proof strategy language and goal oriented conjecturing
play

Proof Strategy Language and Goal-Oriented Conjecturing for - PowerPoint PPT Presentation

Dec 19, 2023 •215 likes •558 views

Proof Strategy Language and Goal-Oriented Conjecturing for Isabelle/HOL Yutaka Nagashima and Julian Parsert Czech Technical University in Prague University of Innsbruck Isabelle/HOL before PSL Isabelle/HOL before PSL context proof goal

  1. Proof Strategy Language and Goal-Oriented Conjecturing for Isabelle/HOL Yutaka Nagashima and Julian Parsert Czech Technical University in Prague University of Innsbruck

  2. Isabelle/HOL before PSL

  3. Isabelle/HOL before PSL context proof goal optimal for proof automation tactic / sub-tool

  4. Isabelle/HOL before PSL context proof goal optimal for proof automation tactic / sub-tool error-message subgoals

  5. Isabelle/HOL before PSL context proof goal optimal for proof automation tactic / sub-tool error-message subgoals

  6. Isabelle/HOL before PSL context proof goal optimal for proof automation tactic / sub-tool error-message subgoals no sub-goal!

  7. Isabelle/HOL before PSL context proof goal optimal for proof automation tactic / sub-tool error-message subgoals no sub-goal!

  8. Isabelle/HOL before PSL context proof goal optimal for proof automation tactic / sub-tool error-message subgoals no sub-goal!

  9. Isabelle/HOL before PSL context proof goal optimal for proof automation tactic / sub-tool error-message subgoals no sub-goal!

  10. Isabelle/HOL before PSL context proof goal optimal for proof automation tactic / sub-tool error-message subgoals no sub-goal!

  11. Isabelle/HOL before PSL context proof goal optimal for proof automation tactic / sub-tool error-message It's blatantly clear subgoals no sub-goal! You stupid machine, that what I tell you is true (Michael Norrish)

  12. PSL (Proof Strategy Language) PSL

  13. PSL (Proof Strategy Language) meta-tool approach PSL

  14. PSL (Proof Strategy Language) tactics meta-tool approach PSL

  15. PSL (Proof Strategy Language) tactics meta-tool approach quickcheck PSL

  16. PSL (Proof Strategy Language) tactics meta-tool approach quickcheck sledgehammer PSL

  17. PSL (Proof Strategy Language) tactics meta-tool approach quickcheck sledgehammer programming language PSL

  18. PSL (Proof Strategy Language) tactics meta-tool approach quickcheck sledgehammer programming language extensible PSL (Eisbach)

  19. PSL (Proof Strategy Language) tactics meta-tool approach quickcheck sledgehammer programming language runtime tactic extensible generation PSL (Eisbach)

  20. PSL (Proof Strategy Language) tactics meta-tool approach quickcheck sledgehammer programming language runtime tactic extensible generation PSL (Eisbach) extensive proof search

  21. PSL (Proof Strategy Language) tactics meta-tool approach quickcheck sledgehammer programming language runtime tactic extensible generation PSL (Eisbach) extensive proof search low memory usage

  22. PSL (Proof Strategy Language) tactics meta-tool approach quickcheck sledgehammer programming language runtime tactic extensible generation PSL (Eisbach) extensive parallel proof search search low memory usage

  23. PSL (Proof Strategy Language) tactics meta-tool approach quickcheck sledgehammer programming language runtime tactic extensible generation PSL (Eisbach) efficient proof generation extensive parallel proof search search low memory usage

  24. PSL (Proof Strategy Language) tactics meta-tool approach quickcheck sledgehammer programming language runtime tactic extensible generation PSL (Eisbach) efficient proof generation extensive parallel proof search native Isabelle search low memory proof script usage

  25. PSL (Proof Strategy Language) tactics meta-tool approach quickcheck sledgehammer programming language runtime tactic extensible generation PSL (Eisbach) efficient proof generation extensive parallel proof search native Isabelle search low memory proof script usage easy installation

  26. PSL (Proof Strategy Language) tactics meta-tool approach quickcheck sledgehammer programming language runtime tactic extensible generation PSL (Eisbach) efficient proof generation extensive parallel proof search native Isabelle search low memory proof script usage easy installation badly specified proof goals

  27. PSL (Proof Strategy Language) tactics meta-tool approach quickcheck sledgehammer programming language runtime tactic extensible generation PSL (Eisbach) efficient proof generation extensive parallel proof search native Isabelle search low memory proof script usage easy installation badly specified proof goals proof goals optimal for Isabelle

  28. No background in Isabelle is necessary! PSL: Proof Strategy Language and Proof Script Generation � 4

  29. PSL with PGT PGT

  30. PSL with PGT proof goal sub-optimal for proof automation context PGT strategy PGT

  31. PSL with PGT proof goal sub-optimal proof goal context for proof automation tactic / sub-tool context PGT strategy PGT

  32. PSL with PGT proof goal sub-optimal proof goal context for proof automation tactic / sub-tool context PGT strategy PGT proved theorem / subgoals / message

  33. PSL with PGT proof goal sub-optimal proof goal context for proof automation tactic / sub-tool context PGT strategy PGT proof for the original goal, proved theorem / and auxiliary lemma subgoals / message optimal for proof automation

Recommend

Automated Conjecturing for Proof Discovery Craig Larson (joint work with Nico Van Cleemput)

Automated Conjecturing for Proof Discovery Craig Larson (joint work with Nico Van Cleemput)

Automated Conjecturing for Proof Discovery Craig Larson (joint work with Nico Van Cleemput) Virginia Commonwealth University Ghent University CombinaTexas Texas A&M University 8 May 2016 Kiran ChilakamarriOn Conjectures Goal To tell

1.43k views • 75 slides
An Implicational Logic for Conjecturing and Distributed Proof Attempts Lucas Dixon 1 Nov 2007

An Implicational Logic for Conjecturing and Distributed Proof Attempts Lucas Dixon 1 Nov 2007

An Implicational Logic for Conjecturing and Distributed Proof Attempts Lucas Dixon 1 Nov 2007 Lucas Dixon An Implicational Logic of Conjecturing (ILC) 1 Nov 2007 1 The Issue Asynchronous and distributed contribution to a formalisation.

440 views • 13 slides
First Experiments with Data Driven Conjecturing Karel Chvalovsk, Thibault Gauthier, and Josef

First Experiments with Data Driven Conjecturing Karel Chvalovsk, Thibault Gauthier, and Josef

First Experiments with Data Driven Conjecturing Karel Chvalovsk, Thibault Gauthier, and Josef Urban CIIRC CTU Conjecturing some bits from history There have been various attempts, e.g., Wang in the late 1950s novel and

540 views • 15 slides
SOL Shape Oriented Language Aditya Narayanamoorthy - Language Guru Gergana Alteva - Project

SOL Shape Oriented Language Aditya Narayanamoorthy - Language Guru Gergana Alteva - Project

SOL Shape Oriented Language Aditya Narayanamoorthy - Language Guru Gergana Alteva - Project Manager Erik Dyer - System Architect Kunal Baweja - Testing Why SOL? We wanted: - a simple, lightweight object-oriented language for creating 2D

447 views • 10 slides
Conjecturing over large corpora Thibault Gauthier Cezary Kaliszyk Josef Urban April 6, 2016 1

Conjecturing over large corpora Thibault Gauthier Cezary Kaliszyk Josef Urban April 6, 2016 1

Conjecturing over large corpora Thibault Gauthier Cezary Kaliszyk Josef Urban April 6, 2016 1 Goal Automatically discover conjectures in formalized libraries. Which formalized libraries ? theorems constants types theories Mizar 51086

587 views • 22 slides
Conjecturing over large corpora Thibault Gauthier Cezary Kaliszyk Josef Urban July 14, 2017 1

Conjecturing over large corpora Thibault Gauthier Cezary Kaliszyk Josef Urban July 14, 2017 1

Conjecturing over large corpora Thibault Gauthier Cezary Kaliszyk Josef Urban July 14, 2017 1 Goal Automatically discover conjectures in formalized libraries. Which formalized libraries ? theorems constants types theories Mizar 51086

449 views • 27 slides
Goal-Oriented Buffer Management Revisited Andr e Riedel 21 January 2004 Goal-Oriented Buffer

Goal-Oriented Buffer Management Revisited Andr e Riedel 21 January 2004 Goal-Oriented Buffer

Otto-von-Guericke-Universit at Magdeburg Seminar Self-Tuning Databases Goal-Oriented Buffer Management Revisited Andr e Riedel 21 January 2004 Goal-Oriented Buffer Management Revisited Contents Contents 1. Introduction 2. Previous

532 views • 22 slides
OOP PHP PHP is an object-oriented language See:

OOP PHP PHP is an object-oriented language See:

OOP PHP PHP is an object-oriented language See: h8p://us.php.net/manual/en/language.oop5.php Has classes + objects Has inheritance and method

708 views • 17 slides
Designing Games of Theorems Who am I? What do I like? automating proof search in expressive

Designing Games of Theorems Who am I? What do I like? automating proof search in expressive

Designing Games of Theorems Who am I? What do I like? automating proof search in expressive logic (HOL) using heuristics / ML What did I develop? PSL/PaMpeR for Isabelle/HOL Proof Strategy Language (PSL) for Isabelle/HOL meta-tool tactics

380 views • 19 slides
ProverBot9000 A proof assistant assistant Proofs are hard Proof assistants are hard Big Idea:

ProverBot9000 A proof assistant assistant Proofs are hard Proof assistants are hard Big Idea:

ProverBot9000 A proof assistant assistant Proofs are hard Proof assistants are hard Big Idea: Proofs are hard, make computers do them Proofs are just language with lots of structure Local Context Global Goal Context Want to generate this!

288 views • 18 slides
C2 language Bas van den Berg Fosdem 2015, Brussels Bas van den Berg C2 language Goal Goal of

C2 language Bas van den Berg Fosdem 2015, Brussels Bas van den Berg C2 language Goal Goal of

C2 language Bas van den Berg Fosdem 2015, Brussels Bas van den Berg C2 language Goal Goal of this presentation: show the C2 language show how you can re-use LLVM/Clang components get feedback/ideas Bas van den Berg C2 language

686 views • 40 slides
Object-Oriented Databases Object Oriented Databases ODMG Standard Object Model, Object

Object-Oriented Databases Object Oriented Databases ODMG Standard Object Model, Object

Object-Oriented Databases Object Oriented Databases ODMG Standard Object Model, Object Definition Language, Object Query Language Programming Language Bindings Outlook October 17, 2008 Michael Grossniklaus Department of

786 views • 27 slides
Adaptive FEM, Approach with hp- and Goal-Oriented A Posteriori Error Estimator Arezou Ghesmati

Adaptive FEM, Approach with hp- and Goal-Oriented A Posteriori Error Estimator Arezou Ghesmati

Adaptive FEM, Approach with hp- and Goal-Oriented A Posteriori Error Estimator Arezou Ghesmati Dept. of Mathematics Texas A&M University 5 th deal.II Users and Developers Workshop Aug. 6, 2015 Arezou Ghesmati (TAMU) hp- and Goal-Oriented

770 views • 47 slides
Language-Independent Detection of Object-Oriented Design Patterns Johan Fabry Vrije

Language-Independent Detection of Object-Oriented Design Patterns Johan Fabry Vrije

Language-Independent Detection of Object-Oriented Design Patterns Johan Fabry Vrije Universiteit Brussel, Programming Technology Lab johan.fabry@vub.ac.be 25 Aug 2003 Lang-Indep Detection of OO DP 1 Overview Research Goal DMP and Soul

519 views • 33 slides
UML: Uniform Modeling Language UML is a standardized design language for object-oriented

UML: Uniform Modeling Language UML is a standardized design language for object-oriented

UML: Uniform Modeling Language UML is a standardized design language for object-oriented programming in various languages. The website for UML is http://www.uml.org . UML diagrams can be classified into four types. Class Diagram. Shows

412 views • 18 slides
Language-oriented programming in Racket A cultural anthropology Jesse Alama jesse@lisp.sh

Language-oriented programming in Racket A cultural anthropology Jesse Alama jesse@lisp.sh

Language-oriented programming in Racket A cultural anthropology Jesse Alama jesse@lisp.sh 1 WTF is language-oriented programming?! 2 WTF is language-oriented programming?! I kinda-sorta know. 3 WTF is language-oriented

792 views • 36 slides
The Goal of Object-Oriented (OO) Design Patterns Our goal is to design good OO software

The Goal of Object-Oriented (OO) Design Patterns Our goal is to design good OO software

The Goal of Object-Oriented (OO) Design Patterns Our goal is to design good OO software systems. Here, good means reusable and flexible. We want source files that require no modification when used in future systems. Contrary to

333 views • 15 slides
Proof explanations: using natural language and graph view Fr ed erique GUILHOT Hanane

Proof explanations: using natural language and graph view Fr ed erique GUILHOT Hanane

Proof explanations: using natural language and graph view Fr ed erique GUILHOT Hanane NACIRI Lo c POTTIER September 2003 MOWGLI Proof explanations: document and graph view From a proof tree, we want to provide: a web

562 views • 29 slides
Anisotropic Goal-Oriented Mesh Adaptation in Firedrake Joe Wallwork 1 Nicolas Barral 2 David Ham 1

Anisotropic Goal-Oriented Mesh Adaptation in Firedrake Joe Wallwork 1 Nicolas Barral 2 David Ham 1

Anisotropic Goal-Oriented Mesh Adaptation in Firedrake Anisotropic Goal-Oriented Mesh Adaptation in Firedrake Joe Wallwork 1 Nicolas Barral 2 David Ham 1 Matthew Piggott 1 1 Imperial College London, UK 2 University of Bordeaux, France Firedrake

274 views • 23 slides
The Marvellous Universe of Arithmetization-Oriented Primitives Abdelrahaman Aly, Tomer Ashur , Eli

The Marvellous Universe of Arithmetization-Oriented Primitives Abdelrahaman Aly, Tomer Ashur , Eli

The Marvellous Universe of Arithmetization-Oriented Primitives Abdelrahaman Aly, Tomer Ashur , Eli Ben-Sasson, Siemen Dhooghe, Alan Szepieniec The Goal The goal is to design a hash function that: The Goal The goal is to design a hash

690 views • 49 slides
Uncertainty, Risk, and Conjecturing Daniele Chiffi chiffidaniele@gmail.com Joint work with

Uncertainty, Risk, and Conjecturing Daniele Chiffi chiffidaniele@gmail.com Joint work with

Uncertainty, Risk, and Conjecturing Daniele Chiffi chiffidaniele@gmail.com Joint work with Ahti-Veikko Pietarinen Tallinn University of Technology Uncertainty Epistemology and epistemic logic are not usual topics of discussion in

512 views • 13 slides
Components of a Hammer for Type Theory Goal Translation and Proof Reconstruction ukasz Czajka

Components of a Hammer for Type Theory Goal Translation and Proof Reconstruction ukasz Czajka

Components of a Hammer for Type Theory Goal Translation and Proof Reconstruction ukasz Czajka Cezary Kaliszyk University of Innsbruck May 24, 2016 Interactive Proof in Type Theory Why do we love it? Why do we hate it? 2 / 14

689 views • 46 slides
Web Ontology Language (OWL) Need meaning beyond an object-oriented type system RDF (with

Web Ontology Language (OWL) Need meaning beyond an object-oriented type system RDF (with

Web Ontology Language Web Ontology Language (OWL) Need meaning beyond an object-oriented type system RDF (with RDFS) captures the basics, approximating an object-oriented type system OWL provides some of the rest OWL standardizes

320 views • 20 slides
SSOL Simple Shape Oriented Language Jeevan Farias (Language Designer) Daniel Mesko (System

SSOL Simple Shape Oriented Language Jeevan Farias (Language Designer) Daniel Mesko (System

SSOL Simple Shape Oriented Language Jeevan Farias (Language Designer) Daniel Mesko (System Architect) Madeleine Tipp (Manager/Test Engineer) Motivation Algorithmically create shapes and render in SVG format Concise syntax to

1.21k views • 14 slides

More recommend