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

Alejandro Díaz-Caro, Giulio Manzonetto, Michele Pagani
2013 Lecture Notes in Computer Science  
Inspired 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.  ... 
doi:10.1007/978-3-642-35722-0_12 fatcat:jlxryisb2ja6zopk6mb7mqmhvq

Linearity, Control Effects, and Behavioral Types [chapter]

Luís Caires, Jorge A. Pérez
2017 Lecture Notes in Computer Science  
Designing 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.  ... 
doi:10.1007/978-3-662-54434-1_9 fatcat:hk5yagycr5f55f2gigbs5hwl7a

A Formalization of the Semantics of Functional-Logic Programming in Isabelle [article]

Francisco López Fraguas, Stephan Merz, Juan Rodríguez Hortalá
2009 arXiv   pre-print
Modern functional-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  ... 
arXiv:0908.0494v1 fatcat:vq2yuupdtzdmtmjdku5wg2z2zm

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)}).  ... 

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  ... 

The duality of computation

Pierre-Louis Curien, Hugo Herbelin
2000 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming - ICFP '00  
For λµμ-calculus, choosing 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.  ... 
doi:10.1145/351240.351262 dblp:conf/icfp/CurienH00 fatcat:6wcsxmzjqrd67p5knlom4detqa

The duality of computation

Pierre-Louis Curien, Hugo Herbelin
2000 SIGPLAN notices  
For λµμ-calculus, choosing 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.  ... 
doi:10.1145/357766.351262 fatcat:mpwytpp2b5eejcsdeizvzdcewy

Transdisciplinary Knowledge Creation [chapter]

Sue L. T. McGregor
2015 Transdisciplinary Professional Learning and Practice  
The principle of 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.  ... 
doi:10.1007/978-3-319-11590-0_2 fatcat:orwuo35zcnf7hgoaatijfcnjui

Constructor-based conditional narrowing

Sergio Antoy
2001 Proceedings of the 3rd ACM SIGPLAN international conference on Principles and practice of declarative programming - PPDP '01  
We define 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.  ... 
doi:10.1145/773184.773205 dblp:conf/ppdp/Antoy01 fatcat:wkoqhitlwrdhjmi56y2trarigm

Fab ous Interoperability for ML and a Linear Language [chapter]

Gabriel Scherer, Max New, Nick Rioux, Amal Ahmed
2018 Lecture Notes in Computer Science  
language with 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).  ... 
doi:10.1007/978-3-319-89366-2_8 fatcat:kpu6p5exhfdphdxzfkszurbskm

A Sampling-Aware Interpretation of Linear Logic: Syntax and Categorical Semantics [article]

Pedro H. Azevedo de Amorim
2022 arXiv   pre-print
We accommodate this new interpretation 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 ".  ... 
arXiv:2202.00142v1 fatcat:q4fgw3dehndyjgtokkee4or7n4

Type-Based Security for Mobile Computing Integrity, Secrecy and Liveness

Nobuko Yoshida
2006 Electronical Notes in Theoretical Computer Science  
This paper sketches an idea on how to challenge the three security issues concentrating on code mobility, 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  ... 
doi:10.1016/j.entcs.2005.12.115 fatcat:nuyji5iylbgeli36wjrmm6g35a

Foundations of transdisciplinarity

Manfred A. Max-Neef
2005 Ecological Economics  
The latter represents an epistemological challenge that introduces 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  ... 
doi:10.1016/j.ecolecon.2005.01.014 fatcat:pkdziy6d4vehbmkhzp5v6h5vtm

Semiring Programming: A Declarative Framework for Generalized Sum Product Problems [article]

Vaishak Belle, Luc De Raedt
2020 arXiv   pre-print
To solve hard problems, AI relies on 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.  ... 
arXiv:1609.06954v2 fatcat:jhcfx6adm5achggxa25hwdfkmq

Linear Contexts, Sharing Functors: Techniques for Symbolic Computation [chapter]

Gérard Huet
2003 Applied Logic Series  
This may be considered 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  ... 
doi:10.1007/978-94-017-0253-9_4 fatcat:nhaqrstcpvctpenp6tkvjxnv7e
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