PLDI '88 Proceedings of the ACM SIGPLAN 1988 conference on Programming Language design and Implementation
Proofs and types
Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
A framework for defining logics
Journal of the ACM (JACM)
Computation and reasoning: a type theory for computer science
Computation and reasoning: a type theory for computer science
The ALF proof editor and its proof engine
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
A modal analysis of staged computation
POPL '96 Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Higher-Order Abstract Syntax with Induction in Coq
LPAR '94 Proceedings of the 5th International Conference on Logic Programming and Automated Reasoning
On Mints' Reduction for ccc-Calculus
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Primitive Recursion for Higher-Order Abstract Syntax
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
Automated Theorem Proving in a Simple Meta-Logic for LF
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
A Logic for Reasoning with Higher-Order Abstract Syntax
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Semantical Analysis of Higher-Order Abstract Syntax
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
A Higher-Order Specification of the pi-Calculus
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
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An extension of the simply-typed λ-calculus, allowing iteration and case reasoning over terms of functional types that arise when using higher order abstract syntax, has recently been introduced by F. Pfenning, C. Schürmann and the first author. This thorny mixing is achieved thanks to the help of the operator '□' of modal logic S4. Here we give a new presentation of their system, with reduction rules, instead of evaluation judgments, that compute the canonical forms of terms. Our presentation is based on a modal λ-calculus that is better from the user's point of view. Moreover we do not impose a particular strategy of reduction during the computation. Our system enjoys the decidability of typability, soundness of typed reduction with respect to typing rules, the Church-Rosser and strong normalization properties and it is a conservative extension over the simply-typed λ-calculus.