اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدExtracting verified decision procedures: DPLL and Resolution
269
0
0.0
(
0
)
تأليف
Ulrich Berger
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
This article is concerned with the application of the program extraction technique to a new class of problems: the synthesis of decision procedures for the classical satisfiability problem that are correct by construction. To this end, we formalize a completeness proof for the DPLL proof system and extract a SAT solver from it. When applied to a propositional formula in conjunctive normal form the program produces either a satisfying assignment or a DPLL derivation showing its unsatisfiability. We use non-computational quantifiers to remove redundant computational content from the extracted program and translate it into Haskell to improve performance. We also prove the equivalence between the resolution proof system and the DPLL proof system with a bound on the size of the resulting resolution proof. This demonstrates that it is possible to capture quantitative information about the extracted program on the proof level. The formalization is carried out in the interactive proof assistant Minlog.
قيم البحث
اقرأ أيضاً
We implement extraction of Coq programs to functional languages based on MetaCoqs certified erasure. As part of this, we implement an optimisation pass removing unused arguments. We prove the pass correct wrt. a conventional call-by-value operational
semantics of functional languages. We apply this to two functional smart contract languages, Liquidity and Midlang, and to the functional language Elm. Our development is done in the context of the ConCert framework that enables smart contract verification. We contribute a verified boardroom voting smart contract featuring maximum voter privacy such that each vote is kept private except under collusion of all other parties. We also integrate property-based testing into ConCert using QuickChick and our development is the first to support testing properties of interacting smart contracts. We test several complex contracts such as a DAO-like contract, an escrow contract, an implementation of a Decentralized Finance (DeFi) contract which includes a custom token standard (Tezos FA2), and more. In total, this gives us a way to write dependent programs in Coq, test them semi-automatically, verify, and then extract to functional smart contract languages, while retaining a small trusted computing base of only MetaCoq and the pretty-printers into these languages.
In verified generic programming, one cannot exploit the structure of concrete data types but has to rely on well chosen sets of specifications or abstract data types (ADTs). Functors and monads are at the core of many applications of functional progr
amming. This raises the question of what useful ADTs for verified functors and monads could look like. The functorial map of many important monads preserves extensional equality. For instance, if $f, g : A rightarrow B$ are extensionally equal, that is, $forall x in A, f x = g x$, then $map f : List A rightarrow List B$ and $map g$ are also extensionally equal. This suggests that preservation of extensional equality could be a useful principle in verified generic programming. We explore this possibility with a minimalist approach: we deal with (the lack of) extensional equality in Martin-Lofs intensional type theories without extending the theories or using full-fledged setoids. Perhaps surprisingly, this minimal approach turns out to be extremely useful. It allows one to derive simple generic proofs of monadic laws but also verified, generic results in dynamical systems and control theory. In turn, these results avoid tedious code duplication and ad-hoc proofs. Thus, our work is a contribution towards pragmatic, verified generic programming.
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and displaying imag
es with a computer. In this paper, I build upon existing work about complete metric spaces to define compact sets as the completion of the space of finite sets under the Hausdorff metric. This definition allowed me to quickly develop a computer verified theory of compact sets. I applied this theory to compute provably correct plots of uniformly continuous functions.
We present sqire, a low-level language for quantum computing and verification. sqire uses a global register of quantum bits, allowing easy compilation to and from existing `quantum assembly languages and simplifying the verification process. We demon
strate the power of sqire as an intermediate representation of quantum programs by verifying a number of useful optimizations, and we demonstrate sqires use as a tool for general verification by proving several quantum programs correct.
We provide a computer verified exact monadic functional implementation of the Riemann integral in type theory. Together with previous work by OConnor, this may be seen as the beginning of the realization of Bishops vision to use constructive mathematics as a programming language for exact analysis.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
