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Proofs, Programs, Processes [chapter]

Ulrich Berger, Monika Seisenberger
2010 Lecture Notes in Computer Science  
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
more » ... xact 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.
doi:10.1007/978-3-642-13962-8_5 fatcat:rcvrnid7evgwdcntvdbblrcz64

Proofs, Programs, Processes

Ulrich Berger, Monika Seisenberger
2011 Theory of Computing Systems  
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
more » ... xact 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.
doi:10.1007/s00224-011-9325-8 fatcat:ixtzrva6cnfnzeopffiqolncui

Extracting a DPLL Algorithm

Andrew Lawrence, Ulrich Berger, Monika Seisenberger
2012 Electronical Notes in Theoretical Computer Science  
We formalize a completeness proof for the DPLL proof system and extract a DPLL SAT solver from it. When applied to a propositional formula in conjunctive normal form the program produces either a satisfying assignment or a DPLL derivation which shows that it is unsatisfiable. We use non-computational quantifiers to remove redundant computational content from the extracted program and improve its performance. The formalization is carried out in the Minlog system.
doi:10.1016/j.entcs.2012.08.016 fatcat:bgcj4yddufhrheenzfs5oywihm

Program extraction applied to monadic parsing

Ulrich Berger, Alison Jones, Monika Seisenberger
2015 Journal of Logic and Computation  
doi:10.1093/logcom/exv078 fatcat:5dqhqwqbqnepnbed6tya7d7fsu

Well Quasi-Orders in Computer Science (Dagstuhl Seminar 16031)

Jean Goubault-Larrecq, Monika Seisenberger, Victor Selivanov, Andreas Weiermann, Marc Herbstritt
2016 Dagstuhl Reports  
Monika Seisenberger's proof [2] or Jean Goubault-Larrecq's proof [1] ).  ...  Seisenberger, Victor Selivanov, and Andreas Weiermann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ... 
doi:10.4230/dagrep.6.1.69 dblp:journals/dagstuhl-reports/Goubault-Larrecq16 fatcat:o3uwzu5ptfavfes6kgexpi4a6q

Verification of Solid State Interlocking Programs [chapter]

Phillip James, Andy Lawrence, Faron Moller, Markus Roggenbach, Monika Seisenberger, Anton Setzer, Karim Kanso, Simon Chadwick
2014 Lecture Notes in Computer Science  
We report on the inclusion of a formal method into a design process in industry. Concretely, we suggest carrying out a verification step in railway interlocking design between programming the interlocking and testing this program. Safety still relies on testing, but the burden of guaranteeing completeness and correctness of the verfication is in this way greatly reduced. We present a complete methodology for carrying out this verification step in the case of ladder logic programs and give
more » ... s for real world railway interlockings. As this verification step reduces costs for testing, Invensys Rail is working to include such a verification step into their design process of solid state interlockings.
doi:10.1007/978-3-319-05032-4_19 fatcat:wjm4tsayvzgwxc3enjtfwcttzm

Minlog - A Tool for Program Extraction Supporting Algebras and Coalgebras [chapter]

Ulrich Berger, Kenji Miyamoto, Helmut Schwichtenberg, Monika Seisenberger
2011 Lecture Notes in Computer Science  
doi:10.1007/978-3-642-22944-2_29 fatcat:a52xuqzngjhxrirrqfleudyxgm

An Inductive Version of Nash-Williams' Minimal-Bad-Sequence Argument for Higman's Lemma [chapter]

Monika Seisenberger
2002 Lecture Notes in Computer Science  
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. Research supported by the DFG Graduiertenkolleg "Logik in
more » ... Informatik" † Research supported by the British EPSRC IND 1 (acc A ). Let as be such that acc A as and IH 1 : ∀bs A as, ∀f. acc ≺ f → ∀ws. bs = badsubseq(lasts ws) ∧ f = forest ws → acc A * ws.
doi:10.1007/3-540-45842-5_15 fatcat:2c5l7c7iszdzpg656hrnmnkk5y

APPLICATIONS OF INDUCTIVE DEFINITIONS AND CHOICE PRINCIPLES TO PROGRAM SYNTHESIS [chapter]

Ulrich Berger, Monika Seisenberger
2005 From Sets and Types to Topology and Analysis  
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
more » ... 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 Higman's lemma is used, for example, in term rewriting theory for termination proofs [CTB94,Tou02].
doi:10.1093/acprof:oso/9780198566519.003.0008 fatcat:n4z453pujrenfgte7abt4tkjhi

Extracting Imperative Programs from Proofs: In-place Quicksort

Ulrich Berger, Monika Seisenberger, Gregory J. M. Woods, Marc Herbstritt
2014 Types for Proofs and Programs  
The process of program extraction is primarily associated with functional programs with less focus on imperative program extraction. In this paper we consider a standard problem for imperative programming: In-place Quicksort. We formalize a proof that every array of natural numbers can be sorted and apply a realizability interpretation to extract a program from the proof. Using monads we are able to exhibit the inherent imperative nature of the extracted program. We see this as a first step
more » ... rds an automated extraction of imperative programs. The case study is carried out in the interactive proof assistant Minlog.
doi:10.4230/lipics.types.2013.84 dblp:conf/types/BergerSW13 fatcat:ofhtwmjlsjb5nau5y3lqrkxspa

Towards a Shapley Value Graph Framework for Medical peer-influence [article]

Jamie Duell, Monika Seisenberger, Gert Aarts, Shangming Zhou, Xiuyi Fan
2022 arXiv   pre-print
eXplainable Artificial Intelligence (XAI) is a sub-field of Artificial Intelligence (AI) that is at the forefront of AI research. In XAI, feature attribution methods produce explanations in the form of feature importance. People often use feature importance as guidance for intervention. However, a limitation of existing feature attribution methods is that there is a lack of explanation towards the consequence of intervention. In other words, although contribution towards a certain prediction is
more » ... highlighted by feature attribution methods, the relation between features and the consequence of intervention is not studied. The aim of this paper is to introduce a new framework, called a peer influence framework to look deeper into explanations using graph representation for feature-to-feature interactions to improve the interpretability of black-box Machine Learning models and inform intervention.
arXiv:2112.14624v2 fatcat:g2ho4fwzrreo3jdjmv4akob3rq

On Understanding the Influence of Controllable Factors with a Feature Attribution Algorithm: a Medical Case Study [article]

Veera Raghava Reddy Kovvuri, Siyuan Liu, Monika Seisenberger, Berndt Müller, Xiuyi Fan
2022 arXiv   pre-print
Feature attribution XAI algorithms enable their users to gain insight into the underlying patterns of large datasets through their feature importance calculation. Existing feature attribution algorithms treat all features in a dataset homogeneously, which may lead to misinterpretation of consequences of changing feature values. In this work, we consider partitioning features into controllable and uncontrollable parts and propose the Controllable fActor Feature Attribution (CAFA) approach to
more » ... ute the relative importance of controllable features. We carried out experiments applying CAFA to two existing datasets and our own COVID-19 non-pharmaceutical control measures dataset. Experimental results show that with CAFA, we are able to exclude influences from uncontrollable features in our explanation while keeping the full dataset for prediction.
arXiv:2203.12701v1 fatcat:7gxipf5uyffurir5ynrpiw4a24

Towards Safety Analysis of ERTMS/ETCS Level 2 in Real-Time Maude [chapter]

Phillip James, Andrew Lawrence, Markus Roggenbach, Monika Seisenberger
2016 Communications in Computer and Information Science  
doi:10.1007/978-3-319-29510-7_6 fatcat:ctjwhin63jcu3asepr5z3mz4fm

Verification of the European Rail Traffic Management System in Real-Time Maude

Ulrich Berger, Phillip James, Andrew Lawrence, Markus Roggenbach, Monika Seisenberger
2018 Science of Computer Programming  
doi:10.1016/j.scico.2017.10.011 fatcat:vkc7njfdwjbchg2hzrrx3dekae

Preface to the special issue: Continuity, computability, constructivity: from logic to algorithms 2013

HAJIME ISHIHARA, MARGARITA KOROVINA, ARNO PAULY, MONIKA SEISENBERGER, DIETER SPREEN
2016 Mathematical Structures in Computer Science  
Special issue editors: Hajime Ishihara Margarita Korovina Arno Pauly Monika Seisenberger Dieter Spreen at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0960129516000086 Downloaded  ... 
doi:10.1017/s0960129516000086 fatcat:ogmi3j6zkrhgdh35mauj3m5i7i
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