--- /dev/null
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html>
+<head>
+ <meta content="text/html; charset=UTF-8" http-equiv="content-type">
+ <title>lambda-delta home page</title>
+ <meta content="Ferruccio Guidi" name="author">
+ <meta content="The formal system lambda-delta" name="description">
+ <link rel="shortcut icon" href="download/crux_16.ico">
+</head>
+<body>
+<div style="text-align: center;">
+<br>
+<a href="http://lambda-delta.info"><img alt="[Crux Logo]"
+ title="The Crux" src="download/crux_32.png"
+ style="border: 0px solid ; width: 32px; height: 32px;"></a>
+<h1>The Formal System λδ (lambda-delta)<br>
+</h1>
+<h2>Towards the unification of terms, types, environments and contexts</h2>
+<img style="width: 95%; height: 4px;" alt="[Separator]"
+ title="Separator" src="download/rainbow.png"><br>
+<table
+ style="text-align: left; width: 95%; margin-left: auto; margin-right: auto;"
+ border="0" cellpadding="2" cellspacing="20">
+ <tbody>
+ <tr>
+ <td style="vertical-align: top;">
+ <ul>
+ <li><a href="index.html">Foreword</a></li>
+ </ul>
+ <ul>
+ <li><a href="news.html">News</a></li>
+ </ul>
+ <ul>
+ <li>Papers</li>
+ </ul>
+ <ul>
+ <li><a href="implementation.html">Resources</a><br>
+ </li>
+ </ul>
+ </td>
+ <td style="vertical-align: top; text-align: left;">
+ <h3 style="text-align: right;">Documentation <img
+ style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly"
+ src="download/b5.png"></h3>
+Currently the <span style="font-weight: bold;">main source of
+information</span> on λδ (version 1) is <span
+ style="font-weight: bold;">Resource
+1.1</span> below.<br>
+A <span style="font-weight: bold;">summary</span> of basic λδ (version
+1) is found in <span style="font-weight: bold;">Resource 1.5</span>
+below.<br>
+ <h3><img style="width: 32px; height: 32px;"
+ alt="[Basic lambda-delta Logo]" title="Basic lambda-delta"
+ src="download/basic_32.png"> Basic λδ version 2:</h3>
+ <table style="text-align: left; width: 100%;" border="0"
+ cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td style="vertical-align: top;">2.1.<br>
+ </td>
+ <td style="vertical-align: top;">F. Guidi: <a
+ href="download/cie_2010.pdf"><span style="font-style: italic;">An
+Efficient
+Validation Procedure for the Formal System </span><span
+ style="font-style: italic;">λδ</span></a><span
+ style="font-style: italic;"></span>
+(<span style="font-weight: bold;">2010-07</span>). In <span
+ style="font-style: italic;">CiE 2010 Local Proceedings</span>.
+University of Azores, CMATI Booklet, pp. 204-213. <a
+ href="implementation.html#bibtex">BibTeX entry</a>.<br>
+ <br>
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;">2.2.<br>
+ </td>
+ <td style="vertical-align: top;"> <a name="ublcs-2009-16"></a>F.
+Guidi:
+
+
+
+
+
+
+
+
+ <a
+ href="http://www.cs.unibo.it/pub/TR/UBLCS/ABSTRACTS/2009.bib?ncstrl.cabernet//BOLOGNA-UBLCS-2009-16"><span
+ style="font-style: italic;">Landau's
+"Grundlagen der Analysis" from Automath to lambda-delta</span></a> (<span
+ style="font-weight: bold;">2009-09)</span>. University of
+Bologna, technical report UBLCS-2009-16. <a
+ href="implementation.html#bibtex">BibTeX entry</a>.<br>
+ <br>
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;">2.3.<br>
+ </td>
+ <td style="vertical-align: top;">F. Guidi: <a
+ href="download/ld_talk_7s.pdf"><span style="font-style: italic;">An
+Efficient
+Validation Procedure for the Formal System λδ</span></a> (<span
+ style="font-weight: bold;">2010-07</span>). Presentation
+at
+CiE
+2010
+(slides).<br>
+ <br>
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;">2.4.<br>
+ </td>
+ <td style="vertical-align: top;">F. Guidi: <a
+ href="download/ld_talk_6s.pdf"><span style="font-style: italic;">A
+Validator
+for the Formal System λδ</span></a> (revised <span
+ style="font-weight: bold;">2010-02</span>). Presentation
+at
+the
+University
+of
+Bologna
+(slides). </td>
+ </tr>
+ </tbody>
+ </table>
+ <h3><img style="width: 32px; height: 32px;"
+ alt="[Basic lambda-delta Logo]" title="Basic lambda-delta"
+ src="download/basic_32.png"> Basic λδ version 1:</h3>
+ <table style="text-align: left; width: 100%;" border="0"
+ cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td style="vertical-align: top;">1.1.<br>
+ </td>
+ <td style="vertical-align: top;"><a name="tocl1"></a>F.
+Guidi: <a href="http://doi.acm.org/10.1145/1614431.1614436"><span
+ style="font-style: italic;">The Formal System λδ</span></a> (<span
+ style="font-weight: bold;">2009-10</span>). In ACM ToCL 11(1), Article
+No. 5 (<a href="http://tocl.acm.org/accepted/335guidi.pdf">accepted</a>
+ <span style="font-weight: bold;">2008-07</span>). CoRR
+identifier <a href="http://arxiv.org/abs/cs/0611040"><span
+ style="font-style: italic;"></span>cs/0611040</a> [v10] (revised <span
+ style="font-weight: bold;">2008-09</span>). <a
+ href="implementation.html#bibtex">BibTeX
+entry</a>.<br>
+ <br>
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;">1.2.<br>
+ </td>
+ <td style="vertical-align: top;">F. Guidi: <a
+ href="http://www.cs.unibo.it/%7Efguidi/download/cie_2007.pdf"><span
+ style="font-style: italic;">Lambda Types on the Lambda Calculus with
+Abbreviations</span></a> (<span style="font-weight: bold;">2007-06</span>).
+In
+
+
+
+
+
+
+
+
+
+
+
+
+ <span style="font-style: italic;">CiE 2007 Local Proceedings</span>.
+University
+of
+Siena,
+technical
+report
+487,
+p.
+387
+(abstract
+of
+a
+presentation).
+
+
+
+
+
+
+ <a href="implementation.html#bibtex">BibTeX
+entry</a>.<br>
+ <br>
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;">1.3.<br>
+ </td>
+ <td style="vertical-align: top;">F. Guidi: <a
+ href="http://www.cs.unibo.it/pub/TR/UBLCS/ABSTRACTS/2006.bib?ncstrl.cabernet//BOLOGNA-UBLCS-2006-25"><span
+ style="font-style: italic;">Lambda Types on the Lambda Calculus with
+Abbreviations</span></a> (<span style="font-weight: bold;">2006-11</span>).
+University
+of
+Bologna,
+technical
+report
+UBLCS-2006-25.
+
+
+
+
+
+
+
+
+
+
+
+
+
+ <a href="implementation.html#bibtex">BibTeX
+entry</a>.<br>
+ <br>
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;">1.4.<br>
+ </td>
+ <td style="vertical-align: top;">F. Guidi: <a
+ style="font-style: italic;"
+ href="http://www.cs.unibo.it/pub/TR/UBLCS/ABSTRACTS/2006.bib?ncstrl.cabernet//BOLOGNA-UBLCS-2006-01">Lambda
+Types
+on
+the
+Lambda
+Calculus
+with
+Abbreviations:
+a
+Certified
+Specification</a> (<span style="font-weight: bold;">2006-01</span>).
+University of
+Bologna, technical report UBLCS-2006-01. <a
+ href="implementation.html#bibtex">BibTeX entry</a>.<br>
+ <br>
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;">1.5.<br>
+ </td>
+ <td style="vertical-align: top;">F. Guidi: <a
+ style="font-style: italic;" href="download/ld_talk_5s.pdf">The
+Formal
+System lambda-delta</a>
+(<span style="font-weight: bold;">2008-10</span>). Presentation at
+"Advances in Constructive Topology and Logical Foundations" (slides).<br>
+ <br>
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;">1.6.<br>
+ </td>
+ <td style="vertical-align: top;">F. Guidi: <a
+ href="http://www.cs.unibo.it/%7Efguidi/download/ld-talk-4.pdf"><span
+ style="font-style: italic;">Towards the Unification of Terms, Types
+and Contexts</span></a> (<span style="font-weight: bold;">2008-03</span>).
+Presentation
+at
+Types
+2008
+(slides).<br>
+ <br>
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;">1.7.<br>
+ </td>
+ <td style="vertical-align: top;">F. Guidi: <a
+ href="http://www.cs.unibo.it/%7Efguidi/download/ld-talk-3.pdf"><span
+ style="font-style: italic;">Lambda Types on the Lambda Calculus with
+Abbreviations</span></a> (<span style="font-weight: bold;">2007-06</span>).
+Presentation
+at
+CiE
+2007
+(slides).<br>
+ <br>
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;">1.8.<br>
+ </td>
+ <td style="vertical-align: top;">F. Guidi: <a
+ href="http://www.cs.unibo.it/%7Efguidi/download/ld-talk-2.pdf"><span
+ style="font-style: italic;">Lambda Tipi sul Lambda Calcolo con
+Abbreviazioni</span></a> (<span style="font-weight: bold;">2007-01</span>).
+Presentation
+at
+the
+University
+of
+Padova
+(slides
+
+
+
+
+
+
+ <span style="font-weight: bold;">in
+Italian</span>).<br>
+ <br>
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;">1.9.<br>
+ </td>
+ <td style="vertical-align: top;"><a name="bologna1"></a>F.
+Guidi: <a
+ href="http://www.cs.unibo.it/%7Efguidi/download/ld-talk-1.pdf"><span
+ style="font-style: italic;">Lambda Tipi sul Lambda Calcolo con
+Abbreviazioni: una Specifica Certificata</span></a> (<span
+ style="font-weight: bold;">2005-12</span>). Presentation at
+the University of Bologna (slides <span style="font-weight: bold;">in
+Italian</span>).<br>
+ </td>
+ </tr>
+ </tbody>
+ </table>
+ </td>
+ </tr>
+ </tbody>
+</table>
+<br>
+<a href="http://validator.w3.org/check?uri=referer"><img
+ alt="[Valid HTML 4.01 Transitional]"
+ title="Valid HTML 4.01 Transitional"
+ src="http://www.w3.org/Icons/valid-html401"
+ style="border: 0px solid ; width: 88px; height: 31px;"></a> <a
+ href="http://www.anybrowser.org/campaign/"><img
+ alt="[Use Any Browser Here]" title="Use Any Browser Here"
+ src="http://www.cs.unibo.it/%7Efguidi/download/globe-trans.png"
+ style="border: 0px solid ; width: 147px; height: 42px;"></a> <img
+ style="width: 88px; height: 31px;" alt="[PNG Used Here]"
+ title="PNG Used Here]"
+ src="http://www.cs.unibo.it/%7Efguidi/download/PNGnow2.png"><br>
+<br>
+Last update 2010-12-14 by <a href="http://www.cs.unibo.it/%7Efguidi/">Ferruccio
+Guidi</a><br>
+</div>
+</body>
+</html>
--- /dev/null
+$1 = "Automath";
+
+create_syntax_table ($1);
+
+define_syntax ("{","}",'%', $1); % comments
+define_syntax ("#","",'%', $1); % comments
+define_syntax ("%","",'%', $1); % comments
+define_syntax ("([<", ")]>", '(', $1); % brackets
+define_syntax ('"', '"', $1); % strings
+define_syntax ("a-zA-Z_0-9`'", 'w', $1); % words
+define_syntax (":+-=*@~,;.?", '+', $1); % operators
+
+
+() = define_keywords_n ($1, "EBPN_E", 2, 0);
+() = define_keywords_n ($1, "'_E''eb''pn'PRIMPROPTYPE", 4, 0);
+() = define_keywords_n ($1, "'prim''prop''type'", 6, 0);
+
+define Automath_mode ()
+{
+ variable kmap = "Automath";
+
+ set_mode(kmap, 0x04);
+ use_syntax_table (kmap);
+ runhooks("Automath_mode_hook");
+}
+
+add_mode_for_extension ("Automath", "aut");
--- /dev/null
+$1 = "Helena";
+
+create_syntax_table ($1);
+
+define_syntax ("\\*","*\\",'%', $1); % comments
+define_syntax ("([{<", ")]}>", '(', $1); % brackets
+define_syntax ('"', '"', $1); % strings
+define_syntax ("\\a-zA-Z_0-9", 'w', $1); % words
+
+set_syntax_flags ($1, 4);
+
+() = define_keywords_n ($1, "\\ax\\th", 3, 0);
+() = define_keywords_n ($1, "\\def", 4, 0);
+() = define_keywords_n ($1, "\\cong\\decl\\open", 5, 0);
+() = define_keywords_n ($1, "\\close\\graph\\sorts", 6, 0);
+() = define_keywords_n ($1, "\\require", 8, 0);
+() = define_keywords_n ($1, "\\generate", 9, 0);
+
+define helena_mode ()
+{
+ variable kmap = "Helena";
+
+ set_mode(kmap, 0x04);
+ use_syntax_table (kmap);
+ runhooks("helena_mode_hook");
+}
+
+add_mode_for_extension ("helena", "hln");
--- /dev/null
+@incollection{lambdadelta7,
+ author="F. {Guidi}",
+ title="{An Efficient Validation Procedure for the Formal System $\lambda\delta$}",
+ publisher="Centre for Applied Mathematics and Information Technology, Department of Mathematics, University of Azores",
+ address="Ponta Delgada, Portugal",
+ editor="F. {Ferreira} and H. {Guerra} and E. {Mayordomo} and J. {Rasga}",
+ booktitle="Local Proceedings of 6th Conference on Computability in Europe (CiE 2010)",
+ pages="204-213",
+ year="2010",
+ month="July"
+}
+
+@techreport{lambdadelta6,
+ author="F. {Guidi}",
+ title="{Landau's ``Grundlagen der Analysis'' from Automath to lambda-delta}",
+ type="Technical Report",
+ institution="University of Bologna",
+ address="Bologna, Italy",
+ number="UBLCS 2009-16",
+ year="2009",
+ month="September"
+}
+
+@article{lambdadelta5,
+ author="F. {Guidi}",
+ title="{The Formal System $\lambda\delta$}",
+ publisher="ACM",
+ address="New York, NY, USA",
+ journal="Transactions on Computational Logic",
+ volume="11",
+ number="1",
+ year="2009",
+ month="October",
+ pages="Article No. 5"
+}
+
+@incollection{lambdadelta4,
+ author="F. {Guidi}",
+ title="{Lambda Types on the Lambda Calculus with Abbreviations}",
+ publisher="Universit\`a di Siena",
+ address="Siena, Italy",
+ editor="S. {Barry Cooper} and T. F. {Kent} and B. {L\"owe} and A. {Sorbi}", @comment="{\"}",
+ booktitle="Local Proceedings of 3rd Conference on Computability in Europe (CiE 2007) Technical Report 487",
+ pages="387-387",
+ year="2007",
+ month="June"
+}
+
+@techreport{lambdadelta3,
+ author="F. {Guidi}",
+ title="{Lambda-Types on the Lambda-Calculus with Abbreviations}",
+ type="Technical Report",
+ institution="University of Bologna",
+ address="Bologna, Italy",
+ number="UBLCS 2006-25",
+ year="2006",
+ month="November"
+}
+
+@techreport{lambdadelta2,
+ author="F. {Guidi}",
+ title="{Lambda-Types on the Lambda-Calculus with Abbreviations: a Certified Specification}",
+ type="Technical Report",
+ institution="University of Bologna",
+ address="Bologna, Italy",
+ number="UBLCS 2006-01",
+ year="2006",
+ month="January"
+}
+
+@misc{lambdadelta1,
+ author="F. {Guidi}",
+ title="{lambda-delta}",
+ howpublished="Formal specification with the proof assistant \textsc{coq} 7.3.1",
+ year="2007",
+ month="January",
+ note="Available at the lambda-delta Web site: {http://helm.cs.unibo.it/lambda-delta/}"
+}
--- /dev/null
+@incollection{lambdadelta7,
+ author="F. {Guidi}",
+ title="{An Efficient Validation Procedure for the Formal System $\lambda\delta$}",
+ publisher="Centre for Applied Mathematics and Information Technology, Department of Mathematics, University of Azores",
+ address="Ponta Delgada, Portugal",
+ editor="F. {Ferreira} and H. {Guerra} and E. {Mayordomo} and J. {Rasga}",
+ booktitle="Local Proceedings of 6th Conference on Computability in Europe (CiE 2010)",
+ pages="204-213",
+ year="2010",
+ month="July"
+}
+
+@techreport{lambdadelta6,
+ author="F. {Guidi}",
+ title="{Landau's ``Grundlagen der Analysis'' from Automath to lambda-delta}",
+ type="Technical Report",
+ institution="University of Bologna",
+ address="Bologna, Italy",
+ number="UBLCS 2009-16",
+ year="2009",
+ month="September"
+}
+
+@article{lambdadelta5,
+ author="F. {Guidi}",
+ title="{The Formal System $\lambda\delta$}",
+ publisher="ACM",
+ address="New York, NY, USA",
+ journal="Transactions on Computational Logic",
+ volume="11",
+ number="1",
+ year="2009",
+ month="October",
+ pages="Article No. 5"
+}
+
+@incollection{lambdadelta4,
+ author="F. {Guidi}",
+ title="{Lambda Types on the Lambda Calculus with Abbreviations}",
+ publisher="Universit\`a di Siena",
+ address="Siena, Italy",
+ editor="S. {Barry Cooper} and T. F. {Kent} and B. {L\"owe} and A. {Sorbi}", @comment="{\"}",
+ booktitle="Local Proceedings of 3rd Conference on Computability in Europe (CiE 2007) Technical Report 487",
+ pages="387-387",
+ year="2007",
+ month="June"
+}
+
+@techreport{lambdadelta3,
+ author="F. {Guidi}",
+ title="{Lambda-Types on the Lambda-Calculus with Abbreviations}",
+ type="Technical Report",
+ institution="University of Bologna",
+ address="Bologna, Italy",
+ number="UBLCS 2006-25",
+ year="2006",
+ month="November"
+}
+
+@techreport{lambdadelta2,
+ author="F. {Guidi}",
+ title="{Lambda-Types on the Lambda-Calculus with Abbreviations: a Certified Specification}",
+ type="Technical Report",
+ institution="University of Bologna",
+ address="Bologna, Italy",
+ number="UBLCS 2006-01",
+ year="2006",
+ month="January"
+}
+
+@misc{lambdadelta1,
+ author="F. {Guidi}",
+ title="{lambda-delta}",
+ howpublished="Formal specification with the proof assistant \textsc{coq} 7.3.1",
+ year="2007",
+ month="January",
+ note="Available at the lambda-delta Web site: {http://helm.cs.unibo.it/lambda-delta/}"
+}
--- /dev/null
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html>
+<head>
+ <meta content="text/html; charset=UTF-8" http-equiv="content-type">
+ <title>lambda-delta home page</title>
+ <meta content="Ferruccio Guidi" name="author">
+ <meta content="The formal system lambda-delta" name="description">
+ <link rel="shortcut icon" href="download/crux_16.ico">
+</head>
+<body>
+<div style="text-align: center;">
+<br>
+<a href="http://lambda-delta.info"><img alt="[Crux Logo]"
+ title="The Crux" src="download/crux_32.png"
+ style="border: 0px solid ; width: 32px; height: 32px;"></a>
+<h1>The Formal System λδ (lambda-delta)<br>
+</h1>
+<h2>Towards the unification of terms, types, environments and contexts</h2>
+<img style="width: 95%; height: 4px;" alt="[Separator]"
+ title="Separator" src="download/rainbow.png"><br>
+<table
+ style="text-align: left; width: 95%; margin-left: auto; margin-right: auto;"
+ border="0" cellpadding="2" cellspacing="20">
+ <tbody>
+ <tr>
+ <td style="vertical-align: top;">
+ <ul>
+ <li><a href="index.html">Foreword</a></li>
+ </ul>
+ <ul>
+ <li><a href="news.html">News</a></li>
+ </ul>
+ <ul>
+ <li><a href="documentation.html">Papers</a></li>
+ </ul>
+ <ul>
+ <li>Resources<br>
+ </li>
+ </ul>
+ </td>
+ <td style="vertical-align: top; text-align: left;">
+ <h3 style="text-align: right;">Computer-checked formal
+specifications <img style="width: 37px; height: 37px;"
+ alt="[Butterfly]" title="Butterfly" src="download/b9.png"></h3>
+ <span style="font-weight: bold;">Resource
+1</span> below provides for the statically generated <span
+ style="font-weight: bold;">natural language representation</span> of
+λδ meta-theory (faster rendering w.r.t. resource 2 below).<br>
+ <span style="font-weight: bold;">Resource 2</span> below provides
+for the dynamically generated <span style="font-weight: bold;">natural
+language representation</span> of
+λδ meta-theory (powered by the <a href="http://helm.cs.unibo.it/">HELM</a>
+rendering engine).<br>
+Remarkably λδ was born and developed in the digital format of <span
+ style="font-weight: bold;">resource 3</span> below, which is not the
+formal counterpart of some informal material previously written on
+paper (as it happens for most currently digitalized Mathematics).<br>
+ <ol>
+ <li><a name="static"></a>F. Guidi: <a
+ style="font-style: italic;" href="static/matita/LAMBDA-TYPES/">LAMBDA-TYPES</a>
+(revised <span style="font-weight: bold;">2008-06</span>). Formal
+specification with the proof assistant <a
+ href="http://matita.cs.unibo.it/">Matita</a> 0.5 (HTML pages generated
+by the <a href="http://helm.cs.unibo.it/">HELM</a>
+rendering engine)<br>
+Here are the most relevant theorems proved in the formal specification:
+ <ul>
+ <li><a
+ href="static/matita/LAMBDA-TYPES/LambdaDelta-1/pr3/pr3/pr3_confluence.con.html">Confluence
+of
+reduction</a> (Church-Rosser property).</li>
+ <li><a
+ href="static/matita/LAMBDA-TYPES/LambdaDelta-1/ty3/props/ty3_correct.con.html">Correctness
+of
+types</a>.</li>
+ <li><a
+ href="static/matita/LAMBDA-TYPES/LambdaDelta-1/ty3/props/ty3_unique.con.html">Uniqueness
+of
+types
+up
+to
+conversion</a>.<br>
+ </li>
+ <li><a
+ href="static/matita/LAMBDA-TYPES/LambdaDelta-1/ty3/pr3/ty3_sred_pr3.con.html">Subject
+reduction
+of
+the
+type
+assignment</a>.</li>
+ <li><a
+ href="static/matita/LAMBDA-TYPES/LambdaDelta-1/ty3/arity_props/ty3_sn3.con.html">Strong
+normalization
+of
+the
+typed
+terms</a>.</li>
+ <li><a
+ href="static/matita/LAMBDA-TYPES/LambdaDelta-1/ty3/dec/ty3_inference.con.html">Decidability
+of
+the
+type
+inference
+problem</a>.<br>
+ <br>
+ </li>
+ </ul>
+ </li>
+ <li><a name="dynamic"></a>F. Guidi: <a
+ style="font-style: italic;"
+ href="http://mowgli.cs.unibo.it:58080/apply?keys=RT&xmluri=http://helm.cs.unibo.it/helm//html/folder/index.html&prop.media-type=text/html&param.thmedia-type=text/html&param.thkeys=T1%2CT2%2CL%2CE&param.embedkeys=d_c%2CTC1%2CHC2%2CL&param.thencoding=UTF-8&prop.encoding=UTF-8&prop.doctype-public=-//W3C//DTD%20XHTML%201.0%20Transitional//EN&param.doctype-public=-//W3C//DTD%20XHTML%201.0%20Transitional//EN&param.encoding=UTF-8&param.media-type=text/html&param.keys=d_c%2CC1%2CHC2%2CL&profile=default&param.profile=default&param.CICURI=theory:/matita/LAMBDA-TYPES/">LAMBDA-TYPES</a>
+(revised <span style="font-weight: bold;">2008-06</span>). Formal
+specification with the proof assistant <a
+ href="http://matita.cs.unibo.it/">Matita</a> 0.5 (<a
+ href="http://helm.cs.unibo.it/">HELM</a> directory).<br>
+ <br>
+ </li>
+ <li><a name="source"></a>F. Guidi: <a
+ href="http://www.cs.unibo.it/%7Efguidi/download/LAMBDA-TYPES.tgz"><span
+ style="font-style: italic;">LAMBDA-TYPES</span></a> (revised <span
+ style="font-weight: bold;">2008-03</span>).
+Formal specification with the proof assistant <span
+ style="font-weight: bold;">Coq 7.3.1</span> (source
+proof scripts). <a href="#bibtex">BibTeX entry</a>.<br>
+ </li>
+ </ol>
+ <h3 style="text-align: right;">Tools <img
+ style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly"
+ src="download/b5.png"></h3>
+ <a name="lddl"></a><img style="width: 32px; height: 32px;"
+ alt="[Crux Logo]" title="The Crux" src="download/crux_32.png"><span
+ style="font-weight: bold;"> </span>The <span
+ style="font-weight: bold;"><span style="text-decoration: underline;">λδ
+Digital
+Library
+(LDDL)</span></span> is part of <a href="http://helm.cs.unibo.it/">HELM</a>
+and contains a set of
+resources expressed in λδ.<br>
+ <ul>
+ <li><span style="font-weight: bold;">Contents:</span> Landau's "<span
+ style="font-style: italic;">Grundlagen der Analysis</span>" (from
+Jutting's specification in <a href="http://www.win.tue.nl/automath/">Automath</a>).<br>
+ <span style="font-weight: bold;"></span></li>
+ </ul>
+ <ul>
+ <li><span style="font-weight: bold;">Access:</span> <a
+ href="static/lddl/">static pages</a> (updated <span
+ style="font-weight: bold;">2010-11</span>), <a
+ href="download/lddl.tar.bz2">data set</a> (updated <span
+ style="font-weight: bold;">2010-11</span>), <a
+ href="http://helm.cs.unibo.it/lambda-delta/xml">HELM server URL</a>
+(updated <span style="font-weight: bold;">2010-11</span>).</li>
+ </ul>
+ <ul>
+ <li><span style="font-weight: bold;">Examples:</span> <a
+ href="static/lddl/brg-si/grundlagen/l/e/st/eq/landau/n/rt/rp/r/c/8283/t234.ld.html">Grundlagen's
+definition
+"t234"</a> (in "basic_rg" λδ), <a
+ href="static/lddl/crg-si/grundlagen/l/e/st/eq/landau/n/rt/rp/r/c/8283/t234.ld.html">Grundlagen's
+definition
+"t234"</a> (in "complete_rg" λδ).<br>
+ </li>
+ </ul>
+ <br>
+ <a name="helena"></a><span style="font-weight: bold;"><img
+ style="width: 32px; height: 32px;" alt="[Helena Logo]" title="Helena"
+ src="download/helena_32.png"> <span
+ style="text-decoration: underline;">Helena</span></span> is a λδ
+processor,
+implemented in <a href="http://caml.inria.fr/">Caml</a> as a part of
+the <a href="http://helm.cs.unibo.it/">HELM</a> software, meant for
+testing the stable features of the calculus as well as the unstable
+ones.<br>
+The processor source code is available in the directory <a
+ href="http://helm.cs.unibo.it/websvn/listing.php?repname=helm&path=%2Ftrunk%2Fhelm%2Fsoftware%2Flambda-delta%2F&rev=0&sc=0">/trunk/helm/software/lambda-delta/</a>
+of the <a href="http://helm.cs.unibo.it/software/index.html">HELM Svn
+repository</a>. The Svn revisions containing the stable versions
+of Helena are indicated below. <br>
+ <ul>
+ <li><span style="font-weight: bold;">Version 0.8.1 (2010-11).</span>
+Exploits a subset of "complete_rg" λδ as the intermediate language.
+Features importation from ".hln" files containing λδ textual syntax.
+The overall validation speed of the "<span style="font-style: italic;">Grundlagen
+der
+Analysis</span>" increases of 22% with respect to version 0.8.0. [Svn
+revision: 11032] (<a href="download/helena_0.8.1.tar.gz">archived
+source code</a>)
+ <ul>
+ <li><span style="font-weight: bold;">2009-12.</span> Helena
+appears in F. Wiedijk's <a
+ href="http://www.cs.ru.nl/%7Efreek/digimath/index.html">index of
+computer math systems</a>.</li>
+ </ul>
+ </li>
+ </ul>
+ <ul>
+ <li><a style="font-weight: bold;"
+ href="documentation.html#ublcs-2009-16">Version 0.8.0</a><span
+ style="font-weight: bold;"> (2009-09).</span> Supports
+"basic_rg" λδ with naive implementation of impredicative sort
+inclusion. Features
+importation from <a href="http://www.win.tue.nl/automath/">Automath</a>
+and exportation to <a href="http://www.w3.org/XML/">XML</a>. [Svn
+revision: 10304] (<a href="download/helena_0.8.0.tar.gz">archived
+source code</a>)<br>
+ <ul>
+ <li><span style="font-weight: bold;">2009-09.</span>
+Jutting's specification of Landau's "<span style="font-style: italic;">Grundlagen
+der
+Analysis</span>" enters λδ Digital Library.<br>
+ <span style="font-weight: bold;"></span></li>
+ <li><span style="font-weight: bold;">2009-06.</span>
+Jutting's specification of Landau's "<span style="font-style: italic;">Grundlagen
+der
+Analysis</span>" is
+successfully processed, enabling sort inclusion<span
+ style="font-weight: bold;"></span>.</li>
+ </ul>
+ </li>
+ </ul>
+ <h3 style="text-align: right;">Other resources <img
+ style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly"
+ src="download/b4.png"></h3>
+ <ul>
+ <li><a name="bibtex"></a>A
+BibTeX database of λδ documentation: <a
+ href="download/lambda_delta.bib"><span style="font-style: italic;">lambda-delta.bib</span></a>,
+
+ <a style="font-style: italic;"
+ href="download/lambda_delta.txt">lambda-delta.txt</a> (revised <span
+ style="font-weight: bold;">2010-07</span>).</li>
+ </ul>
+ <ul>
+ <li>A <a href="http://www.jedsoft.org/jed/">Jed mode</a> for
+editing ".hln" files (containing λδ textual syntax): <a
+ style="font-style: italic;" href="download/helena.sl">helena.sl</a>
+(revised <span style="font-weight: bold;">2010-11</span>).</li>
+ </ul>
+ <ul>
+ <li>A <a href="http://www.jedsoft.org/jed/">Jed mode</a> for
+editing ".aut" files (containing <a
+ href="http://www.win.tue.nl/automath/">Automath</a> textual syntax): <a
+ style="font-style: italic;" href="download/automath.sl">automath.sl</a>
+(revised <span style="font-weight: bold;">2008-07</span>).</li>
+ </ul>
+ <ul>
+ <li>A logo for "basic" λδ: <a href="download/bld.pdf"><span
+ style="font-style: italic;">bld.pdf</span></a> (revised <span
+ style="font-weight: bold;">2008-07</span>).<br>
+ </li>
+ </ul>
+ </td>
+ </tr>
+ </tbody>
+</table>
+<br>
+<a href="http://validator.w3.org/check?uri=referer"><img
+ alt="[Valid HTML 4.01 Transitional]"
+ title="Valid HTML 4.01 Transitional"
+ src="http://www.w3.org/Icons/valid-html401"
+ style="border: 0px solid ; width: 88px; height: 31px;"></a> <a
+ href="http://www.anybrowser.org/campaign/"><img
+ alt="[Use Any Browser Here]" title="Use Any Browser Here"
+ src="http://www.cs.unibo.it/%7Efguidi/download/globe-trans.png"
+ style="border: 0px solid ; width: 147px; height: 42px;"></a> <img
+ style="width: 88px; height: 31px;" alt="[PNG Used Here]"
+ title="PNG Used Here"
+ src="http://www.cs.unibo.it/%7Efguidi/download/PNGnow2.png"><br>
+<br>
+Last update 2010-12-14 by <a href="http://www.cs.unibo.it/%7Efguidi/">Ferruccio
+Guidi</a><br>
+</div>
+</body>
+</html>
--- /dev/null
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html>
+<head>
+ <meta content="text/html; charset=UTF-8" http-equiv="content-type">
+ <title>lambda-delta home page</title>
+ <meta content="Ferruccio Guidi" name="author">
+ <meta content="The formal system lambda-delta" name="description">
+ <link rel="shortcut icon" href="download/crux_16.ico">
+</head>
+<body>
+<div style="text-align: center;">
+<br>
+<a href="http://lambda-delta.info"><img alt="[Crux Logo]"
+ title="The Crux" src="download/crux_32.png"
+ style="border: 0px solid ; width: 32px; height: 32px;"></a>
+<h1>The Formal System λδ (lambda-delta)<br>
+</h1>
+<h2>Towards the unification of terms, types, environments and contexts</h2>
+<img style="width: 95%; height: 4px;" alt="[Separator]"
+ title="Separator" src="download/rainbow.png"><br>
+<table
+ style="text-align: left; width: 95%; margin-left: auto; margin-right: auto;"
+ border="0" cellpadding="2" cellspacing="20">
+ <tbody>
+ <tr>
+ <td style="vertical-align: top;">
+ <ul>
+ <li>Foreword</li>
+ </ul>
+ <ul>
+ <li><a href="news.html">News</a></li>
+ </ul>
+ <ul>
+ <li><a href="documentation.html">Papers</a></li>
+ </ul>
+ <ul>
+ <li><a href="implementation.html">Resources</a><br>
+ </li>
+ </ul>
+ </td>
+ <td style="vertical-align: top; text-align: left;">
+ <h3 style="text-align: right;">Foreword <img
+ style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly"
+ src="download/b9.png"></h3>
+The formal system λδ
+(lambda-delta) is a typed lambda calculus that pursues the static and
+dynamic unification of terms, types, environments and contexts while
+enjoying a well-conceived meta-theory, which includes the commonly
+desired properties.<br>
+ <br>
+λδ takes some features from the calculi of the Automath family and
+some from the pure type systems, but it differs from both in that it
+does not include the Π construction while it provides for an
+abbreviation mechanism at the level of terms.<br>
+ <br>
+λδ features explicit type annotations, which are borrowed from
+realistic type checker implementations and with which type checking is
+reduced to type inference.<br>
+ <br>
+The reduction steps of λδ include β-contraction, δ-expansion,
+ζ-contraction and θ-swap. On the other hand,
+η-contraction is not included.<br>
+ <br>
+The meta-theory of λδ includes important properties such as the
+confluence of reduction, the correctness of types, the
+uniqueness of types up to conversion, the subject reduction of the type
+assignment, the strong normalization of the typed terms. The
+decidability of type inference and of type checking come as corollaries.<br>
+ <br>
+λδ features uniformly dependent types and a predicative abstraction
+mechanism, so the calculus can serve as a formal specification language
+for the type theories that need a predicative foundation. λδ is
+expected to have the expressive power of λ→.<br>
+ <h3 style="text-align: right;">Notice
+for
+the
+Internet
+Explorer
+user <img style="width: 37px; height: 37px;" alt="[Butterfly]"
+ title="Butterfly" src="download/b3.png"></h3>
+To view this site
+correctly, please select a font with <a href="http://www.unicode.org/">Unicode</a>
+support.<br>
+For example <span style="font-weight: bold;">Lucida Sans Unicode</span>
+(it should be already installed on your system).<br>
+To change the current font follow: <br>
+ <span style="font-weight: bold;">"Tools" menu → "Internet
+Options" entry → "General" tab → "Fonts" button.</span><br>
+ </td>
+ </tr>
+ </tbody>
+</table>
+<br>
+<a href="http://validator.w3.org/check?uri=referer"><img
+ alt="[Valid HTML 4.01 Transitional]"
+ title="Valid HTML 4.01 Transitional"
+ src="http://www.w3.org/Icons/valid-html401"
+ style="border: 0px solid ; width: 88px; height: 31px;"></a> <a
+ href="http://www.anybrowser.org/campaign/"><img
+ alt="[Use Any Browser Here]" title="Use Any Browser Here"
+ src="http://www.cs.unibo.it/%7Efguidi/download/globe-trans.png"
+ style="border: 0px solid ; width: 147px; height: 42px;"></a> <img
+ style="width: 88px; height: 31px;" alt="[PNG Used Here]"
+ title="PNG Used Here"
+ src="http://www.cs.unibo.it/%7Efguidi/download/PNGnow2.png"><br>
+<br>
+Last update 2010-12-14 by <a href="http://www.cs.unibo.it/%7Efguidi/">Ferruccio
+Guidi</a><br>
+</div>
+</body>
+</html>
--- /dev/null
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html>
+<head>
+ <meta content="text/html; charset=UTF-8" http-equiv="content-type">
+ <title>lambda-delta home page</title>
+ <meta content="Ferruccio Guidi" name="author">
+ <meta content="The formal system lambda-delta" name="description">
+ <link rel="shortcut icon" href="download/crux_16.ico">
+</head>
+<body>
+<div style="text-align: center;">
+<br>
+<a href="http://lambda-delta.info"><img alt="[Crux Logo]"
+ title="The Crux" src="download/crux_32.png"
+ style="border: 0px solid ; width: 32px; height: 32px;"></a>
+<h1>The Formal System λδ (lambda-delta)<br>
+</h1>
+<h2>Towards the unification of terms, types, environments and contexts</h2>
+<img style="width: 95%; height: 4px;" alt="[Separator]"
+ title="Separator" src="download/rainbow.png"><br>
+<table
+ style="text-align: left; width: 95%; margin-left: auto; margin-right: auto;"
+ border="0" cellpadding="2" cellspacing="20">
+ <tbody>
+ <tr>
+ <td style="vertical-align: top;">
+ <ul>
+ <li><a href="index.html">Foreword</a></li>
+ </ul>
+ <ul>
+ <li>News</li>
+ </ul>
+ <ul>
+ <li><a href="documentation.html">Papers</a></li>
+ </ul>
+ <ul>
+ <li><a href="implementation.html">Resources</a><br>
+ </li>
+ </ul>
+ </td>
+ <td style="vertical-align: top; text-align: left;">
+ <h3 style="text-align: right;">News <img
+ style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly"
+ src="download/b5.png"></h3>
+ <ul>
+ <li><span style="font-weight: bold;">December 2010.</span>
+Permanent λδ URL acquired: <a href="http://lambda-delta.info">http://lambda-delta.info</a>
+(pointing at this site). <br>
+ <span style="font-weight: bold;"></span></li>
+ </ul>
+ <ul>
+ <li><span style="font-weight: bold;">November 2010.</span> <span
+ style="font-style: italic;">Helena 0.8.1</span> is released. <br>
+ </li>
+ </ul>
+ <ul>
+ <li><span style="font-weight: bold;">September 2009.</span> <span
+ style="font-style: italic;">Helena 0.8.0</span> is released and the <a
+ href="implementation.html#lddl">λδ Digital Library</a> is
+started.<br>
+ <span style="font-weight: bold;"></span></li>
+ </ul>
+ <ul>
+ <li><span style="font-weight: bold;">June 2009.</span> <span
+ style="font-style: italic;">Helena</span>, A <a
+ href="implementation.html#helena">validator for </a><a
+ href="implementation.html#helena">λδ</a><span
+ style="font-style: italic;"></span>, <span style="font-style: italic;"></span>is
+available
+as a
+part of the <a href="http://helm.cs.unibo.it/">HELM</a> software. <br>
+ </li>
+ </ul>
+ <span style="font-weight: bold;"></span>
+ <ul>
+ <li><span style="font-weight: bold;">September 2008.</span>
+This site is online.<br>
+ </li>
+ </ul>
+ <span style="font-weight: bold;"></span>
+ <ul>
+ <li><span style="font-weight: bold;">July 2008.</span> <a
+ href="documentation.html#tocl1">First journal paper on λδ</a> accepted
+for publication.</li>
+ </ul>
+ <ul>
+ <li><span style="font-weight: bold;">July 2008.</span> First <a
+ href="http://helm.cs.unibo.it/procedural/">procedural
+reconstruction</a> in <a href="http://matita.cs.unibo.it/">Matita 0.5</a>
+of the <a href="implementation.html#source">λδ proof scripts in
+Coq 7.3.1</a>.<br>
+ </li>
+ </ul>
+ <ul>
+ <li><span style="font-weight: bold;">June 2008.</span> The <a
+ href="implementation.html#static">HTML
+pages of the specification of λδ in Matita 0.5</a> are online.<br>
+ <span style="font-weight: bold;"></span></li>
+ </ul>
+ <ul>
+ <li><span style="font-weight: bold;">March 2008.</span> An
+improvement of the
+specification of λδ in Coq 7.3.1 begins:
+ <ul>
+ <li>native type assignment with new rules for application: <span
+ style="font-style: italic;">nty</span> (it replaces <span
+ style="font-style: italic;">ty3</span>);<br>
+ </li>
+ <li>parallel conversion on focalized terms: <span
+ style="font-style: italic;">fpcs</span> (it replaces <span
+ style="font-style: italic;"></span><span style="font-style: italic;">pc3</span>);
+
+
+
+
+
+
+
+ <br>
+ </li>
+ <li>new weak parallel reduction on environments: <span
+ style="font-style: italic;">wcpr</span> <span
+ style="font-style: italic;"></span>(it is based on <span
+ style="font-style: italic;">fpr</span> and replaces <span
+ style="font-style: italic;">wcpr0</span>); <br>
+ </li>
+ <li>parallel reduction on focalized terms: <span
+ style="font-style: italic;">fpr</span> and <span
+ style="font-style: italic;">fprs</span> (they replace <span
+ style="font-style: italic;"></span><span style="font-style: italic;"></span><span
+ style="font-style: italic;">pr2</span>, <span
+ style="font-style: italic;">pr3</span>); <br>
+ </li>
+ </ul>
+ <ul>
+ <li>new thinning relation: <span
+ style="font-style: italic;">drop</span>
+(it replaces the old <span style="font-style: italic;">drop</span>, <span
+ style="font-style: italic;">clear</span>, <span
+ style="font-style: italic;">getl</span>, <span
+ style="font-style: italic;">cimp</span>, <span
+ style="font-style: italic;">drop1</span>);</li>
+ <li>new shift function: <span style="font-style: italic;">shift</span>:
+(it
+replaces
+ <span style="font-style: italic;">app1</span>);</li>
+ <li>new length function for environments: <span
+ style="font-style: italic;">clen</span>;<br>
+ </li>
+ <li>new relocation function: <span
+ style="font-style: italic;">lift</span> (it replaces old <span
+ style="font-style: italic;">lift</span>, <span
+ style="font-style: italic;">lift1</span>);<br>
+ </li>
+ <li>new term structure with polarity indicators and no
+distinction between binding and flat items;</li>
+ <li>new general theory of relocation (comprises new
+relocation functions: <span style="font-style: italic;">s</span>, <span
+ style="font-style: italic;">r</span>);</li>
+ <li>we removed context-free reduction and conversion (<span
+ style="font-style: italic;">pr0</span>, <span
+ style="font-style: italic;">pr1</span>, <span
+ style="font-style: italic;">pc1</span>);<br>
+ </li>
+ <li>we removed greedy substitution (<span
+ style="font-style: italic;"></span><span style="font-style: italic;">csubst0</span>,
+
+
+ <span style="font-style: italic;">csubst1</span>, <span
+ style="font-style: italic;">fsubst0</span>, <span
+ style="font-style: italic;">subst0</span>, <span
+ style="font-style: italic;">subst1</span>);<br>
+ </li>
+ <li>we removed level indicators on environments (<span
+ style="font-style: italic;">cbk</span>).</li>
+ </ul>
+ </li>
+ </ul>
+ <ul>
+ <li><span style="font-weight: bold;">September 2007.</span>
+The <a href="implementation.html#dynamic">specification of λδ in
+Matita 0.4</a> is online.<br>
+ </li>
+ </ul>
+ <ul>
+ <li><span style="font-weight: bold;">December 2005.</span> <a
+ href="documentation.html#bologna1">First communication on λδ</a>.<br>
+ </li>
+ </ul>
+ <ul>
+ <li><span style="font-weight: bold;">May 2004.</span> The <a
+ href="implementation.html#source">specification of λδ in
+Coq 7.3.1</a> begins.<br>
+ </li>
+ </ul>
+ <h3 style="text-align: right;">Visibility <img
+ style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly"
+ src="download/b4.png"></h3>
+ <ul>
+ <li><span style="font-weight: bold;">November 2010.</span> The <a
+ href="http://www.google.com/">Google</a>
+search <span style="color: rgb(255, 0, 0);">formal system lambda delta</span>
+gives 8 resources about λδ as the first results.<br>
+ </li>
+ </ul>
+ <ul>
+ <li><span style="font-weight: bold;">November 2010.</span> The <a
+ href="http://www.yahoo.com/">Yahoo</a>
+search <span style="color: rgb(255, 0, 0);">formal system lambda delta</span>
+gives 4 resources and 2 sub-resources about λδ as the first results.</li>
+ </ul>
+ </td>
+ </tr>
+ </tbody>
+</table>
+<br>
+<a href="http://validator.w3.org/check?uri=referer"><img
+ alt="[Valid HTML 4.01 Transitional]"
+ title="Valid HTML 4.01 Transitional"
+ src="http://www.w3.org/Icons/valid-html401"
+ style="border: 0px solid ; width: 88px; height: 31px;"></a> <a
+ href="http://www.anybrowser.org/campaign/"><img
+ alt="[Use Any Browser Here]" title="Use Any Browser Here"
+ src="http://www.cs.unibo.it/%7Efguidi/download/globe-trans.png"
+ style="border: 0px solid ; width: 147px; height: 42px;"></a> <img
+ style="width: 88px; height: 31px;" alt="[PNG Used Here]"
+ title="PNG Used Here"
+ src="http://www.cs.unibo.it/%7Efguidi/download/PNGnow2.png"><br>
+<br>
+Last update 2010-12-14 by <a href="http://www.cs.unibo.it/%7Efguidi/">Ferruccio
+Guidi</a><br>
+</div>
+</body>
+</html>
projects / helm.git / commitdiff
