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Intersection Type Discipline
In mathematical logic, the intersection type discipline is a branch of type theory encompassing type systems that use the intersection type constructor (\cap) to assign multiple types to a single term. In particular, if a term M can be assigned ''both'' the type \varphi_1 and the type \varphi_2, then M can be assigned the intersection type \varphi_1 \cap \varphi_2 (and vice versa). Therefore, the intersection type constructor can be used to express finite heterogeneous ad hoc polymorphism (as opposed to parametric polymorphism). For example, the Lambda_calculus_definition#Definition, λ-term \lambda x.\!(x\;x) can be assigned the type ((\alpha \to \beta) \cap \alpha) \to \beta in most intersection type systems, assuming for the term variable x both the function type \alpha \to \beta and the corresponding argument type \alpha. Prominent intersection type systems include the Coppo–Dezani type assignment system, the Barendregt-Coppo–Dezani type assignment system, and the ess ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion 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 uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and Mathematical analysis, analysis. In the early 20th century it was shaped by David Hilbert's Hilbert's program, program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |