Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
The ALF proof editor and its proof engine
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Formalization of a lamda-Calculus with Explicit Substitutions in Coq
TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
From Semantics to Rules: A Machine Assisted Analysis
CSL '93 Selected Papers from the 7th Workshop on Computer Science Logic
Categorical Reconstruction of a Reduction Free Normalization Proof
CTCS '95 Proceedings of the 6th International Conference on Category Theory and Computer Science
Normalization and the Yoneda embedding
Mathematical Structures in Computer Science
Intuitionistic model constructions and normalization proofs
Mathematical Structures in Computer Science
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We describe a formalisation of the Curry-Howard-Lawvere correspondence between the natural deduction system for minimal logic, the typed lambda calculus and Cartesian closed categories. We formalise the type of natural deduction proof trees as a family of sets Γ ⊢ A indexed by the current assumption list Γ and the conclusion A and organise numerous useful lemmas about proof trees categorically. We prove categorical properties about proof trees up to (syntactic) identity as well as up to βη-convertibility. We prove that our notion of proof trees is equivalent in an appropriate sense to more traditional representations of lambda terms. The formalisation is carried out in the proof assistant ALF for Martin-Löf type theory.