helm/www/lambdadelta/basic_2.html

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  10     <title>lambdadelta version 2</title>
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  22     <div class="head1">cic:/matita/lambdadelta/basic_2/ (λδ version 2)</div>
  23     <div class="spacer">
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  25     </div>
  26    <div xmlns:ld="http://lambdadelta.info/" class="head2">System's Syntax and Behavior</div>
  27    <div xmlns:ld="http://lambdadelta.info/" class="text">This is a summary of the "block structure"
  28          of the System's syntactic items and reductions.
  29    </div>
  30    <div xmlns:ld="http://lambdadelta.info/" class="text">
  31       <table cellpadding="4" cellspacing="0">
  32         <tbody>
  33           <tr>
  34             <td class="snns text grey">domain</td>
  35             <td class="snns plane grey">block</td>
  36             <td class="snns text grey">leader</td>
  37             <td class="snns text grey">applicator (with →θ)*</td>
  38             <td class="snns text grey">reduction</td>
  39             <td class="snns text grey">→ζ *</td>
  40             <td class="ssns text grey">reference *</td>
  41           </tr>
  42           <tr>
  43             <td class="snns text">{X | Γ ⊢ X : W}</td>
  44             <td class="snns plane wine">local typed abstraction *</td>
  45             <td class="snns text wine">Γ ⊢ +λW</td>
  46             <td class="snns text wine">ⓐV</td>
  47             <td class="snns text wine">→β</td>
  48             <td class="snns text wine">no</td>
  49             <td class="ssns text wine">#i</td>
  50           </tr>
  51           <tr>
  52             <td class="nnns text">
  53               <br />
  54             </td>
  55             <td class="snns plane magenta">local typed declaration **</td>
  56             <td class="snns text magenta">Γ ⊢ -λW</td>
  57             <td class="snns text magenta">ⓐV</td>
  58             <td class="snns text magenta">→β</td>
  59             <td class="snns text magenta">no</td>
  60             <td class="ssns text magenta">#i</td>
  61           </tr>
  62           <tr>
  63             <td class="nnns text">
  64               <br />
  65             </td>
  66             <td class="snns plane prune">global typed declaration ***</td>
  67             <td class="snns text prune">Γ ⊢ pλW</td>
  68             <td class="snns text prune">no</td>
  69             <td class="snns text prune">no</td>
  70             <td class="snns text prune">no</td>
  71             <td class="ssns text prune">$p</td>
  72           </tr>
  73           <tr>
  74             <td class="nnns text">
  75               <br />
  76             </td>
  77             <td class="snns plane blue">native type annotation *</td>
  78             <td class="snns text blue">Γ ⊢ ⓝW</td>
  79             <td class="snns text blue">no</td>
  80             <td class="snns text blue">no</td>
  81             <td class="snns text blue">yes</td>
  82             <td class="ssns text blue">no</td>
  83           </tr>
  84           <tr>
  85             <td class="snns text">{X | Γ ⊢ X = V}</td>
  86             <td class="snns plane sky">local abbreviation *</td>
  87             <td class="snns text sky">Γ ⊢ +δV</td>
  88             <td class="snns text sky">no</td>
  89             <td class="snns text sky">local →δ</td>
  90             <td class="snns text sky">yes</td>
  91             <td class="ssns text sky">#i</td>
  92           </tr>
  93           <tr>
  94             <td class="nnns text">
  95               <br />
  96             </td>
  97             <td class="snns plane cyan">local definition **</td>
  98             <td class="snns text cyan">Γ ⊢ -δV</td>
  99             <td class="snns text cyan">no</td>
 100             <td class="snns text cyan">local →δ</td>
 101             <td class="snns text cyan">no</td>
 102             <td class="ssns text cyan">#i</td>
 103           </tr>
 104           <tr>
 105             <td class="nnns text">
 106               <br />
 107             </td>
 108             <td class="snns plane water">global definition ***</td>
 109             <td class="snns text water">Γ ⊢ pδV</td>
 110             <td class="snns text water">no</td>
 111             <td class="snns text water">global →δ</td>
 112             <td class="snns text water">no</td>
 113             <td class="ssns text water">$p</td>
 114           </tr>
 115           <tr>
 116             <td class="snss text">no</td>
 117             <td class="snss plane green">sort ****</td>
 118             <td class="snss text green">Γ ⊢ ⋆k</td>
 119             <td class="snss text green">no</td>
 120             <td class="snss text green">no</td>
 121             <td class="snss text green">no</td>
 122             <td class="ssss text green">no</td>
 123           </tr>
 124         </tbody>
 125       </table>
 126     </div>
 127    <div xmlns:ld="http://lambdadelta.info/" class="text">* In terms only.
 128          ** In terms and local environments only.
 129          *** In global environments only.
 130          **** Sort level k in terms only.
 131    </div>
 132
 133    <div xmlns:ld="http://lambdadelta.info/" class="head2">Summary of the Specification</div>
 134    <div xmlns:ld="http://lambdadelta.info/" class="text">Here is a numerical acount of the specification's contents
 135          and its timeline.
 136          Nodes are counted according to the "intrinsinc complexity measure"
 137          [F. Guidi: "Procedural Representation of CIC Proof Terms"
 138          Journal of Automated Reasoning 44(1-2), Springer (February 2010),
 139          pp. 53-78].
 140    </div>
 141    <div xmlns:ld="http://lambdadelta.info/" class="text">
 142       <table cellpadding="4" cellspacing="0">
 143         <tbody>
 144           <tr>
 145             <td class="snns component grey">category</td>
 146             <td class="snns plane grey">objects</td>
 147             <td class="snnn number grey">
 148               <br />
 149             </td>
 150             <td class="snnn plane grey">
 151               <br />
 152             </td>
 153             <td class="snnn number grey">
 154               <br />
 155             </td>
 156             <td class="snnn plane grey">
 157               <br />
 158             </td>
 159             <td class="ssnn number grey">
 160               <br />
 161             </td>
 162           </tr>
 163           <tr>
 164             <td class="snns component cyan">sizes</td>
 165             <td class="snns plane cyan">files</td>
 166             <td class="snnn number cyan">247  </td>
 167             <td class="snns plane cyan">characters</td>
 168             <td class="snnn number cyan">350287</td>
 169             <td class="snns plane cyan">nodes</td>
 170             <td class="ssnn number cyan">1035865</td>
 171           </tr>
 172           <tr>
 173             <td class="snns component green">propositions</td>
 174             <td class="snns plane green">theorems</td>
 175             <td class="snnn number green">76</td>
 176             <td class="snns plane green">lemmas</td>
 177             <td class="snnn number green">748</td>
 178             <td class="snns plane green">total</td>
 179             <td class="ssnn number green">824</td>
 180           </tr>
 181           <tr>
 182             <td class="snss component yellow">concepts</td>
 183             <td class="snss plane yellow">declared</td>
 184             <td class="snsn number yellow">41</td>
 185             <td class="snss plane yellow">defined</td>
 186             <td class="snsn number yellow">77</td>
 187             <td class="snss plane yellow">total</td>
 188             <td class="sssn number yellow">118</td>
 189           </tr>
 190         </tbody>
 191       </table>
 192     </div>
 193    <ul xmlns:ld="http://lambdadelta.info/">
 194       <li>
 195         <span class="date">In progress.</span>
 196          Context-sensitive subject equivalence
 197          for native type assignment.
 198    </li>
 199     </ul>
 200    <ul xmlns:ld="http://lambdadelta.info/">
 201       <li>
 202         <span class="date">In progress.</span>
 203          Closure of context-sensitive extended computation
 204          for native validity.
 205    </li>
 206     </ul>
 207    <ul xmlns:ld="http://lambdadelta.info/">
 208       <li>
 209         <span class="date">In progress.</span>
 210          Passive support for global environments.
 211    </li>
 212     </ul>
 213    <ul xmlns:ld="http://lambdadelta.info/">
 214       <li>
 215         <span class="date">2013 July 27.</span>
 216          Reaxiomatized β-reductum as in extended β-reduction
 217    </li>
 218     </ul>
 219    <ul xmlns:ld="http://lambdadelta.info/">
 220       <li>
 221         <span class="date">2013 July 20.</span>
 222          Context-sensitive extended strong normalization
 223          for simply typed terms.
 224    </li>
 225     </ul>
 226    <ul xmlns:ld="http://lambdadelta.info/">
 227       <li>
 228         <span class="date">2013 April 16.</span>
 229          Reaxiomatized substitution and reduction
 230          commute with respect to subclosure
 231          (anniversary milestone).
 232    </li>
 233     </ul>
 234    <ul xmlns:ld="http://lambdadelta.info/">
 235       <li>
 236         <span class="date">2013 March 16.</span>
 237          Mutual recursive preservation of stratified native validity
 238          for hyper computation on closures.
 239    </li>
 240     </ul>
 241    <ul xmlns:ld="http://lambdadelta.info/">
 242       <li>
 243         <span class="date">2012 October 16.</span>
 244          Confluence for context-free parallel reduction on closures.
 245    </li>
 246     </ul>
 247    <ul xmlns:ld="http://lambdadelta.info/">
 248       <li>
 249         <span class="date">2012 July 26.</span>
 250          Term binders polarized to control ζ-reduction.
 251    </li>
 252     </ul>
 253    <ul xmlns:ld="http://lambdadelta.info/">
 254       <li>
 255         <span class="date">2012 April 16.</span>
 256          Context-sensitive subject equivalence
 257          for atomic arity assignment
 258          (anniversary milestone).
 259    </li>
 260     </ul>
 261    <ul xmlns:ld="http://lambdadelta.info/">
 262       <li>
 263         <span class="date">2012 March 15.</span>
 264          Context-sensitive strong normalization
 265          for simply typed terms.
 266    </li>
 267     </ul>
 268    <ul xmlns:ld="http://lambdadelta.info/">
 269       <li>
 270         <span class="date">2012 January 27.</span>
 271          Support for abstract candidates of reducibility.
 272    </li>
 273     </ul>
 274    <ul xmlns:ld="http://lambdadelta.info/">
 275       <li>
 276         <span class="date">2011 September 21.</span>
 277          Confluence for context-sensitive parallel reduction on terms.
 278    </li>
 279     </ul>
 280    <ul xmlns:ld="http://lambdadelta.info/">
 281       <li>
 282         <span class="date">2011 September 6.</span>
 283          Confluence for context-free parallel reduction on terms.
 284    </li>
 285     </ul>
 286    <ul xmlns:ld="http://lambdadelta.info/">
 287       <li>
 288         <span class="date">2011 April 17.</span>
 289          Specification starts.
 290    </li>
 291     </ul>
 292
 293    <div xmlns:ld="http://lambdadelta.info/" class="head2">Logical Structure of the Specification</div>
 294    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in planes and components
 295          according to the following table.
 296          A notation file covering the whole specification is provided.
 297          The notation for the relations or functions introduced in each file
 298          is shown in parentheses (? are placeholders).
 299    </div>
 300    <div xmlns:ld="http://lambdadelta.info/" class="text">
 301       <table cellpadding="4" cellspacing="0">
 302         <tbody>
 303           <tr>
 304             <td class="snns component grey">component</td>
 305             <td class="snns plane grey">plane</td>
 306             <td class="snns file grey">files</td>
 307             <td class="snnn file grey">
 308               <br />
 309             </td>
 310             <td class="snnn file grey">
 311               <br />
 312             </td>
 313             <td class="ssnn file grey">
 314               <br />
 315             </td>
 316           </tr>
 317           <tr>
 318             <td class="snns component prune">dynamic typing</td>
 319             <td class="snns plane prune">"big tree" parallel computation</td>
 320             <td class="snns file prune">yprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )</td>
 321             <td class="snnn file prune">yprs_yprs</td>
 322             <td class="snnn file prune">ygt ( ? ⊢ ⦃?,?⦄ &gt;[g] ⦃?,?⦄ )</td>
 323             <td class="ssnn file prune">ygt_ygt</td>
 324           </tr>
 325           <tr>
 326             <td class="nnns component prune">
 327               <br />
 328             </td>
 329             <td class="snns plane prune">"big tree" parallel reduction</td>
 330             <td class="snns file prune">ypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )</td>
 331             <td class="snnn file prune">ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ )</td>
 332             <td class="snnn file prune">
 333               <br />
 334             </td>
 335             <td class="ssnn file prune">
 336               <br />
 337             </td>
 338           </tr>
 339           <tr>
 340             <td class="nnns component prune">
 341               <br />
 342             </td>
 343             <td class="snns plane prune">local env. ref. for stratified native validity</td>
 344             <td class="snns file prune">lsubsv ( ? ⊢ ? ¡⊑[?] ? )</td>
 345             <td class="snnn file prune">lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv</td>
 346             <td class="snnn file prune">
 347               <br />
 348             </td>
 349             <td class="ssnn file prune">
 350               <br />
 351             </td>
 352           </tr>
 353           <tr>
 354             <td class="nnns component prune">
 355               <br />
 356             </td>
 357             <td class="snns plane prune">stratified native validity</td>
 358             <td class="snns file prune">snv ( ⦃?,?⦄ ⊢ ? ¡[?] )</td>
 359             <td class="snnn file prune">snv_lift snv_aaa snv_ssta snv_sstas snv_ssta_lpr snv_lpr snv_cpcs</td>
 360             <td class="snnn file prune">
 361               <br />
 362             </td>
 363             <td class="ssnn file prune">
 364               <br />
 365             </td>
 366           </tr>
 367           <tr>
 368             <td class="snns component blue">equivalence</td>
 369             <td class="snns plane blue">context-sensitive equivalence</td>
 370             <td class="snns file blue">cpcs ( ? ⊢ ? ⬌* ? )</td>
 371             <td class="snnn file blue">cpcs_aaa cpcs_cprs cpcs_cpcs</td>
 372             <td class="snnn file blue">
 373               <br />
 374             </td>
 375             <td class="ssnn file blue">
 376               <br />
 377             </td>
 378           </tr>
 379           <tr>
 380             <td class="snns component sky">conversion</td>
 381             <td class="snns plane sky">context-sensitive conversion</td>
 382             <td class="snns file sky">cpc ( ? ⊢ ? ⬌ ? )</td>
 383             <td class="snnn file sky">cpc_cpc</td>
 384             <td class="snnn file sky">
 385               <br />
 386             </td>
 387             <td class="ssnn file sky">
 388               <br />
 389             </td>
 390           </tr>
 391           <tr>
 392             <td class="snns component cyan">computation</td>
 393             <td class="snns plane cyan">context-sensitive extended evaluation</td>
 394             <td class="snns file cyan">cpxe ( ⦃?,?⦄ ⊢ ➡*[?] 𝐍⦃?⦄ )</td>
 395             <td class="snnn file cyan">
 396               <br />
 397             </td>
 398             <td class="snnn file cyan">
 399               <br />
 400             </td>
 401             <td class="ssnn file cyan">
 402               <br />
 403             </td>
 404           </tr>
 405           <tr>
 406             <td class="nnns component cyan">
 407               <br />
 408             </td>
 409             <td class="snns plane cyan">context-sensitive evaluation</td>
 410             <td class="snns file cyan">cpre ( ? ⊢ ➡* 𝐍⦃?⦄ )</td>
 411             <td class="snnn file cyan">cpre_cpre</td>
 412             <td class="snnn file cyan">
 413               <br />
 414             </td>
 415             <td class="ssnn file cyan">
 416               <br />
 417             </td>
 418           </tr>
 419           <tr>
 420             <td class="nnns component cyan">
 421               <br />
 422             </td>
 423             <td class="snns plane cyan">strongly normalizing computation</td>
 424             <td class="snns file cyan">csn_vector ( ? ⊢ ⬊* ? )</td>
 425             <td class="snnn file cyan">csn_tstc_vector csn_aaa</td>
 426             <td class="snnn file cyan">
 427               <br />
 428             </td>
 429             <td class="ssnn file cyan">
 430               <br />
 431             </td>
 432           </tr>
 433           <tr>
 434             <td class="nnns component cyan">
 435               <br />
 436             </td>
 437             <td class="nnns plane cyan">
 438               <br />
 439             </td>
 440             <td class="snns file cyan">csn ( ? ⊢ ⬊* ? )</td>
 441             <td class="snnn file cyan">csn_alt ( ? ⊢ ⬊⬊* ? )</td>
 442             <td class="snnn file cyan">csn_lift csn_lpx</td>
 443             <td class="ssnn file cyan">
 444               <br />
 445             </td>
 446           </tr>
 447           <tr>
 448             <td class="nnns component cyan">
 449               <br />
 450             </td>
 451             <td class="snns plane cyan">decomposed extended computation</td>
 452             <td class="snns file cyan">dxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )</td>
 453             <td class="snnn file cyan">dxprs_lift dxprs_aaa dxprs_dxprs</td>
 454             <td class="snnn file cyan">
 455               <br />
 456             </td>
 457             <td class="ssnn file cyan">
 458               <br />
 459             </td>
 460           </tr>
 461           <tr>
 462             <td class="nnns component cyan">
 463               <br />
 464             </td>
 465             <td class="snns plane cyan">context-sensitive extended computation</td>
 466             <td class="snns file cyan">lpxs ( ⦃?,?⦄ ⊢ ➡*[?] ? )</td>
 467             <td class="snnn file cyan">lpxs_alt ( ⦃?,?⦄ ⊢ ➡➡*[?] ? )</td>
 468             <td class="snnn file cyan">lpxs_ldrop lpxs_aaa lpxs_cpxs lpxs_lpxs</td>
 469             <td class="ssnn file cyan">
 470               <br />
 471             </td>
 472           </tr>
 473           <tr>
 474             <td class="nnns component cyan">
 475               <br />
 476             </td>
 477             <td class="nnns plane cyan">
 478               <br />
 479             </td>
 480             <td class="snns file cyan">cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?] ? )</td>
 481             <td class="snnn file cyan">cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_aaa cpxs_cpxs</td>
 482             <td class="snnn file cyan">
 483               <br />
 484             </td>
 485             <td class="ssnn file cyan">
 486               <br />
 487             </td>
 488           </tr>
 489           <tr>
 490             <td class="nnns component cyan">
 491               <br />
 492             </td>
 493             <td class="snns plane cyan">context-sensitive computation</td>
 494             <td class="snns file cyan">lprs ( ? ⊢ ➡* ? )</td>
 495             <td class="snnn file cyan">lprs_alt ( ? ⊢ ➡➡* ? )</td>
 496             <td class="snnn file cyan">lprs_ldrop lprs_cprs lprs_lprs</td>
 497             <td class="ssnn file cyan">
 498               <br />
 499             </td>
 500           </tr>
 501           <tr>
 502             <td class="nnns component cyan">
 503               <br />
 504             </td>
 505             <td class="nnns plane cyan">
 506               <br />
 507             </td>
 508             <td class="snns file cyan">cprs ( ? ⊢ ? ➡* ?)</td>
 509             <td class="snnn file cyan">cprs_lift cprs_cprs</td>
 510             <td class="snnn file cyan">
 511               <br />
 512             </td>
 513             <td class="ssnn file cyan">
 514               <br />
 515             </td>
 516           </tr>
 517           <tr>
 518             <td class="nnns component cyan">
 519               <br />
 520             </td>
 521             <td class="snns plane cyan">local env. ref. for abstract candidates of reducibility</td>
 522             <td class="snns file cyan">lsubc ( ? ⊑[?] ? )</td>
 523             <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
 524             <td class="snnn file cyan">
 525               <br />
 526             </td>
 527             <td class="ssnn file cyan">
 528               <br />
 529             </td>
 530           </tr>
 531           <tr>
 532             <td class="nnns component cyan">
 533               <br />
 534             </td>
 535             <td class="snns plane cyan">support for abstract computation properties</td>
 536             <td class="snns file cyan">acp</td>
 537             <td class="snnn file cyan">acp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )</td>
 538             <td class="snnn file cyan">acp_aaa</td>
 539             <td class="ssnn file cyan">
 540               <br />
 541             </td>
 542           </tr>
 543           <tr>
 544             <td class="snns component water">reduction</td>
 545             <td class="snns plane water">context-sensitive extended normal forms</td>
 546             <td class="snns file water">cnx ( ⦃?,?⦄ ⊢ 𝐍[?]⦃?⦄ )</td>
 547             <td class="snnn file water">cnx_lift cnx_crx cnx_cix</td>
 548             <td class="snnn file water">
 549               <br />
 550             </td>
 551             <td class="ssnn file water">
 552               <br />
 553             </td>
 554           </tr>
 555           <tr>
 556             <td class="nnns component water">
 557               <br />
 558             </td>
 559             <td class="snns plane water">context-sensitive extended reduction</td>
 560             <td class="snns file water">lpx ( ⦃?,?⦄ ⊢ ➡[?] ? )</td>
 561             <td class="snnn file water">lpx_ldrop lpx_aaa</td>
 562             <td class="snnn file water">
 563               <br />
 564             </td>
 565             <td class="ssnn file water">
 566               <br />
 567             </td>
 568           </tr>
 569           <tr>
 570             <td class="nnns component water">
 571               <br />
 572             </td>
 573             <td class="nnns plane water">
 574               <br />
 575             </td>
 576             <td class="snns file water">cpx ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
 577             <td class="snnn file water">cpx_lift cpx_cix</td>
 578             <td class="snnn file water">
 579               <br />
 580             </td>
 581             <td class="ssnn file water">
 582               <br />
 583             </td>
 584           </tr>
 585           <tr>
 586             <td class="nnns component water">
 587               <br />
 588             </td>
 589             <td class="snns plane water">context-sensitive extended irreducible forms</td>
 590             <td class="snns file water">cix ( ⦃?,?⦄ ⊢ 𝐈[?]⦃?⦄ )</td>
 591             <td class="snnn file water">cix_append cix_lift</td>
 592             <td class="snnn file water">
 593               <br />
 594             </td>
 595             <td class="ssnn file water">
 596               <br />
 597             </td>
 598           </tr>
 599           <tr>
 600             <td class="nnns component water">
 601               <br />
 602             </td>
 603             <td class="snns plane water">context-sensitive extended reducible forms</td>
 604             <td class="snns file water">crx ( ⦃?,?⦄ ⊢ 𝐑[?]⦃?⦄ )</td>
 605             <td class="snnn file water">crx_append crx_lift</td>
 606             <td class="snnn file water">
 607               <br />
 608             </td>
 609             <td class="ssnn file water">
 610               <br />
 611             </td>
 612           </tr>
 613           <tr>
 614             <td class="nnns component water">
 615               <br />
 616             </td>
 617             <td class="snns plane water">context-sensitive normal forms</td>
 618             <td class="snns file water">cnr ( ? ⊢ 𝐍⦃?⦄ )</td>
 619             <td class="snnn file water">cnr_lift cnr_crr cnr_cir</td>
 620             <td class="snnn file water">
 621               <br />
 622             </td>
 623             <td class="ssnn file water">
 624               <br />
 625             </td>
 626           </tr>
 627           <tr>
 628             <td class="nnns component water">
 629               <br />
 630             </td>
 631             <td class="snns plane water">context-sensitive reduction</td>
 632             <td class="snns file water">lpr ( ? ⊢ ➡ ? )</td>
 633             <td class="snnn file water">lpr_ldrop lpr_lpr</td>
 634             <td class="snnn file water">
 635               <br />
 636             </td>
 637             <td class="ssnn file water">
 638               <br />
 639             </td>
 640           </tr>
 641           <tr>
 642             <td class="nnns component water">
 643               <br />
 644             </td>
 645             <td class="nnns plane water">
 646               <br />
 647             </td>
 648             <td class="snns file water">cpr ( ? ⊢ ? ➡ ? )</td>
 649             <td class="snnn file water">cpr_lift cpr_cir</td>
 650             <td class="snnn file water">
 651               <br />
 652             </td>
 653             <td class="ssnn file water">
 654               <br />
 655             </td>
 656           </tr>
 657           <tr>
 658             <td class="nnns component water">
 659               <br />
 660             </td>
 661             <td class="snns plane water">context-sensitive irreducible forms</td>
 662             <td class="snns file water">cir ( ? ⊢ 𝐈⦃?⦄ )</td>
 663             <td class="snnn file water">cir_append cir_lift</td>
 664             <td class="snnn file water">
 665               <br />
 666             </td>
 667             <td class="ssnn file water">
 668               <br />
 669             </td>
 670           </tr>
 671           <tr>
 672             <td class="nnns component water">
 673               <br />
 674             </td>
 675             <td class="snns plane water">context-sensitive reducible forms</td>
 676             <td class="snns file water">crr ( ? ⊢ 𝐑⦃?⦄ )</td>
 677             <td class="snnn file water">crr_append crr_lift</td>
 678             <td class="snnn file water">
 679               <br />
 680             </td>
 681             <td class="ssnn file water">
 682               <br />
 683             </td>
 684           </tr>
 685           <tr>
 686             <td class="snns component green">unfold</td>
 687             <td class="snns plane green">unfold</td>
 688             <td class="snns file green">unfold ( ? ⊢ ? ⧫* ? )</td>
 689             <td class="snnn file green">
 690               <br />
 691             </td>
 692             <td class="snnn file green">
 693               <br />
 694             </td>
 695             <td class="ssnn file green">
 696               <br />
 697             </td>
 698           </tr>
 699           <tr>
 700             <td class="nnns component green">
 701               <br />
 702             </td>
 703             <td class="snns plane green">iterated stratified static type assignment</td>
 704             <td class="snns file green">sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )</td>
 705             <td class="snnn file green">sstas_lift sstas_aaa sstas_sstas</td>
 706             <td class="snnn file green">
 707               <br />
 708             </td>
 709             <td class="ssnn file green">
 710               <br />
 711             </td>
 712           </tr>
 713           <tr>
 714             <td class="snns component grass">static typing</td>
 715             <td class="snns plane grass">stratified static type assignment</td>
 716             <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
 717             <td class="snnn file grass">ssta_lift ssta_aaa ssta_ssta</td>
 718             <td class="snnn file grass">
 719               <br />
 720             </td>
 721             <td class="ssnn file grass">
 722               <br />
 723             </td>
 724           </tr>
 725           <tr>
 726             <td class="nnns component grass">
 727               <br />
 728             </td>
 729             <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
 730             <td class="snns file grass">lsuba ( ? ⁝⊑ ? )</td>
 731             <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
 732             <td class="snnn file grass">
 733               <br />
 734             </td>
 735             <td class="ssnn file grass">
 736               <br />
 737             </td>
 738           </tr>
 739           <tr>
 740             <td class="nnns component grass">
 741               <br />
 742             </td>
 743             <td class="snns plane grass">atomic arity assignment</td>
 744             <td class="snns file grass">aaa ( ? ⊢ ? ⁝ ? )</td>
 745             <td class="snnn file grass">aaa_lift aaa_lifts aaa_aaa</td>
 746             <td class="snnn file grass">
 747               <br />
 748             </td>
 749             <td class="ssnn file grass">
 750               <br />
 751             </td>
 752           </tr>
 753           <tr>
 754             <td class="nnns component grass">
 755               <br />
 756             </td>
 757             <td class="snns plane grass">parameters</td>
 758             <td class="snns file grass">sh</td>
 759             <td class="snnn file grass">sd</td>
 760             <td class="snnn file grass">
 761               <br />
 762             </td>
 763             <td class="ssnn file grass">
 764               <br />
 765             </td>
 766           </tr>
 767           <tr>
 768             <td class="snns component yellow">substitution</td>
 769             <td class="snns plane yellow">restricted local env. ref.</td>
 770             <td class="snns file yellow">lsubr ( ? ⊑ ? )</td>
 771             <td class="snnn file yellow">lsubr_lsubr</td>
 772             <td class="snnn file yellow">
 773               <br />
 774             </td>
 775             <td class="ssnn file yellow">
 776               <br />
 777             </td>
 778           </tr>
 779           <tr>
 780             <td class="nnns component yellow">
 781               <br />
 782             </td>
 783             <td class="snns plane yellow">iterated structural successor for closures</td>
 784             <td class="snns file yellow">fsups ( ⦃?,?⦄ ⊃* ⦃?,?⦄ )</td>
 785             <td class="snnn file yellow">fsups_fsups</td>
 786             <td class="snnn file yellow">
 787               <br />
 788             </td>
 789             <td class="ssnn file yellow">
 790               <br />
 791             </td>
 792           </tr>
 793           <tr>
 794             <td class="nnns component yellow">
 795               <br />
 796             </td>
 797             <td class="nnns plane yellow">
 798               <br />
 799             </td>
 800             <td class="snns file yellow">fsupp ( ⦃?,?⦄ ⊃+ ⦃?,?⦄ )</td>
 801             <td class="snnn file yellow">fsupp_fsupp</td>
 802             <td class="snnn file yellow">
 803               <br />
 804             </td>
 805             <td class="ssnn file yellow">
 806               <br />
 807             </td>
 808           </tr>
 809           <tr>
 810             <td class="nnns component yellow">
 811               <br />
 812             </td>
 813             <td class="snns plane yellow">generic local env. slicing</td>
 814             <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
 815             <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</td>
 816             <td class="snnn file yellow">
 817               <br />
 818             </td>
 819             <td class="ssnn file yellow">
 820               <br />
 821             </td>
 822           </tr>
 823           <tr>
 824             <td class="nnns component yellow">
 825               <br />
 826             </td>
 827             <td class="snns plane yellow">generic term relocation</td>
 828             <td class="snns file yellow">lifts_vector ( ⇧*[?] ? ≡ ? )</td>
 829             <td class="snnn file yellow">lifts_lift_vector</td>
 830             <td class="snnn file yellow">
 831               <br />
 832             </td>
 833             <td class="ssnn file yellow">
 834               <br />
 835             </td>
 836           </tr>
 837           <tr>
 838             <td class="nnns component yellow">
 839               <br />
 840             </td>
 841             <td class="nnns plane yellow">
 842               <br />
 843             </td>
 844             <td class="snns file yellow">lifts ( ⇧*[?] ? ≡ ? )</td>
 845             <td class="snnn file yellow">lifts_lift lifts_lifts</td>
 846             <td class="snnn file yellow">
 847               <br />
 848             </td>
 849             <td class="ssnn file yellow">
 850               <br />
 851             </td>
 852           </tr>
 853           <tr>
 854             <td class="nnns component yellow">
 855               <br />
 856             </td>
 857             <td class="snns plane yellow">support for generic relocation</td>
 858             <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
 859             <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
 860             <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
 861             <td class="ssnn file yellow">gr2_gr2</td>
 862           </tr>
 863           <tr>
 864             <td class="snns component orange">relocation</td>
 865             <td class="snns plane orange">structural successor for closures</td>
 866             <td class="snns file orange">fsup ( ⦃?,?⦄ ⊃ ⦃?,?⦄ )</td>
 867             <td class="snnn file orange">fsupq ( ⦃?,?⦄ ⊃⸮ ⦃?,?⦄ )</td>
 868             <td class="snnn file orange">fsupq_alt</td>
 869             <td class="ssnn file orange">
 870               <br />
 871             </td>
 872           </tr>
 873           <tr>
 874             <td class="nnns component orange">
 875               <br />
 876             </td>
 877             <td class="snns plane orange">global env. slicing</td>
 878             <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
 879             <td class="snnn file orange">gdrop_gdrop</td>
 880             <td class="snnn file orange">
 881               <br />
 882             </td>
 883             <td class="ssnn file orange">
 884               <br />
 885             </td>
 886           </tr>
 887           <tr>
 888             <td class="nnns component orange">
 889               <br />
 890             </td>
 891             <td class="snns plane orange">basic local env. slicing</td>
 892             <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
 893             <td class="snnn file orange">ldrop_append ldrop_lpx_sn ldrop_ldrop</td>
 894             <td class="snnn file orange">
 895               <br />
 896             </td>
 897             <td class="ssnn file orange">
 898               <br />
 899             </td>
 900           </tr>
 901           <tr>
 902             <td class="nnns component orange">
 903               <br />
 904             </td>
 905             <td class="snns plane orange">basic term relocation</td>
 906             <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
 907             <td class="snnn file orange">lift_lift_vector</td>
 908             <td class="snnn file orange">
 909               <br />
 910             </td>
 911             <td class="ssnn file orange">
 912               <br />
 913             </td>
 914           </tr>
 915           <tr>
 916             <td class="nnns component orange">
 917               <br />
 918             </td>
 919             <td class="nnns plane orange">
 920               <br />
 921             </td>
 922             <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
 923             <td class="snnn file orange">lift_lift</td>
 924             <td class="snnn file orange">
 925               <br />
 926             </td>
 927             <td class="ssnn file orange">
 928               <br />
 929             </td>
 930           </tr>
 931           <tr>
 932             <td class="snns component red">grammar</td>
 933             <td class="snns plane red">pointwise extension of a relation</td>
 934             <td class="snns file red">lpx_sn</td>
 935             <td class="snnn file red">lpx_sn_tc lpx_sn_lpx_sn</td>
 936             <td class="snnn file red">
 937               <br />
 938             </td>
 939             <td class="ssnn file red">
 940               <br />
 941             </td>
 942           </tr>
 943           <tr>
 944             <td class="nnns component red">
 945               <br />
 946             </td>
 947             <td class="snns plane red">same top term constructor</td>
 948             <td class="snns file red">tstc ( ? ≃ ? )</td>
 949             <td class="snnn file red">tstc_tstc tstc_vector</td>
 950             <td class="snnn file red">
 951               <br />
 952             </td>
 953             <td class="ssnn file red">
 954               <br />
 955             </td>
 956           </tr>
 957           <tr>
 958             <td class="nnns component red">
 959               <br />
 960             </td>
 961             <td class="snns plane red">closures</td>
 962             <td class="snns file red">cl_shift ( ? @@ ? )</td>
 963             <td class="snnn file red">cl_weight ( ♯{?,?} )</td>
 964             <td class="snnn file red">
 965               <br />
 966             </td>
 967             <td class="ssnn file red">
 968               <br />
 969             </td>
 970           </tr>
 971           <tr>
 972             <td class="nnns component red">
 973               <br />
 974             </td>
 975             <td class="snns plane red">internal syntax</td>
 976             <td class="snns file red">genv</td>
 977             <td class="snnn file red">
 978               <br />
 979             </td>
 980             <td class="snnn file red">
 981               <br />
 982             </td>
 983             <td class="ssnn file red">
 984               <br />
 985             </td>
 986           </tr>
 987           <tr>
 988             <td class="nnns component red">
 989               <br />
 990             </td>
 991             <td class="nnns plane red">
 992               <br />
 993             </td>
 994             <td class="snns file red">lenv</td>
 995             <td class="snnn file red">lenv_weight ( ♯{?} )</td>
 996             <td class="snnn file red">lenv_length ( |?| )</td>
 997             <td class="ssnn file red">lenv_append ( ? @@ ? )</td>
 998           </tr>
 999           <tr>
1000             <td class="nnns component red">
1001               <br />
1002             </td>
1003             <td class="nnns plane red">
1004               <br />
1005             </td>
1006             <td class="snns file red">term</td>
1007             <td class="snnn file red">term_weight ( ♯{?} )</td>
1008             <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
1009             <td class="ssnn file red">term_vector</td>
1010           </tr>
1011           <tr>
1012             <td class="nnns component red">
1013               <br />
1014             </td>
1015             <td class="nnns plane red">
1016               <br />
1017             </td>
1018             <td class="snns file red">item</td>
1019             <td class="snnn file red">
1020               <br />
1021             </td>
1022             <td class="snnn file red">
1023               <br />
1024             </td>
1025             <td class="ssnn file red">
1026               <br />
1027             </td>
1028           </tr>
1029           <tr>
1030             <td class="nnss component red">
1031               <br />
1032             </td>
1033             <td class="snss plane red">external syntax</td>
1034             <td class="snss file red">aarity</td>
1035             <td class="snsn file red">
1036               <br />
1037             </td>
1038             <td class="snsn file red">
1039               <br />
1040             </td>
1041             <td class="sssn file red">
1042               <br />
1043             </td>
1044           </tr>
1045         </tbody>
1046       </table>
1047     </div>
1048
1049    <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
1050    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
1051          one for each component.
1052    </div>
1053    <div class="spacer">
1054       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
1055     </div>
1056     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1057       <br />
1058     </div>
1059     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1060       <a href="http://validator.w3.org/check?uri=referer">
1061         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
1062       </a>
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1065       </a>
1066       <a href="http://www.w3.org/XML/">
1067         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
1068       </a>
1069       <a href="http://www.w3.org/Graphics/PNG/">
1070         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
1071       </a>
1072       <a href="http://www.anybrowser.org/campaign/">
1073         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
1074       </a>
1075     </div>
1076     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1077       <br />
1078     </div>
1079     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sat, 27 Jul 2013 18:22:47 +0200</div>
1080 </body>
1081 </html>