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CALCO brings together researchers and practitioners to exchange new results related to foundational aspects and both traditional and emerging uses of algebras and coalgebras in computer science. The study of algebra and coalgebra relates to the data, process and structural aspects of software systems. This is a high-level, bi-annual conference f...

CALCO brings together researchers and practitioners to exchange new results related to foundational aspects and both traditional and emerging uses of algebras and coalgebras in computer science. The study of algebra and coalgebra relates to the data, process and structural aspects of software systems. This is a high-level, bi-annual conference formed by joining the forces and reputations of CMCS (the International Workshop on Coalgebraic Methods in Computer Science), and WADT (the Workshop on Algebraic Development Techniques). The first CALCO conference was held in Swansea, Wales, in 2005; the second takes place in Bergen, Norway. The CALCO Young Researchers Workshop, CALCO-jnr, is a CALCO satellite event dedicated to presentations by PhD students and by those who completed their doctoral studies within the past few years. Attendance at the workshop is open to all- it is anticipated that many CALCO conference participants attend the CALCO-jnr workshop (and vice versa). CALCO-jnr presentations have been selected on the basis of submitted 2page abstracts, by the CALCO-jnr PC. This booklet contains the abstracts of the accepted contributions. After the workshop, the author(s) of each presentation will be invited to submit a full 10-15 page paper on the same topic. They will also be asked to write (anonymous) reviews of papers submitted by other authors on related topics. Additional reviewing and the final selection of papers will be carried out by the CALCO-jnr PC. The volume of selected papers from the workshop will be published as a Department of Informatics, University of Bergen, technical report, and it will also be made available through the open access database Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

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http://www.ii.uib.no/calco07/calcojnr-p/calco07-jnr-abstracts.pdf

http://www.ii.uib.no/calco07/calcojnr-p/calco07-jnr-abstracts.pdf Minimize

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en

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Sponsoring Institutions Working Group 1.3: Foundations of System Specification The British Computer Society specialist group on Formal Aspects of Computer Science Preface

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and WADT – the Workshop on Algebraic Development Techniques, have joined their forces and reputations into a new high-level bi-annual conference. Starting in 2005, CALCO brings together researchers and practitioners to exchange new results related to foundational aspects and both traditional and emerging uses of algebras and coalgebras in comput...

and WADT – the Workshop on Algebraic Development Techniques, have joined their forces and reputations into a new high-level bi-annual conference. Starting in 2005, CALCO brings together researchers and practitioners to exchange new results related to foundational aspects and both traditional and emerging uses of algebras and coalgebras in computer science. The CALCO Young Researchers Workshop, CALCO-jnr, was a CALCO 2005 satellite event dedicated to presentations by PhD students and by those who completed their doctoral studies within the past few years. Attendance at the workshop was open to all – many CALCO conference participants attended the CALCO-jnr workshop and vice versa. Overall, CALCO-jnr received 23 submissions and had 37 participants. CALCO-jnr presentations were selected according to originality, significance, and general interest, on the basis of 2-page abstracts, by the organisers. After the workshop, the author(s) of each presentation were invited to submit a full 10-15 page paper on the same topic. They were also asked to write (anonymous) reviews of papers submitted by other authors on related topics; further reviewing was provided mainly by members of the CALCO Programme Committee and of IFIP WG 1.3. This volume of selected papers from the workshop is published as a technical report at Swansea. Authors retain copyright, and are also encouraged to disseminate the results reported at CALCO-jnr by subsequent publication elsewhere. The organisers of CALCO-jnr would like to thank the workshop participants, the reviewers, and the CALCO 2005 organisers José Fiadeiro, Neal Harman, Markus Roggenbach, and Jan Rutten for their efforts to make this event a success. The support of the sponsoring institutions listed on the preceding page is Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

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http://www-compsci.swan.ac.uk/~csmona/CALCO-jnr-Proceedings.pdf

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Verification of railway interlockings in scade

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Abstract: We present two modelling approaches for the application of model checking to verify railway interlockings. The first translates so-called Ladder Logic into Scade language, the second models a segment of railway from scratch. The verification tool used is Scade. Keywords: Verification, Model Checking, Scade, Data-flow, Lustre, Railway T...

Abstract: We present two modelling approaches for the application of model checking to verify railway interlockings. The first translates so-called Ladder Logic into Scade language, the second models a segment of railway from scratch. The verification tool used is Scade. Keywords: Verification, Model Checking, Scade, Data-flow, Lustre, Railway The aim of our research is to investigate the use of Scade Suite (Esterel Technologies) for the verification of railway interlockings. This is a feasibility study done in co-operation with Invensys Rail, a leading international company for the design, construction, and validation of railway control systems. We concentrate on the application of modelling and model checking [CGP99]; specifically we present the development of two different modelling approaches. In the first approach, we translate existing specifications written in so-called Ladder Logic into Scade and verify them. In the second, we model a segment of railway from scratch. We applied the first approach to two real world railway interlockings, however, for confidentially reasons, we can only demonstrate the method with a toy example. The track plan and control table of one of these two real world interlockings were simplified and led to the model considered in the second Minimize

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Springer

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-05-09

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http://cs.swan.ac.uk/%7Ecsal/AVOCS2010.pdf

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an der Fakultät für Mathematik und Informatik der Ludwig–Maximilians–Universität München

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This thesis aims at exploring the scopes and limits of techniques for extracting programs from proofs. We focus on constructive theories of inductive definitions and classical systems allowing choice principles. Special emphasis is put on optimizations that allow for the extraction of realistic programs. Our main field of application is infinita...

This thesis aims at exploring the scopes and limits of techniques for extracting programs from proofs. We focus on constructive theories of inductive definitions and classical systems allowing choice principles. Special emphasis is put on optimizations that allow for the extraction of realistic programs. Our main field of application is infinitary combinatorics. Higman’s Lemma, having an elegant non-constructive proof due to Nash-Williams, constitutes an interesting case for the problem of discovering the constructive content behind a classical proof. We give two distinct solutions to this problem. First, we present a proof of Higman’s Lemma for an arbitrary alphabet in a theory of inductive definitions. This proof may be considered as a constructive counterpart to Nash-Williams ’ minimal-bad-sequence proof. Secondly, using a refined A-translation method, we directly transform the classical proof into a constructive one and extract a program. The crucial point in the latter is that we do not need to avoid the axiom of classical dependent choice but directly assign a realizer to its translation. A generalization of Higman’s Lemma is Kruskal’s Theorem. We present a constructive proof of Kruskal’s Theorem that is completely formalized in a theory of inductive definitions. As a practical part, we show that these methods can be carried out in an interactive theorem prover. Both approaches to Higman’s Lemma have been implemented in Minlog. ii Minimize

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The Pennsylvania State University CiteSeerX Archives

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2008-07-01

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http://edoc.ub.uni-muenchen.de/1619/1/seisenberger_monika.pdf

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DOI 10.1007/s00224-011-9325-8 Proofs, Programs, Processes

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Abstract The objective of this paper is to provide a theoretical foundation for program extraction from inductive and coinductive proofs geared to practical applications. The novelties consist in the addition of inductive and coinductive definitions to a realizability interpretation for first-order proofs, a soundness proof for this system, and ...

Abstract The objective of this paper is to provide a theoretical foundation for program extraction from inductive and coinductive proofs geared to practical applications. The novelties consist in the addition of inductive and coinductive definitions to a realizability interpretation for first-order proofs, a soundness proof for this system, and applications to the synthesis of non-trivial provably correct programs in the area of exact real number computation. We show that realizers, although per se untyped, can be assigned polymorphic recursive types and hence represent valid programs in a lazy functional programming language such as Haskell. Programs extracted from proofs using coinduction can be understood as perpetual processes producing infinite streams of data. Typical applications of such processes are computations in exact real arithmetic. As an example we show how to extract a program computing the average of two real numbers w.r.t. the binary signed digit representation. Minimize

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The Pennsylvania State University CiteSeerX Archives

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2013-09-24

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http://link.springer.com/content/pdf/10.1007/s00224-011-9325-8.pdf

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

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Proofs, programs, processes

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Abstract. We study a realisability interpretation for inductive and coinductive definitions and discuss its application to program extraction from proofs. A speciality of this interpretation is that realisers are given by terms that correspond directly to programs in a lazy functional programming language such as Haskell. Programs extracted from...

Abstract. We study a realisability interpretation for inductive and coinductive definitions and discuss its application to program extraction from proofs. A speciality of this interpretation is that realisers are given by terms that correspond directly to programs in a lazy functional programming language such as Haskell. Programs extracted from proofs using coinduction can be understood as perpetual processes producing infinite streams of data. Typical applications of such processes are computations in exact real arithmetic. As an example we show how to extract a program computing the average of two real numbers w.r.t. to the binary signed digit representation. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-04-15

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http://www-compsci.swan.ac.uk/%7Ecsulrich/ftp/cie10r.pdf

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Program extraction via typed realisability for induction and coinduction

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and coinduction

and coinduction Minimize

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The Pennsylvania State University CiteSeerX Archives

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2012-03-19

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http://wwwmath.uni-muenster.de/logik/Personen/rds/pohlers_volume/Berger_Seisenberger.pdf

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An Inductive Version of Nash-Williams’ Minimal-Bad-Sequence Argument for Higman’s Lemma

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Higman’s lemma has a very elegant, non-constructive proof due to Nash-Williams [NW63] using the so-called minimal-bad-sequence argument. The objective of the present paper is to give a proof that uses the same combinatorial idea, but is constructive. For a two letter alphabet this was done by Coquand and Fridlender [CF94]. Here we present a proo...

Higman’s lemma has a very elegant, non-constructive proof due to Nash-Williams [NW63] using the so-called minimal-bad-sequence argument. The objective of the present paper is to give a proof that uses the same combinatorial idea, but is constructive. For a two letter alphabet this was done by Coquand and Fridlender [CF94]. Here we present a proof in a theory of inductive definitions that works for arbitrary decidable well quasiorders. Minimize

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Springer

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-06-20

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http://www-compsci.swan.ac.uk/~csmona/articles/nash-williams.pdf

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Applications of inductive definitions and choice principles to program synthesis

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Abstract. We describe two methods of extracting constructive content from classical proofs, focusing on theorems involving infinite sequences and nonconstructive choice principles. The first method removes any reference to infinite sequences and transforms the theorem into a system of inductive definitions, the other applies a combination of Göd...

Abstract. We describe two methods of extracting constructive content from classical proofs, focusing on theorems involving infinite sequences and nonconstructive choice principles. The first method removes any reference to infinite sequences and transforms the theorem into a system of inductive definitions, the other applies a combination of Gödel’s negativeand Friedman’s A-translation. Both approaches are explained by means of a case study on Higman’s Lemma and its well-known classical proof due to Nash-Williams. We also discuss some proof-theoretic optimizations that were crucial for the formalization and implementation of this work in the interactive proof system Minlog. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://www-compsci.swan.ac.uk/~csmona/claco.pdf

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The Warshall Algorithm and Dickson's Lemma: Two Examples of realistic program extraction

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. By means of two well-known examples it is demonstrated that the method of extracting programs from proofs is manageable in practise and may yield efficient and sometimes unexpected programs. The Warshall algorithm computing the transitive closure of a relation is extracted from a constructive proof that repetitions in a path can always be avoi...

. By means of two well-known examples it is demonstrated that the method of extracting programs from proofs is manageable in practise and may yield efficient and sometimes unexpected programs. The Warshall algorithm computing the transitive closure of a relation is extracted from a constructive proof that repetitions in a path can always be avoided. Secondly, we extract a program from a classical (i.e. non constructive) proof of a special case of Dickson's Lemma, by transforming the classical proof into a constructive one. These techniques (as well as the examples) are implemented in the interactive theorem prover Minlog developed at the University of Munich. 1. Introduction The objective of this paper is to show that the method of extracting programs from proofs is not only a powerful metamathematical tool, but also is of considerable practical interest. By means of two nontrivial examples we demonstrate that, applied in a refined way, the method is applicable to rather involved pro. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-13

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http://www.mathematik.uni-muenchen.de/~schwicht/papers/jar97/jar99.ps.Z

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