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Cons
In computer programming, ( or ) is a fundamental function in most dialects of the Lisp programming language. ''constructs'' memory objects which hold two values or pointers to two values. These objects are referred to as (cons) cells, conses, non-atomic s-expressions ("NATSes"), or (cons) pairs. In Lisp jargon, the expression "to cons ''x'' onto ''y''" means to construct a new object with (cons ''x'' ''y''). The resulting pair has a left half, referred to as the (the first element, or ''contents of the address part of register''), and a right half, referred to as the (the second element, or ''contents of the decrement part of register''). It is loosely related to the object-oriented notion of a constructor, which creates a new object given arguments, and more closely related to the constructor function of an algebraic data type system. The word "cons" and expressions like "to cons onto" are also part of a more general functional programming jargon. Sometimes operators t ...
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Computer Programming
Computer programming is the process of performing a particular computation (or more generally, accomplishing a specific computing result), usually by designing and building an executable computer program. Programming involves tasks such as analysis, generating algorithms, profiling algorithms' accuracy and resource consumption, and the implementation of algorithms (usually in a chosen programming language, commonly referred to as coding). The source code of a program is written in one or more languages that are intelligible to programmers, rather than machine code, which is directly executed by the central processing unit. The purpose of programming is to find a sequence of instructions that will automate the performance of a task (which can be as complex as an operating system) on a computer, often for solving a given problem. Proficient programming thus usually requires expertise in several different subjects, including knowledge of the application domain, specialized algorit ...
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Linked List
In computer science, a linked list is a linear collection of data elements whose order is not given by their physical placement in memory. Instead, each element points to the next. It is a data structure consisting of a collection of nodes which together represent a sequence. In its most basic form, each node contains: data, and a reference (in other words, a ''link'') to the next node in the sequence. This structure allows for efficient insertion or removal of elements from any position in the sequence during iteration. More complex variants add additional links, allowing more efficient insertion or removal of nodes at arbitrary positions. A drawback of linked lists is that access time is linear (and difficult to pipeline). Faster access, such as random access, is not feasible. Arrays have better cache locality compared to linked lists. Linked lists are among the simplest and most common data structures. They can be used to implement several other common abstract data types, ...
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Lambda Calculus
Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine. It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics. Lambda calculus consists of constructing § lambda terms and performing § reduction operations on them. In the simplest form of lambda calculus, terms are built using only the following rules: * x – variable, a character or string representing a parameter or mathematical/logical value. * (\lambda x.M) – abstraction, function definition (M is a lambda term). The variable x becomes bound in the expression. * (M\ N) – application, applying a function M to an argument N. M and N are lambda terms. The reduction operations include: * (\lambda x.M \rightarrow(\ ...
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Church Encoding
In mathematics, Church encoding is a means of representing data and operators in the lambda calculus. The Church numerals are a representation of the natural numbers using lambda notation. The method is named for Alonzo Church, who first encoded data in the lambda calculus this way. Terms that are usually considered primitive in other notations (such as integers, booleans, pairs, lists, and tagged unions) are mapped to higher-order functions under Church encoding. The Church-Turing thesis asserts that any computable operator (and its operands) can be represented under Church encoding. In the untyped lambda calculus the only primitive data type is the function. Use A straightforward implementation of Church encoding slows some access operations from O(1) to O(n), where n is the size of the data structure, making Church encoding impractical. Research has shown that this can be addressed by targeted optimizations, but most functional programming languages instead expand their in ...
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Scheme (programming Language)
Scheme is a dialect of the Lisp family of programming languages. Scheme was created during the 1970s at the MIT AI Lab and released by its developers, Guy L. Steele and Gerald Jay Sussman, via a series of memos now known as the Lambda Papers. It was the first dialect of Lisp to choose lexical scope and the first to require implementations to perform tail-call optimization, giving stronger support for functional programming and associated techniques such as recursive algorithms. It was also one of the first programming languages to support first-class continuations. It had a significant influence on the effort that led to the development of Common Lisp.Common LISP: The Language, 2nd Ed., Guy L. Steele Jr. Digital Press; 1981. . "Common Lisp is a new dialect of Lisp, a successor to MacLisp, influenced strongly by ZetaLisp and to some extent by Scheme and InterLisp." The Scheme language is standardized in the official IEEE standard1178-1990 (Reaff 2008) IEEE Standard for t ...
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First-class Function
In computer science, a programming language is said to have first-class functions if it treats functions as first-class citizens. This means the language supports passing functions as arguments to other functions, returning them as the values from other functions, and assigning them to variables or storing them in data structures. Some programming language theorists require support for anonymous functions (function literals) as well. b) -> -> map f [] = [] map f (x:xs) = f x : map f xs Languages where functions are not first-class often still allow one to write higher-order functions through the use of features such as function pointers or delegates. In the language C: void map(int (*f)(int), int x[], size_t n) There are a number of differences between the two approaches that are ''not'' directly related to the support of first-class functions. The Haskell sample operates on lists, while the C sample operates on arrays. Both are the most natural compound data struct ...
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Side Effect (computer Science)
In computer science, an operation, function or expression is said to have a side effect if it modifies some state variable value(s) outside its local environment, which is to say if it has any observable effect other than its primary effect of returning a value to the invoker of the operation. Example side effects include modifying a non-local variable, modifying a static local variable, modifying a mutable argument passed by reference, performing I/O or calling other functions with side-effects. In the presence of side effects, a program's behaviour may depend on history; that is, the order of evaluation matters. Understanding and debugging a function with side effects requires knowledge about the context and its possible histories. Side effects play an important role in the design and analysis of programming languages. The degree to which side effects are used depends on the programming paradigm. For example, imperative programming is commonly used to produce side effect ...
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Dynamic Memory Allocation
Memory management is a form of resource management applied to computer memory. The essential requirement of memory management is to provide ways to dynamically allocate portions of memory to programs at their request, and free it for reuse when no longer needed. This is critical to any advanced computer system where more than a single process might be underway at any time. Several methods have been devised that increase the effectiveness of memory management. Virtual memory systems separate the memory addresses used by a process from actual physical addresses, allowing separation of processes and increasing the size of the virtual address space beyond the available amount of RAM using paging or swapping to secondary storage. The quality of the virtual memory manager can have an extensive effect on overall system performance. In some operating systems, e.g. OS/360 and successors, memory is managed by the operating system. In other operating systems, e.g. Unix-like operating s ...
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Leaf Node
In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the ''root'' node, which has no parent. These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes in a single straight line. Binary trees are a commonly used type, which constrain the number of children for each parent to exactly two. When the order of the children is specified, this data structure corresponds to an ordered tree in graph theory. A value or pointer to other data may be associated with every node in the tr ...
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Binary Tree
In computer science, a binary tree is a k-ary k = 2 tree data structure in which each node has at most two children, which are referred to as the ' and the '. A recursive definition using just set theory notions is that a (non-empty) binary tree is a tuple (''L'', ''S'', ''R''), where ''L'' and ''R'' are binary trees or the empty set and ''S'' is a singleton set containing the root. Some authors allow the binary tree to be the empty set as well. From a graph theory perspective, binary (and K-ary) trees as defined here are arborescences. A binary tree may thus be also called a bifurcating arborescence—a term which appears in some very old programming books, before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than a directed graph, in which case a binary tree is an ordered, rooted tree. Some authors use rooted binary tree instead of ''binary tree'' to emphasize the fact that the tree is rooted, b ...
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Concatenation
In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end. For example, the concatenation of "snow" and "ball" is "snowball". In certain formalisations of concatenation theory, also called string theory, string concatenation is a primitive notion. Syntax In many programming languages, string concatenation is a binary infix operator. The + (plus) operator is often overloaded to denote concatenation for string arguments: "Hello, " + "World" has the value "Hello, World". In other languages there is a separate operator, particularly to specify implicit type conversion to string, as opposed to more complicated behavior for generic plus. Examples include . in Edinburgh IMP, Perl, and PHP, .. in Lua, and & in Ada, AppleScript, and Visual Basic. Other syntax exists, like , , in PL/I and Oracle Database SQL. In a few languages, notably C, C++, and Python, there is string literal concatenation, mea ...
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Append
In computer programming, append is the operation for concatenating linked lists or arrays in some high-level programming languages. Lisp Append originates in the Lisp programming language. The append procedure takes zero or more (linked) lists as arguments, and returns the concatenation of these lists. (append '(1 2 3) '(a b) '() '(6)) ;Output: (1 2 3 a b 6) Since the append procedure must completely copy all of its arguments except the last, both its time and space complexity are O(''n'') for a list of n elements. It may thus be a source of inefficiency if used injudiciously in code. The nconc procedure (called append! in Scheme) performs the same function as append, but destructively: it alters the cdr of each argument (save the last), pointing it to the next list. Implementation Append can easily be defined recursively in terms of cons. The following is a simple implementation in Scheme, for two arguments only: (define append (lambda (ls1 ls2) (if (null? ls1) ...
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