Curry–Howard correspondence

Target entity: Curry–Howard correspondence
Context triple: [Curry encoding, influencedBy, Curry–Howard correspondence]

• A. 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.
• B. Hilbert’s program
  Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
• C. Church–Rosser property
  The Church–Rosser property is a confluence property of rewriting systems stating that if an expression can be reduced in different ways, all reduction paths can be further reduced to a common equivalent form.
• D. Hoare logic
  Hoare logic is a formal system in computer science used to reason rigorously about the correctness of computer programs using logical assertions about program states.
• E. Recherches sur la théorie de la démonstration
  Recherches sur la théorie de la démonstration is Jacques Herbrand’s foundational work in mathematical logic, introducing key results in proof theory and what is now known as Herbrand’s theorem.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Curry–Howard correspondence
Target entity description: 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.

• A. 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.
• B. Hilbert’s program
  Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
• C. Church–Rosser property
  The Church–Rosser property is a confluence property of rewriting systems stating that if an expression can be reduced in different ways, all reduction paths can be further reduced to a common equivalent form.
• D. Hoare logic
  Hoare logic is a formal system in computer science used to reason rigorously about the correctness of computer programs using logical assertions about program states.
• E. Recherches sur la théorie de la démonstration
  Recherches sur la théorie de la démonstration is Jacques Herbrand’s foundational work in mathematical logic, introducing key results in proof theory and what is now known as Herbrand’s theorem.
• F. None of above. chosen