A notation for lambda terms. A generalization of environment
Theoretical Computer Science
Implementing typed intermediate languages
ICFP '98 Proceedings of the third ACM SIGPLAN international conference on Functional programming
Typed lambda-calculi with explicit substitutions may not terminate
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
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TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
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CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
System Description: Twelf - A Meta-Logical Framework for Deductive Systems
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
FreshML: programming with binders made simple
ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
The Bedwyr System for Model Checking over Syntactic Expressions
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
The Abella Interactive Theorem Prover (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Celf --- A Logical Framework for Deductive and Concurrent Systems (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
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ACM SIGPLAN Notices
Practical programming with higher-order encodings and dependent types
ESOP'08/ETAPS'08 Proceedings of the Theory and practice of software, 17th European conference on Programming languages and systems
The theory of calculi with explicit substitutions revisited
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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We introduce a calculus of explicit substitutions for the λ-calculus with linear, affine, and intuitionistic variables and meta-variables. Using a Curry-style formulation, we redesign and extend previously suggested type systems for linear explicit substitutions. This way, we obtain a fine-grained small-step reduction semantics suitable for efficient implementation. We prove that subject reduction, confluence, and termination holds. All theorems have been formally verified in the Twelf proof assistant.