From: acondolu Date: Fri, 7 Jul 2017 16:04:21 +0000 (+0200) Subject: Added new calculus X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=537f15490817fe9e6d9e8e9c6a647d21df5942c3;p=fireball-separation.git Added new calculus --- diff --git a/calculus/main.aux b/calculus/main.aux new file mode 100644 index 0000000..b8a33e5 --- /dev/null +++ b/calculus/main.aux @@ -0,0 +1,5 @@ +\relax +\select@language{english} +\@writefile{toc}{\select@language{english}} +\@writefile{lof}{\select@language{english}} +\@writefile{lot}{\select@language{english}} diff --git a/calculus/main.fdb_latexmk b/calculus/main.fdb_latexmk new file mode 100644 index 0000000..d484be9 --- /dev/null +++ b/calculus/main.fdb_latexmk @@ -0,0 +1,64 @@ +# Fdb version 3 +["pdflatex"] 1499443424 "main.tex" "main.pdf" "main" 1499443425 + "C:/Program Files (x86)/MiKTeX 2.9/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1233955448 1004 54797486969f23fa377b128694d548df "" + "C:/Program Files (x86)/MiKTeX 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defining Unicode char U+00E4 (decimal 228) + defining Unicode char U+00E5 (decimal 229) + defining Unicode char U+00E6 (decimal 230) + defining Unicode char U+00E7 (decimal 231) + defining Unicode char U+00E8 (decimal 232) + defining Unicode char U+00E9 (decimal 233) + defining Unicode char U+00EA (decimal 234) + defining Unicode char U+00EB (decimal 235) + defining Unicode char U+00EC (decimal 236) + defining Unicode char U+00ED (decimal 237) + defining Unicode char U+00EE (decimal 238) + defining Unicode char U+00EF (decimal 239) + defining Unicode char U+00F0 (decimal 240) + defining Unicode char U+00F1 (decimal 241) + defining Unicode char U+00F2 (decimal 242) + defining Unicode char U+00F3 (decimal 243) + defining Unicode char U+00F4 (decimal 244) + defining Unicode char U+00F5 (decimal 245) + defining Unicode char U+00F6 (decimal 246) + defining Unicode char U+00F8 (decimal 248) + defining Unicode char U+00F9 (decimal 249) + defining Unicode char U+00FA (decimal 250) + defining Unicode char U+00FB (decimal 251) + defining Unicode char U+00FC (decimal 252) + defining Unicode char U+00FD (decimal 253) + defining Unicode char U+00FE (decimal 254) + defining Unicode char U+00FF (decimal 255) + defining Unicode char U+0100 (decimal 256) + defining Unicode char U+0101 (decimal 257) + defining Unicode char U+0102 (decimal 258) + defining Unicode char U+0103 (decimal 259) + defining Unicode char U+0104 (decimal 260) + defining Unicode char U+0105 (decimal 261) + defining Unicode char U+0106 (decimal 262) + defining Unicode char U+0107 (decimal 263) + defining Unicode char U+0108 (decimal 264) + defining Unicode char U+0109 (decimal 265) + defining Unicode char U+010A (decimal 266) + defining Unicode char U+010B (decimal 267) + defining Unicode char U+010C (decimal 268) + defining Unicode char U+010D (decimal 269) + defining Unicode char U+010E (decimal 270) + defining Unicode char U+010F (decimal 271) + defining Unicode char U+0110 (decimal 272) + defining Unicode char U+0111 (decimal 273) + defining Unicode char U+0112 (decimal 274) + defining Unicode char U+0113 (decimal 275) + defining Unicode char U+0114 (decimal 276) + defining Unicode char U+0115 (decimal 277) + defining Unicode char U+0116 (decimal 278) + defining Unicode char U+0117 (decimal 279) + defining Unicode char U+0118 (decimal 280) + defining Unicode char U+0119 (decimal 281) + defining Unicode char U+011A (decimal 282) + defining Unicode char U+011B (decimal 283) + defining Unicode char U+011C (decimal 284) + defining Unicode char U+011D (decimal 285) + defining Unicode char U+011E (decimal 286) + defining Unicode char U+011F (decimal 287) + defining Unicode char U+0120 (decimal 288) + defining Unicode char U+0121 (decimal 289) + defining Unicode char U+0122 (decimal 290) + defining Unicode char U+0123 (decimal 291) + defining Unicode char U+0124 (decimal 292) + defining Unicode char U+0125 (decimal 293) + defining Unicode char U+0128 (decimal 296) + defining Unicode char 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345) + defining Unicode char U+015A (decimal 346) + defining Unicode char U+015B (decimal 347) + defining Unicode char U+015C (decimal 348) + defining Unicode char U+015D (decimal 349) + defining Unicode char U+015E (decimal 350) + defining Unicode char U+015F (decimal 351) + defining Unicode char U+0160 (decimal 352) + defining Unicode char U+0161 (decimal 353) + defining Unicode char U+0162 (decimal 354) + defining Unicode char U+0163 (decimal 355) + defining Unicode char U+0164 (decimal 356) + defining Unicode char U+0165 (decimal 357) + defining Unicode char U+0168 (decimal 360) + defining Unicode char U+0169 (decimal 361) + defining Unicode char U+016A (decimal 362) + defining Unicode char U+016B (decimal 363) + defining Unicode char U+016C (decimal 364) + defining Unicode char U+016D (decimal 365) + defining Unicode char U+016E (decimal 366) + defining Unicode char U+016F (decimal 367) + defining Unicode char U+0170 (decimal 368) + defining Unicode char U+0171 (decimal 369) + defining Unicode char U+0172 (decimal 370) + defining Unicode char U+0173 (decimal 371) + defining Unicode char U+0174 (decimal 372) + defining Unicode char U+0175 (decimal 373) + defining Unicode char U+0176 (decimal 374) + defining Unicode char U+0177 (decimal 375) + defining Unicode char U+0178 (decimal 376) + defining Unicode char U+0179 (decimal 377) + defining Unicode char U+017A (decimal 378) + defining Unicode char U+017B (decimal 379) + defining Unicode char U+017C (decimal 380) + defining Unicode char U+017D (decimal 381) + defining Unicode char U+017E (decimal 382) + defining Unicode char U+01CD (decimal 461) + defining Unicode char U+01CE (decimal 462) + defining Unicode char U+01CF (decimal 463) + defining Unicode char U+01D0 (decimal 464) + defining Unicode char U+01D1 (decimal 465) + defining Unicode char U+01D2 (decimal 466) + defining Unicode char U+01D3 (decimal 467) + defining Unicode char U+01D4 (decimal 468) + defining Unicode char U+01E2 (decimal 482) + defining Unicode char U+01E3 (decimal 483) + defining Unicode char U+01E6 (decimal 486) + defining Unicode char U+01E7 (decimal 487) + defining Unicode char U+01E8 (decimal 488) + defining Unicode char U+01E9 (decimal 489) + defining Unicode char U+01EA (decimal 490) + defining Unicode char U+01EB (decimal 491) + defining Unicode char U+01F0 (decimal 496) + defining Unicode char U+01F4 (decimal 500) + defining Unicode char U+01F5 (decimal 501) + defining Unicode char U+0218 (decimal 536) + defining Unicode char U+0219 (decimal 537) + defining Unicode char U+021A (decimal 538) + defining Unicode char U+021B (decimal 539) + defining Unicode char U+1E02 (decimal 7682) + defining Unicode char U+1E03 (decimal 7683) + defining Unicode char U+200C (decimal 8204) + defining Unicode char U+2010 (decimal 8208) + defining Unicode char U+2011 (decimal 8209) + defining Unicode char U+2012 (decimal 8210) + defining Unicode char U+2013 (decimal 8211) + defining Unicode char U+2014 (decimal 8212) + defining Unicode char U+2015 (decimal 8213) + defining Unicode char U+2018 (decimal 8216) + defining Unicode char U+2019 (decimal 8217) + defining Unicode char U+201A (decimal 8218) + defining Unicode char U+201C (decimal 8220) + defining Unicode char U+201D (decimal 8221) + defining Unicode char U+201E (decimal 8222) + defining Unicode char U+2030 (decimal 8240) + defining Unicode char U+2031 (decimal 8241) + defining Unicode char U+2039 (decimal 8249) + defining Unicode char U+203A (decimal 8250) + defining Unicode char U+2423 (decimal 9251) +) +Now handling font encoding OT1 ... +... processing UTF-8 mapping file for font encoding OT1 + +("C:\Program Files (x86)\MiKTeX 2.9\tex\latex\base\ot1enc.dfu" +File: ot1enc.dfu 2016/02/28 v1.1s UTF-8 support for inputenc + defining Unicode char U+00A0 (decimal 160) + defining Unicode char U+00A1 (decimal 161) + defining Unicode char U+00A3 (decimal 163) + defining Unicode char U+00AD (decimal 173) + defining Unicode char U+00B8 (decimal 184) + defining 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char U+021A (decimal 538) + defining Unicode char U+021B (decimal 539) + defining Unicode char U+2013 (decimal 8211) + defining Unicode char U+2014 (decimal 8212) + defining Unicode char U+2018 (decimal 8216) + defining Unicode char U+2019 (decimal 8217) + defining Unicode char U+201C (decimal 8220) + defining Unicode char U+201D (decimal 8221) +) +Now handling font encoding OMS ... +... processing UTF-8 mapping file for font encoding OMS + +("C:\Program Files (x86)\MiKTeX 2.9\tex\latex\base\omsenc.dfu" +File: omsenc.dfu 2016/02/28 v1.1s UTF-8 support for inputenc + defining Unicode char U+00A7 (decimal 167) + defining Unicode char U+00B6 (decimal 182) + defining Unicode char U+00B7 (decimal 183) + defining Unicode char U+2020 (decimal 8224) + defining Unicode char U+2021 (decimal 8225) + defining Unicode char U+2022 (decimal 8226) +) +Now handling font encoding OMX ... +... no UTF-8 mapping file for font encoding OMX +Now handling font encoding U ... +... no UTF-8 mapping file for 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0000000..811a3bd Binary files /dev/null and b/calculus/main.pdf differ diff --git a/calculus/main.synctex.gz b/calculus/main.synctex.gz new file mode 100644 index 0000000..c16d6af Binary files /dev/null and b/calculus/main.synctex.gz differ diff --git a/calculus/main.tex b/calculus/main.tex new file mode 100644 index 0000000..38cacf3 --- /dev/null +++ b/calculus/main.tex @@ -0,0 +1,55 @@ +\documentclass[10pt]{article} +\input{preambolo.tex} + +% \usepackage{tikz} + +\newcommand{\true}{\operatorname{tt}} +\newcommand{\false}{\operatorname{ff}} + +\newcommand{\ddef}{\mathrel{::=}} +\newcommand{\semi}{\mathrel{;}} + +\newtheorem{example}[theorem]{Example} + + + +\begin{document} + +Terms: +\[t, u \ddef x \mid t\,u \mid \lambda x.\, t\] + +Fireballs, inerts and normal forms: + +\[\begin{array}{lll} +f & \ddef & x \mid i \mid \lambda x.\, t \\ +i & \ddef & x\,F_1\cdots F_n \\ +F & \ddef & K\langle f\rangle \\ +\end{array}\] + +Contexts $K$: +\[K \ddef [\,] \mid i \semi K\] + + +\[\begin{array}{lll} + K_1\langle\lambda x.\,t\rangle \, K_2\langle \lambda y.\, u\rangle & + \mapsto_{\beta_\lambda} & + K_1\langle K_2\langle t\{x\leftarrow \lambda y.\, u\}\rangle\rangle +\\ + K_1\langle\lambda x.\,t\rangle \, K_2\langle y \,\,\,\,\,\,\,\,\,\,\rangle & + \mapsto_{\beta_v} & + K_1\langle K_2\langle t\{x\leftarrow y\}\rangle\rangle +\\ + K_1\langle\lambda x.\,t\rangle \, K_2\langle i\,\,\,\,\,\,\,\,\,\,\,\rangle & + \mapsto_{\beta_i} & + \begin{cases} + K_1\langle K_2\langle t\{x\leftarrow i\}\rangle\rangle & + \text{ if } x \text{ occurs in } t \\ + K_1\langle K_2\langle i \semi t\rangle\rangle & + \text{ otherwise } \\ + \end{cases} +\end{array}\] + +Evaluation contexts $E$: +\[E \ddef [\,] \mid t\,E \mid E\,t\] + +\end{document} diff --git a/calculus/preambolo.tex b/calculus/preambolo.tex new file mode 100644 index 0000000..c7d653e --- /dev/null +++ b/calculus/preambolo.tex @@ -0,0 +1,20 @@ +\usepackage[english]{babel} +\usepackage[utf8]{inputenc} +\usepackage{amsmath, amsthm, amssymb} +\usepackage[ruled,vlined]{algorithm2e} +\usepackage{verbatim} +\usepackage{xcolor} +\usepackage{stmaryrd} +\usepackage[normalem]{ulem} + +% \theoremstyle{definition} +\newtheorem{theorem}{Theorem} +\newtheorem{lemma}[theorem]{Lemma} +% \newtheorem{corollary}[theorem]{Corollary} +\newtheorem{notation}[theorem]{Notation} +\newtheorem{definition}[theorem]{Definition} +\newtheorem{fact}[theorem]{Fact} + + + +\newcommand{\commento}[1]{\textcolor{orange}{#1}}