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Theorem about a certain class of control-flow graphs
In programming language theory, the structured program theorem, generally called the Böhm–Jacopini theorem, states that a class of control-flow graphs
Structured_program_theorem
Programming paradigm based on block-based control flow
who coined the term structured programming. The structured program theorem provides the theoretical basis of structured programming. It states that three
Structured_programming
Topics referred to by the same term
Structure theorem may refer to: Structured program theorem, a result in programming language theory Structure theorem for finitely generated modules over
Structure_theorem
Italian computer scientist (1923–2017)
mechanism of a programming language, written in that same language. His most influential contribution is the so-called structured program theorem, published
Corrado_Böhm
Numerical measure of program structure
the structuredness of a program" in his words) rather than a yes/no answer to the question of whether a program's control-flow graph is structured or not
Essential_complexity
Space hierarchy theorem (computational complexity theory) Speedup theorem (computational complexity theory) Structured program theorem (computer science)
List_of_theorems
How software progresses through its implementation
Kosaraju refined the structured program theorem by proving that it is possible to avoid adding additional variables in structured programming, as long as arbitrary-depth
Control_flow
Measure of the structural complexity of a software program
(CFGs) of non-structured programs look like in terms of their subgraphs, which McCabe identified. (For details, see structured program theorem.) McCabe concluded
Cyclomatic_complexity
Primitive programming language created in 1964
formulations of the single-entry single-exit principle central to structured programming. P′′ is formally defined as a set of words on the four-instruction
P′′
One-way software control-flow statement
limited to specific scenarios. The structured program theorem proved that the goto statement is not necessary to write programs that can be expressed as flow
Goto
Ability of a computing system to simulate Turing machines
Loop (computing) Machine that always halts Rice's theorem S m n theorem Structured program theorem Turing tarpit Virtualization Emulation (computing)
Turing_completeness
Proof assistant and programming language
programming language. It is based on the calculus of constructions with inductive types, the foundational type theory developed with the Coq theorem prover
Lean_(proof_assistant)
Limitative results in mathematical logic
mathematical logic and in philosophy of mathematics. The theorems are interpreted as showing that Hilbert's program to find a complete and consistent set of axioms
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
17th-century conjecture proved by Andrew Wiles in 1994
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers a
Fermat's_Last_Theorem
Proof assistant
The Rocq Prover (formerly named Coq) is an interactive theorem prover first released in 1989. It allows the expression of mathematical assertions, mechanical
Rocq
Property of artificial neural networks
machine learning, the universal approximation theorems (UATs) state that neural networks with a certain structure can, in principle, approximate any continuous
Universal approximation theorem
Universal_approximation_theorem
language, the first meta-circular evaluator, contributed the structured program theorem Grady Booch, developer of Unified Modeling Language (UML) Kathleen
List of programming language researchers
List_of_programming_language_researchers
In mathematics, a statement that has been proven
mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses
Theorem
Measure of algorithmic complexity
diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem. In particular, no program P computing a lower bound for each text's Kolmogorov
Kolmogorov_complexity
Theorem classifying finite simple groups
classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite simple group is
Classification of finite simple groups
Classification_of_finite_simple_groups
correctness. Control-flow graph Program slicing Program dependence graph Structured programming Structured program theorem Ferrante, Ottenstein & Warren
Single-entry_single-exit
Theorem relating graph minors and topological embeddings
In mathematics, the graph structure theorem is a major result in the area of graph theory. The result establishes a deep and fundamental connection between
Graph_structure_theorem
index is a data structure to facilitate fast lookup of terms and clauses in a logic program, deductive database, or automated theorem prover. Many operations
Term_indexing
On bipartite matching and vertex cover
In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Computer programming paradigm
Functional programming (contrast) Imperative programming Logic programming Object-oriented programming Programming paradigms Programming language Structured programming
Procedural_programming
Interactive theorem prover software
computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs
Proof_assistant
Doignon's theorem in geometry is an analogue of Helly's theorem for the integer lattice. It states that, if a family of convex sets in d {\displaystyle
Doignon's_theorem
Theorem in topology
In topology, a discipline within mathematics, the Jordan curve theorem (JCT), formulated by Camille Jordan in 1887, asserts that every simple closed curve
Jordan_curve_theorem
Planar maps require at most four colors
In mathematics, the four color theorem, or the four-color map theorem, states that no more than four colors are required to color the regions of any map
Four_color_theorem
Statement in mathematical combinatorics
In combinatorics, Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours)
Ramsey's_theorem
Counterintuitive result in probability
random programs can produce highly structured outputs more often than classical probability suggests, aligning with Gregory Chaitin's modern theorem and
Infinite_monkey_theorem
Data table used to control program flow
be tested in the next table entry. See Structured program theorem Multiway branching is an important programming technique which is all too often replaced
Control_table
Mathematical result in differential geometry
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential
Atiyah–Singer_index_theorem
Impossible task in computing
valid in every structure. Such an algorithm was proven to be impossible by Alonzo Church and Alan Turing in 1936. By the completeness theorem of First-order
Entscheidungsproblem
Relationship between programs and proofs
to a proof of that theorem. This sets a form of logic programming on a rigorous foundation: proofs can be represented as programs, and especially as lambda
Curry–Howard_correspondence
Programming language
(RTMs), laying the foundation for reversible programming. The reversible variant of the structured program theorem, for instance, can be effectively analyzed
Flow_chart_language
Type of software system
applications of theorem provers include verification of the correctness of integrated circuits, software programs, engineering designs, etc. Logic programs (LPs)
Reasoning_system
Methodology of programming
Eriksson, Johannes (2012). "An Exercise in Invariant-based Programming with Interactive and Automatic Theorem Prover Support". arXiv:1202.4829 [cs.SE].
Invariant-based_programming
Overview of and topical guide to algorithms
algorithms and The Art of Computer Programming Edsger W. Dijkstra — Dijkstra's algorithm and structured programming Robert W. Floyd — Floyd–Warshall algorithm
Outline_of_algorithms
Theorem in quantum information science
In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement
No-cloning_theorem
Programming language
negation of the theorem to be proved. Using only resolution as the rule of inference is problematical because it hides the underlying structure of proofs.
Planner (programming language)
Planner_(programming_language)
Software projects developed at universities
language (MIT) ML – functional programming language developed for theorem proving (Edinburgh) Modula-2 – systems programming language (ETH Zurich) NESL –
List of software developed at universities
List_of_software_developed_at_universities
Analysis of computer programs without executing them
syntax trees (ASTs) are commonly used, since they provide a structured representation of a program's syntactic elements. [citation needed] Formal methods is
Static_program_analysis
Self-replicating program
programs into their outputs. Quines are possible in any Turing-complete programming language, as a direct consequence of Kleene's recursion theorem.
Quine_(computing)
Programming language that uses first order logic
Prolog is a logic programming language that has its origins in artificial intelligence, automated theorem proving, and computational linguistics. Prolog
Prolog
Constructs a fiber bundle from a base space, fiber and a set of transition functions
mathematics, the fiber bundle construction theorem is a theorem which constructs a fiber bundle with a structure group from a given base space, fiber, group
Fiber bundle construction theorem
Fiber_bundle_construction_theorem
Russian mathematician (born 1966)
Polikanova, he established a measure-theoretic formulation of Helly's theorem.[PP86] In 1987, the year he began graduate studies, he published an article
Grigori_Perelman
spiral development Amber S. Boehnlein Corrado Böhm – author of the structured program theorem Kurt Bollacker Jeff Bonwick – invented slab allocation and ZFS
List_of_computer_scientists
Proving or disproving the correctness of certain intended algorithms
automated theorem proving, type systems, and lightweight formal methods. A promising type-based verification approach is dependently typed programming, in which
Formal_verification
Proof all ranked voting rules have spoilers
Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow. It shows that no group decision-making
Arrow's_impossibility_theorem
Mathematical model for deduction or proof systems
system) is an abstract structure and formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms. In 1921, David
Formal_system
Study of discrete mathematical structures
computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer
Discrete_mathematics
Classification theorem in group theory
In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved in the early 1960s
Feit–Thompson_theorem
Gives general conditions under which sheaf cohomology groups with indices > 0 are zero
In mathematics, the Kodaira vanishing theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions
Kodaira_vanishing_theorem
London. Byron's research interests include program analysis/verification, programming languages, theorem proving, logic, hardware design, and operating
Byron Cook (computer scientist)
Byron_Cook_(computer_scientist)
E is a high-performance theorem prover for full first-order logic with equality. It is based on the equational superposition calculus and uses a purely
E_(theorem_prover)
Software system
Nqthm is a theorem prover sometimes referred to as the Boyer–Moore theorem prover. It was a precursor to ACL2. The system was developed by Robert S. Boyer
Nqthm
Unsolved problem in computer science
classes by logics over finite structures. By Fagin's theorem, NP is exactly the class of properties of finite structures expressible in existential second-order
P_versus_NP_problem
Theorem in mathematics and economics
In mathematics and economics, the envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization
Envelope_theorem
Path in a graph that visits each vertex exactly once
the Bondy–Chvátal theorem, which generalizes earlier results by G. A. Dirac (1952) and Øystein Ore. Both Dirac's and Ore's theorems can also be derived
Hamiltonian_path
High-level computer programming conceptualization
A programming paradigm is a relatively high-level way to conceptualize and structure the implementation of a computer program. A programming language can
Programming_paradigm
Subfield of mathematics
incompleteness theorem, establishes severe limitations on axiomatic foundations for mathematics, striking a strong blow to Hilbert's program. It showed the
Mathematical_logic
Upper bound on intersecting set families
In mathematics, the Erdős–Ko–Rado theorem limits the number of sets in a family of sets for which every two sets have at least one element in common.
Erdős–Ko–Rado_theorem
Computer program for the Boolean satisfiability problem
large number of heuristics and program optimizations to work efficiently. By a result known as the Cook–Levin theorem, Boolean satisfiability is an NP-complete
SAT_solver
Number divisible only by 1 and itself
than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself
Prime_number
Algorithm component in computer science
unification. It causes unification of a variable V and a structure S to fail if S contains V. In theorem proving, unification without the occurs check can lead
Occurs_check
Completes the Langlands program for general linear groups over algebraic function fields
In mathematics, Lafforgue's theorem, due to Laurent Lafforgue, completes the Langlands program for general linear groups over algebraic function fields
Lafforgue's_theorem
Area of mathematical logic
sentences satisfied by a structure is also called the theory of that structure. It's a consequence of Gödel's completeness theorem (not to be confused with
Model_theory
Field of artificial intelligence
systems, frames, rules, logic programs, and ontologies. Examples of automated reasoning engines include inference engines, theorem provers, model generators
Knowledge representation and reasoning
Knowledge_representation_and_reasoning
Area of discrete mathematics
Well-known applications include automatic theorem proving and modeling the elaboration of linguistic structure. Hamiltonian path problem Minimum spanning
Graph_theory
Higher-order logic (HOL) automated theorem prover
The Isabelle automated theorem prover is a higher-order logic (HOL) theorem prover, written in Standard ML and Scala. As a Logic for Computable Functions
Isabelle_(proof_assistant)
Mathematical topics based on the works of George Boole
interpretation that satisfies a given Boolean formula Boolean prime ideal theorem, a theorem which states that ideals in a Boolean algebra can be extended to prime
Boolean
Concept in topology
2003, where he follows Richard S. Hamilton's program using Ricci flow. For n = 1, the h-cobordism theorem is vacuously true, since there is no closed simply-connected
H-cobordism
Casio calculator programming language
calculations, such as the Pythagorean theorem and complex trigonometric calculations.[citation needed] Output from the program can be in the form of scrolling
Casio_BASIC
Graph data structure
David; Nelson, Greg; Saxe, James B. (May 2005). "Simplify: a theorem prover for program checking". Journal of the ACM. 52 (3): 365–473. doi:10.1145/1066100
E-graph
Effort to birationally classify algebraic varieties
result is the cone theorem of Shigefumi Mori, describing the structure of the cone of curves of X {\displaystyle X} . Briefly, the theorem shows that starting
Minimal_model_program
Branch of mathematical logic
Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining
Reverse_mathematics
Proof assistant
step execution of structured tactics allowing a much better management of the proof development, and naturally leading to more structured and readable scripts
Matita
Branch of mathematics that studies the properties of groups
the space X. Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure. This occurs in many
Group_theory
Overview of and topical guide to computer science
query on a fact and rule database, and automated theorem provers that aim to prove mathematical theorems with some assistance from a programmer. Computer
Outline_of_computer_science
Method to solve optimization problems
equivalent. Dantzig provided formal proof in an unpublished report "A Theorem on Linear Inequalities" on January 5, 1948. Dantzig's work was made available
Linear_programming
Term in mathematics
Canonical Form is a characterization, or structure theorem, for complex matrices, and the spectral theorem is likewise for symmetric matrices (if real)
Characterization (mathematics)
Characterization_(mathematics)
Programming paradigm entirely based on functions
artificial intelligence [field]", for writing Logic Theorist, a program which proved theorems from Principia Mathematica automatically. In order to accomplish
Purely_functional_programming
American mathematician (1946–2012)
that orbifold structures naturally arose. Such structures had been studied prior to Thurston, but his work, particularly the next theorem, would bring
William_Thurston
Set of software engineering methods
In computer programming, program slicing is the computation of the set of program statements, the program slice, that may affect the values at some point
Program_slicing
Programming language developed at Cornell University
and best engineering practices and through which methods such as structured programming and stepwise refinement could be taught, and PL/I was a more expressive
PL/C
Pairing where no unchosen pair prefers each other over their choice
and hybrid CPU–GPU execution to reduce overhead. The rural hospitals theorem concerns a more general variant of the stable matching problem, like that
Stable_matching_problem
Automated theorem proving ACL2 theorem prover E equational theorem prover Gandalf theorem prover HOL theorem prover Isabelle theorem prover LCF theorem prover
List of mathematical logic topics
List_of_mathematical_logic_topics
American mathematician (1943–2024)
second fundamental form, which has a simpler structure than the Riemann curvature tensor.[H95c] Hamilton's theorem, which requires strict convexity, is naturally
Richard_S._Hamilton
death paradox Zero Kelvin Kelvin–Stokes theorem Kelvin functions Kelvin problem/Kelvin conjecture/Kelvin structure/Kelvin foam Kelvin transform Kelvin (microarchitecture)
List of things named after Lord Kelvin
List_of_things_named_after_Lord_Kelvin
Functional programming language
which theorems and from which modules can be used, whether the action can use pattern matching, etc. Agda is a total functional programming language
Agda_(programming_language)
Automated software testing technique
memory leaks. Typically, fuzzers are used to test programs that take structured inputs. This structure is specified, such as in a file format or protocol
Fuzzing
Reasoning for mathematical statements
The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic
Mathematical_proof
Computer program that uses a knowledge base and reasoning to solve problems
backward chaining. Other approaches include the use of automated theorem proving, logic programming, blackboard systems, and term rewriting systems such as Constraint
Knowledge-based_systems
Study of rational collective decision-making
impossibility theorem is what often comes to mind when one thinks about impossibility theorems in voting. There are several famous theorems concerning social
Social_choice_theory
Concept in computer science
data structures found in device drivers). Interactive Proof. Proofs have been done using embeddings of Separation Logic into interactive theorem provers
Separation_logic
Venezuelan computer scientist
concrete results like the compression theorem, the gap theorem, the honesty theorem and the Blum speedup theorem. Some of his other work includes a protocol
Manuel_Blum
Logical problem studied in computer science
applications across computer science, including in automated theorem proving, program analysis, program verification, and software testing. Since Boolean satisfiability
Satisfiability modulo theories
Satisfiability_modulo_theories
Graphs of d-dimensional polytopes are d-connected
combinatorics, a branch of mathematics, Balinski's theorem is a statement about the graph-theoretic structure of three-dimensional convex polyhedra and higher-dimensional
Balinski's_theorem
Principle of interchangeability of data and code
computational theory, Kleene's second recursion theorem provides a form of code-is-data, by proving that a program can have access to its own source code. Code-as-data
Code_as_data
travel, tourism, insurance
STRUCTURED PROGRAM-THEOREM
STRUCTURED PROGRAM-THEOREM
Boy/Male
Afghan, Arabic, Gujarati, Indian, Muslim
Solid Structure; Lifetime
Boy/Male
Muslim
Solid structure
Boy/Male
Arabic, Muslim
Way; Program; Road; Path
Surname or Lastname
English and German
English and German : variant spelling of Pilgrim.
Girl/Female
Tamil
Shape, Structure
Boy/Male
Hindu, Indian, Marathi
The Highest Point; Summit
Boy/Male
Muslim
Way. Program.
Boy/Male
Hindu, Indian
Start
Boy/Male
Indian
Good Structure
Boy/Male
Arabic
Way; Program
Girl/Female
Hindu, Indian
Prowess
Girl/Female
Indian
Shape, Structure
Boy/Male
Hindu
Girl/Female
Indian
Shape, Structure
Girl/Female
Indian
Structure
Girl/Female
Indian, Kashmiri
Body Structure
Boy/Male
Indian
Solid structure
Girl/Female
Tamil
Shape, Structure
Surname or Lastname
English (mainly Cambridgeshire)
English (mainly Cambridgeshire) : variant of Pilgrim.
Girl/Female
Hindu, Indian, Telugu
The Structure of God
STRUCTURED PROGRAM-THEOREM
STRUCTURED PROGRAM-THEOREM
STRUCTURED PROGRAM-THEOREM
STRUCTURED PROGRAM-THEOREM
STRUCTURED PROGRAM-THEOREM
STRUCTURED PROGRAM-THEOREM
STRUCTURED PROGRAM-THEOREM
travel, tourism, insurance