In mathematical logic and computer science, the calculus of constructions (CoC) is a type theory created by Thierry Coquand. It can serve as both a typed...
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Rocq works within the theory of the calculus of inductive constructions, a derivative of the calculus of constructions. Rocq is not an automated theorem...
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Helmut (27 April 2024). "Typed Lambda Calculus / Calculus of Constructions" (PDF). Calculus of Constructions. Retrieved 27 April 2024. Lambek, J.; Scott...
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the University of Edinburgh. It implements several type theories: the Edinburgh Logical Framework (LF), the Calculus of Constructions (CoC), the Generalized...
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Calculus of Constructions, a dependent type theory for functions. With inductive types, it would be called "the Calculus of Inductive Constructions"...
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assistant and a functional programming language. It is based on the calculus of constructions with inductive types. It is an open-source project hosted on GitHub...
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Lambda cube (category Lambda calculus)
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...
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Dependent type (redirect from ΛΠ-calculus)
corresponds to the calculus of constructions whose derivative, the calculus of inductive constructions is the underlying system of Rocq. The Curry–Howard...
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systems of typed lambda calculus including the simply typed lambda calculus, Jean-Yves Girard's System F, and Thierry Coquand's calculus of constructions are...
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Church–Rosser theorem Simply typed lambda calculus Typed lambda calculus Curry–Howard isomorphism Calculus of constructions Constructivist analysis Lambda cube...
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type (generalized) Type variable First-class value Polymorphism Calculus of constructions Domain theory Directed complete partial order Knaster–Tarski theorem...
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lambda calculus – Lambda calculus with typed variables (and functions) System F – A typed lambda calculus with type-variables Calculus of constructions – A...
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Calculus 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...
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Constructive proof (redirect from Proof by construction)
intuitionistic type theory, and Thierry Coquand and Gérard Huet's calculus of constructions. Until the end of 19th century, all mathematical proofs were essentially...
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dependent type system known as the calculus of (co)inductive constructions (a derivative of the calculus of constructions), and is compatible, to some extent...
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Type theory (redirect from Theory of types)
known as Coq) and Lean, are based on the calculus for inductive constructions, which is a calculus of constructions with inductive types. The most commonly...
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Pure type system (category Lambda calculus)
as is the case with the calculus of constructions, but this is not generally the case, e.g. the simply typed lambda calculus allows only terms to depend...
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Thierry Coquand (category Academic staff of the University of Gothenburg)
constructive mathematics, especially the calculus of constructions. He received his Ph.D. under the supervision of Gérard Huet, another academic who has...
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Curry–Howard correspondence (category CS1 maint: DOI inactive as of February 2025)
Coquand's calculus of constructions (CoC), two calculi in which proofs are regular objects of the discourse and in which one can state properties of proofs...
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McGruff City of Caterpillar, an Emo/Screamo band Corrosion of Conformity, a heavy metal band from the American South Calculus of constructions, a formal...
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directly in plain System F, in Martin-Löf type theory or the Calculus of Constructions. Termination analysis This term is due to: Turner, D.A. (December...
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Minimal logic (redirect from Minimal calculus)
foremostly depend on the implication connective, see e.g. the calculus of constructions for a predicate logic framework. The system can be defined by...
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Tai's model (redirect from A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves)
to the naming of "Tai's model" and the treatment of a method "used in undergraduate calculus courses" as a novel discovery in the field of diabetes care...
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Natural deduction (redirect from Natural deduction calculus)
deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. This contrasts...
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Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important...
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any of the typed lambda calculi such as the simply typed lambda calculus, Jean-Yves Girard's System F, or Thierry Coquand's calculus of constructions. Here...
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related fields, Malliavin calculus is a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic...
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Calculus, originally called infinitesimal calculus, is a mathematical discipline focused on limits, continuity, derivatives, integrals, and infinite series...
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Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape...
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Gérard Huet (category Members of the French Academy of Sciences)
which developed the Caml programming language. He designed the calculus of constructions in 1984 with Thierry Coquand. He led the Coq project in the 1990s...
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