Lambda calculusLambda 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.
Lambda cubeIn mathematical logic and type theory, the λ-cube (also written lambda cube) is a framework introduced by Henk Barendregt to investigate the different dimensions in which the calculus of constructions is a generalization of the simply typed λ-calculus. Each dimension of the cube corresponds to a new kind of dependency between terms and types. Here, "dependency" refers to the capacity of a term or type to bind a term or type. The respective dimensions of the λ-cube correspond to: x-axis (): types that can bind terms, corresponding to dependent types.
ParsingParsing, syntax analysis, or syntactic analysis is the process of analyzing a string of symbols, either in natural language, computer languages or data structures, conforming to the rules of a formal grammar. The term parsing comes from Latin pars (orationis), meaning part (of speech). The term has slightly different meanings in different branches of linguistics and computer science. Traditional sentence parsing is often performed as a method of understanding the exact meaning of a sentence or word, sometimes with the aid of devices such as sentence diagrams.
LR parserIn computer science, LR parsers are a type of bottom-up parser that analyse deterministic context-free languages in linear time. There are several variants of LR parsers: SLR parsers, LALR parsers, Canonical LR(1) parsers, Minimal LR(1) parsers, and GLR parsers. LR parsers can be generated by a parser generator from a formal grammar defining the syntax of the language to be parsed. They are widely used for the processing of computer languages.
Lazy evaluationIn programming language theory, lazy evaluation, or call-by-need, is an evaluation strategy which delays the evaluation of an expression until its value is needed (non-strict evaluation) and which also avoids repeated evaluations (by the use of sharing). The benefits of lazy evaluation include: The ability to define control flow (structures) as abstractions instead of primitives. The ability to define potentially infinite data structures. This allows for more straightforward implementation of some algorithms.
Parser combinatorIn computer programming, a parser combinator is a higher-order function that accepts several parsers as input and returns a new parser as its output. In this context, a parser is a function accepting strings as input and returning some structure as output, typically a parse tree or a set of indices representing locations in the string where parsing stopped successfully. Parser combinators enable a recursive descent parsing strategy that facilitates modular piecewise construction and testing.
Earley parserIn computer science, the Earley parser is an algorithm for parsing strings that belong to a given context-free language, though (depending on the variant) it may suffer problems with certain nullable grammars. The algorithm, named after its inventor, Jay Earley, is a chart parser that uses dynamic programming; it is mainly used for parsing in computational linguistics. It was first introduced in his dissertation in 1968 (and later appeared in an abbreviated, more legible, form in a journal).
Recursive descent parserIn computer science, a recursive descent parser is a kind of top-down parser built from a set of mutually recursive procedures (or a non-recursive equivalent) where each such procedure implements one of the nonterminals of the grammar. Thus the structure of the resulting program closely mirrors that of the grammar it recognizes. A predictive parser is a recursive descent parser that does not require backtracking.
Evaluation strategyIn a programming language, an evaluation strategy is a set of rules for evaluating expressions. The term is often used to refer to the more specific notion of a parameter-passing strategy that defines the kind of value that is passed to the function for each parameter (the binding strategy) and whether to evaluate the parameters of a function call, and if so in what order (the evaluation order). The notion of reduction strategy is distinct, although some authors conflate the two terms and the definition of each term is not widely agreed upon.
Lambda liftingLambda lifting is a meta-process that restructures a computer program so that functions are defined independently of each other in a global scope. An individual "lift" transforms a local function into a global function. It is a two step process, consisting of; Eliminating free variables in the function by adding parameters. Moving functions from a restricted scope to broader or global scope. The term "lambda lifting" was first introduced by Thomas Johnsson around 1982 and was historically considered as a mechanism for implementing functional programming languages.
Shift-reduce parserA shift-reduce parser is a class of efficient, table-driven bottom-up parsing methods for computer languages and other notations formally defined by a grammar. The parsing methods most commonly used for parsing programming languages, LR parsing and its variations, are shift-reduce methods. The precedence parsers used before the invention of LR parsing are also shift-reduce methods. All shift-reduce parsers have similar outward effects, in the incremental order in which they build a parse tree or call specific output actions.
Type systemIn computer programming, a type system is a logical system comprising a set of rules that assigns a property called a type (for example, integer, floating point, string) to every "term" (a word, phrase, or other set of symbols). Usually the terms are various constructs of a computer program, such as variables, expressions, functions, or modules. A type system dictates the operations that can be performed on a term. For variables, the type system determines the allowed values of that term.
System FSystem F (also polymorphic lambda calculus or second-order lambda calculus) is a typed lambda calculus that introduces, to simply typed lambda calculus, a mechanism of universal quantification over types. System F formalizes parametric polymorphism in programming languages, thus forming a theoretical basis for languages such as Haskell and ML. It was discovered independently by logician Jean-Yves Girard (1972) and computer scientist John C. Reynolds.
Simply typed lambda calculusThe simply typed lambda calculus (), a form of type theory, is a typed interpretation of the lambda calculus with only one type constructor () that builds function types. It is the canonical and simplest example of a typed lambda calculus. The simply typed lambda calculus was originally introduced by Alonzo Church in 1940 as an attempt to avoid paradoxical use of the untyped lambda calculus. The term simple type is also used to refer extensions of the simply typed lambda calculus such as products, coproducts or natural numbers (System T) or even full recursion (like PCF).
Church encodingIn 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.
Combinatory logicCombinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming languages. It is based on combinators, which were introduced by Schönfinkel in 1920 with the idea of providing an analogous way to build up functions—and to remove any mention of variables—particularly in predicate logic.
Comparison of parser generatorsThis is a list of notable lexer generators and parser generators for various language classes. Regular languages are a category of languages (sometimes termed Chomsky Type 3) which can be matched by a state machine (more specifically, by a deterministic finite automaton or a nondeterministic finite automaton) constructed from a regular expression.
Short-circuit evaluationShort-circuit evaluation, minimal evaluation, or McCarthy evaluation (after John McCarthy) is the semantics of some Boolean operators in some programming languages in which the second argument is executed or evaluated only if the first argument does not suffice to determine the value of the expression: when the first argument of the AND function evaluates to false, the overall value must be false; and when the first argument of the OR function evaluates to true, the overall value must be true.
Type safetyIn 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.
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.
