Hipster: Integrating Theory Exploration in a Proof Assistant

Johansson, Moa; Rosén, Dan; Smallbone, Nicholas; Claessen, Koen

doi:10.1007/978-3-319-08434-3_9

Cited by 32 publications

(25 citation statements)

References 15 publications

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“…This ensures that it only generates Theorems and it does not need to filter its conjectures through a counter-example finder, which is the most time-consuming sub-process within IsaCoSy. Hipster is a successor system to IsaCoSy [8]. The main differences between MATHsAiD 2.0 and Hipster are similar to those between MATHsAiD 2.0 and IsaCoSy.…”

Section: Isacosy and Hipstermentioning

confidence: 76%

“…The proof process is guided by sketch plans, which we have abstracted from common patterns of reasoning observed in human proofs 8 These help to ensure that interesting Theorems are generated. There are two kinds of sketch plans: generating and trivial.…”

Section: ∃X : C(x)a(x) P P ∃ : Ementioning

confidence: 99%

“…There are two kinds of sketch plans: generating and trivial. Generating plans are 8 Realising the Human-Like principle.…”

Section: ∃X : C(x)a(x) P P ∃ : Ementioning

confidence: 99%

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MATHsAiD: Automated mathematical theory exploration

2017

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The aim of the MATHsAiD project is to build a tool for automated theorem-discovery; to design and build a tool to automatically conjecture and prove theorems (lemmas, corollaries, etc.) from a set of user-supplied axioms and definitions. No other input is required. This tool would, for instance, allow a mathematician to try several versions of a particular definition, and in a relatively small amount of time, be able to see some of the consequences, in terms of the resulting theorems, of each version. Moreover, the automatically discovered theorems could perhaps help the users to discover and prove further theorems for themselves. The tool could also easily be used by educators (to generate exercise sets, for instance) and by students as well. 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.

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Section: Isacosy and Hipstermentioning

confidence: 76%

Section: ∃X : C(x)a(x) P P ∃ : Ementioning

confidence: 99%

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MATHsAiD: Automated mathematical theory exploration

2017

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“…We have recently seen increased interest in inductive theorem proving, both with specialised provers such as IsaPlanner, Zeno and HipSpec [3,5,13], SMTsolvers such as CVC4 [11], the auto-active prover Dafny [10], recent work on the first-order SPASS prover [14], as well as some support in proof assistants [8,9].…”

Section: Introductionmentioning

confidence: 99%

TIP: Tons of Inductive Problems

Claessen

Johansson

Rosén

et al. 2015

Lecture Notes in Computer Science

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Abstract. This paper describes our collection of benchmarks for inductive theorem provers. The recent spur of interest in automated inductive theorem proving has increased the demands for evaluation and comparison between systems. We expect the benchmark suite to continually grow as more problems are submitted by the community. New challenge problems will promote further development of provers which will greatly benefit both developers and users of inductive theorem provers.

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“…Hipster The Hipster system [12] integrates QuickSpec with the proof assistant Isabelle/HOL. Hipster speeds up and facilitates the development of new theories in Isabelle/HOL by using HipSpec to discover basic lemmas automatically.…”

Section: Related Workmentioning

confidence: 99%

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

BraquehaisRudy

RuncimanColin

2017

SIGPLAN Not.

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This paper presents Speculate, a tool that automatically conjectures laws involving conditional equations and inequalities about Haskell functions. Speculate enumerates expressions involving a given collection of Haskell functions, testing to separate those expressions into apparent equivalence classes. 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. Speculate uses lightweight equational reasoning based on term rewriting to discard redundant laws and to avoid needless testing. Several applications demonstrate the e ectiveness of Speculate.CCS Concepts •Software and its engineering →Software testing and debugging; •Theory of computation →Program speci cations;

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Hipster: Integrating Theory Exploration in a Proof Assistant

Cited by 32 publications

References 15 publications

MATHsAiD: Automated mathematical theory exploration

MATHsAiD: Automated mathematical theory exploration

TIP: Tons of Inductive Problems

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

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