Higher-order functionIn mathematics and computer science, a higher-order function (HOF) is a function that does at least one of the following: takes one or more functions as arguments (i.e. a procedural parameter, which is a parameter of a procedure that is itself a procedure), returns a function as its result. All other functions are first-order functions. In mathematics higher-order functions are also termed operators or functionals. The differential operator in calculus is a common example, since it maps a function to its derivative, also a function.
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.
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.
Kotlin (programming language)Kotlin (ˈkɒtlɪn) is a cross-platform, statically typed, general-purpose high-level programming language with type inference. Kotlin is designed to interoperate fully with Java, and the JVM version of Kotlin's standard library depends on the Java Class Library, but type inference allows its syntax to be more concise. Kotlin mainly targets the JVM, but also compiles to JavaScript (e.g., for frontend web applications using React) or native code via LLVM (e.g., for native iOS apps sharing business logic with Android apps).
Partial applicationIn computer science, partial application (or partial function application) refers to the process of fixing a number of arguments to a function, producing another function of smaller arity. Given a function , we might fix (or 'bind') the first argument, producing a function of type . Evaluation of this function might be represented as . Note that the result of partial function application in this case is a function that takes two arguments. Partial application is sometimes incorrectly called currying, which is a related, but distinct concept.
Macro (computer science)In computer programming, a macro (short for "macro instruction"; ) is a rule or pattern that specifies how a certain input should be mapped to a replacement output. Applying a macro to an input is known as macro expansion. The input and output may be a sequence of lexical tokens or characters, or a syntax tree. Character macros are supported in software applications to make it easy to invoke common command sequences. Token and tree macros are supported in some programming languages to enable code reuse or to extend the language, sometimes for domain-specific languages.
Kappa calculusIn mathematical logic, , and computer science, kappa calculus is a formal system for defining first-order functions. Unlike lambda calculus, kappa calculus has no higher-order functions; its functions are not first class objects. Kappa-calculus can be regarded as "a reformulation of the first-order fragment of typed lambda calculus". Because its functions are not first-class objects, evaluation of kappa calculus expressions does not require closures. The definition below has been adapted from the diagrams on pages 205 and 207 of Hasegawa.
CalculusCalculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus and integral calculus; the former concerns instantaneous rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves.
Object (grammar)In linguistics, an object is any of several types of arguments. In subject-prominent, nominative-accusative languages such as English, a transitive verb typically distinguishes between its subject and any of its objects, which can include but are not limited to direct objects, indirect objects, and arguments of adpositions (prepositions or postpositions); the latter are more accurately termed oblique arguments, thus including other arguments not covered by core grammatical roles, such as those governed by case morphology (as in languages such as Latin) or relational nouns (as is typical for members of the Mesoamerican Linguistic Area).
