Code Generation via Higher-Order Rewrite Systems

Haftmann, Florian; Nipkow, Tobias

doi:10.1007/978-3-642-12251-4_9

Cited by 144 publications

(136 citation statements)

References 16 publications

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“…Code Extraction Isabelle's code generator [29] extracts Haskell code from an executable fragment of HOL, mapping HOL (co)datatypes to lazy Haskell datatypes and HOL functions to Haskell functions. Seven out of our eight case studies fall into this fragment; the extracted code is part of the archive [14].…”

Section: Related Work and Discussionmentioning

confidence: 99%

Friends with Benefits

Blanchette

Bouzy

Lochbihler

et al. 2017

Programming Languages and Systems

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Abstract. We introduce AmiCo, a tool that extends a proof assistant, Isabelle/ HOL, with flexible function definitions well beyond primitive corecursion. All definitions are certified by the assistant's inference kernel to guard against inconsistencies. A central notion is that of friends: functions that preserve the productivity of their arguments and that are allowed in corecursive call contexts. As new friends are registered, corecursion benefits by becoming more expressive. We describe this process and its implementation, from the user's specification to the synthesis of a higher-order definition to the registration of a friend. We show some substantial case studies where our approach makes a difference.

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Section: Related Work and Discussionmentioning

confidence: 99%

Friends with Benefits

Blanchette

Bouzy

Lochbihler

et al. 2017

Programming Languages and Systems

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“…As we want to apply Isabelle's code generator [11] on our certification algorithm, we have to formalize conditional constraints via a deep embedding. Therefore, we had the choice between at least two alternatives how to deal with bound variables: we can use a dedicated approach like Nominal Isabelle [21,22], or we perform renamings, α-equivalence, .…”

Section: Third Problem: Solving Conditional Constraintsmentioning

confidence: 99%

Formalizing Bounded Increase

Thiemann

2013

Interactive Theorem Proving

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Abstract. Bounded increase is a termination technique where it is tried to find an argument x of a recursive function that is increased repeatedly until it reaches a bound b, which might be ensured by a condition x < b. Since the predicates like < may be arbitrary user-defined recursive functions, an induction calculus is utilized to prove conditional constraints. In this paper, we present a full formalization of bounded increase in the theorem prover Isabelle/HOL. It fills one large gap in the pen-andpaper proof, and it includes generalized inference rules for the induction calculus as well as variants of the Babylonian algorithm to compute square roots. These algorithms were required to write executable functions which can certify untrusted termination proofs from termination tools that make use of bounded increase. And indeed, the resulting certifier was already useful: it detected an implementation error that remained undetected since 2007.

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“…In addition, Isabelle/HOL is a framework for certified programming: functional programming (including lazy (co)programming [9]) is supported natively and imperative programming is supported via a monadic extension [10]. Programs can be written and verified in Isabelle/HOL, and efficient code for them (in Haskell, Standard ML, OCaml and Scala) can be produced using a code generator [19]. This certified programming methodology has yielded a wide range of verified software systems, from a Java compiler [32] to an LTL model checker [14] to a conference management system [23].…”

Section: Introductionmentioning

confidence: 99%

Comprehending Isabelle/HOL’s Consistency

KunăźAr¹,

Popescu²

2017

Programming Languages and Systems

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Abstract. The proof assistant Isabelle/HOL is based on an extension of HigherOrder Logic (HOL) with ad hoc overloading of constants. It turns out that the interaction between the standard HOL type definitions and the Isabelle-specific ad hoc overloading is problematic for the logical consistency. In previous work, we have argued that standard HOL semantics is no longer appropriate for capturing this interaction, and have proved consistency using a nonstandard semantics. The use of an exotic semantics makes that proof hard to digest by the community. In this paper, we prove consistency by proof-theoretic means-following the healthy intuition of definitions as abbreviations, realized in HOLC, a logic that augments HOL with comprehension types. We hope that our new proof settles the Isabelle/HOL consistency problem once and for all. In addition, HOLC offers a framework for justifying the consistency of new deduction schemas that address practical user needs.

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Code Generation via Higher-Order Rewrite Systems

Cited by 144 publications

References 16 publications

Friends with Benefits

Friends with Benefits

Formalizing Bounded Increase

Comprehending Isabelle/HOL’s Consistency

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