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Proving Properties about Functions on Lists Involving Element Tests
[chapter]

2012
*
Lecture Notes in Computer Science
*

All these results are restricted to fully polymorphic

doi:10.1007/978-3-642-28412-0_17
fatcat:25zvp5sjjfhsfi5fjhsixfdirq
*functions*. For example,*functions*using equality*tests**on**list**elements*are out of reach. ... Bundy and Richardson [4] developed a method for reasoning*about**functions*manipulating*lists*which is based*on*separating shape from content, and then exploiting a mathematically convenient representation ...*functions**on**lists*to the case of the presence of*element**tests*. ...##
###
Property-Based Testing and Verification: A Catalog of Classroom Examples
[chapter]

2012
*
Lecture Notes in Computer Science
*

Our collection of examples from course records may help shed some light

doi:10.1007/978-3-642-34407-7_9
fatcat:v5g4x2pk7zalnn6k7v74ngz2e4
*on*how closely pedagogy*on**property*-based*testing*matches observations of relative frequencies of various categories of*properties*... Hughes has observed that software*properties*useful for*testing**functional*software often (1) compare the results of different ways of computing the same thing or (2) check that forward and inverse transformations ... Morazán for suggesting a section*on*tips for full verification of prpperties and John Hughes for helpful discussions of*property*categories. ...##
###
Logic against ghosts

2019
*
Proceedings of the 34th ACM/SIGAPP Symposium on Applied Computing - SAC '19
*

The proposed specifications are validated by

doi:10.1145/3297280.3297495
dblp:conf/sac/BlanchardKL19
fatcat:eyb25mrlenctxgauugbe4rdrt4
*proving*a few client*functions*manipulating*lists*. During the verification, a more efficient implementation for*one**function*was found and verified. ... The specifications of all*functions*are now*proved*faster and almost all automatically, only a small number of auxiliary lemmas and a couple of assertions being*proved*interactively in Coq. ... In order to get confidence in our specification of the*list*module*functions*, we wrote 15 valid*test**functions*manipulating*lists*, and*proved*simple*properties**about*them using Frama-C/Wp. ...##
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Ghosts For Lists: A Critical Module Of Contiki Verified In Frama-C

2018
*
Zenodo
*

Finally, we validate the proposed specification by

doi:10.5281/zenodo.1402494
fatcat:q3aslgztnvdx5jjklotmvrpkpm
*proving*a few*functions*manipulating*lists*. ... The proposed verification technique relies*on*a parallel view of a*list*through a companion ghost array. ... Validation of Specification To get confidence in the proposed specification, we have implemented 15 simple valid*test**functions*7 manipulating*lists*, and tried to*prove*simple*properties**on**lists*in them ...##
###
Ghosts for Lists: A Critical Module of Contiki Verified in Frama-C
[chapter]

2018
*
Lecture Notes in Computer Science
*

Finally, we validate the proposed specification by

doi:10.1007/978-3-319-77935-5_3
fatcat:drww6giaqrc37hkfl4gjgjmcwa
*proving*a few*functions*manipulating*lists*. ... The proposed verification technique relies*on*a parallel view of a*list*through a companion ghost array. ... Validation of Specification To get confidence in the proposed specification, we have implemented 15 simple valid*test**functions*7 manipulating*lists*, and tried to*prove*simple*properties**on**lists*in them ...##
###
Verifying haskell programs using constructive type theory

2005
*
Proceedings of the 2005 ACM SIGPLAN workshop on Haskell - Haskell '05
*

Proof assistants based

doi:10.1145/1088348.1088355
dblp:conf/haskell/AbelBBHN05
fatcat:43fip43tijgtpnwlsxrhsh6swu
*on*dependent type theory are closely related to*functional*programming languages, and so it is tempting to use them to*prove*the correctness of*functional*programs. ...*One*begins by expressing a specification as a type; for example, ∀xs ::*List*Integer.∃ys ::*List*Integer. isPermutation(xs, ys) ∧ isOrdered(ys) ... proofs*about*partial programs. ...##
###
Engineering software correctness

2005
*
Proceedings of the 2005 workshop on Functional and declaritive programming in education - FDPE '05
*

The sequence is based

doi:10.1145/1085114.1085123
dblp:conf/icfp/Page05
fatcat:5cepkw3al5fbdaelk2f2a5n2rm
*on**functional*programming using ACL2, a purely*functional*subset of Common Lisp with a built-in, computational logic developed by J Strother Moore and his colleagues over the past ... In the second offering,*about*forty percent of the students gained enough competence with the ACL2 mechanized logic to make significant use of it in verifying*properties*of software. ...*One*such example is a*function*that parcels a*list*into packets. Each packet is a contiguous sublist of the original, containing the*elements*lying between occurrences of a specified delimiter. ...##
###
Engineering Software Correctness

2007
*
Journal of functional programming
*

The sequence is based

doi:10.1017/s095679680700634x
fatcat:ftethwcglvcibprebzo3tzpqsu
*on**functional*programming using ACL2, a purely*functional*subset of Common Lisp with a built-in, computational logic developed by J Strother Moore and his colleagues over the past ... In the second offering,*about*forty percent of the students gained enough competence with the ACL2 mechanized logic to make significant use of it in verifying*properties*of software. ...*One*such example is a*function*that parcels a*list*into packets. Each packet is a contiguous sublist of the original, containing the*elements*lying between occurrences of a specified delimiter. ...##
###
Pi-Ware: Hardware Description and Verification in Agda

2018
*
Types for Proofs and Programs
*

We demonstrate this by defining an algebra of parallel prefix circuits,

doi:10.4230/lipics.types.2015.9
dblp:conf/types/FlorSS15
fatcat:cfswwcfherbinipoj363hl722a
*proving*their correctness and further algebraic*properties*. ... There is a long tradition of modelling digital circuits using*functional*programming languages. ... Acknowledgements We would like to thank the helpful comments and suggestions of the attendants of the TYPES 2015 conference in Tallinn where we presented our initial results*on*Π-Ware. ...##
###
Functional programming and theorem proving for undergraduates

2008
*
Proceedings of the 2008 international workshop on Functional and declarative programming in education - FDPE '08
*

For the past five years, the University of Oklahoma has used the ACL2 theorem prover for a year-long sequence

doi:10.1145/1411260.1411264
dblp:conf/icfp/PageEF08
fatcat:h2fvj7jj3fcipec6n7qgdscxm4
*on*software engineering. ...*One*out of four times, the generator produces nil; three in four times, it extends a recursively chosen tail*list*with an*element*chosen independently from elem-dist. ... Lastly, the library provides a pseudo-random number*function*. The machine perspective is useful for*proving*theorems*about*such GUI programs. ...##
###
Automating Inductive Proofs Using Theory Exploration
[chapter]

2013
*
Lecture Notes in Computer Science
*

HipSpec is a system for automatically deriving and

doi:10.1007/978-3-642-38574-2_27
fatcat:jdb5lnunjnejxkcsjh3bpp5aym
*proving**properties**about**functional*programs. ... It uses a novel approach, combining theory exploration, counterexample*testing*and inductive theorem*proving*. ... The*test*suites consist of conjectures*about*natural numbers,*lists*and binary trees. As they feature a large number of unrelated*functions*, HipSpec was run separately for each*property*. ...##
###
Termination in ACL2 Using Multiset Relations
[chapter]

2003
*
Applied Logic Series
*

We

doi:10.1007/978-94-017-0253-9_9
fatcat:c5apat4qx5amvljyex4gq7pc3u
*prove*this*property*in the ACL2 logic, and use it by*functional*instantiation in order to provide well-founded relations for the admissibility*test*of recursive*functions*. ... Every relation*on*a set A induces a relation*on*finite multisets over A; it can be shown that the multiset relation induced by a well-founded relation is also well-founded. ... For example, the expression (remove-*one*3 '(5 3 7 3)) is evaluated to (5 7 3). But we can also state and*prove*formal*properties**about*the*function*, using the ACL2 logic. ...##
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Accurate Programming: Thinking about programs in terms of properties

2011
*
Electronic Proceedings in Theoretical Computer Science
*

This is achieved by encouraging programmers to think

doi:10.4204/eptcs.66.13
fatcat:2p6qj7o47zatfcd3qblx7rb7ge
*about*programs in terms of*properties*. ... It combines ideas from*test*-automation,*test*-driven development, agile programming, and other state of the art software development methods. ... Finally, Paul Brauner kindly provided us with helpful comments*on*a draft of these notes. Rex's visit would have not been possible without the generous support of the U.S. ...##
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Towards the Formal Reliability Analysis of Oil and Gas Pipelines
[chapter]

2014
*
Lecture Notes in Computer Science
*

The formal reasoning

doi:10.1007/978-3-319-08434-3_4
fatcat:upkuwifzpzberoer4ji2qwycr4
*about*the proof of Theorem 2*involves*some basic axioms of probability theory and a*property*that the CDF is a monotonically increasing*function*. ... The predicate PERM ensures that its two*list*arguments form a permutation of*one*another, the*function*LENGTH returns the length of a*list*, the*function*TAKE returns a*list*that contains the first n*elements*...##
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Learning to Represent Programs with Property Signatures
[article]

2020
*
arXiv
*
pre-print

For instance, if τ_in and τ_out are both

arXiv:2002.09030v1
fatcat:ew5evgqhtjcwdllz4oc5fj75x4
*lists*of the same type,*one**property*might ask 'is the input*list*the same length as the output*list*?'. ... If we have a*list*of such*properties*, we can evaluate them all for our*function*to get a*list*of outputs that we will call the*property*signature. ... Most of all, we owe a substantial debt to Niklas Een,*on*whose Evo programming language (https://github.com/tensorflow/deepmath/tree/master/ deepmath/zz/CodeBreeder) the Searcho language is heavily based ...
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