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Automatic detection of the type of an expression in a formal language
In type theory, type inference (sometimes called type reconstruction) is the automatic detection of the type of an expression. These include programming
Type_inference
Type system used in computer programming and mathematics
most general type of a given program without programmer-supplied type annotations or other hints. Algorithm W is an efficient type inference method in practice
Hindley–Milner_type_system
Steps in reasoning
Aristotle (300s BC). A third type of inference, abduction, has been proposed, notably by Charles Sanders Peirce. Deduction is inference deriving logical conclusions
Inference
Mathematical theory of data types
of type theories is in specifying how terms may be combined by way of inference rules. Type theories which have functions also have the inference rule
Type_theory
General-purpose programming language
(with type inference, and omitting the unnecessary newline): def printValue(x: String) = println("I ate a %s" format x) Due to type inference, the type of
Scala_(programming_language)
Programming language and superset of JavaScript
(annotations) and compile-time type checking Type inference Interfaces Enumerated types Generics Namespaces Tuples Syntactically, TypeScript is very similar to
TypeScript
Process by which explicit type annotations are removed from a program
type inference. Though type erasure can be an easy way to define typing over implicitly typed languages (an implicitly typed term is well-typed if and
Type_erasure
Computer science concept
types, in which type inference is computable. Most Haskell compilers allow arbitrary-rank polymorphism as an extension, but this makes type inference
Type_system
Concept in functional programming
extended algebraic data types which combine GADTs together with the existential data types and type class constraints. Type inference in the absence of any
Generalized algebraic data type
Generalized_algebraic_data_type
Branch of statistics
approaches to causal inference are broadly applicable across all types of scientific disciplines, and many methods of causal inference that were designed
Causal_inference
Basis of generic programming
the type system simple enough that full type inference is always possible. As a practical example, OCaml (a descendant or dialect of ML) performs type inference
Parametric_polymorphism
Study of correct reasoning
formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based
Logic
Extent to which a programming language discourages type errors
Semantics and Polymorphic Type Inference (Thesis). Henriksen, Troels; Elsman, Martin (17 June 2021). "Towards size-dependent types for array programming"
Type_safety
Integer i2) { return i1 + i2; } However, to make single-pass type inference possible, type inference is only allowed for non-toplevel and unshared declarations
Ceylon_(programming_language)
Python to C++ compiler
techniques), until it is fully analyzed. This allows Shed Skin to do type inference on larger programs than previously. It starts with an empty callgraph
Shed_Skin
Type of statistical inference
Frequentist inference is a type of statistical inference based in frequentist probability, which treats "probability" in equivalent terms to "frequency"
Frequentist_inference
Memory-safe dialect of the C programming language
some uses of setjmp and longjmp Namespaces Type inference Pattern matching Templates, parameterized types Cyclone looks, in general, much like C, but
Cyclone (programming language)
Cyclone_(programming_language)
Kind of polymorphism
than nominally) polymorphic on record types and/or variants. A row-polymorphic type system and proof of type inference for records was introduced by Mitchell
Row_polymorphism
Type of types in a type system
with how type schemes with no metavariables are identified with the underlying types, in certain theoretical presentation of ML's type inference algorithm
Kind_(type_theory)
General-purpose functional programming language
modular, functional programming language with compile-time type checking and type inference. It is popular for writing compilers, for programming language
Standard_ML
General-purpose programming language
(/ˈkɒtlɪn/) is a cross-platform, statically typed, general-purpose high-level programming language with type inference. Kotlin is designed to interoperate fully
Kotlin
Programming language
languages: Optional concise variable declaration and initialization through type inference (x := 0 instead of var x int = 0; or var x = 0;) Fast compilation Remote
Go_(programming_language)
Functional programming language
(/ˈhæskəl/) is a general-purpose, statically typed, purely functional programming language with type inference and lazy evaluation. Haskell pioneered several
Haskell
incomparable possible types. Type inference for systems with the principal type property will usually attempt to infer the principal type. For instance, the
Principal_type
Method of deriving conclusions
Rules of inference are ways of deriving conclusions from premises. They are integral parts of formal logic, serving as the logical structure of valid
Rule_of_inference
Language for the .NET platform
detect type errors at compilation time and to perform significant optimizations. For that purpose, it provides type reconstruction (inference), flow-sensitive
StaDyn_(programming_language)
"Learn the fundamentals of the C# type system - C#". learn.microsoft.com. Microsoft. Retrieved 2026-01-25. "Type Inference Crystal". Crystal Language Reference
Comparison of programming languages by type system
Comparison_of_programming_languages_by_type_system
How a type system assigns a type to a syntactic construction
In type theory, a typing rule is an inference rule that describes how a type system assigns a type to a syntactic construction. These rules may be applied
Typing_rule
C++ alternative syntax for return types
the auto keyword indicates type inference. The data type for that x will be deduced from its initialization. The return type of a function can also be
Trailing_return_type
Type information inspection taking place at runtime
Invoke(RttiType.MetaclassType, []).AsObject; try RttiType.GetMethod('Hello').Invoke(Subject, []); finally Subject.Free; end; end; Type inference Type introspection
Run-time_type_information
C programming language standard, current revision
cause type inference while also retaining its old meaning of a storage class specifier if used alongside a type. Unlike C++, C23 allows type inference only
C23_(C_standard_revision)
Types constrained by a predicate
ML, which presents a type system for a subset of Standard ML. The type system "preserves the decidability of ML's type inference" whilst still "allowing
Refinement_type
Object-oriented programming language
dynamic aspects of Ruby. The advanced global type inference used by the Crystal compiler, combined with union types, gives it more the feel of a higher-level
Crystal (programming language)
Crystal_(programming_language)
Formal system in mathematical logic
terms are well-typed via Hindley–Milner type inference. The inference algorithm is terminating, sound, and complete: whenever a term is typable, the algorithm
Simply_typed_lambda_calculus
2011 edition of the C++ programming language standard
element in a: for (int& x : a) { x *= 2; } // similar but also using type inference for array elements for (auto& x : a) { x *= 2; } This form of for, called
C++11
Programming paradigm based on applying and composing functions
intuitionistic type theory, which lets types depend on terms. Such types are called dependent types. These type systems do not have decidable type inference and
Functional_programming
Version of the C# programming language
merely shorthand syntax for anonymous delegates with type inference for parameters and return type. However, depending on the context they are used in
C_Sharp_3.0
Phenomenon in statistics
ill-posed inference problems. Shrinkage is implicit in Bayesian inference and penalized likelihood inference, and explicit in James–Stein-type inference. In
Shrinkage_(statistics)
Concept in programming language design
Shroff, Scott F. Smith. Type Inference for First-Class Messages with Match-Functions Bove, Ana; Dybjer, Peter (2009). "Dependent Types at Work" (PDF). Language
First-class_citizen
Component of artificial intelligence systems
an 'inference engine' could refer to the specific part of the system, or even the hardware, that executes these operations. This type of inference plays
Inference_engine
Class of type systems
expected type is declared (i.e., not inferred), e.g., only substitute for functions that are signature-based polymorphic via type inference. Then it is
Structural_type_system
Microsoft programming language
functional features are: Everything is an expression Type inference (using Hindley–Milner type inference) Functions as first-class citizens Anonymous functions
F Sharp (programming language)
F_Sharp_(programming_language)
changes with each recursive invocation made, instead of staying constant. Type inference for polymorphic recursion is equivalent to semi-unification and therefore
Polymorphic_recursion
Explicit identification of variable type
compile-time type membership of the object and its run-time type identity. In contrast, some programming languages use implicit typing (a.k.a. type inference) where
Manifest_typing
Free and open source compiler for the Python programming language
such as constant folding and propagation, built-in call prediction, type inference, and conditional statement execution. Nuitka initially was designed
Nuitka
In programming languages with Hindley–Milner type inference and imperative features, in particular the ML programming language family, the value restriction
Value_restriction
Set of objects whose state must satisfy limits
problems that can be modeled as a constraint satisfaction problem include: Type inference Eight queens puzzle Map coloring problem Maximum cut problem Sudoku
Constraint satisfaction problem
Constraint_satisfaction_problem
Programming languages with runtime extensibility
with a dynamic type system, runtime inference of types based on values for internal interpretation marks a common task. As value types may change throughout
Dynamic_programming_language
General purpose functional programming language
prover in the 1970s. It is an early statically typed, functional language with polymorphic type inference in the Hindley–Milner style, and other features
ML_(programming_language)
Programming language concept
inference for existential types is a difficult problem. For the compiler implementer, Java wildcards raise issues with type checker termination, type
Type_variance
Gradually typed dialect of Lua
code or leave it dynamically typed. The type system includes type inference, which automatically determines variable types based on usage without requiring
Luau_(programming_language)
Set of rules defining correctly structured programs for the C# programming language
multiple variables of the same type This is a feature of C# 3.0. C# 3.0 introduced type inference, allowing the type specifier of a variable declaration
C_Sharp_syntax
Logical problem studied in computer science
Outside of software verification, SMT solvers have also been used for type inference and for modelling theoretic scenarios, including modelling actor beliefs
Satisfiability modulo theories
Satisfiability_modulo_theories
Memory allocation scheme
type polymorphism and higher-order functions in Standard ML, a functional programming language, using a different algorithm based on type inference and
Region-based memory management
Region-based_memory_management
British logician
Hindley is a prominent British logician best known for the Hindley–Milner type inference algorithm. Since 1998, he has been an Honorary Research Fellow at Swansea
J._Roger_Hindley
Algorithmic process of solving equations
programming and programming language type system implementation, especially in Hindley–Milner based type inference algorithms. In higher-order unification
Unification (computer science)
Unification_(computer_science)
Type system in computer science
the state type accessible from m is uniquely determined. This aids the compiler in type inference, as well as aiding the programmer in type-directed programming
Type_class
Type system
Gradual Type Inference" (PDF). Association for Computing Machinery (ACM). Archived from the original (PDF) on 2017-08-12. Retrieved 2014-09-23. "type-system-j"
Gradual_typing
Logical inference from a single statement
invalid immediate inferences which are syllogistic fallacies. Given a type E statement, "No S are P.", one can make the immediate inference that "No P are
Immediate_inference
List of versions of the Java programming language
these JEP 286 Local-Variable Type Inference, allows the var keyword to be used for local variables with the actual type calculated by the compiler. Due
Java_version_history
Programming language
written in a functional style. Other notable features include: strong type inference a flexible metaprogramming subsystem (using macros) full support for
Nemerle
Representation of an expression as a generalized graph
applications. Term graphs are also used in type inference, where the graph structure aids in implementing type unification. Term (logic) Graph rewriting
Term_graph
Method of statistical inference
Bayesian inference (/ˈbeɪziən/ BAY-zee-ən or /ˈbeɪʒən/ BAY-zhən) is a method of statistical inference in which Bayes' theorem is used to calculate a probability
Bayesian_inference
General-purpose programming language
on a more concise syntax and some additional functionality such as type inference, extension methods, and operator overloading. Being primarily an object-oriented
Xtend
Data type for values having two types
types. Consequently, type inference for infinite-intersection types is undecidable, but it is decidable for all finite rank intersection types. TypeScript
Intersection_type
Form of reasoning
Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that
Deductive_reasoning
type system. The interpreter is written in Modula-3, and provides Obliq with full access to Modula-3's network objects capabilities. A type inference
Obliq
Object Pascal-based programming language
a := 23;// type inference var b := 15; DoSwap<Integer>(a, b); // no downcasting to Object in this method. var aa := 'abc';// type inference var bb := 'def';
Oxygene (programming language)
Oxygene_(programming_language)
Inference seeking the simplest and most likely explanation
Abductive reasoning (also called abduction, abductive inference, or retroduction) is a form of logical inference that seeks the simplest and most likely conclusion
Abductive_reasoning
Universal subtype in logic and computer science
Top and Bot seems to be a natural target for type inference, allowing the constraints on an omitted type parameter to be captured by a pair of bounds:
Bottom_type
Compiler for Haskell programming language
language as possible until after type inference is complete, toward the goal of providing clear error messages to users. After type checking, the Haskell code
Glasgow_Haskell_Compiler
Topics referred to by the same term
language used to declare automatic variables A keyword in C++11 used for type inference Motorists for Themselves (Czech: Motoristé sobě, formally abbreviated
Auto
Multi-paradigm system programming language
design by contract, ranges, built-in container iteration concepts, and type inference. D's declaration, statement and expression syntaxes also closely match
D_(programming_language)
Rules defining correctly structured Java programs
classes and all values are objects. The only exception is the primitive data types, which are not considered to be objects for performance reasons (though
Java_syntax
Language for controlling a computer
on context. The downside of implicit typing is the potential for errors to go undetected. Complete type inference has traditionally been associated with
Programming_language
Numerical programming library for the OCaml programming language
efficiency, flexible module system, static type checking, intelligent garbage collector, and powerful type inference. Owl inherits these features directly
Owl_Scientific_Computing
Programming language
Programming Languages Software Award. OCaml features a static type system, type inference, parametric polymorphism, tail recursion, pattern matching, first
OCaml
Typed lambda calculus
system, System F is strongly normalizing. However, type inference in System F (without explicit type annotations) is undecidable. Under the Curry–Howard
System_F
Programming language
supports interfaces, mixins, abstract classes, reified generics and type inference. The latest version of Dart is 3.12.2 . Dart was unveiled at the GOTO
Dart_(programming_language)
any platform for which an ANSI C compiler exists. Liberty Eiffel uses type inference to make it possible to implement a more efficient compiler. Liberty
LibertyEiffel
Programming language
properties, generics, assisted memory management, exception handling, type inference, and foreach statements. Its developers, Jürg Billeter and Raffaele
Vala_(programming_language)
Proof assistant
implements a bidirectional type inference algorithm exploiting both inferred and expected types. The power of the type inference system (refiner) is further
Matita
Using one interface or symbol with regards to multiple different types
Polymorphism". Types and Programming Languages. MIT Press. pp. 340–1. ISBN 9780262162098. Wand, Mitchell (June 1989). "Type inference for record concatenation
Polymorphism (computer science)
Polymorphism_(computer_science)
Programming language
2012. Since version 2, Groovy can be compiled statically, offering type inference and performance near that of Java. Groovy 2.4 was the last major release
Apache_Groovy
not have a named type, they must be stored in variables declared using the var keyword, telling the C# compiler to use type inference for the variable
Anonymous_type
Theorem in computability theory
In the case of type safety, the former corresponds to type annotations, and the latter corresponds to type inference. Taken beyond type safety, this idea
Rice's_theorem
Programming language for stream generation
webserver back-end and more. The language is functional, statically typed with type inference. The language is an original one, but the interpreter is programmed
Liquidsoap
Functional programming language
dictionaries in the standard library. Elm is statically typed. Type annotations are optional (due to type inference) but strongly encouraged. Annotations exist on
Elm_(programming_language)
Computer algebra system
Within the interpreter environment, Axiom uses type inference and a heuristic algorithm to make explicit type annotations mostly unnecessary. It features
Axiom (computer algebra system)
Axiom_(computer_algebra_system)
Set of rules defining correctly structured programs
compile-time type checking Type inference Interfaces Enumerated types Generics Namespaces Tuples Explicit resource management Syntactically, TypeScript is
JavaScript_syntax
Overview of and topical guide to Rust
matching Serialization Smart pointers Strings Tuples and structs Traits Type inference Unit testing Variables Compile time performance Ecosystem maturity rustc
Outline of the Rust programming language
Outline_of_the_Rust_programming_language
British computer scientist (1934–2010)
the first language with polymorphic type inference, type-safe exception handling, and an automatically inferred type system, using algorithm W. Milner also
Robin_Milner
American computer scientist
WYRE-ik) is an American computer scientist specializing in type theory, type inference, dependent types, and functional programming. She is a professor of computer
Stephanie_Weirich
General-purpose programming language
keywords, additional meaning for auto to provide type inference when declaring variables, new types including nullptr_t and _BitInt(N), and expansions
C_(programming_language)
Examining complex systems as a whole
theory, in constraint satisfaction problems, the unification algorithm, type inference, and so forth. Systems thinking, born from the visionary contributions
Systems_thinking
One of a number of different types of statistical inference
Fiducial inference is one of a number of different types of statistical inference. These are rules, intended for general application, by which conclusions
Fiducial_inference
Method of logical reasoning
provided. The types of inductive reasoning include generalization, prediction, statistical syllogism, argument from analogy, and causal inference. There are
Inductive_reasoning
Branch of computer science
abstract typed functional language. In 1978, Robin Milner introduces the Hindley–Milner type system inference algorithm for ML language. Type theory became
Programming_language_theory
extensibility. Some features of note include type inference, generators, multimethods, optional duck typing, macros, true closures, currying, and first-class
Boo_(programming_language)
Process of logical induction or deduction during reading
the actress fell from the 14th story." This type of inference is also referred to as a "predictive inference" because the reader is inferring something
Text_inferencing
TYPE INFERENCE
TYPE INFERENCE
Girl/Female
Arabic, Muslim, Pashtun
Type of Flower
Girl/Female
Danish, German, Swedish
A City in Phoenicia
Girl/Female
Christian & English(British/American/Australian)
River
Boy/Male
English French
Fiery.
Surname or Lastname
Irish
Irish : reduced Anglicized form of Gaelic Ó Teimhin ‘descendant of Teimhean’, from teimhean ‘dark’, an adjective from teimhe ‘dusk’, ‘darkness’.English : probably a habitational name for someone from Tyneside in northeast England.
Surname or Lastname
English (Devon)
English (Devon) : unexplained.
Girl/Female
Indian
Type of flower
Girl/Female
Tamil
Anemone | அநேமோநே
Type of flower
Anemone | அநேமோநே
Male
Danish
, a female dog; or, the mad, raging.
Surname or Lastname
English (mainly East Anglia)
English (mainly East Anglia) : topographic name for someone who lived by a common pasture, Middle English tye (Old English tēag).North German : from a short form, Tide, of the personal name Dietrich.
Boy/Male
Hindu, Indian
Type of Liquid
Male
Danish
, a female dog; or, the mad, raging.
Male
English
English surname transferred to forename use, derived from the Middle English word tye, TYE means "pasture."
Surname or Lastname
Scottish
Scottish : reduced form of McIntyre.English : variant spelling of Tyer.
Girl/Female
Indian, Telugu
Type of Music
Boy/Male
Sikh
Ok type person
Boy/Male
Biblical Latin
Strength; rock; sharp.
Girl/Female
English
River.
Girl/Female
American, British, English, Jamaican
A River in England; River
Girl/Female
Muslim
Type of flower
TYPE INFERENCE
TYPE INFERENCE
Girl/Female
Hindu, Indian
Render to the God
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Sanskrit, Tamil, Telugu, Traditional
Beautiful; Wish-yielding Cow; Fragrance
Boy/Male
Indian, Sanskrit
Like a Bull
Boy/Male
Indian, Sanskrit
Self Restrained
Girl/Female
Indian, Telugu
Silent
Boy/Male
American, Australian, British, Christian, Dutch, English, French, Greek, Latin, Portuguese, Shakespearean
Strong; Courageous; Healthy
Female
English
German form of Latin Susanna, SUSANNE means "lily."
Girl/Female
Indian
Beautiful, White
Surname or Lastname
English
English : from Cocke in any the senses described + the suffix -s denoting ‘son of’ or ‘servant of’.Irish (Ulster) : mistranslation of Mac Con Coille (‘son of Cú Choille’, a personal name meaning ‘hound of the wood’), as if formed with coileach ‘cock’, ‘rooster’.
Girl/Female
Indian, Sikh
Happy; Happiness
TYPE INFERENCE
TYPE INFERENCE
TYPE INFERENCE
TYPE INFERENCE
TYPE INFERENCE
n.
A simple compound, used as a mode or pattern to which other compounds are conveniently regarded as being related, and from which they may be actually or theoretically derived.
n.
A narrow fillet or band of cotton or linen; a narrow woven fabric used for strings and the like; as, curtains tied with tape.
n.
Form or character impressed; style; semblance.
v. t.
To represent by a type, model, or symbol beforehand; to prefigure.
n.
A grove or clump of trees; as, a toddy tope.
v. t.
To furnish an expression or copy of; to represent; to typify.
imp. & p. p.
of Type
v. t.
To arrange (types) in a composing stick in order for printing; to set (type).
n.
A general form or structure common to a number of individuals; hence, the ideal representation of a species, genus, or other group, combining the essential characteristics; an animal or plant possessing or exemplifying the essential characteristics of a species, genus, or other group. Also, a group or division of animals having a certain typical or characteristic structure of body maintained within the group.
n.
That which possesses or exemplifies characteristic qualities; the representative.
n.
A single type; type, collectively; a style of type.
n.
The mark or impression of something; stamp; impressed sign; emblem.
n.
A raised letter, figure, accent, or other character, cast in metal or cut in wood, used in printing.
n.
Such letters or characters, in general, or the whole quantity of them used in printing, spoken of collectively; any number or mass of such letters or characters, however disposed.
n.
A tapeline; also, a metallic ribbon so marked as to serve as a tapeline; as, a steel tape.
n.
In the antler of a stag, the third tyne above the base. This tyne appears in the third year. In those deer in which the brow tyne does not divide, the tres-tyne is the second tyne above the base. See Illust. under Rucervine, and under Rusine.
n.
The original object, or class of objects, scene, face, or conception, which becomes the subject of a copy; esp., the design on the face of a medal or a coin.
n.
A combining form signifying impressed form; stamp; print; type; typical form; representative; as in stereotype phototype, ferrotype, monotype.
a.
Relating to a type or types; belonging to types; serving as a type; typical.
n.
A figure or representation of something to come; a token; a sign; a symbol; -- correlative to antitype.