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Design pattern in functional programming to build generic types
which lifts a value into the monadic context, and bind : <A,B>(m_a : M(A), f : A -> M(B)) -> M(B) which chains monadic computations. In simpler terms
Monad (functional programming)
Monad_(functional_programming)
Topics referred to by the same term
Look up monadic in Wiktionary, the free dictionary. Monadic may refer to: Monadic, a relation or function having an arity of one in logic, mathematics
Monadic
Form of second-order logic
In mathematical logic, monadic second-order logic (MSO) is the fragment of second-order logic where the second-order quantification is limited to quantification
Monadic_second-order_logic
Theorem in category theory
category theory, a branch of mathematics, Beck's monadicity theorem gives a criterion that characterises monadic functors, introduced by Jonathan Mock Beck (1968)
Beck's_monadicity_theorem
Operation in algebra and mathematics
be monadic if it has a left adjoint F forming a monadic adjunction. For example, the free–forgetful adjunction between groups and sets is monadic, since
Monad_(category_theory)
Fragment of first-order logic
In logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic (also called predicate calculus)
Monadic_predicate_calculus
In mathematics, especially category theory, a monadic descent is roughly an idea to encode descent data using a monad. The Bénabou-Roubaud theorem says
Monadic_descent
Set of rules defining correctly structured programs
by non-textual symbols. Most symbols denote functions or operators. A monadic function takes as its argument the result of evaluating everything to its
APL_syntax_and_symbols
Boolean algebra extended with a unary operator representing existential quantification
In abstract algebra, a monadic Boolean algebra is an algebraic structure A with signature ⟨·, +, ', 0, 1, ∃⟩ of type ⟨2,2,1,0,0,1⟩, where ⟨A, ·, +, '
Monadic_Boolean_algebra
Number of arguments required by a function
Abraham Robinson follows Quine's usage. In philosophy, the adjective monadic is sometimes used to describe a one-place relation such as 'is square-shaped'
Arity
Mathematical operation with only one operand
In mathematics, a unary operation is an operation with only one operand, i.e. a single input. This is in contrast to binary operations, which use two operands
Unary_operation
On linear-time algorithms for graph logic
Courcelle's theorem is the statement that every graph property definable in the monadic second-order logic of graphs can be decided in linear time on graphs of
Courcelle's_theorem
Topics referred to by the same term
Monade Monadic (disambiguation) Monoid, in abstract algebra All pages with titles beginning with Monad, for titles starting "Monad" or "Monadic" All pages
Monad
Innate inclination of a thing to continue to exist and enhance itself
to explain Zeno's paradoxes of motion. Leibniz later defines the term monadic conatus, as the state of change through which his monads perpetually advance
Conatus
Form of logic that allows quantification over predicates
sometimes called full second-order logic to distinguish it from the monadic version. Monadic second-order logic is particularly used in the context of Courcelle's
Second-order_logic
International relations theory
motivating peace between democratic states. Individual theorists maintain "monadic" forms of this theory (democracies are in general more peaceful in their
Democratic_peace_theory
Functional programming language
features including type classes for type-safe operator overloading and monadic input/output (IO). It is named after logician Haskell Curry. Haskell's
Haskell
Algebraization of first-order logic with equality
\exists (x+y)=\exists x+\exists y} of monadic Boolean algebra. The axiom (C4) drops out (becomes a tautology). Thus monadic Boolean algebra can be seen as a
Cylindric_algebra
In mathematics, S2S is the monadic second-order theory with two successors. Its first-order objects are finite binary strings. It is one of the most expressive
S2S_(mathematics)
Functional programming language inspired by ML and aimed at program verification
Science and Automation (Inria). Its type system includes dependent types, monadic effects, and refinement types. This allows expressing precise specifications
F*_(programming_language)
Ways how entities stand to each other
academic literature. Internal relations, like resemblance, depend only on the monadic properties of the relata. They contrast with external relations, like spatial
Relation_(philosophy)
Logical formulation of graph properties
and predicates concern individual vertices and edges of a graph, while monadic second-order graph logic allows quantification over sets of vertices or
Logic_of_graphs
Functional programming language for arrays
variables was done through special privileged "I-beam" functions, using both monadic and dyadic operations. In 1973, IBM released APL.SV, which was a continuation
APL_(programming_language)
Logical principle
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Law_of_excluded_middle
Algebraic manipulation of "true" and "false"
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Boolean_algebra
Branch of mathematics that studies sets
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Set_theory
Limitative results in mathematical logic
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Aasimon, Deva Planescape Monstrous Compendium Appendix (1994) Astral, Monadic and Movanic Aasimon, Light Planescape Monstrous Compendium Appendix (1994)
List of Advanced Dungeons & Dragons 2nd edition monsters
List_of_Advanced_Dungeons_&_Dragons_2nd_edition_monsters
In logic, a statement which is always true
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Tautology_(logic)
View that mind is a ubiquitous feature of reality
(2024), "Monadic panpsychism", Synthese, 203 (38), Springer Kadić, Nino (2022), Phenomenology of Fundamental Reality, King's College London Monadic Panpsychism
Panpsychism
Set of all things that may be the input of a mathematical function
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Domain_of_a_function
Collection of mathematical objects
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Set_(mathematics)
Diagram that shows all possible logical relations between a collection of sets
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Venn_diagram
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Mathematical_object
Concept in functional programming
In functional programming, a result type is a monadic type holding a returned value or an error code. They provide an elegant way of handling errors,
Result_type
3-volume treatise on mathematics, 1910–1913
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Principia_Mathematica
Mathematical function such that every output has at least one input
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Surjective_function
Early Christian and Jewish religious systems
influences. It depicts creation in a series of emanations from a primal monadic source, finally resulting in the creation of the material universe. These
Gnosticism
Set whose elements all belong to another set
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Subset
2023 edition of the C++ programming language standard
synchronous coroutine std::generator for ranges result type std::expected monadic operations for std::optional and std::expected utility function std::to_underlying
C++23
Microsoft .NET Framework component
arbitrary computations, include the construction of event handlers or monadic parsers. It also defines a set of method names (called standard query operators
Language_Integrated_Query
Adaptation of the Greek philosophical concept
persisted that a young man named Epiphanes, who died at 17, was the leader of Monadic Gnosticism. However, scholars think the legend may have come from a misunderstanding
Monad_(Gnosticism)
Vector logic assumes that the truth values map on vectors, and that the monadic and dyadic operations are executed by matrix operators. "Vector logic"
Vector_logic
Function that preserves distinctness
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Injective_function
System of formal deduction in logic
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Hilbert_system
Sequence of words formed by specific rules
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Formal_language
Class of languages studied in formal language theory in computer science
that ω-regular languages are precisely the ones definable in a particular monadic second-order logic called S1S. Wolfgang Thomas, "Automata on infinite objects
Omega-regular_language
Abstract mathematics problem
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Ross–Littlewood_paradox
Process of repeating items in a self-similar way
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Recursion
Computation model defining an abstract machine
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Turing_machine
Problem in computer science
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Halting_problem
Reasoning for mathematical statements
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Mathematical_proof
Study of computable functions and Turing degrees
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Computability_theory
Axiom of set theory
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Axiom_of_choice
Mathematical model for deduction or proof systems
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Formal_system
Mathematical operation with two operands
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Binary_operation
Mathematical symbol for "greater than"
to the C functions getchar and fgets. In Haskell, the >> function is a monadic operator. It is used for sequentially composing two actions, discarding
Greater-than_sign
Mathematical set formed from two given sets
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Cartesian_product
Non-contradiction of a theory
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Consistency
Mathematical set containing no elements
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Empty_set
Mathematical-logic system based on functions
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Lambda_calculus
Extension of propositional modal logic
)&:=\forall y,xR_{a}y\rightarrow ST_{y}(\phi )\end{aligned}}} Recall that monadic second order logic (MSO) extends first-order logic (FO) with second order
Modal_μ-calculus
Set of the elements not in a given subset
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Complement_(set_theory)
Smallest cardinal strictly greater in size than another cardinal
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Successor_cardinal
Concept in model theory
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Amalgamation_property
Subfield of mathematics
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Mathematical_logic
Measure of algorithmic complexity
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Kolmogorov_complexity
Statement that is taken to be true
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Axiom
Field of computer science
introduced by Alonzo Church in 1962, with specifications being formulas in monadic second-order logic and state machines in the form of digital circuits.
Reactive_synthesis
Method of deriving conclusions
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Rule_of_inference
Impossible task in computing
t {\displaystyle {\rm {FinSat}}} (Theorem 3.15), thus undecidable. The monadic predicate calculus is the fragment where each formula contains only 1-ary
Entscheidungsproblem
One-to-one correspondence
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Bijection
Complexity class used to classify decision problems
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
NP_(complexity)
Standard system of axiomatic set theory
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Zermelo–Fraenkel_set_theory
Proposition in mathematical logic
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Continuum_hypothesis
Set of elements common to all of some sets
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Intersection_(set_theory)
Surveys to judge the success of a new product before its introduction to the market
development, monadic concept-testing surveys must be conducted. Frequently concept testing surveys are described as either monadic, sequential monadic, comparative
Concept_testing
Study of the properties of logical systems
logic (Paul Bernays 1918), (Emil Post 1920) Completeness of first-order monadic predicate logic (Leopold Löwenheim 1915) Completeness of first-order predicate
Metalogic
Any one of the distinct objects that make up a set in set theory
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Element_of_a_set
Variable that stores data about other variables or program structure
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Metavariable
Mathematical problem
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Tarski's high school algebra problem
Tarski's_high_school_algebra_problem
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
List_of_mathematical_proofs
Size of a possibly infinite set
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Cardinal_number
Set of elements in any of some sets
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Union_(set_theory)
Formal language theorem
states that a language is regular if and only if it can be defined in monadic second-order logic (MSO). Since a language is regular if and only if it
Büchi–Elgot–Trakhtenbrot theorem
Büchi–Elgot–Trakhtenbrot_theorem
Notion of equality in type theory
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Identity_type
Theorem for proving more complex theorems
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Lemma_(mathematics)
Mathematical lemma
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Rasiowa–Sikorski_lemma
Algebraic structure
This also reflects the relationship between the monadic logic of quantification (for which monadic Boolean algebras provide an algebraic description)
Interior_algebra
Generalization of depth-first search trees
a graph is a planar graph. A characterization of Trémaux trees in the monadic second-order logic of graphs allows graph properties involving orientations
Trémaux_tree
Basic framework of mathematics
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Foundations_of_mathematics
Mathematical set that can be enumerated
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Countable_set
Type of logical system
consequence relation is decidable. These include propositional logic and monadic predicate logic, which is first-order logic restricted to unary predicate
First-order_logic
Mathematical theory of data types
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Type_theory
Mathematical use of "there exists"
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Existential_quantification
Of a function, an additional effect besides returning a value
effects such as I/O and other stateful computations by replacing them with monadic actions. Functional languages such as Standard ML, Scheme and Scala do
Side effect (computer science)
Side_effect_(computer_science)
Proof that only uses basic techniques
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Elementary_proof
Mathematical proposition equivalent to the axiom of choice
Predicate First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary
Zorn's_lemma
Compiler for Haskell programming language
Later releases added a strictness analyzer and language extensions such as monadic I/O, mutable arrays, unboxed data types, concurrent and parallel programming
Glasgow_Haskell_Compiler
Basis of generic programming
Princ. of Prog. Langs., 1983, pp. 88–98. E. Moggi and Amr Sabry. 2001. Monadic Encapsulation of Effects: A Revised Approach (Extended Version). J. Funct
Parametric_polymorphism
MONADIC
MONADIC
MONADIC
MONADIC
Boy/Male
Anglo Saxon English
Defender.
Male
Chinese
honest, loyal.
Boy/Male
Muslim
Peace. Peaceful. Very safe.
Girl/Female
Australian, Greek, Italian, Latin, Portuguese, Romanian
Violet Flower; Vine Branch
Boy/Male
Hindu, Indian, Kashmiri, Sanskrit
Lord Buddha
Boy/Male
Sikh
One who longs for the divine light, Light of the beloved
Boy/Male
Tamil
Servant
Boy/Male
Hindu, Indian
Drumstick Tree
Boy/Male
Hindu, Indian, Punjabi, Sikh
Clean; Pure
Boy/Male
Hindu
A Raga used in indian music
MONADIC
MONADIC
MONADIC
MONADIC
MONADIC
a.
Alt. of Monadical
a.
Of, pertaining to, or like, a monad, in any of its senses. See Monad, n.