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Generic Automatic Proof Tools
, 1997
"... This article explores a synthesis between two distinct traditions in automated reasoning: resolution and interaction. In particular it discusses Isabelle, an interactive theorem prover based upon a form of resolution. It aims to demonstrate the value of proof tools that, compared with traditional re ..."
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Cited by 29 (11 self)
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This article explores a synthesis between two distinct traditions in automated reasoning: resolution and interaction. In particular it discusses Isabelle, an interactive theorem prover based upon a form of resolution. It aims to demonstrate the value of proof tools that, compared with traditional
AUTOMATIC PROOF OF GRAPH NONISOMORPHISM
"... Abstract. We describe automated methods for constructing nonisomorphism proofs for pairs of graphs. The proofs can be humanreadable or machinereadable. We have developed a proof generator for graph nonisomorphism, which allows users to input graphs and construct a proof of (non)isomorphism. 1. ..."
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Cited by 1 (0 self)
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Abstract. We describe automated methods for constructing nonisomorphism proofs for pairs of graphs. The proofs can be humanreadable or machinereadable. We have developed a proof generator for graph nonisomorphism, which allows users to input graphs and construct a proof of (non)isomorphism. 1.
Automatic Proofs of Properties of Simple
"... We address the problem of verifying automatically properties of modules written in the C \Gamma\Gamma language, a very simple imperative language. In this paper, we develop a framework for proving automatically properties of modules written in C \Gamma\Gamma . Our approach consists of two steps. ..."
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the proof of the desired properties. Our system enables to prove many properties completely automatically from the C \Gamma\Gamma code alone. We illustrate computer applications on programs computing on integers and linked lists. 1 Introduction The need to be able to reason about computer programs in a
Automatic Proofs for Scalecharts
"... Abstract. A scalechart is a set of statecharts, operating in a dense time domain, whose behavior is selfsimilar at different scales. The simplicity of extracting proofs of behavior from scalecharts is demonstrated, based on the < and co relationships. An algorithm is presented which automaticall ..."
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Abstract. A scalechart is a set of statecharts, operating in a dense time domain, whose behavior is selfsimilar at different scales. The simplicity of extracting proofs of behavior from scalecharts is demonstrated, based on the < and co relationships. An algorithm is presented which
Automatic Proofs of Identities
, 2011
"... We present the ideas behind algorithmic proofs of identities involving sums and integrals of large classes of special functions. Recent results allowed a new extension of the class of holonomic functions. 1 ..."
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We present the ideas behind algorithmic proofs of identities involving sums and integrals of large classes of special functions. Recent results allowed a new extension of the class of holonomic functions. 1
The Diagonalization Method In Automatic Proof
, 1997
"... In proof planning, common patterns of mathematical reasoning are embodied in tactics. Each of these is associated with a method, specifying its preconditions and effects. Using methods, a plan for a proof can be constructed from tactics. This plan is then used to guide a theorem prover through the p ..."
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In proof planning, common patterns of mathematical reasoning are embodied in tactics. Each of these is associated with a method, specifying its preconditions and effects. Using methods, a plan for a proof can be constructed from tactics. This plan is then used to guide a theorem prover through
Automatic Proofs and Refutations for . . .
, 2012
"... This thesis describes work on two components of the interactive theorem prover Isabelle/HOL that generate proofs and counterexamples for higherorder conjectures by harnessing external firstorder reasoners. Our primary contribution is the development of Nitpick, a counterexample generator that bui ..."
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This thesis describes work on two components of the interactive theorem prover Isabelle/HOL that generate proofs and counterexamples for higherorder conjectures by harnessing external firstorder reasoners. Our primary contribution is the development of Nitpick, a counterexample generator
Automatic Proof and Disproof in Isabelle/HOL
, 2011
"... 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 c ..."
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Cited by 11 (0 self)
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transformed the Isabelle user experience. This paper provides an overview of the main automatic proof and disproof tools.
Automatic proof generation in Kleene algebra
 In Proc. 10th Int. Conf. Relational Methods in Computer Science (RelMiCS10) and 5th Int. Conf Applications of Kleene Algebra (AKA5), volume 4988 of LNCS
, 2008
"... Abstract. In this paper, we develop the basic theory of disimulations, a type of relation between two automata which witnesses equivalence. We show that many standard constructions in the theory of automata such as determinization, minimization, inaccessible state removal, et al., are instances of d ..."
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Cited by 8 (3 self)
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of disimilar automata. Then, using disimulations, we define an “algebraic ” proof system for the equational theory of Kleene algebra in which a proof essentially consists of a sequence of matrices encoding automata and disimulations between them. We show that this proof system is complete for the equational
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