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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 and Scala. See also * Liquid Haskell * Dependent types In computer science and logic, a dependent type i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Theory
In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general 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 were proposed as foundations are Alonzo Church's typed λ-calculus and Per Martin-Löf's intuitionistic type theory. 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 a paradox in a mathematical foundation based on naive set theory and formal logic. Russell's paradox, which was discovered by Bertrand Russell, existed because a set could be defined using "all possible sets", which included itself. Between 1902 and 1908, Bertrand Russell proposed various "theories of type" to fix the problem. By 1908 Russell arrived at a "ramified" theory ... [...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. Security problems can arise due to incorrect preconditions. 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. For example: the factorial is only defined for integers greater than or equal to zero. So a program that calculates the factorial of an input number would have preconditions that the number be an integer and that it be greater than or equal to zero. In object-oriented programming Preconditions in object-oriented software development are an es ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Argument
In computer programming, a parameter or a formal argument is a special kind of variable used in a subroutine to refer to one of the pieces of data provided as input to the subroutine. These pieces of data are the values of the arguments (often called ''actual arguments'' or ''actual parameters'') with which the subroutine is going to be called/invoked. An ordered list of parameters is usually included in the definition of a subroutine, so that, each time the subroutine is called, its arguments for that call are evaluated, and the resulting values can be assigned to the corresponding parameters. Unlike ''argument'' in usual mathematical usage, the ''argument'' in computer science is the actual input expression passed/supplied to a function, procedure, or routine in the invocation/call statement, whereas the ''parameter'' is the variable inside the implementation of the subroutine. For example, if one defines the add subroutine as def add(x, y): return x + y, then x, y are paramet ... [...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 softwar ... [...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) 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 the code that invoked it when it completes all the statements in the method, reaches a return statement, or throws an exception, whichever occurs first. You declare a method's return type in its method declaration. Within the body of the method, you use t ... [...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 Queue ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard ML
Standard ML (SML) is a general-purpose, modular, functional programming language with compile-time type checking and type inference. It is popular among compiler writers and programming language researchers, as well as in the development of theorem provers. Standard ML is a modern dialect of 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 expressions as opposed to statements or commands, although some expressions of type unit are only evaluated for their side-effects. Functions Like all functional languages, a key feature of Standard ML is the function, which is used for abstraction. The factorial function can be expressed as follows: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haskell (programming Language)
Haskell () is a general-purpose, statically-typed, purely functional programming language with type inference and lazy evaluation. Designed for teaching, research and industrial applications, Haskell has pioneered a number of programming language features such as type classes, which enable type-safe operator overloading, and monadic IO. Haskell's main implementation is the Glasgow Haskell Compiler (GHC). It is named after logician Haskell Curry. Haskell's semantics are historically based on those of the 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 academia and industry. , Haskell was the 28th most popular programming language by Google searches for tutorials, and made up less than 1% of active users on the GitHub source code repository. History ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TypeScript
TypeScript is a free and open source programming language A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming ... developed and maintained by Microsoft. It is a strict syntactical superset of JavaScript and adds optional static typing to the language. It is designed for the development of large applications and source-to-source compiler, transpiles to JavaScript. As it is a superset of JavaScript, existing JavaScript programs are also valid TypeScript programs. TypeScript may be used to develop JavaScript applications for both client-side and server-side execution (as with Node.js or Deno (software), Deno). Multiple options are available for transpilation. The default TypeScript Compiler can be used, or the Babel (transcompiler), Babel compiler can be invoked to convert TypeScript to J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scala (programming Language)
Scala ( ) is a strong statically typed general-purpose programming language that supports both object-oriented programming and functional programming. Designed to be concise, many of Scala's design decisions are aimed 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 compiled to JavaScript to run in a browser, or directly to a native executable. 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 Java, Scala has many features of functional prog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liquid Haskell
Liquid Haskell is a program verifier for the programming language Haskell which allows specifying correctness properties by using refinement types. Properties are verified using a satisfiability modulo theories (SMT) solver which is SMTLIB2-compliant, such as the Z3 Theorem Prover. See also * Formal verification In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal met ... References * * Further reading * * External links * * Formal methods tools Static program analysis tools Type systems Free software programmed in Haskell Software using the BSD license {{Free-software-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dependent Types
In computer science and logic, a dependent type is a type whose definition depends on a value. It is an overlapping feature of type theory and type systems. In intuitionistic type theory, dependent types are used to encode logic's quantifiers like "for all" and "there exists". In functional programming languages like Agda, ATS, Coq, F*, Epigram, and Idris, dependent types help reduce bugs by enabling the programmer to assign types that further restrain the set of possible implementations. Two common examples of dependent types are ''dependent functions'' and ''dependent pairs''. The return type of a dependent function may depend on the ''value'' (not just type) of one of its arguments. For instance, a function that takes a positive integer n may return an array of length n, where the array length is part of the type of the array. (Note that this is different from polymorphism and generic programming, both of which include the type as an argument.) A dependent pair may have a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
