Induction principles formalized in the calculus of constructions
The International Joint Conference on theory and practice of software development on TAPSOFT '87
Logic and computation: interactive proof with Cambridge LCF
Logic and computation: interactive proof with Cambridge LCF
Semantics with applications: a formal introduction
Semantics with applications: a formal introduction
The formal semantics of programming languages: an introduction
The formal semantics of programming languages: an introduction
Synthesis of ML programs in the system Coq
Journal of Symbolic Computation - Special issue on automatic programming
A simple applicative language: mini-ML
LFP '86 Proceedings of the 1986 ACM conference on LISP and functional programming
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
HOLCF: Higher Order Logic of Computable Functions
Proceedings of the 8th International Workshop on Higher Order Logic Theorem Proving and Its Applications
Inductive Definitions: Automation and Application
Proceedings of the 8th International Workshop on Higher Order Logic Theorem Proving and Its Applications
Galois connections and fixed point calculus
Algebraic and coalgebraic methods in the mathematics of program construction
Journal of Functional Programming
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
A coinductive monad for prop-bounded recursion
PLPV '07 Proceedings of the 2007 workshop on Programming languages meets program verification
General recursion in type theory
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Mathematical quotients and quotient types in Coq
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
A Formally Verified Compiler Back-end
Journal of Automated Reasoning
Independence results for n-ary recursion theorems
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
The optimal fixed point combinator
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
A Two-Valued Logic for Properties of Strict Functional Programs Allowing Partial Functions
Journal of Automated Reasoning
Proofs you can believe in: proving equivalences between Prolog semantics in Coq
Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming
Combining proofs and programs in a dependently typed language
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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We propose to use the Knasterâ聙聯Tarski least fixed point theorem as a basis to define recursive functions in the Calculus of Inductive Constructions. This widens the class of functions that can be modelled in type-theory based theorem proving tools to potentially nonterminating functions. This is only possible if we extend the logical framework by adding some axioms of classical logic.We claim that the extended framework makes it possible to reason about terminating or non-terminating computations and we show that extraction can also be extended to handle the new functions