homotopy type theory

Target entity: homotopy type theory
Context triple: [Per Martin-Löf, influenced, homotopy type theory]

• A. univalent foundations program
  The univalent foundations program is a research initiative that redefines the foundations of mathematics using homotopy type theory, emphasizing computationally verifiable proofs and new connections between logic, topology, and category theory.
• B. univalence axiom
  The univalence axiom is a principle in homotopy type theory asserting that equivalent mathematical structures can be identified, providing a foundation for a new, homotopical approach to the foundations of mathematics.
• C. 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.
• D. 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.
• E. Brouwer–Heyting–Kolmogorov interpretation
  The Brouwer–Heyting–Kolmogorov interpretation is a foundational explanation of intuitionistic logic that interprets logical connectives and proofs in terms of explicit constructions and algorithms rather than classical truth values.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: homotopy type theory
Target entity description: Homotopy type theory is a branch of mathematical logic and foundations that interprets types as spaces and equalities as paths, connecting type theory with homotopy theory and higher category theory.

• A. univalent foundations program
  The univalent foundations program is a research initiative that redefines the foundations of mathematics using homotopy type theory, emphasizing computationally verifiable proofs and new connections between logic, topology, and category theory.
• B. univalence axiom
  The univalence axiom is a principle in homotopy type theory asserting that equivalent mathematical structures can be identified, providing a foundation for a new, homotopical approach to the foundations of mathematics.
• C. 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.
• D. 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.
• E. Brouwer–Heyting–Kolmogorov interpretation
  The Brouwer–Heyting–Kolmogorov interpretation is a foundational explanation of intuitionistic logic that interprets logical connectives and proofs in terms of explicit constructions and algorithms rather than classical truth values.
• F. None of above. chosen