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The linear abstract machine

Y. Lafont
1988 Theoretical Computer Science
A Linear Logic  provides a refinement 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]

Johan Jeuring, Alex Gerdes, Bastiaan Heeren
2012 Lecture Notes in Computer Science
both: flip f λx y → f y x which explains 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

Patrick Lincoln, John Mitchell, Andre Scedrov, Natarajan Shankar
1992 Annals of Pure and Applied Logic
Further, we prove that without 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]

André Platzer, Jan-David Quesel, Philipp Rümmer
2009 Lecture Notes in Computer Science
To identify strengths and weaknesses, we examine state 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]

Tuomas Kuismin, Keijo Heljanko
2013 Lecture Notes in Computer Science
As model checkers themselves are quite complicated pieces 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]

David Baelde
2009 Lecture Notes in Computer Science
We provide a coinductive characterization 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]

Daniel J. Buehrer
2018 arXiv   pre-print
It is also generalized to a class 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  .  ...

Some axioms for mathematics [article]

Frédéric Blanqui and Gilles Dowek and Emilie Grienenberger and Gabriel Hondet and François Thiré
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.  ...

Jean-Yves Marion
1999 Theoretical Computer Science
This was shown by 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

Atsushi Ohori
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]

Anatoli Degtyarev, Andrei Voronkov
2001 Handbook of Automated Reasoning
We consider 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]

Paolo Mancosu, Richard Zach, Calixto Badesa
2009 The Development of Modern Logic
elements 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]

Gerard Lann
1998 Lecture Notes in Computer Science
Asap, Better, Cheaper (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

Alberto Moraglio
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]

Joseph W. Norman
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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