Function applicationIn mathematics, function application (or evaluation) is the act of taking a function and an input from its domain to obtain the corresponding value from its range. In this sense, function application can be thought of as the opposite of function abstraction. It is central to programming languages derived from lambda calculus, such as LISP and Scheme, and also in functional languages.Fresh variableIn formal reasoning, in particular in mathematical logic, computer algebra, and automated theorem proving, a fresh variable is a variable that did not occur in the context considered so far. The concept is often used without explanation. Fresh variables may be used to replace other variables, to eliminate variable shadowing or capture.
Alonzo ChurchAlonzo Church (June 14, 1903 – August 11, 1995) was an American computer scientist, mathematician, logician, and philosopher who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, the Church–Turing thesis, proving the unsolvability of the Entscheidungsproblem ("decision problem"), the Frege–Church ontology, and the Church–Rosser theorem.
ComputabilityComputability is the ability to solve a problem by an effective procedure. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem.
Model of computationIn computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model that describes how an output of a mathematical function is computed given an input. A model of computation describes how units of computations, memories, and communications are organized. The computational complexity of an algorithm can be measured given a model of computation.Name collisionIn computer programming, a name collision is the nomenclature problem that occurs when the same variable name is used for different things in two separate areas that are joined, merged, or otherwise go from occupying separate namespaces to sharing one. As with the collision of other identifiers, it must be resolved in some way for the new software (such as a mashup) to work right.
Turing machineA Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algorithm. The machine operates on an infinite memory tape divided into discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the alphabet of the machine.
Mathematical logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include usage of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.Formal systemA formal system (or deductive system) is an abstract structure and formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms. In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge in mathematics. However, in 1931 Kurt Gödel proved that any consistent formal system sufficiently powerful to express basic arithmetic cannot prove its own completeness.
Abstraction (computer science)In software, an abstraction provides access while hiding details that otherwise might make access more challenging. It focuses attention on details of greater importance. Examples include the abstract data type which separates use from the representation of data and functions that form a call tree that is more general at the base and more specific towards the leaves.Name bindingIn computer programming, name binding is the association of a data or code entity with an identifier. An identifier bound to an entity is said to reference that entity. A machine language has no built-in notion of identifiers, but name-entity binding as a service and notation for the programmer is implemented by higher-level programming languages.Foundations of mathematicsFoundations of mathematics are the logical and mathematical frameworks that allow the development of mathematics without generating self-contradictory theories, and to have reliable concepts of theorems, proofs, algorithms, etc. in particular. This may also include the philosophical study of the relation of this framework with reality.
Universal Turing machineIn computer science, a universal Turing machine (UTM) is a Turing machine capable of computing any computable sequence, as described by Alan Turing in his seminal paper "On Computable Numbers, with an Application to the Entscheidungsproblem". Or, in other words, a Turing machine that is capable of simulating any other specialized Turing machines. Common sense might say that a universal machine is impossible, but Turing proves that it is possible.*As an Amazon Associate I earn from qualifying purchases.