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Call-by-Value Non-determinism in a Linear Logic Type Discipline
[chapter]

2013
*
Lecture Notes in Computer Science
*

Inspired

doi:10.1007/978-3-642-35722-0_12
fatcat:jlxryisb2ja6zopk6mb7mqmhvq
*by*recent works on the relational semantics of*linear**logic*and*non*-idempotent intersection*types*, we endow this calculus with*a**type*system based on the so-*called*Girard's second translation ... We consider the*call*-*by*-*value*lambda-calculus extended with*a*may-convergent*non*-deterministic choice and*a*must-convergent parallel composition. ...*Logic*Based*Type*System*In*this section we introduce our*type*system based on*linear**logic*. ...##
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Linearity, Control Effects, and Behavioral Types
[chapter]

2017
*
Lecture Notes in Computer Science
*

Designing

doi:10.1007/978-3-662-54434-1_9
fatcat:hk5yagycr5f55f2gigbs5hwl7a
*type*systems for handling and*disciplining*such idioms is challenging, due to long known conflicts between internal*non*-*determinism*,*linearity*, and control effects such as exceptions. ... The expressivity of our system is illustrated*by*several examples, including*a**typed*encoding of*a*higher-order functional language with threads, session channels,*non*-*determinism*, and exceptions. ... with built-*in*internal*non*-*determinism*. ...##
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A Formalization of the Semantics of Functional-Logic Programming in Isabelle
[article]

2009
*
arXiv
*
pre-print

Modern functional-

arXiv:0908.0494v1
fatcat:vq2yuupdtzdmtmjdku5wg2z2zm
*logic*programming languages like Toy or Curry feature*non*-strict*non*-deterministic functions that behave under*call*-time choice semantics. ...*In*this paper we present*a*formalization of that calculus*in*the Isabelle/HOL proof assistant. ... It is also not very natural that f (*a*, b) could yield the*value**a*for the arguments*a*and b being different*values*, which implies that the semantics defined*by*CRWL for*non*left-*linear*programs is pretty ...##
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Page 1275 of Mathematical Reviews Vol. , Issue 91C
[page]

1991
*
Mathematical Reviews
*

The authors present

*a*criterion for*a*set £ of modal formulas to be formula-complete*in*the*logic*L(B)*determined**by*B. ... The 4-*valued*extension of PM4 considered*by*the authors is*determined**by*the 4-element topological Boolean algebra B the Kripke frame of which is ({*a*, b}, {(*a*,*a*), (b, b), (*a*, b)}). ...##
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Page 3540 of Mathematical Reviews Vol. , Issue 2004e
[page]

2004
*
Mathematical Reviews
*

Later on

*in*Section 3 we are occupied with*a*subset of*non*-tautologies whose asymptotic den- sity is positive*by*the*linear*definition of the length of*a**type*, and moreover, this density tends to | as ...*In*Section 2 we prove that the asymptotic probability (defined precisely there) that*a*random one-variable formula is valid*in*intuitionistic*logic*(with implication only) is exactly 1, while*by*the*linear*...##
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The duality of computation

2000
*
Proceedings of the fifth ACM SIGPLAN international conference on Functional programming - ICFP '00
*

For λµμ-calculus, choosing

doi:10.1145/351240.351262
dblp:conf/icfp/CurienH00
fatcat:6wcsxmzjqrd67p5knlom4detqa
*a**call*-*by*-name or*call*-*by*-*value**discipline*for reduction amounts to choosing one of the two possible symmetric orientations of*a*critical pair. ... We present the λµμ-calculus,*a*syntax for λ-calculus + control operators exhibiting symmetries such as program/context and*call*-*by*-name/*call*-*by*-*value*. ...*In*[1] and [24] , the*non*-*determinism*of classical*logic*is encapsulated*in*critical pairs similar to the (µ) − (μ) pair. ...##
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The duality of computation

2000
*
SIGPLAN notices
*

For λµμ-calculus, choosing

doi:10.1145/357766.351262
fatcat:mpwytpp2b5eejcsdeizvzdcewy
*a**call*-*by*-name or*call*-*by*-*value**discipline*for reduction amounts to choosing one of the two possible symmetric orientations of*a*critical pair. ... We present the λµμ-calculus,*a*syntax for λ-calculus + control operators exhibiting symmetries such as program/context and*call*-*by*-name/*call*-*by*-*value*. ...*In*[1] and [24] , the*non*-*determinism*of classical*logic*is encapsulated*in*critical pairs similar to the (µ) − (μ) pair. ...##
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Transdisciplinary Knowledge Creation
[chapter]

2015
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Transdisciplinary Professional Learning and Practice
*

The principle of

doi:10.1007/978-3-319-11590-0_2
fatcat:orwuo35zcnf7hgoaatijfcnjui
*determinism*(aiding predictability) holds that any event is completely*determined**by*previous events (*linear*cause and effect). ... Classical, exclusive*logic*says*A*and*non*-*A*cannot exist at the same time; classical scholars*call*this idea consistency. ...##
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Constructor-based conditional narrowing

2001
*
Proceedings of the 3rd ACM SIGPLAN international conference on Principles and practice of declarative programming - PPDP '01
*

We define

doi:10.1145/773184.773205
dblp:conf/ppdp/Antoy01
fatcat:wkoqhitlwrdhjmi56y2trarigm
*a*transformation from*a*left-*linear*constructor-based conditional rewrite system into an overlapping inductively sequential rewrite system. ...*In*this context, we analyze the efficiency and practicality of using our transformation for the implementation of functional*logic*programming languages. ... Furthermore, let t and v be*a*term and*a**value**in*R such that*A*: t * → R v. The proof is*by*induction on*a*cost function, denoted*by*α, that takes*a*computation and returns*a**non*-negative integer. ...##
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Fab ous Interoperability for ML and a Linear Language
[chapter]

2018
*
Lecture Notes in Computer Science
*

language with

doi:10.1007/978-3-319-89366-2_8
fatcat:kpu6p5exhfdphdxzfkszurbskm
*linear**types*and*linear*state. ... We propose*a*formal specification for what it means for*a*given language*in**a*multi-language system to be usable without leaks: it should embed into the multi-language*in**a*fully abstract way, that is, ... This work was supported*in*part*by*the National Science Foundation under grants CCF-1422133 and CCF-1453796, and the European Research Council under ERC Starting Grant SECOMP (715753). ...##
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A Sampling-Aware Interpretation of Linear Logic: Syntax and Categorical Semantics
[article]

2022
*
arXiv
*
pre-print

We accommodate this new interpretation

arXiv:2202.00142v1
fatcat:q4fgw3dehndyjgtokkee4or7n4
*by*defining*a*multilanguage syntax and its categorical semantics that bridges the Markov kernel and*linear**logic*interpretations of probabilistic programs. ...*In*this work we show how*in*probabilistic models of*linear**logic*the correct resource interpretation should be sampling, i.e. the*linear*arrow should be read as "the output may only sample once from its ... One such example is*non*-*determinism*, where*linear*morphisms ⊸ should be seen as "*by*observing the*non*-deterministic*value*of once I get ". ...##
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Type-Based Security for Mobile Computing Integrity, Secrecy and Liveness

2006
*
Electronical Notes in Theoretical Computer Science
*

This paper sketches an idea on how to challenge the three security issues concentrating on code mobility,

doi:10.1016/j.entcs.2005.12.115
fatcat:nuyji5iylbgeli36wjrmm6g35a
*by*the development of*a*general theory of*types*of the π-calculus and the higher-order π-calculus ...*call*-*by*-*value*Game Semantics via an encoding of the*call*-*by*-*value*λ-calculus into the π-calculus [26] . ...*In*fact, there is*a*lack of formal foundations of*typing*,*logics*and semantics to even express (not to speak of proving) desired security properties of mobile programs when they include*non*-*determinism*...##
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Foundations of transdisciplinarity

2005
*
Ecological Economics
*

The latter represents an epistemological challenge that introduces

doi:10.1016/j.ecolecon.2005.01.014
fatcat:pkdziy6d4vehbmkhzp5v6h5vtm
*a*kind of quantum*logic*, as*a*substitute for*linear**logic*, and breaks with the assumption of*a*single reality. ... Two possibilities are proposed*in*this paper,*in*terms of*a*weak and*a*strong transdisciplinarity. The former can be applied following traditional methods and*logic*, and is essentially practical. ... It goes without saying (evidences are clear) that*linear**logic*and reductionism 6 Recursive definition (also*called*inductive definition and definition*by*recursion) is*a*definition*in*three clauses ...##
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Semiring Programming: A Declarative Framework for Generalized Sum Product Problems
[article]

2020
*
arXiv
*
pre-print

To solve hard problems, AI relies on

arXiv:1609.06954v2
fatcat:jhcfx6adm5achggxa25hwdfkmq
*a*variety of*disciplines*such as*logic*, probabilistic reasoning, machine learning and mathematical programming. ... The semantics of programs is defined*in*terms of first-order structures with semiring labels, which allows us to freely combine and integrate problems from different AI*disciplines*. ... Formally, quantifier-free*linear*integer arithmetic and propositional*logic*are specified as the underlying*logical*systems, and the domains of constants are*typed*. ...##
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Linear Contexts, Sharing Functors: Techniques for Symbolic Computation
[chapter]

2003
*
Applied Logic Series
*

This may be considered

doi:10.1007/978-94-017-0253-9_4
fatcat:nhaqrstcpvctpenp6tkvjxnv7e
*a**disciplined*use of pointer reversal techniques. ... We present*in*this paper two design issues concerning fundamental representation structures for symbolic and*logic*computations. ... Links with*Linear**Logic**A*focused tree is analogous to*a**linear**logic*box: T T T T or,*in**a*multisorted algebra, where*non*-homogeneous substructures may be edited: B*A*B*A*The zipper is seen as representing ...
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