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Higher-Order Separation Logic in Isabelle/HOLCF

Carsten Varming, Lars Birkedal
2008 Electronical Notes in Theoretical Computer Science  
We formalize higher-order separation logic for a first-order imperative language with procedures and local variables in Isabelle/HOLCF.  ...  The higher-order logic ensures that we can show non-trivial algorithms correct without having to extend the semantics of the language as was done previously in verifications based on first-order separation  ...  In [1] higher-order separation logic was proposed.  ... 
doi:10.1016/j.entcs.2008.10.022 fatcat:dxrjw4q46nfmvk2k6rkgq7z7pi

Axiomatic Constructor Classes in Isabelle/HOLCF [chapter]

Brian Huffman, John Matthews, Peter White
2005 Lecture Notes in Computer Science  
We have definitionally extended Isabelle/HOLCF to support axiomatic Haskell-style constructor classes.  ...  Isabelle/HOLCF.  ...  Background Isabelle is a generic interactive theorem prover, which can be instantiated with various kinds of object-logics. Isabelle/HOL is an instantiation of higher order logic.  ... 
doi:10.1007/11541868_10 fatcat:saqpeqvxtrd5fbgtkzgds5dqsu

The Isabelle Framework [chapter]

Makarius Wenzel, Lawrence C. Paulson, Tobias Nipkow
2008 Lecture Notes in Computer Science  
Other notable object-logics are Isabelle/ZF (Zermelo-Fraenkel set-theory, see [34, 36] ) and Isabelle/HOLCF [26] (Scott's domain theory within HOL).  ...  Specification Mechanisms Isabelle/Pure is a minimal version of higher-order logic; object-logics are specified by stating their characteristic rules as new axioms.  ...  The basic framework is centered around higher-order unification. The Simplifier supports higher-order rewriting, with plug-in interfaces for extra simplification procedures written in ML.  ... 
doi:10.1007/978-3-540-71067-7_7 fatcat:y75g4zyzmjdgbkmosmujtq7yra

Formal Verification of Monad Transformers [article]

Brian Huffman
2012 arXiv   pre-print
We do not require a logic with first-class type constructors, first-class polymorphism, or type quantification; instead, we rely on a domain-theoretic model of the type system in a universal domain to  ...  These ideas are implemented in the Tycon library for the Isabelle theorem prover, which builds on the HOLCF library of domain theory.  ...  Acknowledgments Thanks to John Matthews for many discussions about HOLCF which helped to develop the ideas in this paper.  ... 
arXiv:1207.3208v1 fatcat:4i25rjaosncsdftbfndlyv75ci

Separation logic for sequential programs (functional pearl)

Arthur Charguéraud
2020 Proceedings of the ACM on Programming Languages (PACMPL)  
This paper presents a simple mechanized formalization of Separation Logic for sequential programs.  ...  This formalization is aimed for teaching the ideas of Separation Logic, including its soundness proof and its recent enhancements.  ...  Varming and Birkedal [2008] demonstrate the possibility to formalize higher-order Separation Logic as a shallow embedding in Isabelle/HOLCF.  ... 
doi:10.1145/3408998 fatcat:do7vjcwo2rc4pmqpdcnq6leshy

ALICE: An Advanced Logic for Interactive Component Engineering [article]

Borislav Gajanovic, Bernhard Rumpe
2014 arXiv   pre-print
This paper presents an overview of the verification framework ALICE in its current version 0.7. It is based on the generic theorem prover Isabelle [Pau03a].  ...  The behavior of a component is generally described as a relation on the observations in form of streams of messages flowing over its input and output channels.  ...  ALICE is embedded in the higher order logic HOL, which itself is formalized using the Isabelle generic theorem prover.  ... 
arXiv:1410.4381v1 fatcat:qb533mr6pbdgtojikbafje4tbi

Partiality and recursion in interactive theorem provers – an overview

ANA BOVE, ALEXANDER KRAUSS, MATTHIEU SOZEAU
2014 Mathematical Structures in Computer Science  
We focus on theorem provers based on constructive type theory (in particular, Agda and Coq) and higher-order logic (in particular Isabelle/HOL).  ...  Other systems and logics are covered to a certain extent, but not exhaustively.  ...  Higher-Order Logic In what follows, we introduce higher-order logic (HOL), which we will use to describe the techniques that require classical reasoning.  ... 
doi:10.1017/s0960129514000115 fatcat:y3gdgilgd5bvlev3haw4l3fyxi

Imperative Functional Programming with Isabelle/HOL [chapter]

Lukas Bulwahn, Alexander Krauss, Florian Haftmann, Levent Erkök, John Matthews
2008 Lecture Notes in Computer Science  
Imperative language features have previously been embedded in higher order logic via a state monad [7, 14] .  ...  A more pragmatic option is to store only a representable subset of the full function space in the heap, for example just the continuous functions as is done in Isabelle/HOLCF [8] .  ... 
doi:10.1007/978-3-540-71067-7_14 fatcat:lcedkeoly5fzxol5ttbj6ezv24

HasCasl: Integrated higher-order specification and program development

Lutz Schröder, Till Mossakowski
2009 Theoretical Computer Science  
, in particular but not exclusively in modern functional programming languages, and as an expressive standard language for higher-order logic.  ...  is both a generalisation of classical higher-order logic and can be used as a specification logic for Haskell programs.  ...  higher order logic.  ... 
doi:10.1016/j.tcs.2008.11.020 fatcat:fvluuyjf7ra2dk2izvb2br4uou

The Design of a Practical Proof Checker for a Lazy Functional Language [chapter]

Adam Procter, William L. Harrison, Aaron Stump
2013 Lecture Notes in Computer Science  
Pure, lazy functional languages like Haskell provide a sound basis for formal reasoning about programs in an equational style. In practice, however, equational reasoning is underutilized.  ...  MProver features first-class support for reasoning about potentially undefined computations (particularly important in a lazy setting), and an extended notion of Haskell-like type classes, enabling a highly  ...  Type classes originated in Haskell [23] as a means of enabling ad-hoc polymorphism, and the idea has been reimplemented in Coq [19] and Isabelle/HOLCF [11] .  ... 
doi:10.1007/978-3-642-40447-4_8 fatcat:atmr7h7rmrg7tc4y5qn45ltsru

History of Interactive Theorem Proving [chapter]

John Harrison, Josef Urban, Freek Wiedijk
2014 Handbook of the History of Logic  
ACKNOWLEDGEMENTS The authors are grateful to Jörg Siekmann for inviting them to prepare this chapter and for his patience in the face of our lengthy delays.  ...  Gordon modified Cambridge LCF to support classical higher order logic, and so HOL (for Higher Order Logic) was born.  ...  ) • Constructive type theory (Coq, NuPRL) • First-order set theory (Mizar, EVES, Isabelle/ZF) • Logics of partial terms (LCF, IMPS, Isabelle/HOLCF) Some of this diversity arises because of specific philosophical  ... 
doi:10.1016/b978-0-444-51624-4.50004-6 fatcat:sngnxnl3ivectj5taj3dgsaa7m

Model-Based Engineering for Avionics: Will Specification and Formal Verification e.g. Based on Broy's Streams Become Feasible?

Stefan Kriebel, Deni Raco, Bernhard Rumpe, Sebastian Stüber
2019 Software Engineering  
This again raises the question, whether developing software the same way as we did the last 30 years is still appropriate, or in the times of much better formal methods and cheap and powerful computational  ...  capabilities, it would be feasible to use clear and model-based specification techniques for an integrated systems engineering approach and formally verify any physical and logical implementation of functionality  ...  All above mentioned domain-theoretical concepts has been formalized in the theorem prover Isabelle/HOLCF (HOL stands for higher-order logic, CF stands for computable functions) in [33] , [34] and [  ... 
dblp:conf/se/KriebelRRS19 fatcat:zna7toi2jzhjpa2oq425gmw52q

Consistent graphical specification of distributed systems [chapter]

Franz Huber, Bernhard Schätz, Geralf Einert
1997 Lecture Notes in Computer Science  
We show how such an indirect approach can be incorporated in a CASE tool prototype by basing it upon formally defined hierarchical description techniques.  ...  Since these notions are used in the Isabelle HOLCF-implementation of Focus, a corresponding notion of equivalence and refinement has to be defined for STDs using the relational µ calculus.  ...  Definition of Consistency Conditions In AUTOFOCUS, the actual conditions upon which consistency checks are based, are defined using a declarative textual notation, similar to first order predicate logic  ... 
doi:10.1007/3-540-63533-5_7 fatcat:f6dkfjkzbvbyfnsxo6nwjd2rtu

Partial type constructors: or, making ad hoc datatypes less ad hoc

Mark P. Jones, J. Garrett Morris, Richard A. Eisenberg
2019 Proceedings of the ACM on Programming Languages (PACMPL)  
., requiring computable equality or ordering functions) to type families with defining equations only over certain choices of arguments.  ...  experimental analysis of a body of Haskell code, using a proof-of-concept implementation of our system; while there are cases where our system requires additional annotations, these cases are rarely encountered in  ...  This material is based in part upon work supported by the National Science Foundation under Grant No. CCF-1704041 and Grant No. CNS-1422979.  ... 
doi:10.1145/3371108 fatcat:xz7nreyxjrftrcxxrudsy3fuwy

Witnessing (Co)datatypes [chapter]

Jasmin Christian Blanchette, Andrei Popescu, Dmitriy Traytel
2015 Lecture Notes in Computer Science  
Here we describe a complete procedure for deriving nonemptiness witnesses in the general mutually recursive, nested case-nonemptiness being a proviso for introducing new types in higher-order logic.  ...  General Terms Algorithms, Theory, Verification Keywords (Co)datatypes, higher-order logic, interactive theorem proving, Isabelle/HOL, category theory datatype (α, β) tree = Leaf β | Branch ((α + (α, β)  ...  Conventions We work informally in a mathematical universe S of sets but adopt many conventions from higher-order logic and functional programming.  ... 
doi:10.1007/978-3-662-46669-8_15 fatcat:fl3y3sxomfbq5eunt3tvtem7oa
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