Efficient resource management for linear logic proof search

Cervesato, Iliano; Hodas, Joshua S.; Pfenning, Frank

doi:10.1007/3-540-60983-0_5

Cited by 41 publications

(43 citation statements)

References 13 publications

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“…Hence it is important to realize this CL interpreter in an efficient way, taking advantages of some techniques discussed in [1,2,4].…”

Section: Resultsmentioning

confidence: 99%

Expressing Algorithms as Concise as Possible via Computability Logic

Kwon

2014

IEICE Trans. Fundamentals

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This paper proposes a new approach to defining and expressing algorithms: the notion of task logical algorithms. This notion allows the user to define an algorithm for a task T as a set of agents who can collectively perform T . This notion considerably simplifies the algorithm development process and can be seen as an integration of the sequential pseudocode and logical algorithms.This observation requires some changes to algorithm development process. We propose a two-step approach: the first step is to define an algorithm for a task T via a set of agents that can collectively perform T . The second step is to translate these agents into (higher-order) computability logic.

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“…Hence it is important to realize this CL interpreter in an efficient way, taking advantages of some techniques discussed in [1,2,4].…”

Section: Resultsmentioning

confidence: 99%

Expressing Algorithms as Concise as Possible via Computability Logic

Kwon

2014

IEICE Trans. Fundamentals

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“…A strict logical framework can be directly implemented with very minor adaptations of well-known techniques used for its linear cousins such as Lolli [Hod94,CHP97] and LLF [Cer96]. Although we argue that strictness is a useful and ubiquitous concept which deserves to be offered as a primitive notion in a logical framework, this is not the only choice.…”

Section: Implementation Issuesmentioning

confidence: 99%

Elimination of Negation in a Logical Framework

Momigliano

2000

Computer Science Logic

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We address the issue of endowing a logical framework with a logically justified notion of negation. Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae cannot directly express negative information, although negation is a useful specification tool. Since negation-as-failure does not fit well in a logical framework, especially one endowed with hypothetical and parametric judgments, we adapt the idea of elimination of negation from Horn logic to a fragment of higher-order hereditary Harrop formulae. The idea is to replace occurrences of negative predicates with positive ones which are operationally equivalent. This entails two separate phases.Complementing terms, i.e. in our case higher-order patterns. Due the presence of partially applied lambda terms, intuitionistic lambda calculi are not closed under complementation. We thus develop a strict lambda calculus, where we can directly express whether a function depends on its argument.Complementing clauses. This can be seen as a negation normal form procedure which is consistent with intuitionistic provability. It entails finding a middle ground between the Closed World Assumption usually associated with negation and the Open World Assumption typical of logical frameworks. As this is in general not possible, we restrict ourselves to a fragment in which clause complementation is viable and that has proven to be expressive enough for the practice of logical frameworks. The main technical idea is to isolate a set of programs where static and dynamic clauses do not overlap.

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“…Their type system presents challenges similar to Fuzz, which they handle with algebraic manipulations. More precisely, their algorithmic version uses a technique similar to the one developed in Cervesato et al [2] for the splitting of resources: when a rule with multiple premises is encountered the algorithmic system, first allocate all the resources to the first branch and then allocate the remaining resources to the second branch. Unfortunately, this approach cannot be easily applied to DFuzz due to the presence of index variables and dependent pattern matching.…”

Section: Related Workmentioning

confidence: 99%

Really Natural Linear Indexed Type Checking

Amorim

Gaboardi

Arias

et al. 2014

Proceedings of the 26nd 2014 International Symposium on Implementation and Application of Functional Languages

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Recent works have shown the power of linear indexed type systems for capturing complex safety properties. These systems combine linear type systems with a language of indices that appear in the types, allowing more fine-grained analysis. For example, linear indexed types have been fruitfully applied to verify differential privacy in the Fuzz type system.A natural way to enhance the expressiveness of this approach is by allowing the indices to depend on runtime information, in the spirit of dependent types. This approach is used in DFuzz, an extension of Fuzz. The DFuzz type system relies on an index-level language supporting real and natural number arithmetic over constants and dependent variables. Moreover, DFuzz uses a subtyping mechanism to semantically manipulate indices. By themselves, linearity, dependency, and subtyping each require delicate handling when performing type checking or type inference; their combination increases this challenge substantially, as the features can interact in non-trivial ways.In this paper, we study the type-checking problem for DFuzz. We show how we can reduce type checking for (a simple extension of) DFuzz to constraint solving over a first-order theory of naturals and real numbers which, although undecidable, can often be handled in practice by standard numeric solvers.

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Efficient resource management for linear logic proof search

Cited by 41 publications

References 13 publications

Expressing Algorithms as Concise as Possible via Computability Logic

Expressing Algorithms as Concise as Possible via Computability Logic

Elimination of Negation in a Logical Framework

Really Natural Linear Indexed Type Checking

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