book
12_(number)
Computer science field
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Model_checking
Analysis of computer programs without executing them
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Static_program_analysis
Fundamental problem in computer science
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Path_explosion
Concepts in theoretical computer science
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Safety and liveness properties
Safety_and_liveness_properties
Of a function, an additional effect besides returning a value
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Side effect (computer science)
Side_effect_(computer_science)
Graph data structure
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
E-graph
Computer program for the Boolean satisfiability problem
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
SAT_solver
English-based creole spoken in Hawaii
Shakespeare's Twelfth Night, or What You Will, titled in Hawaiian Pidgin "twelf nite o' WATEVA!" Several theater companies in Hawaiʻi produce plays written
Hawaiian_Pidgin
implementation of the LF logical framework is provided by the Twelf system at Carnegie Mellon University. Twelf includes a logic programming engine meta-theoretic
Logical_framework
Concept in computer science
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Separation_logic
Validates computer program operations
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Typestate_analysis
Interactive theorem prover software
Yes Yes No Yes No Unknown Rocq 9.0 INRIA OCaml Yes Yes Yes Yes Yes Yes Twelf 1.7.1 Frank Pfenning, Carsten Schürmann Standard ML Yes Yes Unknown No No
Proof_assistant
Set of software engineering methods
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Program_slicing
Subfield of automated reasoning and mathematical logic
IsaPlanner LCF Mizar NuPRL Paradox Prover9 PVS SPARK (programming language) Twelf Z3 Theorem Prover CARINE Wolfram Mathematica ResearchCyc Curry–Howard correspondence
Automated_theorem_proving
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Dependence_analysis
Rules to verify computer program correctness
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Hoare_logic
Algorithmic process of solving equations
proof assistants and higher-order logic programming, for example Isabelle, Twelf, and lambdaProlog. Finally, in semantic unification or E-unification, equality
Unification (computer science)
Unification_(computer_science)
Type whose definition depends on a value
Archived 2020-11-09 at the Wayback Machine No Purely functional No No No ? No ? ? ? Twelf Yes Logic programming ? Yes Yes (optional) Any (LF) term No No ? ?
Dependent_type
Higher-order logic (HOL) automated theorem prover
written in ANSI C Prover9, written in C, with a GUI written in Python Twelf, written in Standard ML /ˌɪzəˈbɛl/ /ˈmiːtɪs/ Paulson, L. C. (1986). "Natural
Isabelle_(proof_assistant)
Ancient practice of dividing the night into periods
on ðære feorðan wæccan. An wæcce hæfð þreo tida; feower wæccan gefyllað twelf tida; swa fela tida hæfð seo niht", which translates to "In the fourth watch
Watches_of_the_night
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Hyperproperty
IsaPlanner LCF Mizar NuPRL Paradox Prover9 PVS SPARK (programming language) Twelf Z3 Theorem Prover Golly List of arbitrary-precision arithmetic software
List of open-source software for mathematics
List_of_open-source_software_for_mathematics
Vowel sound represented by ⟨æ⟩ in IPA
front [a]. See Kurdish phonology Lakon rävräv [ræβræβ] 'evening' Limburgish twelf [ˈtβ̞æ̠ləf] 'twelve' Front or near-front, depending on the dialect. The
Near-open front unrounded vowel
Near-open_front_unrounded_vowel
Process of analyzing computer program behavior
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Program_analysis
General-purpose functional programming language
self-service interfaces. The proof assistants HOL4, Isabelle, LEGO, and Twelf are written in Standard ML. It is also used by compiler writers and integrated
Standard_ML
Crown of Tudor monarchs and heraldic device
pearlis and two Collettys the Balace wt the king Item oon the Diademe above twelf poynted diamoundys some better then the other thre Tryangled diamoundys
Tudor_Crown
Mathematical theory of data types
connection between type theory and programming languages: LF is used by Twelf, often to define other type theories; many type theories which fall under
Type_theory
Approach to static program analysis
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Abstract_interpretation
German-American computer scientist
deduction, and trustworthy computing. He is one of the principal authors of the Twelf system. He also developed Carnegie Mellon's introductory imperative programming
Frank_Pfenning
Swedish logician, philosopher, and mathematical statistician
are based on type theory, for example NuPRL, LEGO, Rocq, Lean, ALF, Agda, Twelf, Epigram, and Idris. Martin-Löf is a member of the Royal Swedish Academy
Per_Martin-Löf
Asian-American theatre company
Tales Judy SooHoo S.A.M. I Am Garrett Omata Cleveland Raining Sung J. Rho Twelf Nite O Wateva! James Grant Benton 1995-1996, 30th Season Merrily We Roll
East_West_Players
allows to bind variables var with definition exp in expressions exp'. In Twelf syntax, we could do as follows: exp : type. var : type. v : var -> exp.
Higher-order_abstract_syntax
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Polyvariance
Software projects developed at universities
formal modelling tool for Event-B (Newcastle and other project partners) Twelf – logical framework and theorem-proving environment (Carnegie Mellon) UPPAAL
List of software developed at universities
List_of_software_developed_at_universities
Danish printmaker and publisher
Biographies", 1805–06) Tolv Blade Figurer til Tegne-Øvelser efter Thorvaldsen (Twelf Sheets with Figures for Drawing Lessons after Thorvaldsen, 1814) Elementarværk
Gerhard_Ludvig_Lahde
Pronunciation and sounds of Old English
port, prēost, plega -b- b br bl bōc, blōd, brād -t- t tr — tw tōþ, trēow, twelf -d- d dr dw dæġ, drincan, dwola -k- k — kn kr kl kw cuman, cniht, cræft
Old_English_phonology
Hebrew inscription in Yemen
Eliašīv, Cohen Qanah, the elev[enth] ward Yaqīm Pašḥūr, Ṣefaṯ (Safed), the twelf[th] ward [Ḥū]ppah, Beṯ-Ma‘on, the (thirteenth) ward the thirteenth (ward)
DJE_23
for parts of the POPLmark challenge, using following tools: Isabelle/HOL, Twelf, Rocq, αProlog, ATS, Abella and Matita. Expression problem QED manifesto
POPLmark_challenge
1513 Middle Scots translation of the Aeneid
the heading of a manuscript at Cambridge University, which refers to the "twelf bukis of Eneados". The title of the first printed edition (London, 1553)
Eneados
Work divisions of Jewish priests in the Temple
ward אֶלְיָשִׁיב כהן קנה משמר אחד עשר Yaqīm Pašḥūr, Ṣefaṯ (Safed), the twelf[th] ward יָקִים פַּשְׁחוּר צפת משמר שנים עשר [Ḥū]ppah, Beṯ-Ma‘on, the (thirteenth)
Priestly_divisions
(west), wadge (wedge), twal (twelve) and dwall (dwell) from web, west, weċġ, twelf and dwellan. Old English o in close position became /o̞/ in Older Scots
Phonological_history_of_Scots
First Book of Chronicles, chapter 24
ward אֶלְיָשִׁיב כהן קנה משמר אחד עשר Yaqīm Pašḥūr, Ṣefaṯ (Safed), the twelf[th] ward יָקִים פַּשְׁחוּר צפת משמר שנים עשר [Ḥū]ppah, Beṯ-Ma'on, the (thirteenth)
1_Chronicles_24
Musical artist
tombeau d'Orphée, danse élégiaque pour harpe seule 1951 Kleine suite, for twelf harps (in cooperation with Lex van Delden) Prelude Allegro Valse lente Fughetta
Marius_Flothuis
Limburgish dialect
Numerals between 101 and 999 are constructed as follows: 112 hóngerdj-èn-twèlf 698 zèshóngerdj-èn-ach-èn-neugetig ("six hundred and eight and ninety")
Montfortian_dialect
TWELF
TWELF
Girl/Female
American, Australian, British, Chinese, Christian, Czechoslovakian, Danish, Dutch, English, Finnish, French, German, Italian, Latin, Netherlands, Shakespearean, Swedish
Form of Violet; Violet Flower; Purple; Twelfth Night; Musical; Talanted
Surname or Lastname
English and Scottish
English and Scottish : from the Middle English personal name Ma(t)thew, vernacular form of the Greek New Testament name Matthias, Matthaios, which is ultimately from the Hebrew personal name Matityahu ‘gift of God’. This was taken into Latin as Mat(t)hias and Matthaeus respectively, the former being used for the twelfth apostle (who replaced Judas Iscariot) and the latter for the author of the first Gospel. In many European languages this distinction is reflected in different surname forms. The commonest vernacular forms of the personal name, including English Matthew, Old French Matheu, Spanish Mateo, Italian Matteo, Portuguese Mateus, Catalan and Occitan Mateu are generally derived from the form Matthaeus. The American surname Matthew has also absorbed European cognates from other languages, including Greek Mathias and Mattheos.It is found as a personal name among Christians in India, and in the U.S. is used as a family name among families from southern India.
Boy/Male
Shakespearean
Twelfth Night', also called 'What You Will' Steward to Olivia.
Boy/Male
Shakespearean American Scottish Biblical English Greek
Twelfth Night', also called 'What You Will' Sir Andrew Aguecheek.
Girl/Female
Irish
From caomh â€gentle, beautiful, precious.†The same root as Kevin, the name has become very popular in Ireland with the original Irish spelling. In 2003 it was the twelfth most popular Irish girl name for baby girls.
Boy/Male
African Egyptian
Ghanian name given to the twelfth-born son.
Surname or Lastname
Vietnamese (HÃ )
Vietnamese (HÃ ) : unexplained.Korean : there are two Ha clans, each with a unique Chinese character. The founding ancestor of the larger Ha clan was named Ha Kong-jin and settled in the Chinju area around ad 1010. Most of the modern descendants of Ha Kong-jin live in the KyÅngsang and ChÅlla provinces. The founding ancestor of the smaller of the two clans was named Ha HÅm, and he settled in the Taegu area after emigrating from Song China some time in the early part of the twelfth century. Most of the modern descendants of Ha HÅm still live in the Taegu area.Chinese : variant of Xia.English : unexplained.
Boy/Male
Greek Latin
Revered. The twin brother of Viola in Shakespeare's Twelfth Night. A third-century martyred...
Boy/Male
Shakespearean Italian
Twelfth Night', also called 'What You Will' Orsino, Duke of Illyria.
Girl/Female
English
Violet. Viola was one of the heroine's in Shakespeare's play 'Twelfth Night'.
Boy/Male
Shakespearean
Twelfth Night', also called 'What You Will' A clown, servant to Olivia.
Boy/Male
Shakespearean
Twelfth Night', also called 'What You Will' Sir Toby Belch, uncle of Olivia.
Girl/Female
English American
Violet. Viola was one of the heroine's in Shakespeare's play 'Twelfth Night'.
Girl/Female
Irish
From caomh â€gentle, beautiful, precious.†The same root as Kevin, the name has become very popular in Ireland with the original Irish spelling. In 2003 it was the twelfth most popular Irish girl name for baby girls.
Boy/Male
Shakespearean American English Hebrew
Twelfth Night', also called 'What You Will' Sir Toby Belch, uncle of Olivia.
Girl/Female
Irish
From caomh â€gentle, beautiful, precious.†The same root as Kevin, the name has become very popular in Ireland with the original Irish spelling. In 2003 it was the twelfth most popular Irish girl name for baby girls.
Boy/Male
Shakespearean
Twelfth Night', also called 'What You Will' Orsino, Duke of Illyria.
Boy/Male
Shakespearean
Twelfth Night', also called 'What You Will' Gentleman attending on the Duke.
Male
Italian
Italian name invented by Shakespeare for a character in his play "Twelfth Night," MALVOLIO means "ill-will."
Boy/Male
Shakespearean
Twelfth Night', also called 'What You Will' Sir Andrew Aguecheek.
TWELF
TWELF
Boy/Male
English American
From the cliff land.
Girl/Female
Spanish Latin French
Heavenly.
Boy/Male
Hindu
Made of pearls
Girl/Female
Indian, Kannada
Lovely; Pleasing
Boy/Male
Hindu
Lord Vishnu
Boy/Male
Arabic, Muslim
Lion Cub
Boy/Male
Hindu, Indian, Malayalam, Marathi
Lord Shiva
Female
English
Variant spelling of English Calantha, CALANTHE means "beautiful flower." This is the name of a genus of orchid flowers.
Boy/Male
Indian, Sanskrit
Excelling
Boy/Male
English
From Wade's estate.
TWELF
TWELF
TWELF
TWELF
TWELF
n.
The next in order after the eleventh.
n.
The evening of Epiphany, or the twelfth day after Christmas, observed as a festival by various churches.
n.
The twelfth day after Christmas; Epiphany; -- called also Twelfth-day.
n.
See Twelfthtide.
a.
Under the tongue; -- applied esp., in the higher vertebrates, to the twelfth or last pair of cranial nerves, which are distributed to the base of the tongue.
n.
The quotient of a unit divided by twelve; one of twelve equal parts of one whole.
n.
An ornamented cake distributed among friends or visitors on the festival of Twelfth-night.
n.
A twelfth part, as of the Roman as; an ounce.
n.
A measure of length; one twelfth of an inch.
n.
The twelfth part of the ecliptic or zodiac.
a.
Next in order after the eleventh; coming after eleven others; -- the ordinal of twelve.
a.
Next in order after the twelfth; the third after the tenth; -- the ordinal of thirteen; as, the thirteenth day of the month.
n.
A twelfth part of the heavens, as divided by six circles intersecting at the north and south points of the horizon, used by astrologers in noting the positions of the heavenly bodies, and casting horoscopes or nativities. The houses were regarded as fixed in respect to the horizon, and numbered from the one at the eastern horizon, called the ascendant, first house, or house of life, downward, or in the direction of the earth's revolution, the stars and planets passing through them in the reverse order every twenty-four hours.
a.
In the duodecimal system of mensuration, the twelfth part of an inch or prime; a line. See Inch, and Prime, n., 8.
n.
A unit for the measurement of small intervals of time, such that 1012 (ten trillion) of these units make one second.
n.
A twelfth part of the heavens; a house. See 1st House, 8.
n.
The next in order after the twelfth.
n.
An aspect of the planets when they are distant from each other the twelfth part of a circle, or thirty degrees.
n.
An interval comprising an octave and a fifth.
a.
Consisting, or being one of, twelve equal parts into which anything is divided.