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Refinement Type
In type theory, a refinement type is a type endowed with a predicate which is assumed to hold for any element of the refined type. Refinement types can express preconditions when used as function arguments or postconditions when used as return types: for instance, the type of a function which accepts natural numbers and returns natural numbers greater than 5 may be written as f: \mathbb \rarr \. Refinement types are thus related to behavioral subtyping. History The concept of refinement types was first introduced in Freeman and Pfenning's 1991 ''Refinement types for 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 more errors to be detected at compile-time". In more recent times, refinement type systems have been developed for languages such as Haskell, TypeScript, Rust Rust is an iron oxide, a usually reddish-brown oxide formed by the reaction of iron and oxygen in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Theory
In mathematics and theoretical computer science, a type theory is the formal presentation of a specific type system. Type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that have been proposed as foundations are: * Typed λ-calculus of Alonzo Church * Intuitionistic type theory of Per Martin-Löf Most computerized proof-writing systems use a type theory for their foundation. A common one is Thierry Coquand's Calculus of Inductive Constructions. History Type theory was created to avoid paradoxes in naive set theory and formal logic, such as Russell's paradox which demonstrates that, without proper axioms, it is possible to define the set of all sets that are not members of themselves; this set both contains itself and does not contain itself. Between 1902 and 1908, Bertrand Russell proposed various solutions to this problem. By 1908, Russell arrive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Precondition
In computer programming, a precondition is a condition or predicate that must always be true just prior to the execution of some section of code or before an operation in a formal specification. If a precondition is violated, the effect of the section of code becomes undefined and thus may or may not carry out its intended work. Preconditions that are missing, insufficient, or not formally proved (or have an incorrect attempted proof), or are not checked statically or dynamically, can give rise to Security problems, particularly in unsafe languages that are not strongly typed. Often, preconditions are simply included in the documentation of the affected section of code. Preconditions are sometimes tested using guards or assertions within the code itself, and some languages have specific syntactic constructions for doing so. Example The factorial function is only defined where its parameter is an integer greater than or equal to zero. So an implementation of the factorial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Argument
In mathematics, an argument of a function is a value provided to obtain the function's result. It is also called an independent variable. For example, the binary function f(x,y) = x^2 + y^2 has two arguments, x and y, in an ordered pair (x, y). The hypergeometric function is an example of a four-argument function. The number of arguments that a function takes is called the ''arity'' of the function. A function that takes a single argument as input, such as f(x) = x^2, is called a unary function. A function of two or more variables is considered to have a domain consisting of ordered pairs or tuples of argument values. The argument of a circular function is an angle. The argument of a hyperbolic function is a hyperbolic angle. A mathematical function has one or more arguments in the form of independent variables designated in the definition, which can also contain parameters. The independent variables are mentioned in the list of arguments that the function takes, whereas the par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Postcondition
In computer programming, a postcondition is a condition or predicate that must always be true just after the execution of some section of code or after an operation in a formal specification. Postconditions are sometimes tested using assertions within the code itself. Often, postconditions are simply included in the documentation of the affected section of code. For example: The result of a factorial is always an integer and greater than or equal to 1. So a program that calculates the factorial of an input number would have postconditions that the result after the calculation be an integer and that it be greater than or equal to 1. Another example: a program that calculates the square root of an input number might have the postconditions that the result be a number and that its square be equal to the input. Postconditions in object-oriented programming In some software design approaches, postconditions, along with preconditions and class invariants, are components of the softw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Return Type
In computer programming, the return type (or result type) defines and constrains the data type of the value returned from a subroutine or method. In many programming languages (especially statically-typed programming languages such as C, C++, Java Java is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea (a part of Pacific Ocean) to the north. With a population of 156.9 million people (including Madura) in mid 2024, proje ...) the return type must be explicitly specified when declaring a function. In the Java example: public void setShuma(int n1, int n2) public int getShuma() the return type is . The program can therefore rely on the method returning a value of type . Various mechanisms are used for the case where a subroutine does not return any value, e.g., a return type of is used in some programming languages: public void returnNothing() Returning a value from a method A method returns to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Behavioral Subtyping
In object-oriented programming, behavioral subtyping is the principle that subclasses should satisfy the expectations of clients accessing subclass objects through references of superclass type, not just as regards syntactic safety (such as the absence of "method-not-found" errors) but also as regards behavioral correctness. Specifically, properties that clients can prove using the specification of an object's presumed type should hold even though the object is actually a member of a subtype of that type. For example, consider a type Stack and a type Queue, which both have a ''put'' method to add an element and a ''get'' method to remove one. Suppose the documentation associated with these types specifies that type Stack's methods shall behave as expected for stacks (i.e. they shall exhibit LIFO behavior), and that type Queue's methods shall behave as expected for queues (i.e. they shall exhibit FIFO behavior). Suppose, now, that type Stack was declared as a subclass of type Queu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frank Pfenning
Frank Pfenning is a German-American professor of computer science, adjunct professor in philosophy, and was head of the Computer Science Department at Carnegie Mellon University from 2013 to 2018. Education and career Pfenning grew up in Rüsselsheim am Main, Rüsselsheim in Germany and studied mathematics and computer science at Technische Universität Darmstadt in Germany. He attended Carnegie Mellon University after receiving a Fulbright Scholarship, and subsequently became a professor in Carnegie Mellon's Computer Science Department. His research includes work in the area of programming language theory, programming languages, logic and type theory, LF (logical framework), logical frameworks, automated theorem proving, automated deduction, and trustworthy computing. He is one of the principal authors of the Twelf system. He also developed Carnegie Mellon's introductory imperative programming course for undergraduates and the C0 programming language used in this course. Hono ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard ML
Standard ML (SML) is a General-purpose programming language, general-purpose, High-level programming language, high-level, Modular programming, modular, Functional programming, functional programming language with compile-time type checking and type inference. It is popular for writing compilers, for programming language research, and for developing automated theorem proving, theorem provers. Standard ML is a modern dialect of ML (programming language), ML, the language used in the Logic for Computable Functions (LCF) theorem-proving project. It is distinctive among widely used languages in that it has a formal specification, given as typing rules and operational semantics in ''The Definition of Standard ML''. Language Standard ML is a functional programming language with some impure features. Programs written in Standard ML consist of Expression (computer science), expressions in contrast to statements or commands, although some expressions of type Unit type, unit are only eva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haskell (programming Language)
Haskell () is a General-purpose programming language, general-purpose, static typing, statically typed, purely functional programming, purely functional programming language with type inference and lazy evaluation. Designed for teaching, research, and industrial applications, Haskell pioneered several programming language #Features, features such as type classes, which enable type safety, type-safe operator overloading, and Monad (functional programming), monadic input/output (IO). It is named after logician Haskell Curry. Haskell's main implementation is the Glasgow Haskell Compiler (GHC). Haskell's Semantics (computer science), semantics are historically based on those of the Miranda (programming language), Miranda programming language, which served to focus the efforts of the initial Haskell working group. The last formal specification of the language was made in July 2010, while the development of GHC continues to expand Haskell via language extensions. Haskell is used in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TypeScript
TypeScript (abbreviated as TS) is a high-level programming language that adds static typing with optional type annotations to JavaScript. It is designed for developing large applications and transpiles to JavaScript. It is developed by Microsoft as free and open-source software released under an Apache License 2.0. TypeScript may be used to develop JavaScript applications for both client-side and server-side execution (as with Node.js, Deno or Bun). Multiple options are available for transpiling. The default TypeScript Compiler can be used, or the Babel compiler can be invoked to convert TypeScript to JavaScript. TypeScript supports definition files that can contain type information of existing JavaScript libraries, much like C++ header files can describe the structure of existing object files. This enables other programs to use the values defined in the files as if they were statically typed TypeScript entities. There are third-party header files for popular li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rust (programming Language)
Rust is a General-purpose programming language, general-purpose programming language emphasizing Computer performance, performance, type safety, and Concurrency (computer science), concurrency. It enforces memory safety, meaning that all Reference (computer science), references point to valid memory. It does so without a conventional Garbage collection (computer science), garbage collector; instead, memory safety errors and data races are prevented by the "borrow checker", which tracks the object lifetime of references Compiler, at compile time. Rust does not enforce a programming paradigm, but was influenced by ideas from functional programming, including Immutable object, immutability, higher-order functions, algebraic data types, and pattern matching. It also supports object-oriented programming via structs, Enumerated type, enums, traits, and methods. It is popular for systems programming. Software developer Graydon Hoare created Rust as a personal project while working at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scala (programming Language)
Scala ( ) is a strongly statically typed high-level general-purpose programming language that supports both object-oriented programming and functional programming. Designed to be concise, many of Scala's design decisions are intended to address criticisms of Java. Scala source code can be compiled to Java bytecode and run on a Java virtual machine (JVM). Scala can also be transpiled to JavaScript to run in a browser, or compiled directly to a native executable. When running on the JVM, Scala provides language interoperability with Java so that libraries written in either language may be referenced directly in Scala or Java code. Like Java, Scala is object-oriented, and uses a syntax termed '' curly-brace'' which is similar to the language C. Since Scala 3, there is also an option to use the off-side rule (indenting) to structure blocks, and its use is advised. Martin Odersky has said that this turned out to be the most productive change introduced in Scala 3. Unlike J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
