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
An axiomatic basis for computer programming
Communications of the ACM
A Calculus of Communicating Systems
A Calculus of Communicating Systems
Computer-Aided Reasoning: An Approach
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HOL Light: A Tutorial Introduction
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
Possibly Infinite Sequences in Theorem Provers: A Comparative Study
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
The KIV System: Systematic Construction of Verified Software
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
PVS: A Prototype Verification System
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
System Description: Twelf - A Meta-Logical Framework for Deductive Systems
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Interactive Theorem Proving and Program Development
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Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
Ynot: dependent types for imperative programs
Proceedings of the 13th ACM SIGPLAN international conference on Functional programming
A Hoare Logic for Call-by-Value Functional Programs
MPC '08 Proceedings of the 9th international conference on Mathematics of Program Construction
Proceedings of the 3rd workshop on Programming languages meets program verification
Implementing polymorphism in SMT solvers
SMT '08/BPR '08 Proceedings of the Joint Workshops of the 6th International Workshop on Satisfiability Modulo Theories and 1st International Workshop on Bit-Precise Reasoning
A Basis for Verifying Multi-threaded Programs
ESOP '09 Proceedings of the 18th European Symposium on Programming Languages and Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Who: a verifier for effectful higher-order programs
Proceedings of the 2009 ACM SIGPLAN workshop on ML
VCC: A Practical System for Verifying Concurrent C
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
A Brief Overview of Agda --- A Functional Language with Dependent Types
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
The Why/Krakatoa/Caduceus platform for deductive program verification
CAV'07 Proceedings of the 19th international conference on Computer aided verification
CAV'07 Proceedings of the 19th international conference on Computer aided verification
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Verification of object-oriented software: The KeY approach
Verification of object-oriented software: The KeY approach
Dafny: an automatic program verifier for functional correctness
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Specification and verification: the Spec# experience
Communications of the ACM
Secure distributed programming with value-dependent types
Proceedings of the 16th ACM SIGPLAN international conference on Functional programming
Boogie: a modular reusable verifier for object-oriented programs
FMCO'05 Proceedings of the 4th international conference on Formal Methods for Components and Objects
Filters on coinductive streams, an application to eratosthenes' sieve
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Automating induction with an SMT solver
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
Frama-C: a software analysis perspective
SEFM'12 Proceedings of the 10th international conference on Software Engineering and Formal Methods
Why3: where programs meet provers
ESOP'13 Proceedings of the 22nd European conference on Programming Languages and Systems
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The power and automation offered by modern satisfiability-modulo-theories (SMT) solvers is changing the landscape for mechanized formal theorem proving. For instance, the SMT-based program verifier Dafny supports a number of proof features traditionally found only in interactive proof assistants, like inductive, co-inductive, and declarative proofs. To show that proof tools rooted in SMT are growing up, this paper presents, using Dafny, a series of examples that illustrate how theorems are expressed and proved. Since the SMT solver takes care of many formal trivialities automatically, users can focus more of their time on the creative ingredients of proofs.