Theorem Proving and Proof Verification in the System SAD

Lyaletski, Alexander V.; Paskevich, Andrey; Verchinine, Konstantin

doi:10.1007/978-3-540-27818-4_17

Cited by 11 publications

(6 citation statements)

References 12 publications

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“…Naproche-SAD is a recent tool by Frerix and Koepke [8], based on the original System for Automated Deduction (SAD) by Paskevich and others [11]. It processes the Formal Theory Language (ForTheL), which is designed to look like mathematical text, but it is restricted to a small subset of natural language.…”

Section: Isabelle/naproche For Automatic Proof-checking Of Ordinary M...mentioning

confidence: 99%

Interaction with Formal Mathematical Documents in Isabelle/PIDE

Wenzel¹

2019

Lecture Notes in Computer Science

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Isabelle/PIDE has emerged over more than 10 years as the standard Prover IDE for interactive theorem proving in Isabelle. The well-established Archive of Formal Proofs (AFP) testifies the success of such applications of formalized mathematics in Isabelle/HOL. More recently, the scope of PIDE has widened towards languages that are not connected to logic and proof in Isabelle, but taken from a broader repertoire of mathematics on the computer. The present paper provides a general overview of the PIDE project and its underlying document model, with built-in parallel evaluation and asynchronous interaction. There is also some discussion of original aims and approaches, successes and failures, later changes to the plan, and ideas for the future.

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Section: Isabelle/naproche For Automatic Proof-checking Of Ordinary M...mentioning

confidence: 99%

Interaction with Formal Mathematical Documents in Isabelle/PIDE

Wenzel¹

2019

Lecture Notes in Computer Science

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“…The EA project seems to have run since the beginning of the 1970s, but it hasn't become known outside of Russia and Ukraine and publications about the project are all in Russian. The project has evolved into a system SAD (System for Automated Deduction) [45], which checks mathematical texts written in the language ForTheL (FORmal THEory Language) [67]. The latter is a declarative formal language for writing definitions, lemmas and proofs, very much in the spirit of Mizar, but developed independently from it.…”

Section: Evidence Algorithmmentioning

confidence: 99%

Proof assistants: History, ideas and future

Geuvers

2009

Sadhana

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In this paper we will discuss the fundamental ideas behind proof assistants: What are they and what is a proof anyway? We give a short history of the main ideas, emphasizing the way they ensure the correctness of the mathematics formalized. We will also briefly discuss the places where proof assistants are used and how we envision their extended use in the future. While being an introduction into the world of proof assistants and the main issues behind them, this paper is also a position paper that pushes the further use of proof assistants. We believe that these systems will become the future of mathematics, where definitions, statements, computations and proofs are all available in a computerized form. An important application is and will be in computer supported modelling and verification of systems. But their is still along road ahead and we will indicate what we believe is needed for the further proliferation of proof assistants.

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“…Below we present the current incarnation of the Evidence Algorithm, the System for Automated Deduction (SAD) [5,6], in its current state of development. We start by describing the design of the SAD system and the services it provides (Section 2).…”

Section: Introductionmentioning

confidence: 99%

SAD as a mathematical assistant—how should we go from here to there?

Lyaletski

Paskevich

Verchinine³

2006

Journal of Applied Logic

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The System for Automated Deduction (SAD) is developed in the framework of the Evidence Algorithm research project and is intended for automated processing of mathematical texts. The SAD system works on three levels of reasoning: (a) the level of text presentation where proofs are written in a formal natural-like language for subsequent verification; (b) the level of foreground reasoning where a particular theorem proving problem is simplified and decomposed; (c) the level of background deduction where exhaustive combinatorial inference search in classical first-order logic is applied to prove end subgoals.We present an overview of SAD describing the ideas behind the project, the system's design, and the process of problem formalization in the fashion of SAD. We show that the choice of classical first-order logic as the background logic of SAD is not too restrictive. For example, we can handle binders like Σ or lim without resort to second order or to a full-powered set theory. We illustrate our approach with a series of examples, in particular, with the classical problem √ 2 / ∈ Q.

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Theorem Proving and Proof Verification in the System SAD

Cited by 11 publications

References 12 publications

Interaction with Formal Mathematical Documents in Isabelle/PIDE

Interaction with Formal Mathematical Documents in Isabelle/PIDE

Proof assistants: History, ideas and future

SAD as a mathematical assistant—how should we go from here to there?

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