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.
There is a growing amount of evidence-based research supporting various botanicals; and/or primary evidence comes from a long medicinal use. Evidence-based research may be limited, but we shouldn't ignore botanicals that have been used for 1000s of years,
Isabelle is a generic proof assistant. It allows mathematical formulas to be expressed in a formal language and provides tools for proving those formulas in a logical calculus. Isabelle is developed at University of Cambridge (Larry Paulson) and Technische Universität München (Tobias Nipkow). See the Isabelle overview for a brief introduction. Now available: Isabelle2008 Some notable improvements: * HOL: significant speedup of Metis prover; proper support for multithreading. * HOL: new version of primrec command supporting type-inference and local theory targets. * HOL: improved support for termination proofs of recursive function definitions. * New local theory targets for class instantiation and overloading. * Support for named dynamic lists of theorems.
IsaPlanner is a generic framework for proof planning in the interactive theorem prover Isabelle. It facilitates the encoding of reasoning techniques, which can be used to conjecture and prove theorems automatically. The system provides an interactive tracing tool that allows you to interact the proof planning attempt. (see the screenshot of IsaPlanner being used with Isabelle and Proof General) It is based on the Isabelle theorem prover and the Isar language. The main proof technique written in IsaPlanner is an inductive theorem prover based on Rippling. This is applicable within Isabelle's Higher Order Logic, and can easily be adapted to Isabelle's other logics. The system now the main platform for proof planning research in the Edinburgh mathematical reasoning group
This site is an experimental HTML rendering of fragments of the IsarMathLib project. IsarMathLib is a library of mathematical proofs formally verified by the Isabelle theorem proving environment. The formalization is based on the Zermelo-Fraenkel set theory. The Introduction provides more information about IsarMathLib. The software for exporting Isabelle's Isar language to HTML markup is at an early beta stage, so some proofs may be rendered incorrectly. In case of doubts, compare with the Isabelle generated IsarMathLib proof document.
LambdaCLAM is a tool for automated theorem proving in higher order domains. In particular LambdaCLAM specialises in proof using induction based on the rippling heuristic. LambdaCLAM is a higher-order version of CLAM. Both CLAM and LambdaCLAM use proof planning to guide the search for a proof A proof plan is a proof of a theorem at some level of abstraction presented as a tree. Each node in this tree is justified by a tactic. The exact nature of these tactics is unspecified, they may be sequences of inference rules, programs for generating sequences of inferences or a further proof plan at some lower level of abstraction. In principle while the generation of the proof tree may have involved heuristics and (possibly) unsound inference steps, it can be justified by executing the tactics attached to the nodes.
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