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Value Restriction
In programming languages with Hindley–Milner type system, Hindley-Milner type inference and Imperative programming, imperative features, in particular the ML (programming language), ML programming language family, the value restriction means that declaration (computer science), declarations are only parametric polymorphism, polymorphically let generalization, generalized if they are syntactic values (also called ''non-expansive''). The value restriction prevents reference cells from holding values of different types and preserves type safety. A Counter Example to Type Safety In the Hindley–Milner type system, expressions can be given multiple types through parametric polymorphism. But naively giving multiple types to references breaks type safety. The following are typing rules for references and related operators in ML (programming language), ML-like languages. \begin \mathtt &: \forall \alpha . \alpha \to (\alpha\ \mathtt) \\ \mathtt &: \forall \alpha . (\alpha\ \mathtt) \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hindley–Milner Type System
A Hindley–Milner (HM) type system is a classical type system for the lambda calculus with parametric polymorphism. It is also known as Damas–Milner or Damas–Hindley–Milner. It was first described by J. Roger Hindley and later rediscovered by Robin Milner. Luis Damas contributed a close formal analysis and proof of the method in his PhD thesis. Among HM's more notable properties are its completeness and its ability to infer the 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, and has been successfully applied on large code bases, although it has a high theoretical complexity.Hindley–Milner type inference is DEXPTIME-complete. In fact, merely deciding whether an ML program is typeable (without having to infer a type) is itself DEXPTIME-complete. Non-linear behaviour does manifest itself, yet mostly on pathological inputs. Thus the complexity theoretic proofs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Type
In the area of mathematical logic and computer science known as type theory, a unit type is a type that allows only one value (and thus can hold no information). The carrier (underlying set) associated with a unit type can be any singleton set. There is an isomorphism between any two such sets, so it is customary to talk about ''the'' unit type and ignore the details of its value. One may also regard the unit type as the type of 0-tuples, i.e. the product of no types. The unit type is the terminal object in the category of types and typed functions. It should not be confused with the ''zero'' or bottom type, which allows ''no'' values and is the initial object in this category. Similarly, the Boolean is the type with ''two'' values. The unit type is implemented in most functional programming languages. The void type that is used in some imperative programming languages serves some of its functions, but because its carrier set is empty, it has some limitations (as detailed b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LISP And Symbolic Computation
''Higher-Order and Symbolic Computation'' (formerly ''LISP and Symbolic Computation''; print: , online: ) was a computer science academic journal, journal published by Springer Science+Business Media. It focuses on programming concepts and abstractions and programming language theory. The final issue appeared in 2013. Editors Former Editor-in-chief, editors-in-chief of the journal have been: * Richard P. Gabriel, Sun Microsystems, Inc., USA (1988 – 1991) * Guy L. Steele, Jr., Guy L. Steele Jr., Sun Microsystems, Inc., USA (1988 – 1991) * Robert R. Kessler, University of Utah, USA (1991 – 1998) The last editors-in-chief were Olivier Danvy (Aarhus University) and Carolyn Talcott (SRI International). Abstracting and indexing The journal is abstracted and indexed in InfoTrac, Academic OneFile, ACM Computing Reviews, Association for Computing Machinery, ACM Digital Library, Computer Abstracts International Database, Computer Science Index, Current Abstracts, EB ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John C
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died c. AD 30), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (lived c. AD 30), one of the twelve apostles of Jesus * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mads Tofte
Mads Tofte (born 20 April 1959) is a Danish computer scientist who has contributed in particular to functional programming and the Standard ML programming language. Education Tofte was born in Lyngby, Denmark and grew up in Holbæk, Denmark. He studied computer science and mathematics at the University of Copenhagen where he obtained an MSc degree (with supervisor Neil D. Jones) in 1984; then at University of Edinburgh where he obtained a PhD degree in 1988 (advised by Robin Milner). He is doctor honoris causa 2007 from Kingston University. Research and career In his 1984 MSc thesis and prior work he investigated and formalized the CERES compiler generator (with Neil D. Jones), and showed that (1) a compiler generator is itself a compiler from language definitions to compilers; and (2) under suitable assumptions there exists a language definition that, when applied to itself, generates a compiler generator. This has close connections to self-application in partial evaluati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unification (computer Science)
In logic and computer science, unification is an algorithmic process of solving equations between symbolic expressions. Depending on which expressions (also called ''terms'') are allowed to occur in an equation set (also called ''unification problem''), and which expressions are considered equal, several frameworks of unification are distinguished. If higher-order variables, that is, variables representing functions, are allowed in an expression, the process is called higher-order unification, otherwise first-order unification. If a solution is required to make both sides of each equation literally equal, the process is called syntactic or free unification, otherwise semantic or equational unification, or E-unification, or unification modulo theory. A ''solution'' of a unification problem is denoted as a substitution, that is, a mapping assigning a symbolic value to each variable of the problem's expressions. A unification algorithm should compute for a given problem a ''complete' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Variables And Bound Variables
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively. The idea is related to a placeholder (a symbol that will later be replaced by some value), or a wildcard character that stands for an unspecified symbol. In computer programming, the term free variable refers to variables used in a function that are neither local variables nor parameters of that function. The term non-local variable is often a synonym in this context. A bound variable, in contrast, is a variable that has been ''bound'' to a specific value or range of values in the domain of discourse or universe. This may be achieved through the use of logical q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operational Semantics
Operational semantics is a category of formal programming language semantics in which certain desired properties of a program, such as correctness, safety or security, are verified by constructing proofs from logical statements about its execution and procedures, rather than by attaching mathematical meanings to its terms ( denotational semantics). Operational semantics are classified in two categories: structural operational semantics (or small-step semantics) formally describe how the ''individual steps'' of a computation take place in a computer-based system; by opposition natural semantics (or big-step semantics) describe how the ''overall results'' of the executions are obtained. Other approaches to providing a formal semantics of programming languages include axiomatic semantics and denotational semantics. The operational semantics for a programming language describes how a valid program is interpreted as sequences of computational steps. These sequences then ''are'' t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imperative Programming
In computer science, imperative programming is a programming paradigm of software that uses statements that change a program's state. In much the same way that the imperative mood in natural languages expresses commands, an imperative program consists of commands for the computer to perform. Imperative programming focuses on describing ''how'' a program operates step by step, rather than on high-level descriptions of its expected results. The term is often used in contrast to declarative programming, which focuses on ''what'' the program should accomplish without specifying all the details of ''how'' the program should achieve the result. Imperative and procedural programming Procedural programming is a type of imperative programming in which the program is built from one or more procedures (also termed subroutines or functions). The terms are often used as synonyms, but the use of procedures has a dramatic effect on how imperative programs appear and how they are constructed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Typing Rule
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 by the type system to determine if a program is well-typed and what type expressions have. A prototypical example of the use of typing rules is in defining type inference in the simply typed lambda calculus, which is the internal language of Cartesian closed categories. Notation Typing rules specify the structure of a ''typing relation'' that relates syntactic terms to their types. Syntactically, the typing relation is usually denoted by a colon, so for example e\!:\!\tau denotes that an expression e has type \tau. The rules themselves are usually specified using the notation of natural deduction. For example, the following typing rules specify the typing relation for a simple language of booleans: : \frac \qquad \frac \qquad \frac Each rule states that the conclusion below the line may be derived from the premises above t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Safety
In computer science, type safety and type soundness are the extent to which a programming language discourages or prevents type errors. Type safety is sometimes alternatively considered to be a property of facilities of a computer language; that is, some facilities are type-safe and their usage will not result in type errors, while other facilities in the same language may be type-unsafe and a program using them may encounter type errors. The behaviors classified as type errors by a given programming language are usually those that result from attempts to perform operations on values that are not of the appropriate data type, e.g., adding a string to an integer when there's no definition on how to handle this case. This classification is partly based on opinion. Type enforcement can be static, catching potential errors at compile time, or dynamic, associating type information with values at run-time and consulting them as needed to detect imminent errors, or a combination of both ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
