A framework for defining logics
Journal of the ACM (JACM)
Computational foundations of basic recursive function theory
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Lambda calculus characterizations of poly-time
Fundamenta Informaticae - Special issue: lambda calculus and type theory
A new recursion-theoretic characterization of the polytime functions
Computational Complexity
Information and Computation
Fixed point equations inside the algebra of normal forms
Fundamenta Informaticae
Unification via &lgr;se-style of explicit substitution
Proceedings of the 2nd ACM SIGPLAN international conference on Principles and practice of declarative programming
Lambda-Definition of Function(al)s by Normal Forms
ESOP '94 Proceedings of the 5th European Symposium on Programming: Programming Languages and Systems
Primitive Recursion for Higher-Order Abstract Syntax
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
Lambda-Definable Term rewriting Systems
ASIAN '96 Proceedings of the Second Asian Computing Science Conference on Concurrency and Parallelism, Programming, Networking, and Security
A Self-Interpreter of Lambda Calculus Having a Normal Form
CSL '92 Selected Papers from the 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
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
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Extensions of the simply typed lambda calculus have been used as a metalanguage to represent "higher order term algebras", such as, for instance, formulas of the predicate calculus. In this representation bound variables of the object language are represented by bound variables of the metalanguage. This choice has various advantages but makes the notion of "recursive definition" on higher order term algebras more subtle than the corresponding notion on first order term algebras. Despeyroux, Pfenning and Schürmann pointed out the problems that arise in the proof of a canonical form theorem when one combines higher order representations with primitive recursion. In this paper we consider a stronger scheme of recursion and we prove that it captures all partial recursive functions on second order term algebras. We illustrate the system by considering typed programs to reduce to normal form terms of the untyped lambda calculus, encoded as elements of a second order term algebra. First order encodings based on de Bruijn indexes are also considered. The examples also show that a version of the intersection type disciplines can be helpful in some cases to prove the existence of a canonical form. Finally we consider interpretations of our typed systems in the pure lambda calculus and a new gödelization of the pure lambda calculus.