On understanding types, data abstraction, and polymorphism
ACM Computing Surveys (CSUR) - The MIT Press scientific computation series
Structure and interpretation of computer programs
Structure and interpretation of computer programs
Pebble, a kernel language for modules and abstract data types
Information and Computation - Semantics of Data Types
Proofs and types
Parallel reductions in λ-calculus
Journal of Symbolic Computation
Confluence results for the pure strong categorical logic CCL. &lgr;-calculi as subsystems of CCL
Theoretical Computer Science
Explicit substitution on the edge of strong normalization
Theoretical Computer Science
Recursive functions of symbolic expressions and their computation by machine, Part I
Communications of the ACM
Theoretical Computer Science
Typed lambda-calculi with explicit substitutions may not terminate
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Strong Normalization of Explicit Substitutions via Cut Elimination in Proof Nets
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Journal of Functional Programming
PPDP '05 Proceedings of the 7th ACM SIGPLAN international conference on Principles and practice of declarative programming
Functional Programming With Higher-order Abstract Syntax and Explicit Substitutions
Electronic Notes in Theoretical Computer Science (ENTCS)
The lambda-context calculus (extended version)
Information and Computation
First-class substitutions in contextual type theory
Proceedings of the Eighth ACM SIGPLAN international workshop on Logical frameworks & meta-languages: theory & practice
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We introduce λε, a simply typed calculus with environments as first class values. As well as the usual constructs of λ and application, we have e[a] which evaluates term a in an environment e. Our environments are sets of variable-value pairs, but environments can also be computed by function application and evaluation in some other environments. The notion of environments here is a generalization of explicit substitutions and records. We show that the calculus has desirable properties such as subject reduction, confluence, conservativity over the simply typed λβ-calculus and strong normalizability.