An introduction to functional programming systems using Haskell
An introduction to functional programming systems using Haskell
Synthesis of ML programs in the system Coq
Journal of Symbolic Computation - Special issue on automatic programming
Infinite objects in type theory
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Programming with streams in Coq: a case study: the Sieve of Eratosthenes
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
A Transformation System for Developing Recursive Programs
Journal of the ACM (JACM)
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Codifying Guarded Definitions with Recursive Schemes
TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
An Application of Co-inductive Types in Coq: Verification of the Alternating Bit Protocol
TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
Simple general recursion in type theory
Nordic Journal of Computing
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
A unifying approach to recursive and co-recursive definitions
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
Affine functions and series with co-inductive real numbers
Mathematical Structures in Computer Science
Constructive analysis, types and exact real numbers
Mathematical Structures in Computer Science
Inductive and Coinductive Components of Corecursive Functions in Coq
Electronic Notes in Theoretical Computer Science (ENTCS)
Dependent Types, Theorem Proving, and Applications for a Verifying Compiler
Verified Software: Theories, Tools, Experiments
Coinductive big-step operational semantics
Information and Computation
Using Structural Recursion for Corecursion
Types for Proofs and Programs
Trace-Based Coinductive Operational Semantics for While
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Coinductive correctness of homographic and quadratic algorithms for exact real numbers
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Formal polytypic programs and proofs
Journal of Functional Programming
The optimal fixed point combinator
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Coinductive big-step operational semantics
ESOP'06 Proceedings of the 15th European conference on Programming Languages and Systems
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Automating theorem proving with SMT
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
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We present the formal description of an algorithm to filter values from an infinite steam using a type theory based prover. The key aspect is that filters are partial co-recursive functions and we solve the problem of expressing partiality. We then show how to prove properties of this filter algorithm and we study an application computing the stream of all prime numbers.