Formalising Bitonic Sort in Type Theory
We discuss two complete formalisations of bitonic sort in constructive type theory. Bitonic sort is one of the fastest sorting algorithms where the sequence of comparisons is not data-dependent. In addition, it is a general recursive algorithm. In the formalisation we face two main problems: only st...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Tagungsbericht |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 97 |
|---|---|
| container_issue | |
| container_start_page | 82 |
| container_title | |
| container_volume | |
| creator | Bove, Ana Coquand, Thierry |
| description | We discuss two complete formalisations of bitonic sort in constructive type theory. Bitonic sort is one of the fastest sorting algorithms where the sequence of comparisons is not data-dependent. In addition, it is a general recursive algorithm. In the formalisation we face two main problems: only structural recursion is allowed in type theory, and a formal proof of the correctness of the algorithm needs to consider quite a number of cases. In our first formalisation we define bitonic sort over dependently-typed binary trees with information in the leaves and we make use of the 0-1-principle to prove that the algorithm sorts inputs of arbitrary types. In our second formalisation we use notions from linear orders, lattice theory and monoids. The correctness proof is directly performed for any ordered set and not only for Boolean values. |
| doi_str_mv | 10.1007/11617990_6 |
| format | Conference Proceeding |
| fullrecord | <record><control><sourceid>pascalfrancis_sprin</sourceid><recordid>TN_cdi_pascalfrancis_primary_19938563</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>19938563</sourcerecordid><originalsourceid>FETCH-LOGICAL-p218t-5c99061bd50552e5f12d7f453172810b4e4ea4acad3b06a47d5c8d34edcd49163</originalsourceid><addsrcrecordid>eNpVkD1PwzAYhM2XRFWy8AuyIFgCfv3asT1CRQGpEgNhthzbKYY2iewu_fcEFQlxyw3P6XQ6Qi6B3gKl8g6gBqk1NfURKbRUKDhF4EyLYzKbGFSIXJ_8Y0qdkhlFyiotOZ6TIudPOgkZFRxm5Ho5pK3dxBz7dfkQd0MfXfk2pF0Z-7LZj6FsPsKQ9hfkrLObHIpfn5P35WOzeK5Wr08vi_tVNTJQu0q4aV8NrRdUCBZEB8zLjgsEyRTQlgceLLfOemxpbbn0wimPPHjnuYYa5-Tq0Dva7OymS7Z3MZsxxa1NewNaoxI1TrmbQy5PqF-HZNph-MoGqPn5yvx9hd8RK1PG</addsrcrecordid><sourcetype>Index Database</sourcetype><iscdi>true</iscdi><recordtype>conference_proceeding</recordtype></control><display><type>conference_proceeding</type><title>Formalising Bitonic Sort in Type Theory</title><source>Springer Books</source><creator>Bove, Ana ; Coquand, Thierry</creator><contributor>Paulin-Mohring, Christine ; Filliâtre, Jean-Christophe ; Werner, Benjamin</contributor><creatorcontrib>Bove, Ana ; Coquand, Thierry ; Paulin-Mohring, Christine ; Filliâtre, Jean-Christophe ; Werner, Benjamin</creatorcontrib><description>We discuss two complete formalisations of bitonic sort in constructive type theory. Bitonic sort is one of the fastest sorting algorithms where the sequence of comparisons is not data-dependent. In addition, it is a general recursive algorithm. In the formalisation we face two main problems: only structural recursion is allowed in type theory, and a formal proof of the correctness of the algorithm needs to consider quite a number of cases. In our first formalisation we define bitonic sort over dependently-typed binary trees with information in the leaves and we make use of the 0-1-principle to prove that the algorithm sorts inputs of arbitrary types. In our second formalisation we use notions from linear orders, lattice theory and monoids. The correctness proof is directly performed for any ordered set and not only for Boolean values.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 9783540314288</identifier><identifier>ISBN: 3540314288</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 9783540314295</identifier><identifier>EISBN: 3540314296</identifier><identifier>DOI: 10.1007/11617990_6</identifier><language>eng</language><publisher>Berlin, Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algorithm Sort ; Applied sciences ; Binary Tree ; Computer science; control theory; systems ; Distributive Lattice ; Exact sciences and technology ; Fundamental areas of phenomenology (including applications) ; Linear Order ; Physics ; Programming languages ; Software ; Solid mechanics ; Structural and continuum mechanics ; Type Theory</subject><ispartof>Lecture notes in computer science, 2006, p.82-97</ispartof><rights>Springer-Verlag Berlin Heidelberg 2006</rights><rights>2008 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/11617990_6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/11617990_6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,779,780,784,789,790,793,4050,4051,27925,38255,41442,42511</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=19938563$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><contributor>Paulin-Mohring, Christine</contributor><contributor>Filliâtre, Jean-Christophe</contributor><contributor>Werner, Benjamin</contributor><creatorcontrib>Bove, Ana</creatorcontrib><creatorcontrib>Coquand, Thierry</creatorcontrib><title>Formalising Bitonic Sort in Type Theory</title><title>Lecture notes in computer science</title><description>We discuss two complete formalisations of bitonic sort in constructive type theory. Bitonic sort is one of the fastest sorting algorithms where the sequence of comparisons is not data-dependent. In addition, it is a general recursive algorithm. In the formalisation we face two main problems: only structural recursion is allowed in type theory, and a formal proof of the correctness of the algorithm needs to consider quite a number of cases. In our first formalisation we define bitonic sort over dependently-typed binary trees with information in the leaves and we make use of the 0-1-principle to prove that the algorithm sorts inputs of arbitrary types. In our second formalisation we use notions from linear orders, lattice theory and monoids. The correctness proof is directly performed for any ordered set and not only for Boolean values.</description><subject>Algorithm Sort</subject><subject>Applied sciences</subject><subject>Binary Tree</subject><subject>Computer science; control theory; systems</subject><subject>Distributive Lattice</subject><subject>Exact sciences and technology</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Linear Order</subject><subject>Physics</subject><subject>Programming languages</subject><subject>Software</subject><subject>Solid mechanics</subject><subject>Structural and continuum mechanics</subject><subject>Type Theory</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>9783540314288</isbn><isbn>3540314288</isbn><isbn>9783540314295</isbn><isbn>3540314296</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2006</creationdate><recordtype>conference_proceeding</recordtype><recordid>eNpVkD1PwzAYhM2XRFWy8AuyIFgCfv3asT1CRQGpEgNhthzbKYY2iewu_fcEFQlxyw3P6XQ6Qi6B3gKl8g6gBqk1NfURKbRUKDhF4EyLYzKbGFSIXJ_8Y0qdkhlFyiotOZ6TIudPOgkZFRxm5Ho5pK3dxBz7dfkQd0MfXfk2pF0Z-7LZj6FsPsKQ9hfkrLObHIpfn5P35WOzeK5Wr08vi_tVNTJQu0q4aV8NrRdUCBZEB8zLjgsEyRTQlgceLLfOemxpbbn0wimPPHjnuYYa5-Tq0Dva7OymS7Z3MZsxxa1NewNaoxI1TrmbQy5PqF-HZNph-MoGqPn5yvx9hd8RK1PG</recordid><startdate>2006</startdate><enddate>2006</enddate><creator>Bove, Ana</creator><creator>Coquand, Thierry</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><scope>IQODW</scope></search><sort><creationdate>2006</creationdate><title>Formalising Bitonic Sort in Type Theory</title><author>Bove, Ana ; Coquand, Thierry</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p218t-5c99061bd50552e5f12d7f453172810b4e4ea4acad3b06a47d5c8d34edcd49163</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Algorithm Sort</topic><topic>Applied sciences</topic><topic>Binary Tree</topic><topic>Computer science; control theory; systems</topic><topic>Distributive Lattice</topic><topic>Exact sciences and technology</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>Linear Order</topic><topic>Physics</topic><topic>Programming languages</topic><topic>Software</topic><topic>Solid mechanics</topic><topic>Structural and continuum mechanics</topic><topic>Type Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bove, Ana</creatorcontrib><creatorcontrib>Coquand, Thierry</creatorcontrib><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bove, Ana</au><au>Coquand, Thierry</au><au>Paulin-Mohring, Christine</au><au>Filliâtre, Jean-Christophe</au><au>Werner, Benjamin</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Formalising Bitonic Sort in Type Theory</atitle><btitle>Lecture notes in computer science</btitle><date>2006</date><risdate>2006</risdate><spage>82</spage><epage>97</epage><pages>82-97</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>9783540314288</isbn><isbn>3540314288</isbn><eisbn>9783540314295</eisbn><eisbn>3540314296</eisbn><abstract>We discuss two complete formalisations of bitonic sort in constructive type theory. Bitonic sort is one of the fastest sorting algorithms where the sequence of comparisons is not data-dependent. In addition, it is a general recursive algorithm. In the formalisation we face two main problems: only structural recursion is allowed in type theory, and a formal proof of the correctness of the algorithm needs to consider quite a number of cases. In our first formalisation we define bitonic sort over dependently-typed binary trees with information in the leaves and we make use of the 0-1-principle to prove that the algorithm sorts inputs of arbitrary types. In our second formalisation we use notions from linear orders, lattice theory and monoids. The correctness proof is directly performed for any ordered set and not only for Boolean values.</abstract><cop>Berlin, Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/11617990_6</doi><tpages>16</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Lecture notes in computer science, 2006, p.82-97 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_19938563 |
| source | Springer Books |
| subjects | Algorithm Sort Applied sciences Binary Tree Computer science control theory systems Distributive Lattice Exact sciences and technology Fundamental areas of phenomenology (including applications) Linear Order Physics Programming languages Software Solid mechanics Structural and continuum mechanics Type Theory |
| title | Formalising Bitonic Sort in Type Theory |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-01T14%3A51%3A54IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-pascalfrancis_sprin&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=proceeding&rft.atitle=Formalising%20Bitonic%20Sort%20in%20Type%20Theory&rft.btitle=Lecture%20notes%20in%20computer%20science&rft.au=Bove,%20Ana&rft.date=2006&rft.spage=82&rft.epage=97&rft.pages=82-97&rft.issn=0302-9743&rft.eissn=1611-3349&rft.isbn=9783540314288&rft.isbn_list=3540314288&rft_id=info:doi/10.1007/11617990_6&rft_dat=%3Cpascalfrancis_sprin%3E19938563%3C/pascalfrancis_sprin%3E%3Curl%3E%3C/url%3E&rft.eisbn=9783540314295&rft.eisbn_list=3540314296&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |