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Adam Chlipala This is the web site for an in-progress textbook about practical engineering with the Coq proof assistant. The focus is on building programs with proofs of correctness, using dependent types and scripted proof automation. This is the text for a Fall 2008 class at Harvard.
Coq'Art is the familiar name for the first book on the Coq proof assistant and its underlying theory the Calculus of Inductive Constructions , written by Yves Bertot and Pierre Castéran. Interactive Theorem Proving and Program Development Coq'Art: The Calculus of Inductive Constructions Series: Texts in Theoretical Computer Science. An EATCS Series Bertot, Yves, Castéran, Pierre 2004, XXV, 469 p., Hardcover ISBN: 3-540-20854-2 This site has been updated for Coq8.2. Warning! Some solutions we propose don't work on versions prior to V8.2gamma. Please find here a tar file fully compatible with coq8.1pl3 and the printed edition of the book. These exercises were written after the release of the book (May 2004). The solution of some of them (e.g. mergesort ) illustrates new features of Coq. For instance, command Function and tactic functional induction.
Supported and ongoing software projects: * IsaPlanner - a proof planner for Isabelle * HiGraph - a system for presenting and manipulating hierarchical proofs/graphs generated by proof planning in IsaPlanner. Currently just an editor/drawing tool for the graphs. * Quantomatic - a tool for graphically reasoning about quantum computation using models based on compact closed categories. Older software projects (no longer being developed): * Lambda Clam - a proof planner written in lambda prolog. * HR - an automated theory formation system * Clam proof planner with oyster - a proof planner written in prolog * Clam version 3.2 * HOL-Clam - a link up between the HOL proof assistant and the Clam proof planner. * Anastasia - a structural program editor * Press - a prolog based system for solving symbolic, transcendental, non-differential equations
Research Interests Programming Languages, Logic and Type Theory, Logical Frameworks, Automated Deduction, Trustworthy Computing (see also Publications, Students & Co-authors) Projects Logosphere A Formal Digital Library Triple Type Refinement in Programming Languages ConCert Language Technology for Trustless Software Dissemination Twelf Logical and Meta-Logical Frameworks SeLF Distributed System Security via Logical Frameworks Manifest Security Logics and Languages for Manifestly Secure Systems Prospero Integrating Types and Specifications
HOL4 is the latest version of the HOL interactive proof assistant for higher order logic: a programming environment in which theorems can be proved and proof tools implemented. Built-in decision procedures and theorem provers can automatically establish many simple theorems (users may have to prove the hard theorems themselves!) An oracle mechanism gives access to external programs such as SAT and BDD engines. HOL 4 is particularly suitable as a platform for implementing combinations of deduction, execution and property checking. several widely used versions of the HOL system: 1. HOL88 from Cambridge; 2. HOL90 from Calgary and Bell Labs; 3. HOL98 from Cambridge, Glasgow and Utah. HOL 4 is the successor to these. Its development was partly supported by the PROSPER project. HOL 4 is based on HOL98 and incorporates ideas and tools from HOL Light. The ProofPower system is another implementation of HOL.
HOL Light is a computer program to help users prove interesting mathematical theorems completely formally in higher order logic. It sets a very exacting standard of correctness, but provides a number of automated tools and pre-proved mathematical theorems (e.g. about arithmetic, basic set theory and real analysis) to save the user work. It is also fully programmable, so users can extend it with new theorems and inference rules without compromising its soundness. There are a number of versions of HOL, going back to Mike Gordon's work in the early 80s. Compared with other HOL systems, HOL Light uses a much simpler logical core and has little legacy code, giving the system a simple and uncluttered feel. Despite its simplicity, it offers theorem proving power comparable to, and in some areas greater than, other versions of HOL, and has been used for some significant industrial-scale verification applications.
In the fully expansive (or LCF-style) approach to theorem proving, theorems are represented by an abstract type whose primitive operations are the axioms and inference rules of a logic. Theorem proving tools are implemented by composing together the inference rules using ML programs. This idea can be generalised to computing valid judgements that represent other kinds of information. In particular, consider judgements (a,r,t,b), where a is a set of boolean terms (assumptions) that are assumed true, r represents a variable order, t is a boolean term all of whose free variables are boolean and b is a BDD. Such a judgement is valid if under the assumptions a, the BDD representing t with respect to r is b, and we will write a r t --> b when this is the case. The derivation of "theorems" like a r t --> b can be viewed as "proof" in the style of LCF by defining an abstract type term_bdd that models judgements a r t --> b analogously to the way the type thm models theorems |- t.
In my experience, proof readers tend to be rather calm individuals, going about their work in an unruffled, dignified manner. Proof readers are rarely confrontational in temperament, because proofreading by its very nature requires a serene and reflective approach. So, it was rare for me, as an Operations Manager supervising, amongst other people, proof readers, to have to intervene in any kind of serious dispute.
Except when it came to hyphens.
This interactive tutorial will teach you how to use the sequent calculus, a simple set of rules with which you can use to show the truth of statements in first order logic. It is geared towards anyone with some background in writing software for computers, with knowledge of basic boolean logic.
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