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Interactive theorem proving systems
Isabelle/HOL: A Proof Assistant for Higher-Order Logic. Berlin, Heidelberg: Springer-Verlag. ISBN 978-3-540-45949-1. "HOL Interactive Theorem Prover". "HOL Light"
HOL_(proof_assistant)
Interactive theorem prover software
language as the metalanguage for a theorem prover, and led to the HOL family of proof assistants. The 1990s saw the rise of Rocq, (then known as Coq), which
Proof_assistant
Higher-order logic (HOL) automated theorem prover
Tobias Nipkow, Lawrence C. Paulson, Markus Wenzel, "Isabelle/HOL – A Proof Assistant for Higher-Order Logic", 2020. Free and open-source software portal
Isabelle_(proof_assistant)
Proof assistant program
HOL Light is a proof assistant for classical higher-order logic. It is a member of the HOL theorem prover family. Compared with other HOL systems, HOL
HOL_Light
Topics referred to by the same term
Norway Hol, Tjeldsund, Norway Hol, Ludhiana, Punjab, India Hol, a community in Duk County in Jonglei State in South Sudan HOL (proof assistant), a family
Hol
General purpose functional programming language
the pair into its three components. HOL (proof assistant) Hope (programming language) Isabelle (proof assistant) Nuprl Gordon, M.; Milner, R.; Wadsworth
ML_(programming_language)
Formal argument for the existence of God
Fuenmayor (May 2017). "Types, Tableaus and Gödel's God in Isabelle/HOL". Archive of Formal Proofs. ISSN 2150-914X. Christoph Benzmüller and Dana Scott. "Notes
Gödel's_ontological_proof
Concept in computer science
Interactive Proof. Proofs have been done using embeddings of Separation Logic into interactive theorem provers such as Rocq (previously known as Coq) and HOL (proof
Separation_logic
Formal system of logic
Type theory Higher-order grammar Higher-order logic programming HOL (proof assistant) Many-sorted logic Typed lambda calculus Modal logic Jacobs, 1999
Higher-order_logic
Branch of computer science
substantial subset of Standard ML programming language using the HOL proof assistant. Another approach to obtain a formally correct compiler is to use
Compiler_correctness
Subfield of computer science and logic
essentially another proof assistant for classical higher order logic. Rocq Developed in France, Rocq is another automated proof assistant, which can automatically
Automated_reasoning
1970s automated theorem prover
functions, leading to HOL, HOL Light, and the Isabelle proof assistant that supports various logics. As of 2019, the Isabelle proof assistant still contains
Logic for Computable Functions
Logic_for_Computable_Functions
Math theorem about sphere packing
of a formal proof of the Kepler conjecture using a combination of the Isabelle and HOL Light proof assistants. In 2017, the formal proof was accepted
Kepler_conjecture
Proof assistant program
for writing mathematical definitions and proofs, a proof assistant, which is able to mechanically check proofs written in this language, and a library
Mizar_system
Proposal for a computer-based database of all mathematical knowledge
limitations of existing theorem provers and proof assistants; the paper finds that the major contenders, Mizar, HOL, and Rocq, have serious shortcomings in
QED_manifesto
Subfield of automated reasoning and mathematical logic
specification. Automated theorem provers have been integrated with proof assistants, including Isabelle/HOL. Applications of theorem provers are also found in natural
Automated_theorem_proving
Proving or disproving the correctness of certain intended algorithms
discharging these obligations using either proof assistants (interactive theorem provers) (such as HOL, ACL2, Isabelle, Rocq (previously known as Coq)
Formal_verification
Limitative results in mathematical logic
(O'Connor 2005) and by John Harrison in 2009 using HOL Light (Harrison 2009). A computer-verified proof of both incompleteness theorems was announced by
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
German computer scientist (born 1958)
Springer. Nipkow T. and Paulson L. and Wenzel M. (2002). Isabelle/HOL — A Proof Assistant for Higher-Order Logic. Springer. Gerwin Klein & Tobias Nipkow
Tobias_Nipkow
Computer science professor
principle that unifies and automates proofs by both induction and coinduction, and has been implemented in Rocq, Isabelle/HOL, Dafny, and as part of the CIRC
Grigore_Roșu
Logic programming language
such, it is closely related to Rocq and Isabelle/HOL/HOL Light. However, unlike those systems, Twelf proofs are typically developed by hand. Despite this
Twelf
Of a function, an additional effect besides returning a value
solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category
Side effect (computer science)
Side_effect_(computer_science)
Rules to verify computer program correctness
deficiency in the axioms and rules quoted above is that they give no basis for a proof that a program successfully terminates. Failure to terminate may be due
Hoare_logic
Apparent logical paradox
reasoning; it is sometimes used to contrast the expressiveness of proof assistants. In the setting with empty domains allowed, the drinker paradox must
Drinker_paradox
Analysis of computer programs without executing them
solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category
Static_program_analysis
American mathematician
vindicate his proof of the Kepler conjecture. His proof relied on computer calculation to verify conjectures. The project used two proof assistants, HOL Light
Thomas_Callister_Hales
System of formal mathematical logic
is a form of higher-order logic and closely related to the logics of the HOL theorem prover family. The theorem proving systems TPS and ETPS Archived
Q0_(mathematical_logic)
Computer program for the Boolean satisfiability problem
used to assist in proving mathematical theorems through computer-assisted proof. In Ramsey theory, several previously unknown Van der Waerden numbers were
SAT_solver
Process of analyzing computer program behavior
solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category
Program_analysis
Validates computer program operations
solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category
Typestate_analysis
Set of software engineering methods
solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category
Program_slicing
solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category
Dependence_analysis
Mathematical theory of data types
theory of types and Per Martin-Löf's intuitionistic type theory. Many proof assistants are based on type theory. For example, the underlying formal language
Type_theory
American mathematician
MR 2584403, S2CID 120886087 Her 1973 proof of a partition theorem for the ordinal ω ω {\displaystyle \omega ^{\omega }} , formalised in Isabelle/HOL
Jean_A._Larson
Approach to static program analysis
solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category
Abstract_interpretation
Concepts in theoretical computer science
the decomposition can be helpful, because the formal definitions enable a proof that different methods must be used for verifying safety properties versus
Safety and liveness properties
Safety_and_liveness_properties
solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category
Polyvariance
Computer science field
the violation is feasible, it is reported to the user. If it is not, the proof of infeasibility is used to refine the abstraction and checking begins again
Model_checking
Software used in mathematical applications
Programming System X-13ARIMA-SEATS XploRe ACL2 Agda Albatross ETPS F* HOL theorem prover HOL Light HOL4 Isabelle Jape Lean LEGO Matita Metamath MINLOG Mizar
Mathematical_software
Graph data structure
known as non-chronological backtracking), e-graphs are extended to produce proof certificates. E-graphs are also used in the Simplify theorem prover of ESC/Java
E-graph
Mathematical program specifications
and symbolic evaluation), optimization for Intel IA-64 architecture using HOL light theorem prover, and verification of high-performance dual-port gigabit
Formal_methods
Chronology of AI-assisted developments in mathematical research
environment and benchmark based on HOL Light, together with the DeepHOL prover. DeepHOL used deep reinforcement learning to guide proof search, making formal higher-order
Timeline of artificial intelligence contributions to mathematics
Timeline_of_artificial_intelligence_contributions_to_mathematics
Software projects developed at universities
Mizar – proof assistant and formal mathematics system (Białystok, Alberta, and Shinshu) Murφ – explicit-state model checker (Stanford) Nuprl – proof development
List of software developed at universities
List_of_software_developed_at_universities
Fundamental problem in computer science
solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category
Path_explosion
allegiances to the good guys, but not Hol Horse, even though he considered the idea. Although he drew a color illustration with Hol Horse alongside the Joestar
List of JoJo's Bizarre Adventure characters
List_of_JoJo's_Bizarre_Adventure_characters
solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category
Hyperproperty
Programming language
with static types. The Haxe programming language compiler. HOL Light, a formal proof assistant. Infer, a static analyzer created at Facebook for Java, C
OCaml
Mathematical notation in lambda calculus
reasoning about the meta-theoretic properties of a deductive system in a proof assistant, it is sometimes desirable to limit oneself to first-order representations
De_Bruijn_index
computers and proof assistants. Even with this modern technology, it may take years of human work for writing down a completely detailed proof. This does
Philosophy_of_mathematics
Diving incident in the Maldives
Biology and Ecology from the University of Genoa, and was a research assistant for the University of Genoa in the 24th and 25th scientific cruises that
2026 Dhekunu Kandu cave diving incident
2026_Dhekunu_Kandu_cave_diving_incident
Hungarian philosopher of mathematics and science (1922–1974)
for his thesis of the fallibility of mathematics and its "methodology of proofs and refutations" in its pre-axiomatic stages of development, and also for
Imre_Lakatos
Subjective attitude that something is true
role to play in this. The disagreement between atomism, molecularism and holism concerns the question of how the content of one belief depends on the contents
Belief
Specialty in philosophy, focused on German language origin
Camposampiero, Matteo Favaretti. "The Boundaries of Existence: Mendelssohn's Proof in Light of Wolff and Boscovich." Journal of the History of Philosophy,
German_philosophy
Logical problem studied in computer science
[citation needed] SMT solvers have been integrated with proof assistants, including Rocq and Isabelle/HOL. SMT solvers are a core building block in program
Satisfiability modulo theories
Satisfiability_modulo_theories
English theoretical physicist (1942–2018)
1968 Gravity Research Foundation competition. In 1970, they published a proof that if the universe obeys the theory of general relativity, and fits any
Stephen_Hawking
Austrian philosopher and logician (1889–1951)
as "all those primitive propositions which are assumed as true without proof by the various sciences". Wittgenstein left Cambridge in 1913, but would
Ludwig_Wittgenstein
American religious leader (born 1933)
Woman", "Stone Cold Man" and calypso standards like "Zombie Jamboree", "Hol 'Em Joe", "Mary Ann" and "Brown Skin Girl". Some were reissued: "Don't Touch
Louis_Farrakhan
Quality of zero being an even number
Tobias; Paulson, Lawrence C.; Wenzel, Markus (2002), Isabelle/Hol: A Proof Assistant for Higher-Order Logic, Springer, ISBN 978-3-540-43376-7 Nuerk,
Parity_of_zero
1955 novel by Ian Fleming
Adaptations include a broadcast on South African radio in 1956 starring Bob Holness and a 1958 Daily Express comic strip. The novel's name was used in 1979
Moonraker_(novel)
German fascist ideology
notions of holism, or how they reflect Germany's troubled path towards modernity. My starting point, instead, is the interwar years. By then, holism had become
Nazism
van. John was able to disarm the bomb. Tara Reagan (portrayed by Karen Holness) – A judge who was pressured by Intergang into having Atom-Man released
List of Superman & Lois characters
List_of_Superman_&_Lois_characters
Austrian–British philosopher of science (1902–1994)
proofs; published as a book 1982), ISBN 0415091128 The Open Universe: An Argument for Indeterminism, 1956–57 (as privately circulated galley proofs;
Karl_Popper
Hungarian-British author and journalist (1905–1983)
Britannica Herbert A. Simon – American academic and Nobel Laureate (1916–2001) Holism – Philosophical theory Holon (philosophy) – Something that is simultaneously
Arthur_Koestler
Austrian philosopher of science (1924–1994)
philosophy of quantum mechanics. Feyerabend argues that von Neumann's 'no-go' proof only shows that the Copenhagen interpretation is consistent with the fundamental
Paul_Feyerabend
German polymath (1646–1716)
Arte Combinatoria was inspired by Ramon Llull's Ars Magna and contained a proof of the existence of God, cast in geometrical form, and based on the argument
Gottfried_Wilhelm_Leibniz
Scottish philosopher, historian, economist and essayist (1711–1776)
suppose the universe, an effect quite singular and unparalleled, to be the proof of a Deity, a cause no less singular and unparalleled". The philosopher
David_Hume
2016 police killing in Falcon Heights, Minnesota
profiled in #WhileBlack, a documentary film by Sidney Fussell and Jennifer Holness. List of killings by law enforcement officers in Minnesota List of killings
Killing_of_Philando_Castile
Diving in water-filled caves
Barrier Reef Great Southern Reef Guadalupe Island Biosphere Reserve Haql Hol Chan Marine Reserve iSimangaliso Marine Protected Area Sodwana Bay John Pennekamp
Cave_diving
1111/sjp.12320. S2CID 197907484. Chu; Glass (2013). <path>'.library.uvic.ca/HOL/Page?lname=&handle=hein.journals/alblr51&collection=&page=101&collection=journals
Prostitution_in_Canada
1998 killing of unarmed man in UK
action for battery had no realistic prospect of success as the burden of proof was on the claimants, who could not negate Sherwood's self-defence claim
Killing_of_James_Ashley
German-born American anthropologist (1858–1942)
they do not really exist. Rather than take alternating sounds as objective proof of different stages in cultural evolution, Boas considered them in terms
Franz_Boas
Romanian sociologist and politician (1882–1947)
(second edition 1941). The work also signified his distancing from both holism and the mainline, positivist, sociological school of Bucharest, turning
Traian_Brăileanu
Malaysian politician and 7th Governor of Sarawak (1936–2024)
gov't deals, but no proof of abuse". Malaysiakini. Archived from the original on 25 August 2014. Retrieved 23 October 2015. "No proof of Taib power abuse
Abdul_Taib_Mahmud
2016 funeral of leader of Cuba
the death of Commander Fidel Castro." Jamaica – Prime Minister Andrew Holness issued a statement which read Castro "will go down in the annals of history
Death and state funeral of Fidel Castro
Death_and_state_funeral_of_Fidel_Castro
Philosophy of the Western world
argued for verifiability, based on the idea that one could recognise the proof of truth when offered it. Alternative to these, Paul Grice put forward a
Western_philosophy
American philosopher (1957–2023)
251–70. doi:10.1111/j.2041-6962.1990.tb00545.x. Varner, Gary (1991). "No holism without pluralism". Environmental Ethics. 13 (2): 175–9. doi:10.5840/enviroethics199113228
Gary_Varner
Philosophical heritage of Russian thinkers
spiritual experience and experience of creativity do not need rational proof of the existence of God. At its core, the deity is irrational and super–rational
Russian_philosophy
Director: Niall Fraser; Producer: Dawn Coulson-Beckett (2 April 2020). "Fire Proof". Doctors. BBC. BBC One. Archived from the original on 1 April 2020. Retrieved
List of Doctors characters introduced in 2020
List_of_Doctors_characters_introduced_in_2020
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