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Monad Transformer
In functional programming, a monad transformer is a type constructor which takes a monads in functional programming, monad as an argument and returns a monad as a result. Monad transformers can be used to compose features encapsulated by monads – such as state, exception handling, and I/O – in a modular way. Typically, a monad transformer is created by generalising an existing monad; applying the resulting monad transformer to the identity monad yields a monad which is equivalent to the original monad (ignoring any necessary boxing and unboxing). Definition A monad transformer consists of: # A type constructor t of kind (type theory), kind (* -> *) -> * -> * # Monad operations return and bind (or an equivalent formulation) for all t m where m is a monad, satisfying the Monad_(functional_programming)#Monad_laws, monad laws # An additional operation, lift :: m a -> t m a, satisfying the following laws: (the notation `bind` below indicates infix application): ## lift . return = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Programming
In computer science, functional programming is a programming paradigm where programs are constructed by Function application, applying and Function composition (computer science), composing Function (computer science), functions. It is a declarative programming paradigm in which function definitions are Tree (data structure), trees of Expression (computer science), expressions that map Value (computer science), values to other values, rather than a sequence of Imperative programming, imperative Statement (computer science), statements which update the State (computer science), running state of the program. In functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local Identifier (computer languages), identifiers), passed as Parameter (computer programming), arguments, and Return value, returned from other functions, just as any other data type can. This allows programs to be written in a Declarative programming, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monads In Functional Programming
In functional programming, a monad is a software design pattern with a structure that combines program fragments ( functions) and wraps their return values in a type with additional computation. In addition to defining a wrapping monadic type, monads define two operators: one to wrap a value in the monad type, and another to compose together functions that output values of the monad type (these are known as monadic functions). General-purpose languages use monads to reduce boilerplate code needed for common operations (such as dealing with undefined values or fallible functions, or encapsulating bookkeeping code). Functional languages use monads to turn complicated sequences of functions into succinct pipelines that abstract away control flow, and side-effects. Both the concept of a monad and the term originally come from category theory, where a monad is defined as a functor with additional structure. Research beginning in the late 1980s and early 1990s established that monads ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exception Handling
In computing and computer programming, exception handling is the process of responding to the occurrence of ''exceptions'' – anomalous or exceptional conditions requiring special processing – during the execution of a program. In general, an exception breaks the normal flow of execution and executes a pre-registered ''exception handler''; the details of how this is done depend on whether it is a hardware or software exception and how the software exception is implemented. Exception handling, if provided, is facilitated by specialized programming language constructs, hardware mechanisms like interrupts, or operating system (OS) inter-process communication (IPC) facilities like signals. Some exceptions, especially hardware ones, may be handled so gracefully that execution can resume where it was interrupted. Definition The definition of an exception is based on the observation that each procedure has a precondition, a set of circumstances for which it will terminate "normal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kind (type Theory)
In the area of mathematical logic and computer science known as type theory, a kind is the type of a type constructor or, less commonly, the type of a higher-order type operator. A kind system is essentially a simply typed lambda calculus "one level up", endowed with a primitive type, denoted * and called "type", which is the kind of any data type which does not need any type parameters. A kind is sometimes confusingly described as the "type of a (data) type", but it is actually more of an arity specifier. Syntactically, it is natural to consider polymorphic types to be type constructors, thus non-polymorphic types to be nullary type constructors. But all nullary constructors, thus all monomorphic types, have the same, simplest kind; namely *. Since higher-order type operators are uncommon in programming languages, in most programming practice, kinds are used to distinguish between data types and the types of constructors which are used to implement parametric polymorphism. Kinds ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monad (functional Programming)
In functional programming, a monad is a software design pattern with a structure that combines program fragments (Function (computer programming), functions) and wraps their return values in a Type system, type with additional computation. In addition to defining a wrapping monadic type, monads define two Operator (computer programming), operators: one to wrap a value in the monad type, and another to compose together functions that output values of the monad type (these are known as monadic functions). General-purpose languages use monads to reduce boilerplate code needed for common operations (such as dealing with undefined values or fallible functions, or encapsulating bookkeeping code). Functional languages use monads to turn complicated sequences of functions into succinct pipelines that abstract away control flow, and side-effect (computer science), side-effects. Both the concept of a monad and the term originally come from category theory, where a monad is defined as a Func ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Option Type
In programming languages (especially functional programming languages) and type theory, an option type or maybe type is a polymorphic type that represents encapsulation of an optional value; e.g., it is used as the return type of functions which may or may not return a meaningful value when they are applied. It consists of a constructor which either is empty (often named None or Nothing), or which encapsulates the original data type A (often written Just A or Some A). A distinct, but related concept outside of functional programming, which is popular in object-oriented programming, is called nullable types (often expressed as A?). The core difference between option types and nullable types is that option types support nesting (e.g. Maybe (Maybe String) ≠ Maybe String), while nullable types do not (e.g. String?? = String?). Theoretical aspects In type theory, it may be written as: A^ = A + 1. This expresses the fact that for a given set of values in A, an option type adds ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monoid
In abstract algebra, a branch of mathematics, a monoid is a set equipped with an associative binary operation and an identity element. For example, the nonnegative integers with addition form a monoid, the identity element being 0. Monoids are semigroups with identity. Such algebraic structures occur in several branches of mathematics. The functions from a set into itself form a monoid with respect to function composition. More generally, in category theory, the morphisms of an object to itself form a monoid, and, conversely, a monoid may be viewed as a category with a single object. In computer science and computer programming, the set of strings built from a given set of characters is a free monoid. Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation for process calculi and concurrent computing. In theoretical computer science, the study of monoids is fundamental for automata ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Commutative
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name of the property that says something like or , the property can also be used in more advanced settings. The name is needed because there are operations, such as division and subtraction, that do not have it (for example, ); such operations are ''not'' commutative, and so are referred to as ''noncommutative operations''. The idea that simple operations, such as the multiplication and addition of numbers, are commutative was for many years implicitly assumed. Thus, this property was not named until the 19th century, when mathematics started to become formalized. A similar property exists for binary relations; a binary relation is said to be symmetric if the relation applies regardless of the order of its operands; for example, equality is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monads In Functional Programming
In functional programming, a monad is a software design pattern with a structure that combines program fragments ( functions) and wraps their return values in a type with additional computation. In addition to defining a wrapping monadic type, monads define two operators: one to wrap a value in the monad type, and another to compose together functions that output values of the monad type (these are known as monadic functions). General-purpose languages use monads to reduce boilerplate code needed for common operations (such as dealing with undefined values or fallible functions, or encapsulating bookkeeping code). Functional languages use monads to turn complicated sequences of functions into succinct pipelines that abstract away control flow, and side-effects. Both the concept of a monad and the term originally come from category theory, where a monad is defined as a functor with additional structure. Research beginning in the late 1980s and early 1990s established that monads ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
