Logic programming in the LF logical framework
Logical frameworks
An algorithm for testing conversion in type theory
Logical frameworks
A framework for defining logics
Journal of the ACM (JACM)
&pgr;-calculus in (Co)inductive-type theory
Theoretical Computer Science - Special issues on models and paradigms for concurrency
Higher-Order Abstract Syntax with Induction in Coq
LPAR '94 Proceedings of the 5th International Conference on Logic Programming and Automated Reasoning
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
Five Axioms of Alpha-Conversion
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
A Metalanguage for Programming with Bound Names Modulo Renaming
MPC '00 Proceedings of the 5th International Conference on Mathematics of Program Construction
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
A New Approach to Abstract Syntax Involving Binders
LICS '99 Proceedings of the 14th 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
Higher-order rewriting with dependent types (lambda calculus)
Higher-order rewriting with dependent types (lambda calculus)
Automating the meta theory of deductive systems
Automating the meta theory of deductive systems
| Hi-index | 0.00 |
Reasoning by induction is common practice in computer science and mathematics. In formal logic, however, standard induction principles exist only for a certain class of inductively defined structures that satisfy the positivity condition. This is a major restriction considering that many structures in programming languages and logics are best expressed using higher-order representation techniques that violate exactly this condition. In this paper we develop induction principles for higherorder encodings in the setting of first-order intuitionistic logic. They differ from standard induction principles in that they rely on the concept of worlds [Sch01] which admits reasoning about open terms in regularly formed contexts. The soundness of these induction principles follows from external termination and coverage considerations about a realizability interpretation of proofs.