Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Systematic software development using VDM (2nd ed.)
Systematic software development using VDM (2nd ed.)
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
A type-theoretical alternative to ISWIM, CUCH, OWHY
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Formal Verification for Fault-Tolerant Architectures: Prolegomena to the Design of PVS
IEEE Transactions on Software Engineering
The B-book: assigning programs to meanings
The B-book: assigning programs to meanings
A high-level derivation of global search algorithms (with constraint propagation)
Science of Computer Programming - Special issue: on formal specifications: foundations, methods, tools and applications: selected papers from the FMTA '95 conference (29–31 May 1995, Konstancin n. Warsaw, Poland)
An axiomatic basis for computer programming
Communications of the ACM
Java Program Verification via a Hoare Logic with Abrupt Termination
FASE '00 Proceedings of the Third Internationsl Conference on Fundamental Approaches to Software Engineering: Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS 2000
HOLCF: Higher Order Logic of Computable Functions
Proceedings of the 8th International Workshop on Higher Order Logic Theorem Proving and Its Applications
An Integration of Model Checking with Automated Proof Checking
Proceedings of the 7th International Conference on Computer Aided Verification
Mathematical Structures Underlying Greedy Algorithms
FCT '81 Proceedings of the 1981 International FCT-Conference on Fundamentals of Computation Theory
Design by Contract: Making Object-Oriented Programs that Work
TOOLS '97 Proceedings of the Technology of Object-Oriented Languages and Systems - Tools-25
Theory Interpretations in PVS
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Planning Algorithms
Trust and Automation in Verification Tools
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Rewriting, inference, and proof
WRLA'10 Proceedings of the 8th international conference on Rewriting logic and its applications
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The Knaster–Tarski theorem asserts the existence of least and greatest fixpoints for any monotonic function on a complete lattice. More strongly, it asserts the existence of a complete lattice of such fixpoints. This fundamental theorem has a fairly straightforward proof. We use a mechanically checked proof of the Knaster–Tarski theorem to illustrate several features of the Prototype Verification System (PVS). We specialize the theorem to the power set lattice, and apply the latter to the verification of a general forward search algorithm and a generalization of Dijkstra's shortest path algorithm. We use these examples to argue that the verification of even simple, widely used algorithms can depend on a fair amount of background theory, human insight, and sophisticated mechanical support.