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What (who) is static type inference - definition

SET OF RULES THAT ASSIGN A PROPERTY CALLED TYPE TO VARIOUS CONSTRUCTS A COMPUTER PROGRAM CONSISTS OF, SUCH AS VARIABLES, EXPRESSIONS, FUNCTIONS OR MODULES

Dynamic typing; Static typing; Type systems; Type checking; Type-checking; Dynamically typed; Statically typed language; Dynamically typed language; Typed language; Dynamically-typed; Statically typed; Compile-time type checking; Statically-typed; Dynamicly typed; Dynamic data typing; Typed (programming languages); Static-typing (programming languages); Typechecker; Type checker; Type-checker; Static type; Static types; Type equivalence; Statically typed programming language; Statically-typed programming language; Dynamically-typed language; Existential type; Existential types; Type error; Typing discipline; Static type system; Optional typing; Typechecking; Static type-checking; Static type checking; Runtime type checking; Run-time type checking; Dynamic type checking; Optional type systems; Computational type system; Unified type system; Optional static typing; Dynamic type

type inference

AUTOMATIC DETECTION OF THE DATA TYPE OF AN EXPRESSION IN A PROGRAMMING LANGUAGE

Inferred typing; Type recontruction; Type reconstruction; Typability; Typability problem; Type deduction

<programming> An algorithm for ascribing types to expressions in some language, based on the types of the constants of the language and a set of type inference rules such as f :: A -> B, x :: A --------------------- (App) f x :: B This rule, called "App" for application, says that if expression f has type A -> B and expression x has type A then we can deduce that expression (f x) has type B. The expressions above the line are the premises and below, the conclusion. An alternative notation often used is: G |- x : A where "|-" is the turnstile symbol (LaTeX vdash) and G is a type assignment for the free variables of expression x. The above can be read "under assumptions G, expression x has type A". (As in Haskell, we use a double "::" for type declarations and a single ":" for the infix list constructor, cons). Given an expression plus (head l) 1 we can label each subexpression with a type, using type variables X, Y, etc. for unknown types: (plus :: Int -> Int -> Int) (((head :: [a] -> a) (l :: Y)) :: X) (1 :: Int) We then use unification on type variables to match the partial application of plus to its first argument against the App rule, yielding a type (Int -> Int) and a substitution X = Int. Re-using App for the application to the second argument gives an overall type Int and no further substitutions. Similarly, matching App against the application (head l) we get Y = [X]. We already know X = Int so therefore Y = [Int]. This process is used both to infer types for expressions and to check that any types given by the user are consistent. See also generic type variable, principal type. (1995-02-03)

Type inference

AUTOMATIC DETECTION OF THE DATA TYPE OF AN EXPRESSION IN A PROGRAMMING LANGUAGE

Inferred typing; Type recontruction; Type reconstruction; Typability; Typability problem; Type deduction

Type inference refers to the automatic detection of the type of an expression in a formal language. These include programming languages and mathematical type systems, but also natural languages in some branches of computer science and linguistics.

https://en.wikipedia.org/wiki/Type_inference

Statistical inference

PROCESS OF DEDUCING PROPERTIES OF AN UNDERLYING PROBABILITY DISTRIBUTION BY ANALYSIS OF DATA

InterpretingStatisticalData; Interpreting statistical data; Inferential statistics; Statistical analysis; Non-parametric inference; Inferential Statistics; Inductive strength; Inductive statistics; Statistical induction; Predictive inference; Statistics/Inference; Interpreting Statistical Data; Statistical Inference; Sampling statistics; Prediction theory; Inference (machine learning)

Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability.Upton, G.

https://en.wikipedia.org/wiki/Statistical_inference

Wikipedia

Type system

In computer programming, a type system is a logical system comprising a set of rules that assigns a property called a type (for example, integer, floating point, string) to every "term" (a word, phrase, or other set of symbols). Usually the terms are various constructs of a computer program, such as variables, expressions, functions, or modules. A type system dictates the operations that can be performed on a term. For variables, the type system determines the allowed values of that term. Type systems formalize and enforce the otherwise implicit categories the programmer uses for algebraic data types, data structures, or other components (e.g. "string", "array of float", "function returning boolean").

Type systems are often specified as part of programming languages and built into interpreters and compilers, although the type system of a language can be extended by optional tools that perform added checks using the language's original type syntax and grammar. The main purpose of a type system in a programming language is to reduce possibilities for bugs in computer programs due to type errors. The given type system in question determines what constitutes a type error, but in general, the aim is to prevent operations expecting a certain kind of value from being used with values for which that operation does not make sense (validity errors). Type systems allow defining interfaces between different parts of a computer program, and then checking that the parts have been connected in a consistent way. This checking can happen statically (at compile time), dynamically (at run time), or as a combination of both. Type systems have other purposes as well, such as expressing business rules, enabling certain compiler optimizations, allowing for multiple dispatch, and providing a form of documentation.

https://en.wikipedia.org/wiki/Type system