Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Parallel reductions in &lgr;-calculus
Information and Computation
Metamathematics, machines, and Go¨del's proof
Metamathematics, machines, and Go¨del's proof
Automated reasoning and its applications
Tree-Manipulating Systems and Church-Rosser Theorems
Journal of the ACM (JACM)
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Formalization of a lamda-Calculus with Explicit Substitutions in Coq
TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
Eta-conversion for the Languages of Explicit Substitutions
Proceedings of the Third International Conference on Algebraic and Logic Programming
More Church-Rosser Proofs (in Isabelle/HOL)
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Formal Proofs About Rewriting Using ACL2
Annals of Mathematics and Artificial Intelligence
Mechanized Operational Semantics via (Co)Induction
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Calculating Church-Rosser Proofs in Kleene Algebra
ReIMICS '01 Revised Papers from the 6th International Conference and 1st Workshop of COST Action 274 TARSKI on Relational Methods in Computer Science
A formalised first-order confluence proof for the λ-calculus using one-sorted variable names
Information and Computation - RTA 2001
Verifying CPS transformations in Isabelle/HOL
MERLIN '03 Proceedings of the 2003 ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
A Head-to-Head Comparison of de Bruijn Indices and Names
Electronic Notes in Theoretical Computer Science (ENTCS)
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Automated Reasoning in Kleene Algebra
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
A PVS Theory for Term Rewriting Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
An Isabelle/HOL-based model of stratego-like traversal strategies
PPDP '09 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming
Diagram Chase in Relational System Development
Electronic Notes in Theoretical Computer Science (ENTCS)
A mechanized model of the theory of objects
FMOODS'07 Proceedings of the 9th IFIP WG 6.1 international conference on Formal methods for open object-based distributed systems
Proof pearl: de Bruijn terms really do work
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Composing safely: a type system for aspects
SC'08 Proceedings of the 7th international conference on Software composition
A Formalization of the Knuth---Bendix(---Huet) Critical Pair Theorem
Journal of Automated Reasoning
Extracting a normalization algorithm in Isabelle/HOL
TYPES'04 Proceedings of the 2004 international conference on Types for Proofs and Programs
Proof pearl: abella formalization of λ-calculus cube property
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
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The proofs of the Church–Rosser theorems for β, η, and β ∪ η reduction in untyped λ-calculus are formalized in Isabelle/HOL, an implementation of Higher Order Logic in the generic theorem prover Isabelle. For β-reduction, both the standard proof and Takahashi's are given and compared. All proofs are based on a general theory of commutating relations that supports an almost geometric style of reasoning about confluence diagrams.