A mechanical proof of the Church-Rosser theorem
Journal of the ACM (JACM)
Theoretical Computer Science
An algorithm for testing conversion in type theory
Logical frameworks
Handbook of logic in computer science (vol. 2)
Information and Computation
Computation and reasoning: a type theory for computer science
Computation and reasoning: a type theory for computer science
Checking algorithms for pure type systems
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Closure under alpha-conversion
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Parallel reductions in &lgr;-calculus
Information and Computation
An algorithm for type-checking dependent types
Science of Computer Programming - Special issue on mathematics of program construction
A Formalization of the Strong Normalization Proof for System F in LEGO
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Synthetic Domain Theory in Type Theory: Another Logic of Computable Functions
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
Five Axioms of Alpha-Conversion
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
Inverting Inductively Defined Relations in LEGO
TYPES '96 Selected papers from the International Workshop on Types for Proofs and Programs
Auxiliary Variables and Recursive Procedures
TAPSOFT '97 Proceedings of the 7th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
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
On the Subject Reduction Property for Algebraic Type Systems
CSL '96 Selected Papers from the10th International Workshop on Computer Science Logic
A New Approach to Abstract Syntax Involving Binders
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
A Proof of the Church-Rosser Theorem and its Representation in a Logical Framework
A Proof of the Church-Rosser Theorem and its Representation in a Logical Framework
Journal of Automated Reasoning
A Framework for the Formalisation of Pi Calculus Type Systems in Isabelle/HOL
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
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 lambda-Calculus Using One-Sorted Variable Names
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
A formalised first-order confluence proof for the λ-calculus using one-sorted variable names
Information and Computation - RTA 2001
Formal Foundations of Operational Semantics
Higher-Order and Symbolic Computation
Nominal logic, a first order theory of names and binding
Information and Computation - TACS 2001
Journal of Functional Programming
A definitional approach to primitivexs recursion over higher order abstract syntax
MERLIN '03 Proceedings of the 2003 ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Verifying CPS transformations in Isabelle/HOL
MERLIN '03 Proceedings of the 2003 ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Mechanising Hankin and Barendregt using the Gordon-Melham axioms
MERLIN '03 Proceedings of the 2003 ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Functional pearl: i am not a number--i am a free variable
Haskell '04 Proceedings of the 2004 ACM SIGPLAN workshop on Haskell
Scrap your nameplate: (functional pearl)
Proceedings of the tenth ACM SIGPLAN international conference on Functional programming
A formal treatment of the barendregt variable convention in rule inductions
Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
ACM SIGACT News
Mechanising λ-calculus using a classical first order theory of terms with permutations
Higher-Order and Symbolic Computation
A Logical Framework with Dependently Typed Records
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
A general mathematics of names
Information and Computation
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Parametric higher-order abstract syntax for mechanized semantics
Proceedings of the 13th ACM SIGPLAN international conference on Functional programming
Barendregt's Variable Convention in Rule Inductions
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A PVS Theory for Term Rewriting Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Reasoning with hypothetical judgments and open terms in hybrid
PPDP '09 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming
External and internal syntax of the λ-calculus
Journal of Symbolic Computation
A logical framework with dependently typed records
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
A formalisation of a dependently typed language as an inductive-recursive family
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Proof pearl: de Bruijn terms really do work
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
ESOP'08/ETAPS'08 Proceedings of the Theory and practice of software, 17th European conference on Programming languages and systems
A Formalization of the Knuth---Bendix(---Huet) Critical Pair Theorem
Journal of Automated Reasoning
Outrageous but meaningful coincidences: dependent type-safe syntax and evaluation
Proceedings of the 6th ACM SIGPLAN workshop on Generic programming
Mechanizing the metatheory of LF
ACM Transactions on Computational Logic (TOCL)
Proceedings of the 16th ACM SIGPLAN international conference on Functional programming
Journal of Automated Reasoning
Mechanized metatheory for the masses: the PoplMark challenge
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
A mechanically verified, sound and complete theorem prover for first order logic
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Formalized metatheory with terms represented by an indexed family of types
TYPES'04 Proceedings of the 2004 international conference on Types for Proofs and Programs
On the role of type decorations in the calculus of inductive constructions
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Theoretical Computer Science
A Canonical Locally Named Representation of Binding
Journal of Automated Reasoning
A Logical Framework with Dependently Typed Records
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
Nominal Lambda Calculus: An Internal Language for FM-Cartesian Closed Categories
Electronic Notes in Theoretical Computer Science (ENTCS)
Mechanizing Metatheory Without Typing Contexts
Journal of Automated Reasoning
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We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified proof of standardization for beta reduction that does not mention redex positions or residuals. Then we outline the meta theory of Pure Type Systems, leading to the strengthening lemma. One novelty is our use of named variables for the formalization. Along the way we point out what we feel has been learned about general issues of formalizing mathematics, emphasizing the search for formal definitions that are convenient for formal proof and convincingly represent the intended informal concepts.