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Title:

A syntactical analysis of non-size-increasing polynomial time computation

Description:

A syntactical proof is given that all functions definable in a certain affine linear typed λ-calculus with iteration in all types are polynomial time computable. The proof provides explicit polynomial bounds that can easily be calculated.

A syntactical proof is given that all functions definable in a certain affine linear typed λ-calculus with iteration in all types are polynomial time computable. The proof provides explicit polynomial bounds that can easily be calculated. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-10-10

Source:

http://www-cgi.cs.cmu.edu/~fp/courses/15816-s12/misc/aehlig02tocl.pdf

http://www-cgi.cs.cmu.edu/~fp/courses/15816-s12/misc/aehlig02tocl.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Categories and Subject Descriptors ; F.4.1 [Mathematical Logic and Formal Languages ; Mathematical Logic—Lambda calculus and related systems ; F.2.2 [Analysis of Algorithms and Problem Complexity ; Nonnumerical Algorithms and Problems General Terms ; Theory ; Languages Additional Key Words and Phrases ; Complexity ; lambda calculus ; linear logic

Categories and Subject Descriptors ; F.4.1 [Mathematical Logic and Formal Languages ; Mathematical Logic—Lambda calculus and related systems ; F.2.2 [Analysis of Algorithms and Problem Complexity ; Nonnumerical Algorithms and Problems General Terms ; Theory ; Languages Additional Key Words and Phrases ; Complexity ; lambda calculus ; linear logic Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

DECORATING PROOFS

Description:

Dedicated to Grigori Mints on occasion of his 70th birthday Abstract. The programs synthesized from proofs are guaranteed to be correct, however at the cost of sometimes introducing irrelevant computations, as a consequence of the fact that the extracted code faithfully reflects the proof. In this paper we extend the work of Ulrich Berger [2], w...

Dedicated to Grigori Mints on occasion of his 70th birthday Abstract. The programs synthesized from proofs are guaranteed to be correct, however at the cost of sometimes introducing irrelevant computations, as a consequence of the fact that the extracted code faithfully reflects the proof. In this paper we extend the work of Ulrich Berger [2], which introduces the concept of “non-computational universal quantifiers”, and propose an algorithm by which we identify at the proof level the components- quantified variables, as well as premises of implications- that are computationally irrelevant and mark them as such. We illustrate the benefits of this (optimal) decorating algorithm in some case studies and present the results obtained with the proof assistant Minlog. We consider proofs in minimal logic, written in natural deduction style. The only rules are introduction and elimination for implication and the universal quantifier. The logical connectives ∃, ∧ are seen as special cases of inductively defined predicates, and hence are defined by the introduction and elimination schemes Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-03-20

Source:

http://www.mathematik.uni-muenchen.de/~schwicht/papers/mints09/deco20090728.pdf

http://www.mathematik.uni-muenchen.de/~schwicht/papers/mints09/deco20090728.pdf Minimize

Document Type:

text

Language:

en

DDC:

005 Computer programming, programs & data *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

A Syntactical Analysis of Non-Size-Increasing Polynomial Time Computation

Description:

A purely syntactical proof is given that all functions definable in a certain affine linear typed -calculus with iteration in all types are polynomial time computable. The proof also gives explicit polynomial bounds that can easily be calculated. 1 Summary In [6] Hofmann presented a linear type system for non-size-increasing polynomial time comp...

A purely syntactical proof is given that all functions definable in a certain affine linear typed -calculus with iteration in all types are polynomial time computable. The proof also gives explicit polynomial bounds that can easily be calculated. 1 Summary In [6] Hofmann presented a linear type system for non-size-increasing polynomial time computation allowing unrestricted recursion for inductive datatypes. The proof that all definable functions of type N ( N are polynomial time computable essentially used semantic concepts, such as the set-theoretic interpretation of terms. We present a different proof of the same result for a slightly modified version of the term system, which uses syntactical arguments only. However, this paper is more than a new proof of an already known result, as the method choosen has several benefits: ffl A reduction relation is defined on the term system such that the term system is closed under reduction. Therefore calculations can be done within the . Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-13

Source:

http://www.mathematik.uni-muenchen.de/~schwicht/papers/lics00/coin.ps.Z

http://www.mathematik.uni-muenchen.de/~schwicht/papers/lics00/coin.ps.Z Minimize

Document Type:

text

Language:

en

DDC:

511 General principles of mathematics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Realizability interpretation of proofs in constructive analysis

Description:

We prove constructively (in the style of Bishop) that every monotone continuous function with a uniform modulus of increase has a continuous inverse. The proof is formalized, and a realizing term extracted. It turns out that even in the logical term language – a version of Gödel’s T – evaluation is reasonably efficient.

We prove constructively (in the style of Bishop) that every monotone continuous function with a uniform modulus of increase has a continuous inverse. The proof is formalized, and a realizing term extracted. It turns out that even in the logical term language – a version of Gödel’s T – evaluation is reasonably efficient. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-07

Source:

http://www.mathematik.uni-muenchen.de/~schwicht/papers/swansea06/cie06.pdf

http://www.mathematik.uni-muenchen.de/~schwicht/papers/swansea06/cie06.pdf Minimize

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text

Language:

en

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Title:

Constructive Analysis with Witnesses

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-08-11

Source:

http://www.mathematik.uni-muenchen.de/~schwicht/papers/mod03/modart03.ps

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text

Language:

en

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Title:

A syntactical analysis of non-size-increasing polynomial time computation

Description:

A syntactical proof is given that all functions definable in a certain affine linear typed λ-calculus with iteration in all types are polynomial time computable. The proof also gives explicit polynomial bounds that can easily be calculated.

A syntactical proof is given that all functions definable in a certain affine linear typed λ-calculus with iteration in all types are polynomial time computable. The proof also gives explicit polynomial bounds that can easily be calculated. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-10-10

Source:

http://arxiv.org/pdf/cs/0011037v1.pdf

http://arxiv.org/pdf/cs/0011037v1.pdf Minimize

Document Type:

text

Language:

en

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Title:

Mathematical Logic

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-05-28

Source:

http://www.mathematik.uni-muenchen.de/%7Eschwicht/lectures/logic/ss10/ml.pdf

http://www.mathematik.uni-muenchen.de/%7Eschwicht/lectures/logic/ss10/ml.pdf Minimize

Document Type:

text

Language:

en

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Title:

Recursion on the partial continuous functionals

Description:

We describe a constructive theory of computable functionals, based on the partial continuous functionals as their intendend domain. Such a task had long ago been started by Dana Scott [28], under the well-known abbreviation

We describe a constructive theory of computable functionals, based on the partial continuous functionals as their intendend domain. Such a task had long ago been started by Dana Scott [28], under the well-known abbreviation Minimize

Publisher:

Springer

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-03-24

Source:

http://www.mathematik.uni-muenchen.de/~schwicht/papers/athen05/total06.pdf

http://www.mathematik.uni-muenchen.de/~schwicht/papers/athen05/total06.pdf Minimize

Document Type:

text

Language:

en

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Title:

Density and Choice for Total Continuous Functionals

Description:

this paper is to give complete proofs of the density theorem and the choice principle for total continuous functionals in the natural and concrete context of the partial continuous functionals [Ers77], essentially by specializing more general treatments in the literature. The proofs obtained are relatively short and hopefully perspicious, and ma...

this paper is to give complete proofs of the density theorem and the choice principle for total continuous functionals in the natural and concrete context of the partial continuous functionals [Ers77], essentially by specializing more general treatments in the literature. The proofs obtained are relatively short and hopefully perspicious, and may contribute to redirect attention to the fundamental questions Kreisel originally was interested in. Obviously this work owes much to other sources. In particular I have made use of work by Scott [Sco82] (whose notion of an information system is taken as a basis to introduce domains), Roscoe [Ros87], Larsen and Winskel [LW84] and Berger [Ber93]. The paper is organized as follows. Section 1 treats information systems, and in section 2 it is shown that the partial orders defined by them are exactly the (Scott) domains with countable basis. Section 3 gives a characterization of the continuous functions between domains, in terms of approximable mappings. In section 4 cartesian products and function spaces of domains and information systems are introduced. In section 5 the partial and total continuous functionals are defined. Section 6 finally contains the proofs of the two theorems above; it will be clear that the same proofs also yield effective versions of these theorems. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-12

Source:

http://www.mathematik.uni-muenchen.de/~schwicht/papers/kreisel93/k.ps.Z

http://www.mathematik.uni-muenchen.de/~schwicht/papers/kreisel93/k.ps.Z Minimize

Document Type:

text

Language:

en

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Title:

Minlog - An Interactive Prover

Description:

normalization-by-evaluation : : : : : : : : : : : : : : : : : : : : : : : : 42 7.2 Implementation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 42 7.2.1 The model : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 42 7.2.2 Interpretation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : ...

normalization-by-evaluation : : : : : : : : : : : : : : : : : : : : : : : : 42 7.2 Implementation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 42 7.2.1 The model : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 42 7.2.2 Interpretation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 42 7.2.3 Quote and unquote : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 43 7.2.4 Animation of program-constants and function-symbols : : : : : : : : : : 43 7.2.5 Normalization-by-evaluation : : : : : : : : : : : : : : : : : : : : : : : : : 43 7.2.6 Normalization-by-evaluation for proof terms : : : : : : : : : : : : : : : : 44 7.2.7 Internals : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 44 8 The T E X-output 45 8.1 How to output : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 45 8.2 How to modify the output of types, terms and formulas : : : : : : : : : : : : : 46 8.2.1 add-groun. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-14

Source:

http://www.mathematik.uni-muenchen.de/~schwicht/minlog/doc/manual.ps.gz

http://www.mathematik.uni-muenchen.de/~schwicht/minlog/doc/manual.ps.gz Minimize

Document Type:

text

Language:

en

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