Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Calculus of Inductive Constructions | Statement: [Coq, implements, 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