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## Filters

##
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The linear abstract machine

1988
*
Theoretical Computer Science
*

A Linear Logic [6] provides a refinement

doi:10.1016/0304-3975(88)90100-4
fatcat:fwler4m2qvejdmhrs7ajir4qvi
*of*functional progammin*implementation*technique, with*the*followin features: 0 a synthesis*of*strict and lazy evaluation, @ a clean semantics*of*side effects, ... Linear h-*Calculus*(S vides*the*basis*of*a programuage that can be*implemented*on th achine. ... For example AU is a*correct*(closed) term, but Amxx is not (independently*of*typing rules). Typing rules*The*typing rules are essentially*the*same as for usual A-*calculus*. ...##
###
A Programming Tutor for Haskell
[chapter]

2012
*
Lecture Notes in Computer Science
*

both: flip f λx y → f y x which explains

doi:10.1007/978-3-642-32096-5_1
fatcat:i536ydacofasllrqohjmw75spy
*the**implementation**of*flipS: Infix operators to (prefix) functions } reverse = let f x y = (:) y x in foldl f [ ] ⇒ { Function bindings to lambda abstractions ...*The*tutor targets first-year computer science students. Our tutor is an environment like*ABC*, with feedback functionality, for a 'mainstream' language. ...##
###
Decision problems for propositional linear logic

1992
*
Annals of Pure and Applied Logic
*

Further, we prove that without

doi:10.1016/0168-0072(92)90075-b
fatcat:rgznokvv2vcj7ax6hbk3ozg6ve
*the*modal storage operator, which indicates unboundedness*of*resources,*the*decision problem becomes PSPACE-Complete. ... We also establish membership in N P for*the*multiplicative fragment, NP-completeness for*the*multiplicative fragment extended with unrestricted weakening, and undecidability for certain fragments*of*noncommutative ...*The*encoding is carried out in a one-sided formulation*of**the*MALL sequent*calculus*where, for example,*the**provable*twcsided sequent A , A 4 B I-B is written as + G? I-A ~, A @ B ~, B . ...##
###
Real World Verification
[chapter]

2009
*
Lecture Notes in Computer Science
*

To identify strengths and weaknesses, we examine state

doi:10.1007/978-3-642-02959-2_35
fatcat:4dd6gqu5bbeopbuwikdprliieq
*of**the*art symbolic techniques and*implementations*for*the*universal fragment*of*real-closed fields: approaches based on quantifier elimination, Gröbner ... Scalable handling*of*real arithmetic is a crucial part*of**the*verification*of*hybrid systems, mathematical algorithms, and mixed analog/digital circuits. ...*The*deduction modulo*calculus**of*KeYmaera gives us a uniform context for comparing*the*performance*of*multiple approaches and*implementations*for real arithmetic. ...##
###
Increasing Confidence in Liveness Model Checking Results with Proofs
[chapter]

2013
*
Lecture Notes in Computer Science
*

As model checkers themselves are quite complicated pieces

doi:10.1007/978-3-319-03077-7_3
fatcat:2pppl2uccfdznbcdfl2komkije
*of*software, there is room for doubt about*the**correctness**of**the*model checking result. ... Model checking is an established technique to get condence in*the**correctness**of*a system when testing is not sucient. Validating safety-critical systems is one*of**the*use cases for model checking. ... Acknowledgements We would like to thankfully acknowledge*the*funding*of**the*SAFIR 2014 project, Helsinki Institute for Information Technology, and*the*Academy*of*Finland project 139402. ...##
###
On the Proof Theory of Regular Fixed Points
[chapter]

2009
*
Lecture Notes in Computer Science
*

We provide a coinductive characterization

doi:10.1007/978-3-642-02716-1_8
fatcat:5iou2rnduvh3jnfwwpowzf2jpe
*of*inclusion that yields a natural bridge to proof-theory. ...*The*author is grateful to Luigi Santocanale, Alwen Tiu and especially Dale Miller for their advices, knowledge and insightful discussions. ...*the**correctness**of*such objects is not trivial, but we probably have most*of**the*tools at hand. ...##
###
A Mathematical Framework for Superintelligent Machines
[article]

2018
*
arXiv
*
pre-print

It is also generalized to a class

arXiv:1804.03301v1
fatcat:nofcd7pfkjhmdhtiihkebostbu
*calculus*involving assignments that change*the*states*of*programs. ... It can improve its own model*of**the*world by checking*the*actual results*of**the*actions*of*its robotic activators. ... and a decimal point, obtaining an*implementation**of*Tarski's theory*of*decidable real closed fields [6] . ...##
###
Some axioms for mathematics
[article]

2021
*
arXiv
*
pre-print

*The*lambda-Pi-

*calculus*modulo theory is a logical framework in which many logical systems can be expressed as theories. ... We present such a theory,

*the*theory U, where proofs

*of*several logical systems can be expressed. ...

*The*authors want to thank Michael Färber, César Muñoz, Thiago Felicissimo, and Makarius Wenzel for helpful remarks on a first version

*of*this paper. ...

##
###
From multiple sequent for additive linear logic to decision procedures for free lattices

1999
*
Theoretical Computer Science
*

This was shown by

doi:10.1016/s0304-3975(98)00311-9
fatcat:xi2nxier7fftbbwchuohcteita
*the*seminal work*of*Whitman [ 16,171 on free lattices.*The*sequent*calculus*ALL is singular. That is, there is only one formula on each side*of**the*deducibility relation t-. ... In*the*last Section 5, we apply additive contexts to suggest a sequent*calculus*for*the*propositional fragment*of*linear logic, called ...*the**calculus*. 0*The*proof*of**correction*goes by induction on size*of*T(E, F). ...##
###
A compilation method for ML-style polymorphic record calculi

1992
*
Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '92
*

*the*polymorphic record

*calculus*and a

*correct*

*implementation*term in

*the*

*implementation*

*calculus*. ... Moreover,

*the*polymorphic type system is shown to be sound with respect to an operational semantics

*of*

*the*translated terms in

*the*

*implementation*

*calculus*. * Appeared in Proc. ...

*The*major technical contribution

*of*

*the*present paper is to establish an inference algorithm that always constructs a

*correct*

*implementation*term for any type

*correct*raw term

*of*a polymorphic record

*calculus*...

##
###
Equality Reasoning in Sequent-Based Calculi
[chapter]

2001
*
Handbook of Automated Reasoning
*

We consider

doi:10.1016/b978-044450813-3/50012-6
fatcat:fix4fevuazaojn7acaoonwg5du
*the*history*of*handling equality in sequent systems, methods based on rigid E-uni cation, paramodulation-based methods,*the*equality elimination method and equality reasoning in nonclassical ... We overview methods*of*equality reasoning in sequent-based systems. ... ; T ' _ j : : : j n C 1 ; T ' j 1 ; T j : : : j n C ( ); and*the*rule (*abc*) is changed to1 ; T A; F B j 2 j : : : j n C 2 j : : : j n C fA = Bg (*abc*);*The**calculus*TBSE consists*of**the*following ...##
###
The Development of Mathematical Logic from Russell to Tarski, 1900–1935
[chapter]

2009
*
The Development of Modern Logic
*

elements

doi:10.1093/acprof:oso/9780195137316.003.0029
fatcat:ygiplet5oraf7fza6fsmf5j5ly
*of*K are also in*the*order*ABC*. ... Also,*the*notion*of*a "*correct*formula" which occurs in*the*presentation*of**the**calculus*is intended not as a concept defined, as it were, by*the**calculus*(as we would nowadays define*the*term "*provable*...##
###
Proof-based system engineering and embedded systems
[chapter]

1998
*
Lecture Notes in Computer Science
*

Asap, Better, Cheaper (

doi:10.1007/3-540-65193-4_23
fatcat:aeqgm5k4yzeplh6ttop467bbn4
*ABC*) now is*the*clients defined rule*of**the*game. ... It is based upon fulfilling proof obligations, notably establishing proofs that decisions regarding system design and system dimensioning are*correct*, before embarking on*the**implementation*or*the*fielding ... For*the*obvious reason that*provably**correct*S/W*implementations**of*specifications that are flawed in*the*first place can only result into incorrect computer-based systems. ...##
###
Geometry of evolutionary algorithms

2011
*
Proceedings of the 13th annual conference companion on Genetic and evolutionary computation - GECCO '11
*

*of*

*the*formal EA on

*the*specific fitness landscape (solution representation, neighbourhood structure and fitness function) 90 Automatic

*Implementation*Automatic

*Implementation*:

*the*

*implementation*

*of*... • FUTURE (theory): formal general theory

*of*design

*of*

*provably*efficient EA • FUTURE (practice): automated design, automated

*implementation*, theory-led parameter settings 85 Magic Evolutionary Meta ...

##
###
Resolving Gödel's Incompleteness Myth: Polynomial Equations and Dynamical Systems for Algebraic Logic
[article]

2011
*
arXiv
*
pre-print

*The*truth value

*of*a logical formula subject to a set

*of*axioms is computed from

*the*solution to

*the*corresponding system

*of*polynomial equations. ... In this framework

*the*truth values

*of*logical formulas and other polynomial objectives have complex data structures: sets

*of*elementary values, or dynamical systems that generate sets

*of*infinite sequences ... We now specify a logical formula z with

*the*following properties: z is not

*provable*; if z is ambiguous, then it is not true; and if z is not

*provable*,

*the*negation

*of*z is not

*provable*, and z is not ambiguous ...

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