Calculus of Inductive Constructions

Target entity: Calculus of Inductive Constructions
Context triple: [Coq, implements, Calculus of Inductive Constructions]

• A. calculus of constructions
  The calculus of constructions is a powerful type theory and foundational formal system that unifies higher-order logic and typed lambda calculus, serving as the basis for several modern proof assistants.
• B. Martin-Löf type theory
  Martin-Löf type theory is a foundational system for constructive mathematics and computer science that integrates logic and computation through dependent types and serves as a basis for proof assistants and functional programming languages.
• C. Curry–Howard correspondence
  The Curry–Howard correspondence is a foundational principle in logic and computer science that establishes a deep analogy between proofs and programs, and between logical propositions and types in programming languages.
• D. The Calculus of Computation
  The Calculus of Computation is a textbook that introduces the mathematical foundations of verification, focusing on logic-based methods for specifying and proving properties of computational systems.
• E. Isabelle proof assistant
  Isabelle proof assistant is a widely used interactive theorem prover and generic proof assistant designed for formal verification and mathematical logic, particularly known for its support of higher-order logic.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Calculus of Inductive Constructions
Target entity description: Calculus of Inductive Constructions is a powerful type theory that combines higher-order logic with inductive types and dependent types, forming the formal foundation of the Coq proof assistant.

• A. calculus of constructions
  The calculus of constructions is a powerful type theory and foundational formal system that unifies higher-order logic and typed lambda calculus, serving as the basis for several modern proof assistants.
• B. Martin-Löf type theory
  Martin-Löf type theory is a foundational system for constructive mathematics and computer science that integrates logic and computation through dependent types and serves as a basis for proof assistants and functional programming languages.
• C. Curry–Howard correspondence
  The Curry–Howard correspondence is a foundational principle in logic and computer science that establishes a deep analogy between proofs and programs, and between logical propositions and types in programming languages.
• D. The Calculus of Computation
  The Calculus of Computation is a textbook that introduces the mathematical foundations of verification, focusing on logic-based methods for specifying and proving properties of computational systems.
• E. Isabelle proof assistant
  Isabelle proof assistant is a widely used interactive theorem prover and generic proof assistant designed for formal verification and mathematical logic, particularly known for its support of higher-order logic.
• F. None of above. chosen