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Hipster: Integrating Theory Exploration in a Proof Assistant [article]

Moa Johansson and Dan Rosen and Nicholas Smallbone and Koen Claessen
2014 arXiv   pre-print
This paper describes Hipster, a system integrating theory exploration with the proof assistant Isabelle/HOL.  ...  Theory exploration is a technique for automatically discovering new interesting lemmas in a given theory development. Hipster can be used in two main modes.  ...  Summary Hipster integrates lemma discovery by theory exploration in the proof assistant Isabelle/HOL.  ... 
arXiv:1405.3426v1 fatcat:zbsrlil6uvaafcolhjjqr5dopi

Hipster: Integrating Theory Exploration in a Proof Assistant [chapter]

Moa Johansson, Dan Rosén, Nicholas Smallbone, Koen Claessen
2014 Lecture Notes in Computer Science  
This paper describes Hipster, a system integrating theory exploration with the proof assistant Isabelle/HOL.  ...  Theory exploration is a technique for automatically discovering new interesting lemmas in a given theory development. Hipster can be used in two main modes.  ...  Summary Hipster integrates lemma discovery by theory exploration in the proof assistant Isabelle/HOL.  ... 
doi:10.1007/978-3-319-08434-3_9 fatcat:n4opckzg2jgk5e3zjafthjy3yy

THE HIPSTER ECONOMY

ALESSANDRO GEROSA
2020
Recently, an ongoing colonisation of labour-intensive sectors by the imaginary of creative economy is observable, resulting in the birth of a new hybrid �hipster economic imaginary�, that combines key  ...  In Chapter 1 we will first outline a critical history of the creative economy imaginary and then illustrate the general [...]  ...  nature, looking for the evolution of the phenomenon to integrate the theory.  ... 
doi:10.13130/gerosa-alessandro_phd2020-02-04 fatcat:opw2tuqq5jaerg4hhtqoggvwgy

Theory Exploration Powered by Deductive Synthesis [chapter]

Eytan Singher, Shachar Itzhaky
2021 Lecture Notes in Computer Science  
This gives rise to the challenge of discovering useful sub-properties that can assist the automated proof process.  ...  This new abstraction-based theory exploration method is a step toward applying theory exploration to software verification and synthesis.  ...  We compare our implementation with a current leading theory exploration system, Hipster [18] , using a novel metric.  ... 
doi:10.1007/978-3-030-81688-9_6 fatcat:6nzwbykqofftlciqg453veclia

Theory Exploration Powered By Deductive Synthesis [article]

Eytan Singher, Shachar Itzhaky
2020 arXiv   pre-print
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi.  ...  Complex properties lead to an ever-growing number of definitions and associated lemmas, which constitute an integral part of proof construction.  ...  In this work, we explore a fully-symbolic method for theory exploration that takes advantage of the characteristics of induction-based proofs.  ... 
arXiv:2009.04826v1 fatcat:q2avwtxx3vcprofivqttinzjc4

Proving Type Class Laws for Haskell [article]

Andreas Arvidsson, Moa Johansson, Robin Touche
2018 arXiv   pre-print
Type classes in Haskell are used to implement ad-hoc polymorphism, i.e. a way to ensure both to the programmer and the compiler that a set of functions are defined for a specific data type.  ...  All instances of such type classes are expected to behave in a certain way and satisfy laws associated with the respective class.  ...  This has however been partially addressed in HipSpec's sister system Hipster, which shares the same theory exploration component, but is integrated in the interactive proof assistant Isabelle/HOL [12,  ... 
arXiv:1808.05789v1 fatcat:27kz3be5fnbehiledzprfkm6u4

Proving Type Class Laws for Haskell [chapter]

Andreas Arvidsson, Moa Johansson, Robin Touche
2019 Msphere  
Type classes in Haskell are used to implement ad-hoc polymorphism, i.e. a way to ensure both to the programmer and the compiler that a set of functions are defined for a specific data type.  ...  All instances of such type classes are expected to behave in a certain way and satisfy laws associated with the respective class.  ...  This has however been partially addressed in HipSpec's sister system Hipster, which shares the same theory exploration component, but is integrated in the interactive proof assistant Isabelle/HOL [12,  ... 
doi:10.1007/978-3-030-14805-8_4 fatcat:vcuhynxukjclnmvnnmupkxlnji

Deduction Beyond First-Order Logic (Dagstuhl Seminar 17371)

Jasmin Christian Blanchette, Carsten Fuhs, Viorica Sofronie-Stokkermans, Cesare Tinelli, Marc Herbstritt
2018 Dagstuhl Reports  
Other practical problems need a mixture of first-order proof search and some more advanced reasoning (for instance, about higher-order formulas), or simply higher-level reasoning steps.  ...  This includes genuinely higher-order reasoning, reasoning in theories that are not finitely axiomatisable in first-order logic (such as those including transitive closure operators or standard arithmetic  ...  We presented an approach to reasoning with large theories which is based on the abstractionrefinement framework [1].  ... 
doi:10.4230/dagrep.7.9.26 dblp:journals/dagstuhl-reports/BlanchetteFST17 fatcat:yfc3wk2fwngc3i2dmjwrz3gsgi

MATHsAiD: Automated mathematical theory exploration

R. L. McCasland, A. Bundy, P. F. Smith
2017 Applied intelligence (Boston)  
In a similar fashion, it might also prove useful in enabling automated theorem provers to dispatch many of the more difficult proof obligations arising in software verification, by automatically generating  ...  lemmas which are needed by the prover, in order to finish these proofs.  ...  Introduction MATHsAiD (Mechanically Ascertaining Theorems from Hypotheses, Axioms and Definitions) is a tool for assisting the working mathematician explore new mathematical theories.  ... 
doi:10.1007/s10489-017-0954-8 fatcat:4zwjqe5io5bxnj3sesv2otsufu

Conjectures, Tests and Proofs: An Overview of Theory Exploration

Moa Johansson, Nicholas Smallbone
2021 Electronic Proceedings in Theoretical Computer Science  
In this paper, we give a brief overview of a theory exploration system called QuickSpec, which is able to automatically discover interesting conjectures about a given set of functions.  ...  A key component of mathematical reasoning is the ability to formulate interesting conjectures about a problem domain at hand.  ...  This is also useful in interactive proof assistants when beginning a new formalisation of some stucture about which few theorems have been proved: QuickSpec has been combined with Isabelle/HOL in the Hipster  ... 
doi:10.4204/eptcs.341.1 fatcat:cvbw7x4egrbxdig3swxvdu4ztu

INT: An Inequality Benchmark for Evaluating Generalization in Theorem Proving [article]

Yuhuai Wu, Albert Qiaochu Jiang, Jimmy Ba, Roger Grosse
2021 arXiv   pre-print
In addition, unlike prior benchmarks for learning-assisted theorem proving, INT provides a lightweight and user-friendly theorem proving environment with fast simulations, conducive to performing learning-based  ...  INT is based on a procedure for generating theorems and proofs; this procedure's knobs allow us to measure 6 different types of generalization, each reflecting a distinct challenge characteristic to automated  ...  AQJ was supported by a Vector Institute research grant.  ... 
arXiv:2007.02924v2 fatcat:5dpl46b7jvhkroeteh3iij4igm

Speculate: discovering conditional equations and inequalities about black-box functions by reasoning from test results

Rudy Braquehais, Colin Runciman
2017 Proceedings of the 10th ACM SIGPLAN International Symposium on Haskell - Haskell 2017  
CCS Concepts •Software and its engineering →Software testing and debugging; •Theory of computation →Program speci cations;  ...  Expressions in the same equivalence class are used to conjecture equations. Representative expressions of di erent equivalence classes are used to conjecture conditional equations and inequalities.  ...  bug in our term uni cation algorithm; and anonymous reviwers for their comments on earlier drafts.  ... 
doi:10.1145/3122955.3122961 dblp:conf/haskell/BraquehaisR17 fatcat:hb3alhejyrckbe7qt7wf32gt64

Speculate: discovering conditional equations and inequalities about black-box functions by reasoning from test results

Rudy Braquehais, Colin Runciman
2017 SIGPLAN notices  
CCS Concepts •Software and its engineering →Software testing and debugging; •Theory of computation →Program speci cations;  ...  Expressions in the same equivalence class are used to conjecture equations. Representative expressions of di erent equivalence classes are used to conjecture conditional equations and inequalities.  ...  bug in our term uni cation algorithm; and anonymous reviwers for their comments on earlier drafts.  ... 
doi:10.1145/3156695.3122961 fatcat:hdsak75vcrfdzaedigqbgewp7q

Anything You Can Do, I Can Do Better––Except in Big Tech?: Antitrust's New Inhospitality Tradition

2020 Kansas Law Review  
theory is full of "existence theorems"-proofs that under certain conditions ordinarily-beneficial practices could have undesirable consequences.  ...  Wright et al., Requiem for a Paradox: The Dubious Rise and Inevitable Fall of Hipster Antitrust, 51 ARIZ. ST.  ... 
doi:10.17161/1808.30527 fatcat:m3aea37lxvhaxoegs6j7xkh54m

Skunkworks finder

Dario Casadevall, Marcus Foth, Ana Bilandzic
2018 Proceedings of the 30th Australian Conference on Computer-Human Interaction - OzCHI '18  
Our focus was on the verification and validation of the developed prototype as a proof of concept.  ...  In general, all participants could imagine the prototype being integrated in a familiar interface such as Google maps rather than being a standalone tool.  ... 
doi:10.1145/3292147.3292169 dblp:conf/ozchi/CasadevallFB18 fatcat:7c7o62p4rrdm5f4fdoiowmqwoe
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