Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Set theory for verification. I: from foundations to functions
Journal of Automated Reasoning
Automated reasoning and its applications
QuickCheck: a lightweight tool for random testing of Haskell programs
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
Computer-Aided Reasoning: An Approach
Computer-Aided Reasoning: An Approach
Symbolic Model Checking without BDDs
TACAS '99 Proceedings of the 5th International Conference on Tools and Algorithms for Construction and Analysis of Systems
Type Classes and Overloading in Higher-Order Logic
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
System Description: SystemOn TPTP
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Combining superposition, sorts and splitting
Handbook of automated reasoning
Random Testing in Isabelle/HOL
SEFM '04 Proceedings of the Software Engineering and Formal Methods, Second International Conference
Relational analysis of algebraic datatypes
Proceedings of the 10th European software engineering conference held jointly with 13th ACM SIGSOFT international symposium on Foundations of software engineering
Software Abstractions: Logic, Language, and Analysis
Software Abstractions: Logic, Language, and Analysis
Tutorial: Automated Formal Methods with PVS, SAL, and Yices
SEFM '06 Proceedings of the Fourth IEEE International Conference on Software Engineering and Formal Methods
The design and implementation of VAMPIRE
AI Communications - CASC
Translating Higher-Order Clauses to First-Order Clauses
Journal of Automated Reasoning
Higher-Order Proof Construction Based on First-Order Narrowing
Electronic Notes in Theoretical Computer Science (ENTCS)
The CADE-21 automated theorem proving system competition
AI Communications
Smallcheck and lazy smallcheck: automatic exhaustive testing for small values
Proceedings of the first ACM SIGPLAN symposium on Haskell
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Purely functional lazy non-deterministic programming
Proceedings of the 14th ACM SIGPLAN international conference on Functional programming
Communications of the ACM
Kodkod: a relational model finder
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Finding lexicographic orders for termination proofs in Isabelle/HOL
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Source-level proof reconstruction for interactive theorem proving
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
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
Integrating an automated theorem prover into agda
NFM'11 Proceedings of the Third international conference on NASA Formal methods
Extending Sledgehammer with SMT solvers
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Sort it out with monotonicity: translating between many-sorted and unsorted first-order logic
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Sine Qua non for large theory reasoning
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Monotonicity Inference for Higher-Order Formulas
Journal of Automated Reasoning
SMT solvers: new oracles for the HOL theorem prover
International Journal on Software Tools for Technology Transfer (STTT) - VSTTE 2009
Code generation via higher-order rewrite systems
FLOPS'10 Proceedings of the 10th international conference on Functional and Logic Programming
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Nitpick: a counterexample generator for higher-order logic based on a relational model finder
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Fast LCF-Style proof reconstruction for z3
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Teaching semantics with a proof assistant: no more LSD trip proofs
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
Automated analysis of regular algebra
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Overview and evaluation of premise selection techniques for large theory mathematics
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Dependently typed programming based on automated theorem proving
MPC'12 Proceedings of the 11th international conference on Mathematics of Program Construction
Automated reasoning in higher-order regular algebra
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
The new quickcheck for isabelle: random, exhaustive and symbolic testing under one roof
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
CADE'13 Proceedings of the 24th international conference on Automated Deduction
Data refinement in Isabelle/HOL
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
Premise Selection for Mathematics by Corpus Analysis and Kernel Methods
Journal of Automated Reasoning
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Isabelle/HOL is a popular interactive theorem prover based on higherorder logic. It owes its success to its ease of use and powerful automation. Much of the automation is performed by external tools: The metaprover Sledgehammer relies on resolution provers and SMT solvers for its proof search, the counterexample generator Quickcheck uses the ML compiler as a fast evaluator for ground formulas, and its rival Nitpick is based on the model finder Kodkod, which performs a reduction to SAT. Together with the Isar structured proof format and a new asynchronous user interface, these tools have radically transformed the Isabelle user experience. This paper provides an overview of the main automatic proof and disproof tools.