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">265  </td>
 167             <td class="snns plane cyan">characters</td>
 168             <td class="snnn number cyan">399492</td>
 169             <td class="snns plane cyan">nodes</td>
 170             <td class="ssnn number cyan">1202574</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">81</td>
 176             <td class="snns plane green">lemmas</td>
 177             <td class="snnn number green">808</td>
 178             <td class="snns plane green">total</td>
 179             <td class="ssnn number green">889</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">44</td>
 185             <td class="snss plane yellow">defined</td>
 186             <td class="snsn number yellow">79</td>
 187             <td class="snss plane yellow">total</td>
 188             <td class="sssn number yellow">123</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">2013 August 7.</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">ygt ( ⦃?,?,?⦄ &gt;[?,?] ⦃?,?,?⦄ )</td>
 321             <td class="snnn file prune">ygt_lift ygt_ygt</td>
 322             <td class="snnn file prune">
 323               <br />
 324             </td>
 325             <td class="ssnn file prune">
 326               <br />
 327             </td>
 328           </tr>
 329           <tr>
 330             <td class="nnns component prune">
 331               <br />
 332             </td>
 333             <td class="nnns plane prune">
 334               <br />
 335             </td>
 336             <td class="snns file prune">yprs ( ? ⊢ ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )</td>
 337             <td class="snnn file prune">yprs_lift yprs_yprs</td>
 338             <td class="snnn file prune">
 339               <br />
 340             </td>
 341             <td class="ssnn file prune">
 342               <br />
 343             </td>
 344           </tr>
 345           <tr>
 346             <td class="nnns component prune">
 347               <br />
 348             </td>
 349             <td class="snns plane prune">"big tree" parallel reduction</td>
 350             <td class="snns file prune">ypr ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )</td>
 351             <td class="snnn file prune">ysc ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )</td>
 352             <td class="snnn file prune">
 353               <br />
 354             </td>
 355             <td class="ssnn file prune">
 356               <br />
 357             </td>
 358           </tr>
 359           <tr>
 360             <td class="nnns component prune">
 361               <br />
 362             </td>
 363             <td class="snns plane prune">local env. ref. for stratified native validity</td>
 364             <td class="snns file prune">lsubsv ( ? ⊢ ? ¡⊑[?,?] ? )</td>
 365             <td class="snnn file prune">lsubsv_ldrop lsubsv_lsubd lsubsv_lsuba lsubsv_lsstas lsubsv_cpds lsubsv_cpcs lsubsv_snv</td>
 366             <td class="snnn file prune">
 367               <br />
 368             </td>
 369             <td class="ssnn file prune">
 370               <br />
 371             </td>
 372           </tr>
 373           <tr>
 374             <td class="nnns component prune">
 375               <br />
 376             </td>
 377             <td class="snns plane prune">stratified native validity</td>
 378             <td class="snns file prune">snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )</td>
 379             <td class="snnn file prune">snv_lift snv_da_lpr snv_aaa snv_lsstas snv_lsstas_lpr snv_lpr snv_cpcs</td>
 380             <td class="snnn file prune">
 381               <br />
 382             </td>
 383             <td class="ssnn file prune">
 384               <br />
 385             </td>
 386           </tr>
 387           <tr>
 388             <td class="snns component blue">equivalence</td>
 389             <td class="snns plane blue">decomposed extended equivalence</td>
 390             <td class="snns file blue">cpes ( ⦃?,?⦄ ⊢ ? •*⬌*[?,?] ? )</td>
 391             <td class="snnn file blue">cpes_cpds</td>
 392             <td class="snnn file blue">
 393               <br />
 394             </td>
 395             <td class="ssnn file blue">
 396               <br />
 397             </td>
 398           </tr>
 399           <tr>
 400             <td class="nnns component blue">
 401               <br />
 402             </td>
 403             <td class="snns plane blue">context-sensitive equivalence</td>
 404             <td class="snns file blue">cpcs ( ⦃?,?⦄ ⊢ ? ⬌* ? )</td>
 405             <td class="snnn file blue">cpcs_aaa cpcs_cprs cpcs_cpcs</td>
 406             <td class="snnn file blue">
 407               <br />
 408             </td>
 409             <td class="ssnn file blue">
 410               <br />
 411             </td>
 412           </tr>
 413           <tr>
 414             <td class="snns component sky">conversion</td>
 415             <td class="snns plane sky">context-sensitive conversion</td>
 416             <td class="snns file sky">cpc ( ⦃?,?⦄ ⊢ ? ⬌ ? )</td>
 417             <td class="snnn file sky">cpc_cpc</td>
 418             <td class="snnn file sky">
 419               <br />
 420             </td>
 421             <td class="ssnn file sky">
 422               <br />
 423             </td>
 424           </tr>
 425           <tr>
 426             <td class="snns component cyan">computation</td>
 427             <td class="snns plane cyan">context-sensitive extended evaluation</td>
 428             <td class="snns file cyan">cpxe ( ⦃?,?⦄ ⊢ ➡*[?,?] 𝐍⦃?⦄ )</td>
 429             <td class="snnn file cyan">
 430               <br />
 431             </td>
 432             <td class="snnn file cyan">
 433               <br />
 434             </td>
 435             <td class="ssnn file cyan">
 436               <br />
 437             </td>
 438           </tr>
 439           <tr>
 440             <td class="nnns component cyan">
 441               <br />
 442             </td>
 443             <td class="snns plane cyan">context-sensitive evaluation</td>
 444             <td class="snns file cyan">cpre ( ⦃?,?⦄ ⊢ ➡* 𝐍⦃?⦄ )</td>
 445             <td class="snnn file cyan">cpre_cpre</td>
 446             <td class="snnn file cyan">
 447               <br />
 448             </td>
 449             <td class="ssnn file cyan">
 450               <br />
 451             </td>
 452           </tr>
 453           <tr>
 454             <td class="nnns component cyan">
 455               <br />
 456             </td>
 457             <td class="snns plane cyan">strongly normalizing computation</td>
 458             <td class="snns file cyan">csn_vector ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )</td>
 459             <td class="snnn file cyan">csn_tstc_vector csn_aaa</td>
 460             <td class="snnn file cyan">
 461               <br />
 462             </td>
 463             <td class="ssnn file cyan">
 464               <br />
 465             </td>
 466           </tr>
 467           <tr>
 468             <td class="nnns component cyan">
 469               <br />
 470             </td>
 471             <td class="nnns plane cyan">
 472               <br />
 473             </td>
 474             <td class="snns file cyan">csn ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )</td>
 475             <td class="snnn file cyan">csn_alt ( ⦃?,?⦄ ⊢ ⬊⬊*[?,?] ? )</td>
 476             <td class="snnn file cyan">csn_lift csn_lpx</td>
 477             <td class="ssnn file cyan">
 478               <br />
 479             </td>
 480           </tr>
 481           <tr>
 482             <td class="nnns component cyan">
 483               <br />
 484             </td>
 485             <td class="snns plane cyan">decomposed extended computation</td>
 486             <td class="snns file cyan">cpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?] ? )</td>
 487             <td class="snnn file cyan">cpds_lift cpds_aaa cpds_cpds</td>
 488             <td class="snnn file cyan">
 489               <br />
 490             </td>
 491             <td class="ssnn file cyan">
 492               <br />
 493             </td>
 494           </tr>
 495           <tr>
 496             <td class="nnns component cyan">
 497               <br />
 498             </td>
 499             <td class="snns plane cyan">context-sensitive extended computation</td>
 500             <td class="snns file cyan">lpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? )</td>
 501             <td class="snnn file cyan">lpxs_alt ( ⦃?,?⦄ ⊢ ➡➡*[?,?] ? )</td>
 502             <td class="snnn file cyan">lpxs_ldrop lpxs_aaa lpxs_cpxs lpxs_lpxs</td>
 503             <td class="ssnn file cyan">
 504               <br />
 505             </td>
 506           </tr>
 507           <tr>
 508             <td class="nnns component cyan">
 509               <br />
 510             </td>
 511             <td class="nnns plane cyan">
 512               <br />
 513             </td>
 514             <td class="snns file cyan">cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )</td>
 515             <td class="snnn file cyan">cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_aaa cpxs_cpxs</td>
 516             <td class="snnn file cyan">
 517               <br />
 518             </td>
 519             <td class="ssnn file cyan">
 520               <br />
 521             </td>
 522           </tr>
 523           <tr>
 524             <td class="nnns component cyan">
 525               <br />
 526             </td>
 527             <td class="snns plane cyan">context-sensitive computation</td>
 528             <td class="snns file cyan">lprs ( ⦃?,?⦄ ⊢ ➡* ? )</td>
 529             <td class="snnn file cyan">lprs_alt ( ⦃?,?⦄ ⊢ ➡➡* ? )</td>
 530             <td class="snnn file cyan">lprs_ldrop lprs_cprs lprs_lprs</td>
 531             <td class="ssnn file cyan">
 532               <br />
 533             </td>
 534           </tr>
 535           <tr>
 536             <td class="nnns component cyan">
 537               <br />
 538             </td>
 539             <td class="nnns plane cyan">
 540               <br />
 541             </td>
 542             <td class="snns file cyan">cprs ( ⦃?,?⦄ ⊢ ? ➡* ?)</td>
 543             <td class="snnn file cyan">cprs_lift cprs_cprs</td>
 544             <td class="snnn file cyan">
 545               <br />
 546             </td>
 547             <td class="ssnn file cyan">
 548               <br />
 549             </td>
 550           </tr>
 551           <tr>
 552             <td class="nnns component cyan">
 553               <br />
 554             </td>
 555             <td class="snns plane cyan">local env. ref. for abstract candidates of reducibility</td>
 556             <td class="snns file cyan">lsubc ( ? ⊢ ? ⊑[?] ? )</td>
 557             <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
 558             <td class="snnn file cyan">
 559               <br />
 560             </td>
 561             <td class="ssnn file cyan">
 562               <br />
 563             </td>
 564           </tr>
 565           <tr>
 566             <td class="nnns component cyan">
 567               <br />
 568             </td>
 569             <td class="snns plane cyan">support for abstract computation properties</td>
 570             <td class="snns file cyan">acp</td>
 571             <td class="snnn file cyan">acp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
 572             <td class="snnn file cyan">acp_aaa</td>
 573             <td class="ssnn file cyan">
 574               <br />
 575             </td>
 576           </tr>
 577           <tr>
 578             <td class="snns component water">reduction</td>
 579             <td class="snns plane water">context-sensitive extended normal forms</td>
 580             <td class="snns file water">cnx ( ⦃?,?⦄ ⊢ 𝐍[?,?]⦃?⦄ )</td>
 581             <td class="snnn file water">cnx_lift cnx_crx cnx_cix</td>
 582             <td class="snnn file water">
 583               <br />
 584             </td>
 585             <td class="ssnn file water">
 586               <br />
 587             </td>
 588           </tr>
 589           <tr>
 590             <td class="nnns component water">
 591               <br />
 592             </td>
 593             <td class="snns plane water">context-sensitive extended reduction</td>
 594             <td class="snns file water">lpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
 595             <td class="snnn file water">lpx_ldrop lpx_aaa</td>
 596             <td class="snnn file water">
 597               <br />
 598             </td>
 599             <td class="ssnn file water">
 600               <br />
 601             </td>
 602           </tr>
 603           <tr>
 604             <td class="nnns component water">
 605               <br />
 606             </td>
 607             <td class="nnns plane water">
 608               <br />
 609             </td>
 610             <td class="snns file water">cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
 611             <td class="snnn file water">cpx_lift cpx_cix</td>
 612             <td class="snnn file water">
 613               <br />
 614             </td>
 615             <td class="ssnn file water">
 616               <br />
 617             </td>
 618           </tr>
 619           <tr>
 620             <td class="nnns component water">
 621               <br />
 622             </td>
 623             <td class="snns plane water">context-sensitive extended irreducible forms</td>
 624             <td class="snns file water">cix ( ⦃?,?⦄ ⊢ 𝐈[?,?]⦃?⦄ )</td>
 625             <td class="snnn file water">cix_append cix_lift</td>
 626             <td class="snnn file water">
 627               <br />
 628             </td>
 629             <td class="ssnn file water">
 630               <br />
 631             </td>
 632           </tr>
 633           <tr>
 634             <td class="nnns component water">
 635               <br />
 636             </td>
 637             <td class="snns plane water">context-sensitive extended reducible forms</td>
 638             <td class="snns file water">crx ( ⦃?,?⦄ ⊢ 𝐑[?,?]⦃?⦄ )</td>
 639             <td class="snnn file water">crx_append crx_lift</td>
 640             <td class="snnn file water">
 641               <br />
 642             </td>
 643             <td class="ssnn file water">
 644               <br />
 645             </td>
 646           </tr>
 647           <tr>
 648             <td class="nnns component water">
 649               <br />
 650             </td>
 651             <td class="snns plane water">context-sensitive normal forms</td>
 652             <td class="snns file water">cnr ( ⦃?,?⦄ ⊢ 𝐍⦃?⦄ )</td>
 653             <td class="snnn file water">cnr_lift cnr_crr cnr_cir</td>
 654             <td class="snnn file water">
 655               <br />
 656             </td>
 657             <td class="ssnn file water">
 658               <br />
 659             </td>
 660           </tr>
 661           <tr>
 662             <td class="nnns component water">
 663               <br />
 664             </td>
 665             <td class="snns plane water">context-sensitive reduction</td>
 666             <td class="snns file water">lpr ( ⦃?,?⦄ ⊢ ➡ ? )</td>
 667             <td class="snnn file water">lpr_ldrop lpr_lpr</td>
 668             <td class="snnn file water">
 669               <br />
 670             </td>
 671             <td class="ssnn file water">
 672               <br />
 673             </td>
 674           </tr>
 675           <tr>
 676             <td class="nnns component water">
 677               <br />
 678             </td>
 679             <td class="nnns plane water">
 680               <br />
 681             </td>
 682             <td class="snns file water">cpr ( ⦃?,?⦄ ⊢ ? ➡ ? )</td>
 683             <td class="snnn file water">cpr_lift cpr_cir</td>
 684             <td class="snnn file water">
 685               <br />
 686             </td>
 687             <td class="ssnn file water">
 688               <br />
 689             </td>
 690           </tr>
 691           <tr>
 692             <td class="nnns component water">
 693               <br />
 694             </td>
 695             <td class="snns plane water">context-sensitive irreducible forms</td>
 696             <td class="snns file water">cir ( ⦃?,?⦄ ⊢ 𝐈⦃?⦄ )</td>
 697             <td class="snnn file water">cir_append cir_lift</td>
 698             <td class="snnn file water">
 699               <br />
 700             </td>
 701             <td class="ssnn file water">
 702               <br />
 703             </td>
 704           </tr>
 705           <tr>
 706             <td class="nnns component water">
 707               <br />
 708             </td>
 709             <td class="snns plane water">context-sensitive reducible forms</td>
 710             <td class="snns file water">crr ( ⦃?,?⦄ ⊢ 𝐑⦃?⦄ )</td>
 711             <td class="snnn file water">crr_append crr_lift</td>
 712             <td class="snnn file water">
 713               <br />
 714             </td>
 715             <td class="ssnn file water">
 716               <br />
 717             </td>
 718           </tr>
 719           <tr>
 720             <td class="snns component green">unfold</td>
 721             <td class="snns plane green">unfold</td>
 722             <td class="snns file green">unfold ( ⦃?,?⦄ ⊢ ? ⧫* ? )</td>
 723             <td class="snnn file green">
 724               <br />
 725             </td>
 726             <td class="snnn file green">
 727               <br />
 728             </td>
 729             <td class="ssnn file green">
 730               <br />
 731             </td>
 732           </tr>
 733           <tr>
 734             <td class="nnns component green">
 735               <br />
 736             </td>
 737             <td class="snns plane green">iterated static type assignment</td>
 738             <td class="snns file green">lsstas ( ⦃?,?⦄ ⊢ ? •*[?,?,?] ? )</td>
 739             <td class="snnn file green">lsstas_alt ( ⦃?,?⦄ ⊢ ? ••*[?,?,?] ? )</td>
 740             <td class="snnn file green">lsstas_lift lsstas_aaa lsstas_lsstas</td>
 741             <td class="ssnn file green">
 742               <br />
 743             </td>
 744           </tr>
 745           <tr>
 746             <td class="snns component grass">static typing</td>
 747             <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
 748             <td class="snns file grass">lsuba ( ? ⊢ ? ⁝⊑ ? )</td>
 749             <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
 750             <td class="snnn file grass">
 751               <br />
 752             </td>
 753             <td class="ssnn file grass">
 754               <br />
 755             </td>
 756           </tr>
 757           <tr>
 758             <td class="nnns component grass">
 759               <br />
 760             </td>
 761             <td class="snns plane grass">atomic arity assignment</td>
 762             <td class="snns file grass">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 763             <td class="snnn file grass">aaa_lift aaa_lifts aaa_da aaa_ssta aaa_aaa</td>
 764             <td class="snnn file grass">
 765               <br />
 766             </td>
 767             <td class="ssnn file grass">
 768               <br />
 769             </td>
 770           </tr>
 771           <tr>
 772             <td class="nnns component grass">
 773               <br />
 774             </td>
 775             <td class="snns plane grass">stratified static type assignment</td>
 776             <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
 777             <td class="snnn file grass">ssta_lift ssta_ssta</td>
 778             <td class="snnn file grass">
 779               <br />
 780             </td>
 781             <td class="ssnn file grass">
 782               <br />
 783             </td>
 784           </tr>
 785           <tr>
 786             <td class="nnns component grass">
 787               <br />
 788             </td>
 789             <td class="snns plane grass">local env. ref. for degree assignment</td>
 790             <td class="snns file grass">lsubd ( ? ⊢ ? ▪⊑ ? )</td>
 791             <td class="snnn file grass">lsubd_da lsubd_lsubd</td>
 792             <td class="snnn file grass">
 793               <br />
 794             </td>
 795             <td class="ssnn file grass">
 796               <br />
 797             </td>
 798           </tr>
 799           <tr>
 800             <td class="nnns component grass">
 801               <br />
 802             </td>
 803             <td class="snns plane grass">degree assignment</td>
 804             <td class="snns file grass">da ( ⦃?,?⦄ ⊢ ? ▪[?,?] ? )</td>
 805             <td class="snnn file grass">da_lift da_da</td>
 806             <td class="snnn file grass">
 807               <br />
 808             </td>
 809             <td class="ssnn file grass">
 810               <br />
 811             </td>
 812           </tr>
 813           <tr>
 814             <td class="nnns component grass">
 815               <br />
 816             </td>
 817             <td class="snns plane grass">parameters</td>
 818             <td class="snns file grass">sh</td>
 819             <td class="snnn file grass">sd</td>
 820             <td class="snnn file grass">
 821               <br />
 822             </td>
 823             <td class="ssnn file grass">
 824               <br />
 825             </td>
 826           </tr>
 827           <tr>
 828             <td class="snns component yellow">substitution</td>
 829             <td class="snns plane yellow">restricted local env. ref.</td>
 830             <td class="snns file yellow">lsubr ( ? ⊑ ? )</td>
 831             <td class="snnn file yellow">lsubr_lsubr</td>
 832             <td class="snnn file yellow">
 833               <br />
 834             </td>
 835             <td class="ssnn file yellow">
 836               <br />
 837             </td>
 838           </tr>
 839           <tr>
 840             <td class="nnns component yellow">
 841               <br />
 842             </td>
 843             <td class="snns plane yellow">iterated structural successor for closures</td>
 844             <td class="snns file yellow">fsups ( ⦃?,?,?⦄ ⊃* ⦃?,?,?⦄ )</td>
 845             <td class="snnn file yellow">fsups_fsups</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="nnns plane yellow">
 858               <br />
 859             </td>
 860             <td class="snns file yellow">fsupp ( ⦃?,?,?⦄ ⊃+ ⦃?,?,?⦄ )</td>
 861             <td class="snnn file yellow">fsupp_fsupp</td>
 862             <td class="snnn file yellow">
 863               <br />
 864             </td>
 865             <td class="ssnn file yellow">
 866               <br />
 867             </td>
 868           </tr>
 869           <tr>
 870             <td class="nnns component yellow">
 871               <br />
 872             </td>
 873             <td class="snns plane yellow">generic local env. slicing</td>
 874             <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
 875             <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</td>
 876             <td class="snnn file yellow">
 877               <br />
 878             </td>
 879             <td class="ssnn file yellow">
 880               <br />
 881             </td>
 882           </tr>
 883           <tr>
 884             <td class="nnns component yellow">
 885               <br />
 886             </td>
 887             <td class="snns plane yellow">generic term relocation</td>
 888             <td class="snns file yellow">lifts_vector ( ⇧*[?] ? ≡ ? )</td>
 889             <td class="snnn file yellow">lifts_lift_vector</td>
 890             <td class="snnn file yellow">
 891               <br />
 892             </td>
 893             <td class="ssnn file yellow">
 894               <br />
 895             </td>
 896           </tr>
 897           <tr>
 898             <td class="nnns component yellow">
 899               <br />
 900             </td>
 901             <td class="nnns plane yellow">
 902               <br />
 903             </td>
 904             <td class="snns file yellow">lifts ( ⇧*[?] ? ≡ ? )</td>
 905             <td class="snnn file yellow">lifts_lift lifts_lifts</td>
 906             <td class="snnn file yellow">
 907               <br />
 908             </td>
 909             <td class="ssnn file yellow">
 910               <br />
 911             </td>
 912           </tr>
 913           <tr>
 914             <td class="nnns component yellow">
 915               <br />
 916             </td>
 917             <td class="snns plane yellow">support for generic relocation</td>
 918             <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
 919             <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
 920             <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
 921             <td class="ssnn file yellow">gr2_gr2</td>
 922           </tr>
 923           <tr>
 924             <td class="snns component orange">relocation</td>
 925             <td class="snns plane orange">structural successor for closures</td>
 926             <td class="snns file orange">fsup ( ⦃?,?,?⦄ ⊃ ⦃?,?,?⦄ )</td>
 927             <td class="snnn file orange">fsupq ( ⦃?,?,?⦄ ⊃⸮ ⦃?,?,?⦄ )</td>
 928             <td class="snnn file orange">fsupq_alt ( ⦃?,?,?⦄ ⊃⊃⸮ ⦃?,?,?⦄ )</td>
 929             <td class="ssnn file orange">
 930               <br />
 931             </td>
 932           </tr>
 933           <tr>
 934             <td class="nnns component orange">
 935               <br />
 936             </td>
 937             <td class="snns plane orange">global env. slicing</td>
 938             <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
 939             <td class="snnn file orange">gdrop_gdrop</td>
 940             <td class="snnn file orange">
 941               <br />
 942             </td>
 943             <td class="ssnn file orange">
 944               <br />
 945             </td>
 946           </tr>
 947           <tr>
 948             <td class="nnns component orange">
 949               <br />
 950             </td>
 951             <td class="snns plane orange">basic local env. slicing</td>
 952             <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
 953             <td class="snnn file orange">ldrop_append ldrop_lpx_sn ldrop_ldrop</td>
 954             <td class="snnn file orange">
 955               <br />
 956             </td>
 957             <td class="ssnn file orange">
 958               <br />
 959             </td>
 960           </tr>
 961           <tr>
 962             <td class="nnns component orange">
 963               <br />
 964             </td>
 965             <td class="snns plane orange">basic term relocation</td>
 966             <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
 967             <td class="snnn file orange">lift_lift_vector</td>
 968             <td class="snnn file orange">
 969               <br />
 970             </td>
 971             <td class="ssnn file orange">
 972               <br />
 973             </td>
 974           </tr>
 975           <tr>
 976             <td class="nnns component orange">
 977               <br />
 978             </td>
 979             <td class="nnns plane orange">
 980               <br />
 981             </td>
 982             <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
 983             <td class="snnn file orange">lift_lift</td>
 984             <td class="snnn file orange">
 985               <br />
 986             </td>
 987             <td class="ssnn file orange">
 988               <br />
 989             </td>
 990           </tr>
 991           <tr>
 992             <td class="snns component red">grammar</td>
 993             <td class="snns plane red">pointwise extension of a relation</td>
 994             <td class="snns file red">lpx_sn</td>
 995             <td class="snnn file red">lpx_sn_tc lpx_sn_lpx_sn</td>
 996             <td class="snnn file red">
 997               <br />
 998             </td>
 999             <td class="ssnn file red">
1000               <br />
1001             </td>
1002           </tr>
1003           <tr>
1004             <td class="nnns component red">
1005               <br />
1006             </td>
1007             <td class="snns plane red">same top term constructor</td>
1008             <td class="snns file red">tstc ( ? ≃ ? )</td>
1009             <td class="snnn file red">tstc_tstc tstc_vector</td>
1010             <td class="snnn file red">
1011               <br />
1012             </td>
1013             <td class="ssnn file red">
1014               <br />
1015             </td>
1016           </tr>
1017           <tr>
1018             <td class="nnns component red">
1019               <br />
1020             </td>
1021             <td class="snns plane red">closures</td>
1022             <td class="snns file red">cl_shift ( ? @@ ? )</td>
1023             <td class="snnn file red">cl_weight ( ♯{?,?,?} )</td>
1024             <td class="snnn file red">
1025               <br />
1026             </td>
1027             <td class="ssnn file red">
1028               <br />
1029             </td>
1030           </tr>
1031           <tr>
1032             <td class="nnns component red">
1033               <br />
1034             </td>
1035             <td class="snns plane red">internal syntax</td>
1036             <td class="snns file red">genv</td>
1037             <td class="snnn file red">
1038               <br />
1039             </td>
1040             <td class="snnn file red">
1041               <br />
1042             </td>
1043             <td class="ssnn file red">
1044               <br />
1045             </td>
1046           </tr>
1047           <tr>
1048             <td class="nnns component red">
1049               <br />
1050             </td>
1051             <td class="nnns plane red">
1052               <br />
1053             </td>
1054             <td class="snns file red">lenv</td>
1055             <td class="snnn file red">lenv_weight ( ♯{?} )</td>
1056             <td class="snnn file red">lenv_length ( |?| )</td>
1057             <td class="ssnn file red">lenv_append ( ? @@ ? )</td>
1058           </tr>
1059           <tr>
1060             <td class="nnns component red">
1061               <br />
1062             </td>
1063             <td class="nnns plane red">
1064               <br />
1065             </td>
1066             <td class="snns file red">term</td>
1067             <td class="snnn file red">term_weight ( ♯{?} )</td>
1068             <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
1069             <td class="ssnn file red">term_vector</td>
1070           </tr>
1071           <tr>
1072             <td class="nnns component red">
1073               <br />
1074             </td>
1075             <td class="nnns plane red">
1076               <br />
1077             </td>
1078             <td class="snns file red">item</td>
1079             <td class="snnn file red">
1080               <br />
1081             </td>
1082             <td class="snnn file red">
1083               <br />
1084             </td>
1085             <td class="ssnn file red">
1086               <br />
1087             </td>
1088           </tr>
1089           <tr>
1090             <td class="nnss component red">
1091               <br />
1092             </td>
1093             <td class="snss plane red">external syntax</td>
1094             <td class="snss file red">aarity</td>
1095             <td class="snsn file red">
1096               <br />
1097             </td>
1098             <td class="snsn file red">
1099               <br />
1100             </td>
1101             <td class="sssn file red">
1102               <br />
1103             </td>
1104           </tr>
1105         </tbody>
1106       </table>
1107     </div>
1108
1109    <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
1110    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
1111          one for each component.
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1139     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Fri, 04 Oct 2013 15:36:48 +0200</div>
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