From 2cf4633988fe480f90b477ddaa586d218afc22d6 Mon Sep 17 00:00:00 2001 From: Stefano Zacchiroli Date: Mon, 6 Feb 2006 17:39:27 +0000 Subject: [PATCH] removed papers dir, now all papers are in the new "papers" repository --- helm/papers/system_T/Latex8.ps | 502 -------------- helm/papers/system_T/Latex8.txt | 21 - helm/papers/system_T/Makefile | 5 - helm/papers/system_T/latex8.bib | 29 - helm/papers/system_T/latex8.bst | 1124 ------------------------------- helm/papers/system_T/latex8.sty | 169 ----- helm/papers/system_T/latex8.tex | 230 ------- helm/papers/system_T/t.tex | 810 ---------------------- 8 files changed, 2890 deletions(-) delete mode 100644 helm/papers/system_T/Latex8.ps delete mode 100644 helm/papers/system_T/Latex8.txt delete mode 100644 helm/papers/system_T/Makefile delete mode 100644 helm/papers/system_T/latex8.bib delete mode 100644 helm/papers/system_T/latex8.bst delete mode 100644 helm/papers/system_T/latex8.sty delete mode 100644 helm/papers/system_T/latex8.tex delete mode 100644 helm/papers/system_T/t.tex diff --git a/helm/papers/system_T/Latex8.ps b/helm/papers/system_T/Latex8.ps deleted file mode 100644 index 391c3906a..000000000 --- a/helm/papers/system_T/Latex8.ps +++ /dev/null @@ -1,502 +0,0 @@ -%!PS-Adobe-2.0 -%%Creator: dvips 5.47 Copyright 1986-91 Radical Eye Software -%%Title: latex8.dvi -%%Pages: 2 1 -%%BoundingBox: 0 0 612 792 -%%DocumentFonts: Times-Roman Times-Bold Times-Italic Helvetica-Bold -%%EndComments -%%BeginProcSet: /usr/local/lib/tex/ps/psfig.pro -/TeXscale { 65536 div } def - 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-The following files contain the LaTeX macros necessary for you to format -your paper based on the instructions/measurements in the INSTRUCT.TXT -attachment in our standard author kit for 8.5 x 11-inch proceedings. -The files appear in the following order: - -latex8.sty -- the style file -latex8.tex -- the main macro set -latex8.bib -- the sample bibliography macros -latex8.bst -- the bibliography main macro set -latex8ps.txt -- this file, when printed out, will give you a sample -of how your paper should look when it's finished. This file is in a -separate attachment from the first four LaTeX files. 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number = "7", - year = "1999", - volume = "99", - pages = "1-100", -} - - -@Book{ex2, - author = "Expert, Andreas Nikolaos", - title = "A Book He Wrote", - publisher = "His Publisher", - address = "Erewhon, NC", - year = "1999" -} - diff --git a/helm/papers/system_T/latex8.bst b/helm/papers/system_T/latex8.bst deleted file mode 100644 index 88e49bf41..000000000 --- a/helm/papers/system_T/latex8.bst +++ /dev/null @@ -1,1124 +0,0 @@ - -% --------------------------------------------------------------- -% -% $Id: latex8.bst,v 1.1 1995/09/15 15:13:49 ienne Exp $ -% -% by Paolo.Ienne@di.epfl.ch -% - -% --------------------------------------------------------------- -% -% no guarantee is given that the format corresponds perfectly to -% IEEE 8.5" x 11" Proceedings, but most features should be ok. -% -% --------------------------------------------------------------- -% -% `latex8' from BibTeX standard bibliography style `abbrv' -% version 0.99a for BibTeX versions 0.99a or later, LaTeX version 2.09. -% Copyright (C) 1985, all rights reserved. -% Copying of this file is authorized only if either -% (1) you make absolutely no changes to your copy, including name, or -% (2) if you do make changes, you name it something other than -% btxbst.doc, plain.bst, unsrt.bst, alpha.bst, and abbrv.bst. -% This restriction helps ensure that all standard styles are identical. -% The file btxbst.doc has the documentation for this style. - -ENTRY - { address - author - booktitle - chapter - edition - editor - howpublished - institution - journal - key - month - note - number - organization - pages - publisher - school - series - title - type - volume - year - } - {} - { label } - -INTEGERS { output.state before.all mid.sentence after.sentence after.block } - -FUNCTION {init.state.consts} -{ #0 'before.all := - #1 'mid.sentence := - #2 'after.sentence := - #3 'after.block := -} - -STRINGS { s t } - -FUNCTION {output.nonnull} -{ 's := - output.state mid.sentence = - { ", " * write$ } - { output.state after.block = - { add.period$ write$ - newline$ - "\newblock " write$ - } - { output.state before.all = - 'write$ - { add.period$ " " * write$ } - if$ - } - if$ - mid.sentence 'output.state := - } - if$ - s -} - -FUNCTION {output} -{ duplicate$ empty$ - 'pop$ - 'output.nonnull - if$ -} - -FUNCTION {output.check} -{ 't := - duplicate$ empty$ - { pop$ "empty " t * " in " * cite$ * warning$ } - 'output.nonnull - if$ -} - -FUNCTION {output.bibitem} -{ newline$ - "\bibitem{" write$ - cite$ write$ - "}" write$ - newline$ - "" - before.all 'output.state := -} - -FUNCTION {fin.entry} -{ add.period$ - write$ - newline$ -} - -FUNCTION {new.block} -{ output.state before.all = - 'skip$ - { after.block 'output.state := } - if$ -} - -FUNCTION {new.sentence} -{ output.state after.block = - 'skip$ - { output.state before.all = - 'skip$ - { after.sentence 'output.state := } - if$ - } - if$ -} - -FUNCTION {not} -{ { #0 } - { #1 } - if$ -} - -FUNCTION {and} -{ 'skip$ - { pop$ #0 } - if$ -} - -FUNCTION {or} -{ { pop$ #1 } - 'skip$ - if$ -} - -FUNCTION {new.block.checka} -{ empty$ - 'skip$ - 'new.block - if$ -} - -FUNCTION {new.block.checkb} -{ empty$ - swap$ empty$ - and - 'skip$ - 'new.block - if$ -} - -FUNCTION {new.sentence.checka} -{ empty$ - 'skip$ - 'new.sentence - if$ -} - -FUNCTION {new.sentence.checkb} -{ empty$ - swap$ empty$ - and - 'skip$ - 'new.sentence - if$ -} - -FUNCTION {field.or.null} -{ duplicate$ empty$ - { pop$ "" } - 'skip$ - if$ -} - -FUNCTION {emphasize} -{ duplicate$ empty$ - { pop$ "" } - { "{\em " swap$ * "}" * } - if$ -} - -INTEGERS { nameptr namesleft numnames } - -FUNCTION {format.names} -{ 's := - #1 'nameptr := - s num.names$ 'numnames := - numnames 'namesleft := - { namesleft #0 > } - { s nameptr "{f.~}{vv~}{ll}{, jj}" format.name$ 't := - nameptr #1 > - { namesleft #1 > - { ", " * t * } - { numnames #2 > - { "," * } - 'skip$ - if$ - t "others" = - { " et~al." * } - { " and " * t * } - if$ - } - if$ - } - 't - if$ - nameptr #1 + 'nameptr := - - namesleft #1 - 'namesleft := - } - while$ -} - -FUNCTION {format.authors} -{ author empty$ - { "" } - { author format.names } - if$ -} - -FUNCTION {format.editors} -{ editor empty$ - { "" } - { editor format.names - editor num.names$ #1 > - { ", editors" * } - { ", editor" * } - if$ - } - if$ -} - -FUNCTION {format.title} -{ title empty$ - { "" } - { title "t" change.case$ } - if$ -} - -FUNCTION {n.dashify} -{ 't := - "" - { t empty$ not } - { t #1 #1 substring$ "-" = - { t #1 #2 substring$ "--" = not - { "--" * - t #2 global.max$ substring$ 't := - } - { { t #1 #1 substring$ "-" = } - { "-" * - t #2 global.max$ substring$ 't := - } - while$ - } - if$ - } - { t #1 #1 substring$ * - t #2 global.max$ substring$ 't := - } - if$ - } - while$ -} - -FUNCTION {format.date} -{ year empty$ - { month empty$ - { "" } - { "there's a month but no year in " cite$ * warning$ - month - } - if$ - } - { month empty$ - 'year - { month " " * year * } - if$ - } - if$ -} - -FUNCTION {format.btitle} -{ title emphasize -} - -FUNCTION {tie.or.space.connect} -{ duplicate$ text.length$ #3 < - { "~" } - { " " } - if$ - swap$ * * -} - -FUNCTION {either.or.check} -{ empty$ - 'pop$ - { "can't use both " swap$ * " fields in " * cite$ * warning$ } - if$ -} - -FUNCTION {format.bvolume} -{ volume empty$ - { "" } - { "volume" volume tie.or.space.connect - series empty$ - 'skip$ - { " of " * series emphasize * } - if$ - "volume and number" number either.or.check - } - if$ -} - -FUNCTION {format.number.series} -{ volume empty$ - { number empty$ - { series field.or.null } - { output.state mid.sentence = - { "number" } - { "Number" } - if$ - number tie.or.space.connect - series empty$ - { "there's a number but no series in " cite$ * warning$ } - { " in " * series * } - if$ - } - if$ - } - { "" } - if$ -} - -FUNCTION {format.edition} -{ edition empty$ - { "" } - { output.state mid.sentence = - { edition "l" change.case$ " edition" * } - { edition "t" change.case$ " edition" * } - if$ - } - if$ -} - -INTEGERS { multiresult } - -FUNCTION {multi.page.check} -{ 't := - #0 'multiresult := - { multiresult not - t empty$ not - and - } - { t #1 #1 substring$ - duplicate$ "-" = - swap$ duplicate$ "," = - swap$ "+" = - or or - { #1 'multiresult := } - { t #2 global.max$ substring$ 't := } - if$ - } - while$ - multiresult -} - -FUNCTION {format.pages} -{ pages empty$ - { "" } - { pages multi.page.check - { "pages" pages n.dashify tie.or.space.connect } - { "page" pages tie.or.space.connect } - if$ - } - if$ -} - -FUNCTION {format.vol.num.pages} -{ volume field.or.null - number empty$ - 'skip$ - { "(" number * ")" * * - volume empty$ - { "there's a number but no volume in " cite$ * warning$ } - 'skip$ - if$ - } - if$ - pages empty$ - 'skip$ - { duplicate$ empty$ - { pop$ format.pages } - { ":" * pages n.dashify * } - if$ - } - if$ -} - -FUNCTION {format.chapter.pages} -{ chapter empty$ - 'format.pages - { type empty$ - { "chapter" } - { type "l" change.case$ } - if$ - chapter tie.or.space.connect - pages empty$ - 'skip$ - { ", " * format.pages * } - if$ - } - if$ -} - -FUNCTION {format.in.ed.booktitle} -{ booktitle empty$ - { "" } - { editor empty$ - { "In " booktitle emphasize * } - { "In " format.editors * ", " * booktitle emphasize * } - if$ - } - if$ -} - -FUNCTION {empty.misc.check} - -{ author empty$ title empty$ howpublished empty$ - month empty$ year empty$ note empty$ - and and and and and - key empty$ not and - { "all relevant fields are empty in " cite$ * warning$ } - 'skip$ - if$ -} - -FUNCTION {format.thesis.type} -{ type empty$ - 'skip$ - { pop$ - type "t" change.case$ - } - if$ -} - -FUNCTION {format.tr.number} -{ type empty$ - { "Technical Report" } - 'type - if$ - number empty$ - { "t" change.case$ } - { number tie.or.space.connect } - if$ -} - -FUNCTION {format.article.crossref} -{ key empty$ - { journal empty$ - { "need key or journal for " cite$ * " to crossref " * crossref * - warning$ - "" - } - { "In {\em " journal * "\/}" * } - if$ - } - { "In " key * } - if$ - " \cite{" * crossref * "}" * -} - -FUNCTION {format.crossref.editor} -{ editor #1 "{vv~}{ll}" format.name$ - editor num.names$ duplicate$ - #2 > - { pop$ " et~al." * } - { #2 < - 'skip$ - { editor #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" = - { " et~al." * } - { " and " * editor #2 "{vv~}{ll}" format.name$ * } - if$ - } - if$ - } - if$ -} - -FUNCTION {format.book.crossref} -{ volume empty$ - { "empty volume in " cite$ * "'s crossref of " * crossref * warning$ - "In " - } - { "Volume" volume tie.or.space.connect - " of " * - } - if$ - editor empty$ - editor field.or.null author field.or.null = - or - { key empty$ - { series empty$ - { "need editor, key, or series for " cite$ * " to crossref " * - crossref * warning$ - "" * - } - { "{\em " * series * "\/}" * } - if$ - } - { key * } - if$ - } - { format.crossref.editor * } - if$ - " \cite{" * crossref * "}" * -} - -FUNCTION {format.incoll.inproc.crossref} -{ editor empty$ - editor field.or.null author field.or.null = - or - { key empty$ - { booktitle empty$ - { "need editor, key, or booktitle for " cite$ * " to crossref " * - crossref * warning$ - "" - } - { "In {\em " booktitle * "\/}" * } - if$ - } - { "In " key * } - if$ - } - { "In " format.crossref.editor * } - if$ - " \cite{" * crossref * "}" * -} - -FUNCTION {article} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.block - crossref missing$ - { journal emphasize "journal" output.check - format.vol.num.pages output - format.date "year" output.check - } - { format.article.crossref output.nonnull - format.pages output - } - if$ - new.block - note output - fin.entry -} - -FUNCTION {book} -{ output.bibitem - author empty$ - { format.editors "author and editor" output.check } - { format.authors output.nonnull - crossref missing$ - { "author and editor" editor either.or.check } - 'skip$ - if$ - } - if$ - new.block - format.btitle "title" output.check - crossref missing$ - { format.bvolume output - new.block - format.number.series output - new.sentence - publisher "publisher" output.check - address output - } - { new.block - format.book.crossref output.nonnull - } - if$ - format.edition output - format.date "year" output.check - new.block - note output - fin.entry -} - -FUNCTION {booklet} -{ output.bibitem - format.authors output - new.block - format.title "title" output.check - howpublished address new.block.checkb - howpublished output - address output - format.date output - new.block - note output - fin.entry -} - -FUNCTION {inbook} -{ output.bibitem - author empty$ - { format.editors "author and editor" output.check } - { format.authors output.nonnull - - crossref missing$ - { "author and editor" editor either.or.check } - 'skip$ - if$ - } - if$ - new.block - format.btitle "title" output.check - crossref missing$ - { format.bvolume output - format.chapter.pages "chapter and pages" output.check - new.block - format.number.series output - new.sentence - publisher "publisher" output.check - address output - } - { format.chapter.pages "chapter and pages" output.check - new.block - format.book.crossref output.nonnull - } - if$ - format.edition output - format.date "year" output.check - new.block - note output - fin.entry -} - -FUNCTION {incollection} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.block - crossref missing$ - { format.in.ed.booktitle "booktitle" output.check - format.bvolume output - format.number.series output - format.chapter.pages output - new.sentence - publisher "publisher" output.check - address output - format.edition output - format.date "year" output.check - } - { format.incoll.inproc.crossref output.nonnull - format.chapter.pages output - } - if$ - new.block - note output - fin.entry -} - -FUNCTION {inproceedings} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.block - crossref missing$ - { format.in.ed.booktitle "booktitle" output.check - format.bvolume output - format.number.series output - format.pages output - address empty$ - { organization publisher new.sentence.checkb - organization output - publisher output - format.date "year" output.check - } - { address output.nonnull - format.date "year" output.check - new.sentence - organization output - publisher output - } - if$ - } - { format.incoll.inproc.crossref output.nonnull - format.pages output - } - if$ - new.block - note output - fin.entry -} - -FUNCTION {conference} { inproceedings } - -FUNCTION {manual} -{ output.bibitem - author empty$ - { organization empty$ - 'skip$ - { organization output.nonnull - address output - } - if$ - } - { format.authors output.nonnull } - if$ - new.block - format.btitle "title" output.check - author empty$ - { organization empty$ - { address new.block.checka - address output - } - 'skip$ - if$ - } - { organization address new.block.checkb - organization output - address output - } - if$ - format.edition output - format.date output - new.block - note output - fin.entry -} - -FUNCTION {mastersthesis} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.block - "Master's thesis" format.thesis.type output.nonnull - school "school" output.check - address output - format.date "year" output.check - new.block - note output - fin.entry -} - -FUNCTION {misc} -{ output.bibitem - format.authors output - title howpublished new.block.checkb - format.title output - howpublished new.block.checka - howpublished output - format.date output - new.block - note output - fin.entry - empty.misc.check -} - -FUNCTION {phdthesis} -{ output.bibitem - format.authors "author" output.check - new.block - format.btitle "title" output.check - new.block - "PhD thesis" format.thesis.type output.nonnull - school "school" output.check - address output - format.date "year" output.check - new.block - note output - fin.entry -} - -FUNCTION {proceedings} -{ output.bibitem - editor empty$ - { organization output } - { format.editors output.nonnull } - - if$ - new.block - format.btitle "title" output.check - format.bvolume output - format.number.series output - address empty$ - { editor empty$ - { publisher new.sentence.checka } - { organization publisher new.sentence.checkb - organization output - } - if$ - publisher output - format.date "year" output.check - } - { address output.nonnull - format.date "year" output.check - new.sentence - editor empty$ - 'skip$ - { organization output } - if$ - publisher output - } - if$ - new.block - note output - fin.entry -} - -FUNCTION {techreport} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.block - format.tr.number output.nonnull - institution "institution" output.check - address output - format.date "year" output.check - new.block - note output - fin.entry -} - -FUNCTION {unpublished} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.block - note "note" output.check - format.date output - fin.entry -} - -FUNCTION {default.type} { misc } - -MACRO {jan} {"Jan."} - -MACRO {feb} {"Feb."} - -MACRO {mar} {"Mar."} - -MACRO {apr} {"Apr."} - -MACRO {may} {"May"} - -MACRO {jun} {"June"} - -MACRO {jul} {"July"} - -MACRO {aug} {"Aug."} - -MACRO {sep} {"Sept."} - -MACRO {oct} {"Oct."} - -MACRO {nov} {"Nov."} - -MACRO {dec} {"Dec."} - -MACRO {acmcs} {"ACM Comput. Surv."} - -MACRO {acta} {"Acta Inf."} - -MACRO {cacm} {"Commun. ACM"} - -MACRO {ibmjrd} {"IBM J. Res. Dev."} - -MACRO {ibmsj} {"IBM Syst.~J."} - -MACRO {ieeese} {"IEEE Trans. Softw. Eng."} - -MACRO {ieeetc} {"IEEE Trans. Comput."} - -MACRO {ieeetcad} - {"IEEE Trans. Comput.-Aided Design Integrated Circuits"} - -MACRO {ipl} {"Inf. Process. Lett."} - -MACRO {jacm} {"J.~ACM"} - -MACRO {jcss} {"J.~Comput. Syst. Sci."} - -MACRO {scp} {"Sci. Comput. Programming"} - -MACRO {sicomp} {"SIAM J. Comput."} - -MACRO {tocs} {"ACM Trans. Comput. Syst."} - -MACRO {tods} {"ACM Trans. Database Syst."} - -MACRO {tog} {"ACM Trans. Gr."} - -MACRO {toms} {"ACM Trans. Math. Softw."} - -MACRO {toois} {"ACM Trans. Office Inf. Syst."} - -MACRO {toplas} {"ACM Trans. Prog. Lang. Syst."} - -MACRO {tcs} {"Theoretical Comput. Sci."} - -READ - -FUNCTION {sortify} -{ purify$ - "l" change.case$ -} - -INTEGERS { len } - -FUNCTION {chop.word} -{ 's := - 'len := - s #1 len substring$ = - { s len #1 + global.max$ substring$ } - 's - if$ -} - -FUNCTION {sort.format.names} -{ 's := - #1 'nameptr := - "" - s num.names$ 'numnames := - numnames 'namesleft := - { namesleft #0 > } - { nameptr #1 > - { " " * } - 'skip$ - if$ - s nameptr "{vv{ } }{ll{ }}{ f{ }}{ jj{ }}" format.name$ 't := - nameptr numnames = t "others" = and - { "et al" * } - { t sortify * } - if$ - nameptr #1 + 'nameptr := - namesleft #1 - 'namesleft := - } - while$ -} - -FUNCTION {sort.format.title} -{ 't := - "A " #2 - "An " #3 - "The " #4 t chop.word - chop.word - chop.word - sortify - #1 global.max$ substring$ -} - -FUNCTION {author.sort} -{ author empty$ - { key empty$ - { "to sort, need author or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { author sort.format.names } - if$ -} - -FUNCTION {author.editor.sort} -{ author empty$ - { editor empty$ - { key empty$ - { "to sort, need author, editor, or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { editor sort.format.names } - if$ - } - { author sort.format.names } - if$ -} - -FUNCTION {author.organization.sort} -{ author empty$ - - { organization empty$ - { key empty$ - { "to sort, need author, organization, or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { "The " #4 organization chop.word sortify } - if$ - } - { author sort.format.names } - if$ -} - -FUNCTION {editor.organization.sort} -{ editor empty$ - { organization empty$ - { key empty$ - { "to sort, need editor, organization, or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { "The " #4 organization chop.word sortify } - if$ - } - { editor sort.format.names } - if$ -} - -FUNCTION {presort} -{ type$ "book" = - type$ "inbook" = - or - 'author.editor.sort - { type$ "proceedings" = - 'editor.organization.sort - { type$ "manual" = - 'author.organization.sort - 'author.sort - if$ - } - if$ - } - if$ - " " - * - year field.or.null sortify - * - " " - * - title field.or.null - sort.format.title - * - #1 entry.max$ substring$ - 'sort.key$ := -} - -ITERATE {presort} - -SORT - -STRINGS { longest.label } - -INTEGERS { number.label longest.label.width } - -FUNCTION {initialize.longest.label} -{ "" 'longest.label := - #1 'number.label := - #0 'longest.label.width := -} - -FUNCTION {longest.label.pass} -{ number.label int.to.str$ 'label := - number.label #1 + 'number.label := - label width$ longest.label.width > - { label 'longest.label := - label width$ 'longest.label.width := - } - 'skip$ - if$ -} - -EXECUTE {initialize.longest.label} - -ITERATE {longest.label.pass} - -FUNCTION {begin.bib} -{ preamble$ empty$ - 'skip$ - { preamble$ write$ newline$ } - if$ - "\begin{thebibliography}{" longest.label * - "}\setlength{\itemsep}{-1ex}\small" * write$ newline$ -} - -EXECUTE {begin.bib} - -EXECUTE {init.state.consts} - -ITERATE {call.type$} - -FUNCTION {end.bib} -{ newline$ - "\end{thebibliography}" write$ newline$ -} - -EXECUTE {end.bib} - -% end of file latex8.bst -% --------------------------------------------------------------- - - - diff --git a/helm/papers/system_T/latex8.sty b/helm/papers/system_T/latex8.sty deleted file mode 100644 index 531053a4a..000000000 --- a/helm/papers/system_T/latex8.sty +++ /dev/null @@ -1,169 +0,0 @@ - -% --------------------------------------------------------------- -% -% $Id: latex8.sty,v 1.2 1995/09/15 15:31:13 ienne Exp $ -% -% by Paolo.Ienne@di.epfl.ch -% -% --------------------------------------------------------------- -% -% no guarantee is given that the format corresponds perfectly to -% IEEE 8.5" x 11" Proceedings, but most features should be ok. -% -% --------------------------------------------------------------- -% with LaTeX2e: -% ============= -% -% use as -% \documentclass[times,10pt,twocolumn]{article} -% \usepackage{latex8} -% \usepackage{times} -% -% --------------------------------------------------------------- - -% with LaTeX 2.09: -% ================ -% -% use as -% \documentstyle[times,art10,twocolumn,latex8]{article} -% -% --------------------------------------------------------------- -% with both versions: -% =================== -% -% specify \pagestyle{empty} to omit page numbers in the final -% version -% -% specify references as -% \bibliographystyle{latex8} -% \bibliography{...your files...} -% -% use Section{} and SubSection{} instead of standard section{} -% and subsection{} to obtain headings in the form -% "1.3. My heading" -% -% --------------------------------------------------------------- - -\typeout{IEEE 8.5 x 11-Inch Proceedings Style `latex8.sty'.} - -% ten point helvetica bold required for captions -% in some sites the name of the helvetica bold font may differ, -% change the name here: -\font\tenhv = phvb at 10pt -%\font\tenhv = phvb7t at 10pt - -% eleven point times bold required for second-order headings -% \font\elvbf = cmbx10 scaled 1100 -\font\elvbf = ptmb scaled 1100 - -% set dimensions of columns, gap between columns, and paragraph indent -\setlength{\textheight}{8.875in} -\setlength{\textwidth}{6.875in} -\setlength{\columnsep}{0.3125in} -\setlength{\topmargin}{0in} -\setlength{\headheight}{0in} -\setlength{\headsep}{0in} -\setlength{\parindent}{1pc} -\setlength{\oddsidemargin}{-.304in} -\setlength{\evensidemargin}{-.304in} - -% memento from size10.clo -% \normalsize{\@setfontsize\normalsize\@xpt\@xiipt} -% \small{\@setfontsize\small\@ixpt{11}} -% \footnotesize{\@setfontsize\footnotesize\@viiipt{9.5}} -% \scriptsize{\@setfontsize\scriptsize\@viipt\@viiipt} -% \tiny{\@setfontsize\tiny\@vpt\@vipt} -% \large{\@setfontsize\large\@xiipt{14}} -% \Large{\@setfontsize\Large\@xivpt{18}} -% \LARGE{\@setfontsize\LARGE\@xviipt{22}} -% \huge{\@setfontsize\huge\@xxpt{25}} -% \Huge{\@setfontsize\Huge\@xxvpt{30}} - -\def\@maketitle - { - \newpage - \null - \vskip .375in - \begin{center} - {\Large \bf \@title \par} - % additional two empty lines at the end of the title - \vspace*{24pt} - { - \large - \lineskip .5em - \begin{tabular}[t]{c} - \@author - \end{tabular} - \par - } - % additional small space at the end of the author name - \vskip .5em - { - \large - \begin{tabular}[t]{c} - \@affiliation - \end{tabular} - \par - \ifx \@empty \@email - \else - \begin{tabular}{r@{~}l} - E-mail: & {\tt \@email} - \end{tabular} - \par - \fi - } - % additional empty line at the end of the title block - \vspace*{12pt} - \end{center} - } - -\def\abstract - {% - \centerline{\large\bf Abstract}% - \vspace*{12pt}% - \it% - } - -\def\endabstract - { - % additional empty line at the end of the abstract - \vspace*{12pt} - } - -\def\affiliation#1{\gdef\@affiliation{#1}} \gdef\@affiliation{} - -\def\email#1{\gdef\@email{#1}} -\gdef\@email{} - -\newlength{\@ctmp} -\newlength{\@figindent} -\setlength{\@figindent}{1pc} - -\long\def\@makecaption#1#2{ - \vskip 10pt - \setbox\@tempboxa\hbox{\tenhv\noindent #1.~#2} - \setlength{\@ctmp}{\hsize} - \addtolength{\@ctmp}{-\@figindent}\addtolength{\@ctmp}{-\@figindent} - % IF longer than one indented paragraph line - \ifdim \wd\@tempboxa >\@ctmp - % THEN set as an indented paragraph - \begin{list}{}{\leftmargin\@figindent \rightmargin\leftmargin} - \item[]\tenhv #1.~#2\par - \end{list} - \else - % ELSE center - \hbox to\hsize{\hfil\box\@tempboxa\hfil} - \fi} - -% correct heading spacing and type -\def\section{\@startsection {section}{1}{\z@} - {14pt plus 2pt minus 2pt}{14pt plus 2pt minus 2pt} {\large\bf}} -\def\subsection{\@startsection {subsection}{2}{\z@} - {13pt plus 2pt minus 2pt}{13pt plus 2pt minus 2pt} {\elvbf}} - -% add the period after section numbers -\newcommand{\Section}[1]{\section{\hskip -1em.~#1}} -\newcommand{\SubSection}[1]{\subsection{\hskip -1em.~#1}} - -% end of file latex8.sty -% --------------------------------------------------------------- diff --git a/helm/papers/system_T/latex8.tex b/helm/papers/system_T/latex8.tex deleted file mode 100644 index fc401d6f3..000000000 --- a/helm/papers/system_T/latex8.tex +++ /dev/null @@ -1,230 +0,0 @@ - -% -% $Description: Author guidelines and sample document in LaTeX 2.09$ -% -% $Author: ienne $ -% $Date: 1995/09/15 15:20:59 $ -% $Revision: 1.4 $ -% - -\documentclass[times, 10pt,twocolumn]{article} -\usepackage{latex8} -\usepackage{times} - -%\documentstyle[times,art10,twocolumn,latex8]{article} - -%------------------------------------------------------------------------- -% take the % away on next line to produce the final camera-ready version -\pagestyle{empty} - -%------------------------------------------------------------------------- -\begin{document} - -\title{\LaTeX\ Author Guidelines - for {\boldmath $8.5 \times 11$-Inch} Proceedings Manuscripts} - -\author{Paolo Ienne\\ -Swiss Federal Institute of Technology\\ Microcomputing Laboratory \\ IN-F -Ecublens, 1015 Lausanne, Switzerland\\ Paolo.Ienne@di.epfl.ch\\ -% For a paper whose authors are all at the same institution, -% omit the following lines up until the closing ``}''. -% Additional authors and addresses can be added with ``\and'', -% just like the second author. -\and -Second Author\\ -Institution2\\ -First line of institution2 address\\ Second line of institution2 address\\ -SecondAuthor@institution2.com\\ -} - -\maketitle -\thispagestyle{empty} - -\begin{abstract} - The ABSTRACT is to be in fully-justified italicized text, at the top - of the left-hand column, below the author and affiliation - information. Use the word ``Abstract'' as the title, in 12-point - Times, boldface type, centered relative to the column, initially - capitalized. The abstract is to be in 10-point, single-spaced type. - The abstract may be up to 3 inches (7.62 cm) long. Leave two blank - lines after the Abstract, then begin the main text. -\end{abstract} - - - -%------------------------------------------------------------------------- -\Section{Introduction} - -Please follow the steps outlined below when submitting your -manuscript to the IEEE Computer Society Press. 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We MUST have this form before your paper can be -published in the proceedings. - -%------------------------------------------------------------------------- -\SubSection{Conclusions} - -Please direct any questions to the production editor in charge of these -proceedings at the IEEE Computer Society Press: Phone (714) 821-8380, or -Fax (714) 761-1784. - -%------------------------------------------------------------------------- -\nocite{ex1,ex2} -\bibliographystyle{latex8} -\bibliography{latex8} - -\end{document} - diff --git a/helm/papers/system_T/t.tex b/helm/papers/system_T/t.tex deleted file mode 100644 index 20ec95149..000000000 --- a/helm/papers/system_T/t.tex +++ /dev/null @@ -1,810 +0,0 @@ -\documentclass[times, 10pt,twocolumn, draft]{article} -\pagestyle{headings} -%\usepackage{graphicx} -\usepackage{amssymb,amsmath,mathrsfs,stmaryrd,amsthm} -%\usepackage{hyperref} -%\usepackage{picins} -\usepackage{latex8} -\usepackage{times} - -\pagestyle{empty} - - -\newcommand{\semT}[1]{\ensuremath{\llbracket #1 \rrbracket}} -\newcommand{\sem}[1]{\llbracket \ensuremath{#1} \rrbracket} -\newcommand{\pair}[2]{<\!#1,#2\!>} -\newcommand{\canonical}{\bot} -\newcommand{\R}{~\mathscr{R}~} -\newcommand{\N}{\,\mathbb{N}\,} -\newcommand{\B}{\,\mathbb{B}\,} -\newcommand{\NT}{\,\mathbb{N}\,} -\newcommand{\NH}{\,\mathbb{N}\,} -\renewcommand{\star}{\ast} -\renewcommand{\vec}{\overrightarrow} -\newcommand{\one}{{\bf 1}} -\newcommand{\mult}{\cdot} -\newcommand{\ind}{Ind(X)} -\newcommand{\indP}{Ind(\vec{P}~|~X)} -\newcommand{\Xind}{\ensuremath{X_{ind}}} -\newcommand{\XindP}{\ensuremath{X_{ind}}} -\renewcommand{\|}{\ensuremath{\quad | \quad}} -\newcommand{\triUP}{\ensuremath{\Delta}} -\newcommand{\triDOWN}{\ensuremath{\nabla}} -\newcommand{\Rx}{\ensuremath{R_X}} - -\newtheorem{thm}{Theorem}[subsection] - -\title{Modified Realizability and Inductive Types} -\author{...} - - -\begin{document} -\maketitle -\thispagestyle{empty} - -\begin{abstract} -In 1959, Kreisel introduced a notion of ``modified'' realizability to -provide an alternative technique to G\"odel functional (dialectica) -interpretation for establishing the connection between Peano Arihtmetic -and System T. While the dialectica interpretation has been widely -studied in the literature, Kreisel's technique, although remarkably -simpler,has apparently been almost neglected (with the only exception -of Troelstra). In this paper we give a modern presentation of the technique, -and generalize it to arbitrary inductive types in a first order setting. -This is part of a larger program, advocating the study -of logical systems with primitive inductive types starting form -weak, predicative logical frameworks and adding little by little small -bits of logical power. - -\end{abstract} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\Section{Introduction} -The characterization of the provable recursive functions of -Peano Arithmetic as the terms of system T is a well known -result of G\"odel \cite{Godel58,Godel90}. Although several authors acknowledge -that the functional interpretation of the Dialectica paper -is not among the major achievements of the author (see e.g. \cite{Girard87}), -the result has been extensively investigated and there is a wide -literature on the -topic (see e.g. \cite{Troelstra,HS86,Girard87}, just to mention textbooks, -and the bibliography therein). - -A different, more neglected, but for many respects much more -direct relation between Peano (or Heyting) Arithmetics and -G\"odel System T is provided -by the so called {\em modified realizability}. Modified realizability -was first introduced by Kreisel in \cite{Kreisel59} - although it will take you -a bit of effort to recognize it in the few lines of paragraph 3.52 - -and later in \cite{Kreisel62} under the name of generalized realizability. -The name of modified realizability seems to be due to Troelstra -\cite{Troelstra} -- who contested Kreisel's name but unfortunately failed in proposing -a valid alternative; we shall reluctantly adopt this latter name -to avoid further confusion. Modified realizability is a typed variant of -realizability, essentially providing interpretations -of $HA^{\omega}$ into itself: each theorem is realized by a typed function -of system T, that also gives the actual computational content extracted -from the proof. -In spite of the simplicity and the elegance of the proof, it is extremely -difficult to find a modern discussion of this result; the most recent -exposition we are aware of is in the encyclopedic work by -Troelstra \cite{Troelstra} (pp.213-229) going back to thirty years ago. -Even modern introductory books -to Type Theory and Proof Theory devoting much space to system T -such as \cite{GLT} and \cite{TS} surprisingly leave out this simple and -illuminating result. Both the previous textbooks -prefer to focus on higher order arithmetics and its relation with -Girard's System $F$ \cite{Girard86}, but the technical complexity and -the didactical value of the two proofs is not comparable: when you -prove that the Induction Principle is realized by the recursor $R$ -of system $T$ you catch a sudden gleam of understanding in the -students eyes; usually, the same does not happen when you show, say, -that the ``forgetful'' interpretation of the higher order predicate defining -the natural numbers is the system $F$ encoding -$\forall X.(X\to X) \to X \to X$ of $\N$. -Moreover, after a first period of enthusiasm, the impredicative -encoding of inductive types in Logical Frameworks has shown several -problems and limitations (see e.g. \cite{Werner} pp.24-25) mostly -solved by assuming inductive types as a primitive logical notion -(leading e.g. form the Calculus of Constructions to the Calculus -of Inductive Constructions - CIC). Even the extraction algorithm of -CIC, strictly based on realizability principles, and in a first time -still oriented towards System F \cite{Paulin87,Paulin89} has been -recently rewritten \cite{Letouzey04} -to take advantage of concrete types and pattern matching of ML-like -languages. Unfortunately, systems like the Calculus of Inductive -Constructions are so complex, from the logical point of view, to -substantially prevent a really neat theoretical exposition (at present, -it does not -even exists a truly complete consistency proofs covering all aspects -of such systems); moreover, not everybody may be interested in all the features -offered by these frameworks, from polymorphism to types depending on -proofs. Our program is to restart the analysis of logical systems with -primitive inductive types in a smooth way, starting form first order -logic and adding little by little small bits of logical power. -This paper is the first step in this direction. - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\Section{G\"odel system T} -We shall use a variant of system T with three atomic types $\N$ (natural -numbers), $\B$ (booleans) and $\one$ (a terminal object), and two binary -type constructors $\times$ (product) and $\to$ (arrow type). - -The terms of the language comprise the usual simply typed lambda terms -with explicit pairs, plus the following additional constants: -\begin{itemize} -\item $*:\one$, -\item $true: \B$, $false:\B$, $D:A\to A \to \B \to A$ -\item $O:\N$, $S:\N \to \N$, $R:A \to (A \to \N \to A) \to \N \to A$, -\end{itemize} -Redexes comprise $\beta$-reduction, projections, -and type specific reductions as reported in table \ref{tab:tredex} - -\begin{table}[!h] -\hrule\vspace{0.1cm} -\begin{tabular}{p{0.34\textwidth}r} - $\lambda x:U.M ~ N \leadsto M[N/x]$ & $(\beta)$ \\ - $fst \pair{M}{N} \leadsto M$ & $(\pi_1)$ \\ - $snd \pair{M}{N} \leadsto N$ & $(\pi_2)$ \\ - $D~M~N~ true \leadsto M$ & $(D_{true})$ \\ - $D~M~N~false \leadsto N$ & $(D_{false})$ \\ - $R~M~F~ 0 \leadsto M$ & $(R_0)$ \\ - $R~M~F~(S~n) \leadsto F~n~(R~M~F~n)$ & $(R_S)$ \\ - $M \leadsto * ~~~~ $ for any M of type $\one$ & $(*)$ -\end{tabular}\vspace{0.1cm} -\hrule -\caption{\label{tab:tredex}Reduction rules for System T} -\end{table} - -Note that using the well known isomorpshims -$\one \to A \cong A$, $A \to \one \cong \one$ -and $A \times \one \cong A \cong \one\times A$ (see \cite{AL91}, pp.231-239) -we may always get rid of $\one$ (apart the trivial case). -The terminal object does not play a major role in our treatment, but -it allows to extract better algorithms. In particular we use it -to realize atomic proposition, and stripping out the terminal object using -the above isomorphisms gives a simple way of just keeping the truly -informative part of the algorithms. - -\Section{Heyting's arithmetics} - -{\bf Axioms} - -\begin{itemize} -\item $nat\_ind: P(0) \to (\forall x.P(x) \to P(S(x))) \to \forall x.P(x)$ -\item $ex\_ind: (\forall x.P(x) \to Q) \to \exists x.P(x) \to Q$ -\item $ex\_intro: \forall x.(P \to \exists x.P)$ -\item $fst: P \land Q \to P$ -\item $snd: P \land Q \to Q$ -\item $conj: P \to Q \to P \land Q$ -\item $false\_ind: \bot \to Q$ -\item $discriminate:\forall x.0 = S(x) \to \bot$ -\item $injS: \forall x,y.S(x) = S(y) \to x=y$ -\item $plus\_O:\forall x.x+0=x$ -\item $plus\_S:\forall x,y.x+S(y)=S(x+y)$ -\item $times\_O:\forall x.x\mult0=0$ -\item $times\_S:\forall x,y.x\mult S(y)=x+(x\mult y)$ -\end{itemize} - -\noindent -{\bf Inference Rules} - -say that ax:AX refers to the previous Axioms list... -%\begin{table}[!h] -%\hrule\vspace{0.1cm} -%\begin{tabular}{p{0.34\textwidth}r} - - $$\Gamma, x:A, \Delta \vdash x:A ~~~ (Proj)$$ - $$ \Gamma \vdash ax : AX~~~ (Const)$$ - $$\frac{\Gamma,x:A \vdash M:Q}{\Gamma \vdash \lambda x:A.M: A \to Q} ~~~ (\to_i)$$ - $$\frac{\Gamma \vdash M: A \to Q \hspace{0.5cm}\Gamma \vdash N: A} - {\Gamma \vdash M N: Q} ~~~ (\to_e)$$ - $$\frac{\Gamma \vdash M:P}{\Gamma \vdash \lambda x:\N.M: \forall x.P}(*) ~~~ - (\forall_i)$$ - $$\frac{\Gamma \vdash M :\forall x.P}{\Gamma \vdash M t: P[t/x]} - ~~~ (\forall_e)$$ - -%\end{tabular}\vspace{0.1cm} -%\hrule -%\caption{\label{tab:HArules}Inference rules} -%\end{table}{lr} - -%\[ -% (\land_i)\frac{\Gamma \vdash M:A \hspace{1cm}\Gamma \vdash N:B} -% {\Gamma \vdash \pair{M}{N} : A \land B} -%\hspace{2cm} -% (\land_{el})\frac{\Gamma \vdash A \land B}{\Gamma \vdash A} -%\hspace{2cm} -% (\land_{er})\frac{\Gamma \vdash A \land B}{\Gamma \vdash B} -%\] - - -%\[ -% (\exists_i)\frac{\Gamma \vdash P[t/x]}{\Gamma \vdash \exists x.P}\hspace{2cm} -% (\exists_e)\frac{\Gamma \vdash \exists x.P\hspace{1cm}\Gamma \vdash \forall x.P \to Q} -%{\Gamma \vdash Q} -%\] - -\Section{Extraction} - -The formulae to types translation function $\sem{\cdot}$, see table -\ref{tab:formulae2types}, takes in input formulae in HA and returns -types in T. In table \ref{tab:structproof} we the proofs to terms -function for structured proofs. Axiom translation is reported in table -\ref{tab:axioms}. In table \ref{tab:canonical} we define how the -canoniac element is formed. - -\begin{table}[!h] -\hrule\vspace{0.1cm} -\begin{tabular}{p{0.21\textwidth}p{0.21\textwidth}} - $\sem{A} = \one$ if A is atomic & - $\sem{A \land B} = \sem{A}\times \sem{B}$ \\ - $\sem{A \to B} = \sem{A}\to \sem{B}$ & - $\sem{\forall x:\N.P} = \N \to \sem{P}$ \\ - $\sem{\exists x:\N.P} = \N \times \sem{P}$ & -\end{tabular}\vspace{0.1cm} -\hrule -\caption{\label{tab:formulae2types}Formulae to types translation} -\end{table} - -\begin{table}[!h] -\hrule\vspace{0.1cm} -\begin{tabular}{p{0.20\textwidth}p{0.20\textwidth}} - $\semT{M N} = \semT{M} \semT{N}$ & - $\semT{M t} = \semT{M} \semT{t}$ \\ - \multicolumn{2}{l}{$\semT{\lambda x:A.M} = \lambda x:\sem{A}.\semT{M}$} \\ - \multicolumn{2}{l}{$\semT{\lambda x:\N.M} = \lambda x:\N.\semT{M}$} -\end{tabular}\vspace{0.1cm} -\hrule -\caption{\label{tab:structproof}Structured proofs} -\end{table} - -\begin{table}[!h] -\hrule\vspace{0.1cm} -\begin{tabular}{l}%{0.47\textwidth}p{0.47\textwidth}} - $\sem{fst} = \pi_1$\\ - $\sem{snd} = \pi_2$\\ - $\sem{conj} = \lambda x:\sem{P}.\lambda y:\sem{Q}.\pair{x}{y}$\\ - $\sem{false\_ind} = \canonical_{\sem{Q}}$\\ - $\sem{discriminate} = \lambda \_:\N.\lambda \_:\one.\star$\\ - $\sem{injS}= \lambda \_:\N. \lambda \_:\N.\lambda \_:\one.\star$\\ - $\sem{plus\_O} = \sem{times\_O} = \lambda \_:\N.\star$\\ - $\sem{nat\_ind} = R$ \\ - $\sem{plus\_S} = \sem{times\_S} = \lambda \_:\N. \lambda \_:\N.\star$ \\ - $\sem{ex\_intro} = \lambda x:\N.\lambda f:\sem{P}.\pair{x}{f}$ \\ - $\sem{ex\_ind} = \lambda f:(\N \to \sem{P} \to \sem{Q}).$\\ - $\qquad\lambda p:\N\times \sem{P}.f~(fst~p)~(snd~p)$ -\end{tabular}\vspace{0.1cm} -\hrule -\caption{\label{tab:axioms}Axioms translation} -\end{table} - -\begin{table}[!h] -\hrule\vspace{0.1cm} -\begin{tabular}{l}%p{0.23\textwidth}p{0.23\textwidth}} - $\canonical_\one = \lambda x:\one.x$ \\ - $\canonical_N = \lambda x:\one.0$ \\ - $\canonical_{U\times V} = \lambda x:\one.\pair{\canonical_{U} - x}{\canonical_{V} x}$ \\ - $\canonical_{U\to V} = \lambda x:\one.\lambda \_:U. \canonical_{V} x$ -\end{tabular}\vspace{0.1cm} -\hrule -\caption{\label{tab:canonical}Canonical element} -\end{table} - - -\Section{Realizability} -The realizability relation is a relation $f \R P$ where $f: \sem{P}$, and -$P$ is a closed formula. -In particular: -\begin{itemize} -\item $\neg (\star \R \bot)$ -\item $* \R (t_1=t_2)$ iff $t_1=t_2$ is true ... -\item $\pair{f}{g} \R (P\land Q)$ iff $f \R P$ and $g \R Q$ -\item $f \R (P\to Q)$ iff for any $m$ such that $m \R P$, $(f \,m) \R Q$ -\item $f \R (\forall x.P)$ iff for any natural number $n$ $(f n) \R P[\underline{n}/x]$ -\item $\pair{n}{g}\R (\exists x.P)$ iff $g \R P[\underline{n}/x]$ -\end{itemize} -%We need to generalize the notion of realizability to sequents. -%Given a sequent $B_1, \ldots, B_n \vdash A$ with free variables in -%$\vec{x} = x_1,\ldots, x_m$, we say that $f \R B1, \ldots, B_n \vdash A$ iff -%forall natural numbers $n_1, \ldots, n_m$, -%if forall $i \in {1,\ldots,n}$ -%$m_i \R B_i[\vec{\underline{n}}/\vec{x}]$ then -%$$f \R A[\vec{\underline{n}}/\vec{x}]$$. -% -\noindent -We need to generalize the notion of realizability to sequents.\\ -Let $\vec{x} = FV_{\N}( B_1, \ldots, B_n, P)$ a vector of variables of type -$\N$ that occur free in $B_1, \ldots, B_n, P$. Let $\vec{b:B}$ the vector -$b_1:B_1, \ldots, b_n:B_n$.\\ -We say that $f \R B_1, \ldots, B_n \vdash A:P$ iff -$$\lambda \vec{x:\N}. \lambda \vec{b:B}.f \R -\forall \vec{x}. B_1 \to \ldots \to B_n \to P$$ -Note that $\forall \vec{x}. B_1 \to \ldots \to B_n \to P$ is a closed formula, -so we can use the previous definition of realizability on it. - -\noindent -We proceed to prove that all axioms $ax:Ax$ are realized by $\sem{ax}$. - -\begin{itemize} -\item $nat\_ind$. - We must prove that the recursion schema $R$ realizes the induction principle. - To this aim we must prove that for any $a$ and $f$ such that $a \R P(0)$ and - $f \R \forall x.(P(x) \to P(S(x)))$, and any natural number $n$, $(R \,a \,f - \,n) \R P(\underline{n})$.\\ - We proceed by induction on n.\\ - If $n=O$, $(R \,a \,f \,O) = a$ and by hypothesis $a \R P(0)$.\\ - Suppose by induction that - $(R \,a \,f \,n) \R P(\underline{n})$, and let us prove that the relation - still holds for $n+1$. By definition - $(R \,a \,f \,(n+1)) = f \,n \,(R \,a \,f \,n)$, - and since $f \R \forall x.(P(x) \to P(S(x)))$, - $(f n (R a f n)) \R P(S(\underline{n}))=P(\underline{n+1})$. - -\item $ex\_ind$. - We must prove that $$\underline{ex\_ind} \R (\forall x:(P x) - \to Q) \to (\exists x:(P x)) \to Q$$ Following the definition of $\R$ we have - to prove that given\\ $f~\R~\forall~x:((P~x)~\to~Q)$ and - $p~\R~\exists~x:(P~x)$, then $\underline{ex\_ind}~f~p \R Q$.\\ - $p$ is a couple $\pair{n_p}{g_p}$ such that $g_p \R P[\underline{n_p}/x]$, while - $f$ is a function such that forall $n$ and for all $m \R P[\underline{n}/x]$ - then $f~n~m \R Q$ (note that $x$ is not free in $Q$ so $[\underline{n}/x]$ - affects only $P$).\\ - Expanding the definition of $\underline{ex\_ind}$, $fst$ - and $snd$ we obtain $f~n_p~g_p$ that we know is in relation $\R$ with $Q$ - since $g_p \R P[\underline{n_p}/x]$. - -\item $ex\_intro$. - We must prove that - $$\lambda x:\N.\lambda f:\sem{P}.\pair{x}{f} \R \forall x.(P\to\exists x.P(x)$$ - that leads to prove that for each n - $\underline{ex\_into}~n \R (P\to\exists x.P(x))[\underline{n}/x]$.\\ - Evaluating the substitution we have - $\underline{ex\_into}~n \R (P[\underline{n}/x]\to\exists x.P(x))$.\\ - Again by definition of $\R$ we have to prove that given a - $m \R P[\underline{n}/x]$ then $\underline{ex\_into}~n~m \R \exists x.P(x)$. - Expanding the definition of $\underline{ex\_intro}$ we have - $\pair{n}{m} \R \exists x.P(x)$ that is true since $m \R P[\underline{n}/x]$. - -\item $fst$. - We have to prove that $\pi_1 \R P \land Q \to P$, that is equal to proving - that for each $m \R P \land Q$ then $\pi_1~m \R P$ . - $m$ must be a couple $\pair{f_m}{g_m}$ such that $f_m \R P$ and $g_m \R Q$. - So we conclude that $\pi_1~m$ reduces to $f_m$ that is in relation $\R$ - with $P$. - -\item $snd$. The same for $fst$. - -\item $conj$. - We have to prove that - $$\lambda x:\sem{P}. \lambda y:\sem{Q}.\pair{x}{y}\R P \to Q \to P \land Q$$ - Following the definition of $\R$ we have to show that - for each $m \R P$ and for each $n \R Q$ then - $(\lambda x:\sem{P}. \lambda y:\sem{Q}.\pair{x}{y})~m~n \R P \land Q$.\\ - This is the same of $\pair{m}{n} \R P \land Q$ that is verified since - $m \R P$ and $n \R Q$. - - -\item $false\_ind$. - We have to prove that $\bot_{\sem{Q}} \R \bot \to Q$. - Trivial, since there is no $m \R \bot$. - -\item $discriminate$. - Since there is no $n$ such that $0 = S n$ is true... \\ - $\underline{discriminate}~n \R 0 = S~\underline{n} \to \bot$ for each n. - -\item $injS$. - We have to prove that for each $n_1$ and $n_2$\\ - $\lambda \_:\N. \lambda \_:\N.\lambda \_:\one.*~n_1~n_2 \R - (S(x)=S(y)\to x=y)[n_1/x][n_2/y]$.\\ - We assume that $m \R S(n_1)=S(n_2)$ and we have to show that - $\lambda \_:\N. \lambda \_:\N.\lambda \_:\one.*~n_1~n_2~m$ that reduces to - $*$ is in relation $\R$ with $n_1=n_2$. Since in the standard model of - natural numbers $S(n_1)=S(n_2)$ implies $n_1=n_2$ we have that - $* \R n_1=n_2$. - -\item $plus\_O$. - Since in the standard model for natural numbers $0$ is the neutral element - for addition $\lambda \_:\N.\star \R \forall x.x + 0 = x$. - -\item $plus\_S$. - In the standard model of natural numbers the addition of two numbers is the - operation of counting the second starting from the first. So - $$\lambda \_:\N. \lambda \_:\N. \star \R \forall x,y.x+S(y)=S(x+y)$$. - -\item $times\_O$. - Since in the standard model for natural numbers $0$ is the absorbing element - for multiplication $\lambda \_:\N.\star \R \forall x.x \mult 0 = 0$. - -\item $times\_S$. - In the standard model of natural numbers the multiplications of two - numbers is the operation of adding the first to himself a number of times - equal to the second number. So - $$\lambda \_:\N. \lambda \_:\N. \star \R \forall x,y.x+S(y)=S(x+y)$$. - -\end{itemize} - - -\noindent -{\bf example}\\ -Let us prove the following principle of well founded induction: -\[(\forall m.(\forall p. p < m \to P~p) \to P~m) \to \forall n.P~n\] -In the following proof we shall make use of proof-terms, since we finally -wish to extract the computational content; we leave to reader the easy -check that the proof object describes the usual and natural proof -of the statement. - -We assume to have already proved the following lemmas (having trivial -realizers):\\ -\[L : \forall p, q.p < q \to q \le 0 \to \bot\] -\[M : \forall p,q,n.p < q \to q \le (S n) \to p \le n \] -Let us assume $h : \forall m.(\forall p. p < m \to P~p) \to P~m$. -We prove by induction on $n$ that $\forall q. q \le n \to P~q$. -For $n=0$, we get a proof of $P ~q$ by -\begin{eqnarray} -B & \equiv & \lambda q.\lambda h_0:q \le 0. h ~q~ \nonumber\\ -& & \quad (\lambda p.\lambda k:p < q. false\_ind ~(L~p~q~k~h_0)) \nonumber -\end{eqnarray} -In the inductive case, we must prove that, for any $n$, -\[(\forall q. q \le n \to P~q) \to (\forall q. q \le S n \to P~q)\] -Assume $h_1: \forall q. q \le n \to P q$ and -$h_2: q \le S ~n$. Let us prove $\forall p. p < q \to P~p$. -If $h_3: p < q$ then $(M~ p~ q~ n~ h_3~ h_2): p \le n$, hence -$h_1 ~p ~ (M~ p~ q~ n~ h_3~ h_2): P~p$.\\ -In conclusion, the proof of the -inductive case is -\begin{eqnarray} -I & \equiv & \lambda n.\lambda h_1:\forall q. q \le n \to P~ q.\lambda q.\lambda h_2:q \le S n. \nonumber\\ - & & \quad h ~ q ~ (\lambda p.\lambda h_3:p < q.h_1 ~p~ (M~ p~ q~ n~ h_3~ h_2)) - \nonumber -\end{eqnarray} -(where $h$ is free in I). -The full proof is -\begin{eqnarray} -& \lambda h:\forall m.(\forall p. p < m\to P~p)\to P~m.\lambda m. &\nonumber\\ -& \quad nat\_ind ~B ~ I ~m~m~ (le\_n ~ m) & \nonumber -\end{eqnarray} - -where $le\_n$ is a proof that $\forall n. n \le n$, and the free $P$ in the definition of $nat_{ind}$ is instantiated with $\forall m.m \le m \to P~m$.\\ -Form the previous proof,after stripping terminal objects, -and a bit of eta-contraction to make -the term more readable, we extract the following term (types are omitted): - -\[R' \equiv \lambda f.\lambda m. -R~ (\lambda n.f ~n~ (\lambda q.*))~ -(\lambda n\lambda g\lambda q.f ~q~g)~m ~m\] - -The intuition of this operator is the following: supose to -have a recursive definition $h q = F[h]$ where $q:\N$ and -$F[h]: A$. This defines a functional -$f: \lambda q.\lambda g.F[g]: N\to(N\to A) \to A$, such that -(morally) $h$ is the fixpoint of $f$. For instance, -in the case of the fibonacci function, $f$ is -\begin{eqnarray} -fibo & \equiv & \lambda q. \lambda g. if~ q = 0~then~ 1~ else \nonumber\\ -& & \quad if~ q = 1~ then~ 1~ else ~ g (q-1)+g (q-2) \nonumber -\end{eqnarray} - -So $f$ build a new -approximation of $h$ from the previous approximation $h$ taken -as input. $R'$ precisely computes the mth-approximation starting -from a dummy function $(\lambda q.*_A)$. Alternatively, -you may look at $g$ as the ``history'' (curse of values) of $h$ -for all values less or equal to $q$; then $f$ extend $g$ to -$q+1$. - -Let's compute for example -\begin{eqnarray} -R'~fibo~2 & \leadsto & - R~ (\lambda n.fibo ~n~ (\lambda q.*))~ - (\lambda n\lambda g\lambda q.fibo ~q~g)~2 ~2\nonumber\\ -& \leadsto & - (\lambda n\lambda g\lambda q.fibo ~q~g)~1~ - (R~ - (\lambda n.fibo ~n~ (\lambda q.*))~ - (\lambda n\lambda g\lambda q.fibo ~q~g)~1)~ - 2 \nonumber\\ -& \leadsto & - \lambda q.fibo ~q~ - (R~ - (\lambda n.fibo ~n~ (\lambda q.*))~ - (\lambda n\lambda g\lambda q.fibo ~q~g)~1)~ - 2 \nonumber\\ -& \leadsto & - \lambda q.fibo ~q~ - ((\lambda n\lambda g\lambda q.fibo ~q~g)~0~ - (R~ - (\lambda n.fibo ~n~ (\lambda q.*))~ - (\lambda n\lambda g\lambda q.fibo ~q~g)~0))~ - 2 \nonumber\\ -& \leadsto & - \lambda q.fibo ~q~ - (\lambda q.fibo ~q~ - (R~ - (\lambda n.fibo ~n~ (\lambda q.*))~ - (\lambda n\lambda g\lambda q.fibo ~q~g)~0) - )2 \nonumber\\ -& \leadsto & - \lambda q.fibo ~q~ - (\lambda q.fibo ~q~ - (\lambda n.fibo ~n~ (\lambda q.*)))2 - \nonumber\\ -& \leadsto & - fibo~2~(\lambda q.fibo ~q~ (\lambda n.fibo ~n~ (\lambda q.*))) \nonumber\\ -& \leadsto & - (\lambda q.fibo ~q~ (\lambda n.fibo ~n~ (\lambda q.*))) 1 + - (\lambda q.fibo ~q~ (\lambda n.fibo ~n~ (\lambda q.*))) 0 \nonumber\\ -& \leadsto & - fibo ~1~ (\lambda n.fibo ~n~ (\lambda q.*)) + - fibo ~0~ (\lambda n.fibo ~n~ (\lambda q.*)) \nonumber\\ -& \leadsto & - 1 + 1 \nonumber -\end{eqnarray} -Note that the second argument of $fibo$ is always a method to calculate all the prvious values of $fibo$. DA CAPIRE (per me) come mai $\lambda n$ non viene usata... -CAPITA CON csc: - -n non serve perche' c'e' una relazione logica di n con q, -in particolare $q <= Sn$ ... quindi $q < n$ (lemma M)... -e quindi posso usare come history $< n$ una history $< q$. -il $\lambda h2$ essendo $[[q <= Sn]]$ = 1 viene scartata. - -se si spiega come array viene decente... forse. lunedi' provo a scrivere -meglio. - -\Section{Inductive types} -The notation we will use is similar to the one used in -\cite{Werner} and \cite{Paulin89} but we prefer -giving a label to each constructor and use that label instead of the -longer $Constr(n,\ind\{\ldots\})$ to indicate the $n^{th}$ constructor. -We adopt the vector notation to make things more readable. -$\vec{m}$ has to be intended as $m_1~\ldots~m_n$ where $n$ may -be equal to 0 (we use $m_1~\vec{m}$ when we want to give a -name to the first $m$ and assert $n>0$). If the vector notation is -used inside an arrow type it has a slightly different meaning, -$A \to \vec{B} \to C$ is a shortcut for -$A \to B_1 \to \ldots \to B_n \to C$. - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\SubSection{Extensions to the logic framework} -To talk about arbitrary inductive types (and not hard coded natural numbers) we -have to extend a bit our framework. - -First we admit quantification over inductive types $T$, thus $\forall x:T.A$ -and $\exists x:T.A$ are allowed. Then rules 4 and 5 of the $\sem{\cdot}$ -definition are replaced by $\sem{\forall x:T.P} = T \to \sem{P}$ and -$\sem{\exists x:T.P} = T \times \sem{P}$. - -For each inductive type we will describe the formation rules and the -corresponding induction principle schema. - -Symmetrically we have to extend System T with arbitrary inductive types and -we will see how theyr recursors are defined in the following sections. - -The definition of $\R$ is modified substituting each occurrence of $\N$ with -a generic inductive type $T$. - -%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\SubSection{Type definition} -$$\ind\{c_1:C(X); \ldots ; c_n:C(X)\}$$ -$$C(X) ::= X \| T \to C(X) \| X \to C(X)$$ -In the second case we mean $T \neq X$. - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\SubSection{Induction principle} -The induction principle for an inductive type $X$ and a predicate $Q$ -is a constant with the following type -$$\Xind:\vec{\triUP\{C(X), c\}} \to \forall t:X.Q(t)$$ -$\triUP$ takes a constructor type $C(X)$ and a term $c$ (initially $c$ is a -constructor of X, and $c:C(X)$) and is defined by recursion as follows: -\begin{eqnarray} -\triUP\{X, c\} & = & Q(c) \nonumber\\ -\triUP\{T \to C(X), c\} & = & - \forall m:T.\triUP\{C(X),c~m\} \nonumber\\ -\triUP\{X \to C(X), c\} & = & - \forall t:X.Q(t) \to \triUP\{C(X), c~t\} \nonumber -\end{eqnarray} - -%%%%%%%%%%%%%%%%%%%%% -\SubSection{Recursor} -%\SubSubSection{Type} -The type of the recursor $\Rx$ on an inductive type $X$ is -$$\Rx : \vec{\square\{C(X)\}} \to X \to \alpha$$ -$\square$ is defined by recursion on the constructor type $C(X)$. -\begin{eqnarray} -\square\{X\} & = & \alpha \nonumber \\ -\square\{T \to C(X)\} & = & T \to \square\{C(X)\}\nonumber \\ -\square\{X \to C(X)\} & = & X \to \alpha \to \square\{C(X)\}\nonumber -\end{eqnarray} -%\SubSubSection{Reduction rules} -We say that -$$\Rx~\vec{f}~(c_i~\vec{m}) \leadsto -\triDOWN\{C(X)_i, f_i, \vec{m}\}$$ -$\triDOWN$ takes a constructor type $C(X)$, a term $f$ -(of type $\square\{C(X)\}$) and is defined by recursion as follows: -\begin{eqnarray} -\triDOWN\{X, f, \} & = & f\nonumber \\ -\triDOWN\{T \to C(X), f, m_1~\vec{m}\} & = & - \triDOWN\{C(X), f~m_1, \vec{m}\}\nonumber \\ -\triDOWN\{X \to C(X), f, m_1~\vec{m}\} & = & - \triDOWN\{C(X), f~m_1~(\Rx~\vec{f}~m_1), - \vec{m}\}\nonumber -\end{eqnarray} -We assume $\Rx~\vec{f}~(c_i~\vec{m})$ is well typed, so in the first case we -can omit $\vec{m}$ since it is an empty sequence. - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\SubSection{Realizability of the induction principle} -Once we have inductive types and their induction principle we want to show that -the recursor $\Rx$ realizes $\Xind$, that is that $\Rx$ has type -$\sem{\Xind}$ and is in relation $\R$ with $\Xind$. - -\begin{thm}$\Rx : \sem{\Xind}$\end{thm} -\begin{proof} -We have to compare the definition of $\square$ and $\triUP$ -since they play the same role in constructing respectively the types of -$\Rx$ and -$\Xind$. If we assume $\alpha = \sem{Q}$ and we apply the $\sem{\cdot}$ -function to each right side of the $\triUP$ definition we obtain -exactly $\square$. The last two elements of the arrows $\Rx$ and -$\Xind$ are again the same up to $\sem{\cdot}$. -\end{proof} - -\begin{thm}$\Rx\R \Xind$\end{thm} -\begin{proof} -To prove that $\Rx\R \Xind$ we must assume that for each $i$ index -of a constructor of $X$, $f_i \R \triUP\{C(X)_i, c_i\}$ and we -have to prove that for each $t:X$ -$$\Rx~\vec{f}~t \R Q(t)$$ -\noindent -We proceed by induction on the structure of $t$. -\\ -The base case is when the -type of the head constructor of $t$ has no recursive arguments (i.e. the type -is generated using only the first two rules $C(X)$), so -$(\Rx~\vec{f}~(c_i~\vec{m}))$ reduces in one step to $(f_i~\vec{m})$. $f_i$ -realizes $\triUP\{C(X)_i, c_i\}$ by assumption and since we are in the base -case $\triUP\{C(X)_i, c_i\}$ is of the form $\vec{\forall t:T}.Q(c_i~\vec{t})$. -Thus $f_i~\vec{m} \R Q(c_i~\vec{m})$. -\\ -In the induction step we have as induction hypothesis that for each recursive -argument $t_i$ of the head constructor $c_i$, $r_i\equiv -\Rx~\vec{f}~t_i \R Q(t_i)$. By the third rule of $\triDOWN$ we obtain the reduct -$f_i~\vec{m}~\vec{t~r}$ (here we write first all the non recursive arguments, -then all the recursive one. In general they can be mixed and the proof is -exactly the same but the notation is really heavier). We know by hypothesis -that $f_i \R \triUP\{C(X)_i, c_i\} \equiv \vec{\forall m:T}.\vec{\forall -t:X.Q(t)} \to Q(c_i~\vec{m}~\vec{t})$, thus $f_i~\vec{m}~\vec{t~r} \R -Q(c_i~\vec{m}~\vec{t})$. -\end{proof} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\Section{Strong normalization of extended system T} -Strong normalization for system T is a well know result\cite{GLT} -that can be easily extended to System T with this kind of inductive -types. The first thing we have to do is to extend the definition of -neutral term to the terms not of the form $$, $\lambda x.u$, -$c_i~\vec{m}$. - -In conformity with the demonstration we are extending we call $\nu(t)$ -the length of the longest reduction path from $t$ and $\ell(t)$ the -number of symbols in the normal form of $t$. - -For an inductive type $\ind\{c_1:C(X); \ldots ; c_n:C(X)\}$ -we have to prove that for each $i$, -given a proper sequence of reducible arguments $\vec{m}$ and $\vec{f}$, -$(c_i~\vec{m})$ and $\Rx~\vec{f}~(c_i~\vec{m})$ are reducible. - -First the simple case of constructors. If the constructor $c_i$ takes -no arguments then it is already in normal form. If it takes -$m_1,\ldots,m_n$ reducible arguments, then $\nu(c_i~\vec{m}) = max \{m_1, -\ldots,m_n\}$ and so $c_i~\vec{m}$ is strongly nomalizable thus -reducible for the definition of reducibility for base types. - -To show that $\Rx~\vec{f}~(c_i~\vec{m})$ is reducible we can use -(\textbf{CR 3}) that states that if $t$ is neutral and every $t'$ obtained by -executing one redex of $t$ is reducible, then $t$ is reducible. - -Now we have to show that each term that can be obtained by a -reduction step is reducible. We can procede induction on -$\Sigma\nu(f_i) + \nu(c_i~\vec{m}) + -\ell(c_i~\vec{m})$ since we know by hypothesis that $\vec{f}$ and -$(c_i~\vec{m})$ are reducible and consequently strongly normalizing. -\\ -The base case is when $c_i$ takes no arguments and $\vec{f}$ are -normal. In this case the only redex we can compute is -$$\Rx~\vec{f}~c_i~\leadsto~f_i$$ that is reducible by hypothesis. -\\ -The interesting inductive case is when $\vec{m}$ and $\vec{f}$ are -normal, so the only reduction step we can execute is -$$\Rx~\vec{f}~(c_i~\vec{m})~\leadsto~f_i~\vec{m}~\vec{(\Rx~\vec{f}~n)}$$ -where $\vec{n}$ are the recursive arguments of $c_i$ (here we wrote -the recursive calls as the last parameters of $f_i$ just to lighten -notation). Since $\ell(n_j)$ is less than $\ell(c_i~\vec{m})$ for -every $j$ we can apply the inductive hypothesis and state that -$\Rx~\vec{f}~n_j$ is reducible. Then by definition of reducibility of -the arrow types and by the hypothesis that $f_i$ and $\vec{m}$ are -reducible, we obtain that $$f_i~\vec{m}~\vec{(\Rx~\vec{f}~n)}$$ is -reducible. -\\ -All other cases, when we execute a redex in $\vec{m}$ or $\vec{f}$, -are straightforward applications of the induction hypothesis. - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\Section{Improving inductive types} -It is possible to parametrise inductive types over other inductive types -without much difficulties since the type $T$ in $C(X)$ is free. Both the -recursor and the induction principle are schemas, parametric over $T$. - -Possiamo anche definire $X_{\vec{P}}\equiv Ind(P|X)={c_i : C(P|X)}$ e poi -fare variare $T$ su $\vec{P}$, ma non ottengo niente di meglio. - -Credo anche che quantificare su eventuali variabili di tipo non cambi niente -visto che non abbiamo funzioni. - -Se ammettiamo che i tipi dipendano da termini di tipo induttivo - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\bibliographystyle{latex8} -%\bibliography{latex8} - -\begin{thebibliography}{} -\bibitem{AL91}A.Asperti, G.Longo. Categories, Types and Structures. -Foundations of Computing, Cambrdidge University press, 1991. -\bibitem{Girard86}G.Y.Girard. The system F of variable types, fifteen -years later. Theoretical Computer Science 45, 1986. -\bibitem{Girard87}G.Y.Girard. Proof Theory and Logical Complexity. -Bibliopolis, Napoli, 1987. -\bibitem{GLT}G.Y.Girard, Y.Lafont, P.Tailor. Proofs and Types. -Cambridge Tracts in Theoretical Computer Science 7.Cambridge University -Press, 1989. -\bibitem{Godel58}K.G\"odel. \"Uber eine bisher noch nicht ben\"utzte Erweiterung -des finiten Standpunktes. Dialectica, 12, pp.34-38, 1958. -\bibitem{Godel90}K.G\"odel. Collected Works. Vol.II, Oxford University Press, -1990. -\bibitem{HS86}J.R.Hindley, J. P. Seldin. Introduction to Combinators and -Lambda-calculus, Cambridge University Press, 1986. -\bibitem{Howard68}W.A.Howard. Functional interpretation of bar induction -by bar recursion. Compositio Mathematica 20, pp.107-124. 1958 -\bibitem{Howard80}W.A.Howard. The formulae-as-types notion of constructions. -in J.P.Seldin and j.R.Hindley editors, to H.B.Curry: Essays on Combinatory -Logic, Lambda calculus and Formalism. Acedemic Press, 1980. -\bibitem{Kleene45}S.C.Kleene. On the interpretation of intuitionistic -number theory. Journal of Symbolic Logic, n.10, pp.109-124, 1945. -\bibitem{Kreisel59} G.Kreisel. Interpretation of analysis by means of -constructive functionals of finite type. In. A.Heyting ed. -{\em Constructivity in mathematics}. North Holland, Amsterdam,1959. - \bibitem{Kreisel62} G.Kreisel. On weak completeness of intuitionistic -predicatelogic. Journal of Symbolic Logic 27, pp. 139-158. 1962. -\bibitem{Letouzey04}P.Letouzey. Programmation fonctionnelle -certifi\'ee; l'extraction -de programmes dans l'assistant Coq. Ph.D. Thesis, Universit\'e de -Paris XI-Orsay, 2004. -\bibitem{Loef}P.Martin-L\"of. Intuitionistic Type Theory. -Bibliopolis, Napoli, 1984. -\bibitem{Paulin87}C.Paulin-Mohring. Extraction de programme dans le Calcul de -Constructions. Ph.D. Thesis, Universit\'e de -Paris 7, 1987. -\bibitem{Paulin89}C.Paulin-Mohring. Extracting $F_{\omega}$ programs -from proofs in the Calculus of Constructions. In proc. of the Sixteenth Annual -ACM Symposium on -Principles of Programming Languages, Austin, January, ACML Press 1989. -\bibitem{Sch}K.Sch\"utte. Proof Theory. Grundlehren der mathematischen -Wissenschaften 225, Springer Verlag, Berlin, 1977. -\bibitem{Troelstra}A.S.Troelstra. Metamathemtical Investigation of -Intuitionistic -Arithmetic and Analysis. Lecture Notes in Mathematics 344, Springer Verlag, -Berlin, 1973. -\bibitem{TS}A.S.Troelstra, H.Schwichtenberg. Basic Proof Theory. -Cambridge Tracts in Theoretical Computer Science 43.Cambridge University -Press, 1996. -\bibitem{Werner}B.Werner. Une Th\'eorie des Constructions Inductives. -Ph.D.Thesis, Universit\'e de Paris 7, 1994. - - -\end{thebibliography} - -\end{document} - -- 2.39.2