helm/www/lambdadelta/basic_2.html

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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">266  </td>
 167             <td class="snns plane cyan">characters</td>
 168             <td class="snnn number cyan">400863</td>
 169             <td class="snns plane cyan">nodes</td>
 170             <td class="ssnn number cyan">1203013</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">814</td>
 178             <td class="snns plane green">total</td>
 179             <td class="ssnn number green">895</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">local env. ref. for stratified native validity</td>
 320             <td class="snns file prune">lsubsv ( ? ⊢ ? ¡⊑[?,?] ? )</td>
 321             <td class="snnn file prune">lsubsv_ldrop lsubsv_lsubd lsubsv_lsuba lsubsv_lsstas lsubsv_cpds lsubsv_cpcs lsubsv_snv</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="snns plane prune">stratified native validity</td>
 334             <td class="snns file prune">snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )</td>
 335             <td class="snnn file prune">snv_lift snv_da_lpr snv_aaa snv_lsstas snv_lsstas_lpr snv_lpr snv_cpcs</td>
 336             <td class="snnn file prune">
 337               <br />
 338             </td>
 339             <td class="ssnn file prune">
 340               <br />
 341             </td>
 342           </tr>
 343           <tr>
 344             <td class="snns component blue">equivalence</td>
 345             <td class="snns plane blue">decomposed extended equivalence</td>
 346             <td class="snns file blue">cpes ( ⦃?,?⦄ ⊢ ? •*⬌*[?,?] ? )</td>
 347             <td class="snnn file blue">cpes_cpds</td>
 348             <td class="snnn file blue">
 349               <br />
 350             </td>
 351             <td class="ssnn file blue">
 352               <br />
 353             </td>
 354           </tr>
 355           <tr>
 356             <td class="nnns component blue">
 357               <br />
 358             </td>
 359             <td class="snns plane blue">context-sensitive equivalence</td>
 360             <td class="snns file blue">cpcs ( ⦃?,?⦄ ⊢ ? ⬌* ? )</td>
 361             <td class="snnn file blue">cpcs_aaa cpcs_cprs cpcs_cpcs</td>
 362             <td class="snnn file blue">
 363               <br />
 364             </td>
 365             <td class="ssnn file blue">
 366               <br />
 367             </td>
 368           </tr>
 369           <tr>
 370             <td class="snns component sky">conversion</td>
 371             <td class="snns plane sky">context-sensitive conversion</td>
 372             <td class="snns file sky">cpc ( ⦃?,?⦄ ⊢ ? ⬌ ? )</td>
 373             <td class="snnn file sky">cpc_cpc</td>
 374             <td class="snnn file sky">
 375               <br />
 376             </td>
 377             <td class="ssnn file sky">
 378               <br />
 379             </td>
 380           </tr>
 381           <tr>
 382             <td class="snns component cyan">computation</td>
 383             <td class="snns plane cyan">context-sensitive extended evaluation</td>
 384             <td class="snns file cyan">cpxe ( ⦃?,?⦄ ⊢ ➡*[?,?] 𝐍⦃?⦄ )</td>
 385             <td class="snnn file cyan">
 386               <br />
 387             </td>
 388             <td class="snnn file cyan">
 389               <br />
 390             </td>
 391             <td class="ssnn file cyan">
 392               <br />
 393             </td>
 394           </tr>
 395           <tr>
 396             <td class="nnns component cyan">
 397               <br />
 398             </td>
 399             <td class="snns plane cyan">context-sensitive evaluation</td>
 400             <td class="snns file cyan">cpre ( ⦃?,?⦄ ⊢ ➡* 𝐍⦃?⦄ )</td>
 401             <td class="snnn file cyan">cpre_cpre</td>
 402             <td class="snnn file cyan">
 403               <br />
 404             </td>
 405             <td class="ssnn file cyan">
 406               <br />
 407             </td>
 408           </tr>
 409           <tr>
 410             <td class="nnns component cyan">
 411               <br />
 412             </td>
 413             <td class="snns plane cyan">strongly normalizing computation</td>
 414             <td class="snns file cyan">csx_vector ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )</td>
 415             <td class="snnn file cyan">csx_tstc_vector csx_aaa</td>
 416             <td class="snnn file cyan">
 417               <br />
 418             </td>
 419             <td class="ssnn file cyan">
 420               <br />
 421             </td>
 422           </tr>
 423           <tr>
 424             <td class="nnns component cyan">
 425               <br />
 426             </td>
 427             <td class="nnns plane cyan">
 428               <br />
 429             </td>
 430             <td class="snns file cyan">csx ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )</td>
 431             <td class="snnn file cyan">csx_alt ( ⦃?,?⦄ ⊢ ⬊⬊*[?,?] ? )</td>
 432             <td class="snnn file cyan">csx_lift csx_lpx</td>
 433             <td class="ssnn file cyan">
 434               <br />
 435             </td>
 436           </tr>
 437           <tr>
 438             <td class="nnns component cyan">
 439               <br />
 440             </td>
 441             <td class="snns plane cyan">"big tree" parallel computation</td>
 442             <td class="snns file cyan">fpbg ( ⦃?,?,?⦄ &gt;[?,?] ⦃?,?,?⦄ )</td>
 443             <td class="snnn file cyan">fpbg_lift fpbg_fpbg</td>
 444             <td class="snnn file cyan">
 445               <br />
 446             </td>
 447             <td class="ssnn file cyan">
 448               <br />
 449             </td>
 450           </tr>
 451           <tr>
 452             <td class="nnns component cyan">
 453               <br />
 454             </td>
 455             <td class="nnns plane cyan">
 456               <br />
 457             </td>
 458             <td class="snns file cyan">fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )</td>
 459             <td class="snnn file cyan">fpbs_lift fpbs_fpbs</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="snns plane cyan">decomposed extended computation</td>
 472             <td class="snns file cyan">cpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?] ? )</td>
 473             <td class="snnn file cyan">cpds_lift cpds_aaa cpds_cpds</td>
 474             <td class="snnn file cyan">
 475               <br />
 476             </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">context-sensitive extended computation</td>
 486             <td class="snns file cyan">lpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? )</td>
 487             <td class="snnn file cyan">lpxs_alt ( ⦃?,?⦄ ⊢ ➡➡*[?,?] ? )</td>
 488             <td class="snnn file cyan">lpxs_ldrop lpxs_aaa lpxs_cpxs lpxs_lpxs</td>
 489             <td class="ssnn file cyan">
 490               <br />
 491             </td>
 492           </tr>
 493           <tr>
 494             <td class="nnns component cyan">
 495               <br />
 496             </td>
 497             <td class="nnns plane cyan">
 498               <br />
 499             </td>
 500             <td class="snns file cyan">cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )</td>
 501             <td class="snnn file cyan">cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_aaa cpxs_cpxs</td>
 502             <td class="snnn file cyan">
 503               <br />
 504             </td>
 505             <td class="ssnn file cyan">
 506               <br />
 507             </td>
 508           </tr>
 509           <tr>
 510             <td class="nnns component cyan">
 511               <br />
 512             </td>
 513             <td class="snns plane cyan">context-sensitive computation</td>
 514             <td class="snns file cyan">lprs ( ⦃?,?⦄ ⊢ ➡* ? )</td>
 515             <td class="snnn file cyan">lprs_alt ( ⦃?,?⦄ ⊢ ➡➡* ? )</td>
 516             <td class="snnn file cyan">lprs_ldrop lprs_cprs lprs_lprs</td>
 517             <td class="ssnn file cyan">
 518               <br />
 519             </td>
 520           </tr>
 521           <tr>
 522             <td class="nnns component cyan">
 523               <br />
 524             </td>
 525             <td class="nnns plane cyan">
 526               <br />
 527             </td>
 528             <td class="snns file cyan">cprs ( ⦃?,?⦄ ⊢ ? ➡* ?)</td>
 529             <td class="snnn file cyan">cprs_lift cprs_cprs</td>
 530             <td class="snnn file cyan">
 531               <br />
 532             </td>
 533             <td class="ssnn file cyan">
 534               <br />
 535             </td>
 536           </tr>
 537           <tr>
 538             <td class="nnns component cyan">
 539               <br />
 540             </td>
 541             <td class="snns plane cyan">local env. ref. for abstract candidates of reducibility</td>
 542             <td class="snns file cyan">lsubc ( ? ⊢ ? ⊑[?] ? )</td>
 543             <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</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">support for abstract computation properties</td>
 556             <td class="snns file cyan">acp</td>
 557             <td class="snnn file cyan">acp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
 558             <td class="snnn file cyan">acp_aaa</td>
 559             <td class="ssnn file cyan">
 560               <br />
 561             </td>
 562           </tr>
 563           <tr>
 564             <td class="snns component water">reduction</td>
 565             <td class="snns plane water">"big tree" parallel reduction</td>
 566             <td class="snns file water">fpbc ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )</td>
 567             <td class="snnn file water">fpbc_lift</td>
 568             <td class="snnn file water">
 569               <br />
 570             </td>
 571             <td class="ssnn file water">
 572               <br />
 573             </td>
 574           </tr>
 575           <tr>
 576             <td class="nnns component water">
 577               <br />
 578             </td>
 579             <td class="nnns plane water">
 580               <br />
 581             </td>
 582             <td class="snns file water">fpb ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )</td>
 583             <td class="snnn file water">fpb_lift</td>
 584             <td class="snnn file water">
 585               <br />
 586             </td>
 587             <td class="ssnn file water">
 588               <br />
 589             </td>
 590           </tr>
 591           <tr>
 592             <td class="nnns component water">
 593               <br />
 594             </td>
 595             <td class="snns plane water">context-sensitive extended normal forms</td>
 596             <td class="snns file water">cnx ( ⦃?,?⦄ ⊢ 𝐍[?,?]⦃?⦄ )</td>
 597             <td class="snnn file water">cnx_lift cnx_crx cnx_cix</td>
 598             <td class="snnn file water">
 599               <br />
 600             </td>
 601             <td class="ssnn file water">
 602               <br />
 603             </td>
 604           </tr>
 605           <tr>
 606             <td class="nnns component water">
 607               <br />
 608             </td>
 609             <td class="snns plane water">context-sensitive extended reduction</td>
 610             <td class="snns file water">lpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
 611             <td class="snnn file water">lpx_ldrop lpx_aaa</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="nnns plane water">
 624               <br />
 625             </td>
 626             <td class="snns file water">cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
 627             <td class="snnn file water">cpx_lift cpx_cix</td>
 628             <td class="snnn file water">
 629               <br />
 630             </td>
 631             <td class="ssnn file water">
 632               <br />
 633             </td>
 634           </tr>
 635           <tr>
 636             <td class="nnns component water">
 637               <br />
 638             </td>
 639             <td class="snns plane water">context-sensitive extended irreducible forms</td>
 640             <td class="snns file water">cix ( ⦃?,?⦄ ⊢ 𝐈[?,?]⦃?⦄ )</td>
 641             <td class="snnn file water">cix_append cix_lift</td>
 642             <td class="snnn file water">
 643               <br />
 644             </td>
 645             <td class="ssnn file water">
 646               <br />
 647             </td>
 648           </tr>
 649           <tr>
 650             <td class="nnns component water">
 651               <br />
 652             </td>
 653             <td class="snns plane water">context-sensitive extended reducible forms</td>
 654             <td class="snns file water">crx ( ⦃?,?⦄ ⊢ 𝐑[?,?]⦃?⦄ )</td>
 655             <td class="snnn file water">crx_append crx_lift</td>
 656             <td class="snnn file water">
 657               <br />
 658             </td>
 659             <td class="ssnn file water">
 660               <br />
 661             </td>
 662           </tr>
 663           <tr>
 664             <td class="nnns component water">
 665               <br />
 666             </td>
 667             <td class="snns plane water">context-sensitive normal forms</td>
 668             <td class="snns file water">cnr ( ⦃?,?⦄ ⊢ 𝐍⦃?⦄ )</td>
 669             <td class="snnn file water">cnr_lift cnr_crr cnr_cir</td>
 670             <td class="snnn file water">
 671               <br />
 672             </td>
 673             <td class="ssnn file water">
 674               <br />
 675             </td>
 676           </tr>
 677           <tr>
 678             <td class="nnns component water">
 679               <br />
 680             </td>
 681             <td class="snns plane water">context-sensitive reduction</td>
 682             <td class="snns file water">lpr ( ⦃?,?⦄ ⊢ ➡ ? )</td>
 683             <td class="snnn file water">lpr_ldrop lpr_lpr</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="nnns plane water">
 696               <br />
 697             </td>
 698             <td class="snns file water">cpr ( ⦃?,?⦄ ⊢ ? ➡ ? )</td>
 699             <td class="snnn file water">cpr_lift cpr_cir</td>
 700             <td class="snnn file water">
 701               <br />
 702             </td>
 703             <td class="ssnn file water">
 704               <br />
 705             </td>
 706           </tr>
 707           <tr>
 708             <td class="nnns component water">
 709               <br />
 710             </td>
 711             <td class="snns plane water">context-sensitive irreducible forms</td>
 712             <td class="snns file water">cir ( ⦃?,?⦄ ⊢ 𝐈⦃?⦄ )</td>
 713             <td class="snnn file water">cir_append cir_lift</td>
 714             <td class="snnn file water">
 715               <br />
 716             </td>
 717             <td class="ssnn file water">
 718               <br />
 719             </td>
 720           </tr>
 721           <tr>
 722             <td class="nnns component water">
 723               <br />
 724             </td>
 725             <td class="snns plane water">context-sensitive reducible forms</td>
 726             <td class="snns file water">crr ( ⦃?,?⦄ ⊢ 𝐑⦃?⦄ )</td>
 727             <td class="snnn file water">crr_append crr_lift</td>
 728             <td class="snnn file water">
 729               <br />
 730             </td>
 731             <td class="ssnn file water">
 732               <br />
 733             </td>
 734           </tr>
 735           <tr>
 736             <td class="snns component green">unfold</td>
 737             <td class="snns plane green">unfold</td>
 738             <td class="snns file green">unfold ( ⦃?,?⦄ ⊢ ? ⧫* ? )</td>
 739             <td class="snnn file green">
 740               <br />
 741             </td>
 742             <td class="snnn file green">
 743               <br />
 744             </td>
 745             <td class="ssnn file green">
 746               <br />
 747             </td>
 748           </tr>
 749           <tr>
 750             <td class="nnns component green">
 751               <br />
 752             </td>
 753             <td class="snns plane green">iterated static type assignment</td>
 754             <td class="snns file green">lsstas ( ⦃?,?⦄ ⊢ ? •*[?,?,?] ? )</td>
 755             <td class="snnn file green">lsstas_alt ( ⦃?,?⦄ ⊢ ? ••*[?,?,?] ? )</td>
 756             <td class="snnn file green">lsstas_lift lsstas_aaa lsstas_lsstas</td>
 757             <td class="ssnn file green">
 758               <br />
 759             </td>
 760           </tr>
 761           <tr>
 762             <td class="snns component grass">static typing</td>
 763             <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
 764             <td class="snns file grass">lsuba ( ? ⊢ ? ⁝⊑ ? )</td>
 765             <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
 766             <td class="snnn file grass">
 767               <br />
 768             </td>
 769             <td class="ssnn file grass">
 770               <br />
 771             </td>
 772           </tr>
 773           <tr>
 774             <td class="nnns component grass">
 775               <br />
 776             </td>
 777             <td class="snns plane grass">atomic arity assignment</td>
 778             <td class="snns file grass">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 779             <td class="snnn file grass">aaa_lift aaa_lifts aaa_da aaa_ssta aaa_aaa</td>
 780             <td class="snnn file grass">
 781               <br />
 782             </td>
 783             <td class="ssnn file grass">
 784               <br />
 785             </td>
 786           </tr>
 787           <tr>
 788             <td class="nnns component grass">
 789               <br />
 790             </td>
 791             <td class="snns plane grass">stratified static type assignment</td>
 792             <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
 793             <td class="snnn file grass">ssta_lift ssta_ssta</td>
 794             <td class="snnn file grass">
 795               <br />
 796             </td>
 797             <td class="ssnn file grass">
 798               <br />
 799             </td>
 800           </tr>
 801           <tr>
 802             <td class="nnns component grass">
 803               <br />
 804             </td>
 805             <td class="snns plane grass">local env. ref. for degree assignment</td>
 806             <td class="snns file grass">lsubd ( ? ⊢ ? ▪⊑ ? )</td>
 807             <td class="snnn file grass">lsubd_da lsubd_lsubd</td>
 808             <td class="snnn file grass">
 809               <br />
 810             </td>
 811             <td class="ssnn file grass">
 812               <br />
 813             </td>
 814           </tr>
 815           <tr>
 816             <td class="nnns component grass">
 817               <br />
 818             </td>
 819             <td class="snns plane grass">degree assignment</td>
 820             <td class="snns file grass">da ( ⦃?,?⦄ ⊢ ? ▪[?,?] ? )</td>
 821             <td class="snnn file grass">da_lift da_da</td>
 822             <td class="snnn file grass">
 823               <br />
 824             </td>
 825             <td class="ssnn file grass">
 826               <br />
 827             </td>
 828           </tr>
 829           <tr>
 830             <td class="nnns component grass">
 831               <br />
 832             </td>
 833             <td class="snns plane grass">parameters</td>
 834             <td class="snns file grass">sh</td>
 835             <td class="snnn file grass">sd</td>
 836             <td class="snnn file grass">
 837               <br />
 838             </td>
 839             <td class="ssnn file grass">
 840               <br />
 841             </td>
 842           </tr>
 843           <tr>
 844             <td class="snns component yellow">substitution</td>
 845             <td class="snns plane yellow">restricted local env. ref.</td>
 846             <td class="snns file yellow">lsubr ( ? ⊑ ? )</td>
 847             <td class="snnn file yellow">lsubr_lsubr</td>
 848             <td class="snnn file yellow">
 849               <br />
 850             </td>
 851             <td class="ssnn file yellow">
 852               <br />
 853             </td>
 854           </tr>
 855           <tr>
 856             <td class="nnns component yellow">
 857               <br />
 858             </td>
 859             <td class="snns plane yellow">iterated structural successor for closures</td>
 860             <td class="snns file yellow">fsups ( ⦃?,?,?⦄ ⊃* ⦃?,?,?⦄ )</td>
 861             <td class="snnn file yellow">fsups_fsups</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="nnns plane yellow">
 874               <br />
 875             </td>
 876             <td class="snns file yellow">fsupp ( ⦃?,?,?⦄ ⊃+ ⦃?,?,?⦄ )</td>
 877             <td class="snnn file yellow">fsupp_fsupp</td>
 878             <td class="snnn file yellow">
 879               <br />
 880             </td>
 881             <td class="ssnn file yellow">
 882               <br />
 883             </td>
 884           </tr>
 885           <tr>
 886             <td class="nnns component yellow">
 887               <br />
 888             </td>
 889             <td class="snns plane yellow">generic local env. slicing</td>
 890             <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
 891             <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</td>
 892             <td class="snnn file yellow">
 893               <br />
 894             </td>
 895             <td class="ssnn file yellow">
 896               <br />
 897             </td>
 898           </tr>
 899           <tr>
 900             <td class="nnns component yellow">
 901               <br />
 902             </td>
 903             <td class="snns plane yellow">generic term relocation</td>
 904             <td class="snns file yellow">lifts_vector ( ⇧*[?] ? ≡ ? )</td>
 905             <td class="snnn file yellow">lifts_lift_vector</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="nnns plane yellow">
 918               <br />
 919             </td>
 920             <td class="snns file yellow">lifts ( ⇧*[?] ? ≡ ? )</td>
 921             <td class="snnn file yellow">lifts_lift lifts_lifts</td>
 922             <td class="snnn file yellow">
 923               <br />
 924             </td>
 925             <td class="ssnn file yellow">
 926               <br />
 927             </td>
 928           </tr>
 929           <tr>
 930             <td class="nnns component yellow">
 931               <br />
 932             </td>
 933             <td class="snns plane yellow">support for generic relocation</td>
 934             <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
 935             <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
 936             <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
 937             <td class="ssnn file yellow">gr2_gr2</td>
 938           </tr>
 939           <tr>
 940             <td class="snns component orange">relocation</td>
 941             <td class="snns plane orange">structural successor for closures</td>
 942             <td class="snns file orange">fsup ( ⦃?,?,?⦄ ⊃ ⦃?,?,?⦄ )</td>
 943             <td class="snnn file orange">fsupq ( ⦃?,?,?⦄ ⊃⸮ ⦃?,?,?⦄ )</td>
 944             <td class="snnn file orange">fsupq_alt ( ⦃?,?,?⦄ ⊃⊃⸮ ⦃?,?,?⦄ )</td>
 945             <td class="ssnn file orange">
 946               <br />
 947             </td>
 948           </tr>
 949           <tr>
 950             <td class="nnns component orange">
 951               <br />
 952             </td>
 953             <td class="snns plane orange">global env. slicing</td>
 954             <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
 955             <td class="snnn file orange">gdrop_gdrop</td>
 956             <td class="snnn file orange">
 957               <br />
 958             </td>
 959             <td class="ssnn file orange">
 960               <br />
 961             </td>
 962           </tr>
 963           <tr>
 964             <td class="nnns component orange">
 965               <br />
 966             </td>
 967             <td class="snns plane orange">basic local env. slicing</td>
 968             <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
 969             <td class="snnn file orange">ldrop_append ldrop_lpx_sn ldrop_ldrop</td>
 970             <td class="snnn file orange">
 971               <br />
 972             </td>
 973             <td class="ssnn file orange">
 974               <br />
 975             </td>
 976           </tr>
 977           <tr>
 978             <td class="nnns component orange">
 979               <br />
 980             </td>
 981             <td class="snns plane orange">basic term relocation</td>
 982             <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
 983             <td class="snnn file orange">lift_lift_vector</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="nnns component orange">
 993               <br />
 994             </td>
 995             <td class="nnns plane orange">
 996               <br />
 997             </td>
 998             <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
 999             <td class="snnn file orange">lift_lift</td>
1000             <td class="snnn file orange">
1001               <br />
1002             </td>
1003             <td class="ssnn file orange">
1004               <br />
1005             </td>
1006           </tr>
1007           <tr>
1008             <td class="snns component red">grammar</td>
1009             <td class="snns plane red">pointwise extension of a relation</td>
1010             <td class="snns file red">lpx_sn</td>
1011             <td class="snnn file red">lpx_sn_tc lpx_sn_lpx_sn</td>
1012             <td class="snnn file red">
1013               <br />
1014             </td>
1015             <td class="ssnn file red">
1016               <br />
1017             </td>
1018           </tr>
1019           <tr>
1020             <td class="nnns component red">
1021               <br />
1022             </td>
1023             <td class="snns plane red">same top term constructor</td>
1024             <td class="snns file red">tstc ( ? ≃ ? )</td>
1025             <td class="snnn file red">tstc_tstc tstc_vector</td>
1026             <td class="snnn file red">
1027               <br />
1028             </td>
1029             <td class="ssnn file red">
1030               <br />
1031             </td>
1032           </tr>
1033           <tr>
1034             <td class="nnns component red">
1035               <br />
1036             </td>
1037             <td class="snns plane red">closures</td>
1038             <td class="snns file red">cl_shift ( ? @@ ? )</td>
1039             <td class="snnn file red">cl_weight ( ♯{?,?,?} )</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="snns plane red">internal syntax</td>
1052             <td class="snns file red">genv</td>
1053             <td class="snnn file red">
1054               <br />
1055             </td>
1056             <td class="snnn file red">
1057               <br />
1058             </td>
1059             <td class="ssnn file red">
1060               <br />
1061             </td>
1062           </tr>
1063           <tr>
1064             <td class="nnns component red">
1065               <br />
1066             </td>
1067             <td class="nnns plane red">
1068               <br />
1069             </td>
1070             <td class="snns file red">lenv</td>
1071             <td class="snnn file red">lenv_weight ( ♯{?} )</td>
1072             <td class="snnn file red">lenv_length ( |?| )</td>
1073             <td class="ssnn file red">lenv_append ( ? @@ ? )</td>
1074           </tr>
1075           <tr>
1076             <td class="nnns component red">
1077               <br />
1078             </td>
1079             <td class="nnns plane red">
1080               <br />
1081             </td>
1082             <td class="snns file red">term</td>
1083             <td class="snnn file red">term_weight ( ♯{?} )</td>
1084             <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
1085             <td class="ssnn file red">term_vector</td>
1086           </tr>
1087           <tr>
1088             <td class="nnns component red">
1089               <br />
1090             </td>
1091             <td class="nnns plane red">
1092               <br />
1093             </td>
1094             <td class="snns file red">item</td>
1095             <td class="snnn file red">
1096               <br />
1097             </td>
1098             <td class="snnn file red">
1099               <br />
1100             </td>
1101             <td class="ssnn file red">
1102               <br />
1103             </td>
1104           </tr>
1105           <tr>
1106             <td class="nnss component red">
1107               <br />
1108             </td>
1109             <td class="snss plane red">external syntax</td>
1110             <td class="snss file red">aarity</td>
1111             <td class="snsn file red">
1112               <br />
1113             </td>
1114             <td class="snsn file red">
1115               <br />
1116             </td>
1117             <td class="sssn file red">
1118               <br />
1119             </td>
1120           </tr>
1121         </tbody>
1122       </table>
1123     </div>
1124
1125    <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
1126    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
1127          one for each component.
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1155     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sun, 06 Oct 2013 13:50:12 +0200</div>
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