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    </div>
 137    <div xmlns:ld="http://lambdadelta.info/" class="text">
 138       <table cellpadding="4" cellspacing="0">
 139         <tbody>
 140           <tr>
 141             <td class="snns component grey">category</td>
 142             <td class="snns plane grey">objects</td>
 143             <td class="snnn number grey">
 144               <br />
 145             </td>
 146             <td class="snnn plane grey">
 147               <br />
 148             </td>
 149             <td class="snnn number grey">
 150               <br />
 151             </td>
 152             <td class="snnn plane grey">
 153               <br />
 154             </td>
 155             <td class="ssnn number grey">
 156               <br />
 157             </td>
 158           </tr>
 159           <tr>
 160             <td class="snns component cyan">sizes</td>
 161             <td class="snns plane cyan">files</td>
 162             <td class="snnn number cyan">187  </td>
 163             <td class="snns plane cyan">characters</td>
 164             <td class="snnn number cyan">363451</td>
 165             <td class="snns plane cyan">nodes</td>
 166             <td class="ssnn number cyan">982229</td>
 167           </tr>
 168           <tr>
 169             <td class="snns component green">propositions</td>
 170             <td class="snns plane green">theorems</td>
 171             <td class="snnn number green">85</td>
 172             <td class="snns plane green">lemmas</td>
 173             <td class="snnn number green">781</td>
 174             <td class="snns plane green">total</td>
 175             <td class="ssnn number green">866</td>
 176           </tr>
 177           <tr>
 178             <td class="snss component yellow">concepts</td>
 179             <td class="snss plane yellow">declared</td>
 180             <td class="snsn number yellow">42</td>
 181             <td class="snss plane yellow">defined</td>
 182             <td class="snsn number yellow">70</td>
 183             <td class="snss plane yellow">total</td>
 184             <td class="sssn number yellow">112</td>
 185           </tr>
 186         </tbody>
 187       </table>
 188     </div>
 189    <ul xmlns:ld="http://lambdadelta.info/">
 190       <li>
 191         <span class="date">In progress.</span>
 192          Context-sensitive subject equivalence
 193          for native type assignment.
 194    </li>
 195     </ul>
 196    <ul xmlns:ld="http://lambdadelta.info/">
 197       <li>
 198         <span class="date">In progress.</span>
 199          Closure of extended context-sensitive computation
 200          for native validity.
 201    </li>
 202     </ul>
 203    <ul xmlns:ld="http://lambdadelta.info/">
 204       <li>
 205         <span class="date">In progress.</span>
 206          Extended context-sensitive strong normalization
 207          for simply typed terms.
 208    </li>
 209     </ul>
 210    <ul xmlns:ld="http://lambdadelta.info/">
 211       <li>
 212         <span class="date">2013 April 16.</span>
 213          Reaxiomatized substitution and reduction
 214          commute with respect to subclosure
 215          (anniversary milestone).
 216    </li>
 217     </ul>
 218    <ul xmlns:ld="http://lambdadelta.info/">
 219       <li>
 220         <span class="date">2013 March 16.</span>
 221          Mutual recursive preservation of stratified native validity
 222          for hyper computation on closures.
 223    </li>
 224     </ul>
 225    <ul xmlns:ld="http://lambdadelta.info/">
 226       <li>
 227         <span class="date">2012 October 16.</span>
 228          Confluence for context-free parallel reduction on closures.
 229    </li>
 230     </ul>
 231    <ul xmlns:ld="http://lambdadelta.info/">
 232       <li>
 233         <span class="date">2012 July 26.</span>
 234          Term binders polarized to control ζ reduction.
 235    </li>
 236     </ul>
 237    <ul xmlns:ld="http://lambdadelta.info/">
 238       <li>
 239         <span class="date">2012 April 16.</span>
 240          Context-sensitive subject equivalence
 241          for atomic arity assignment
 242          (anniversary milestone).
 243    </li>
 244     </ul>
 245    <ul xmlns:ld="http://lambdadelta.info/">
 246       <li>
 247         <span class="date">2012 March 15.</span>
 248          Context-sensitive strong normalization
 249          for simply typed terms.
 250    </li>
 251     </ul>
 252    <ul xmlns:ld="http://lambdadelta.info/">
 253       <li>
 254         <span class="date">2012 January 27.</span>
 255          Support for abstract candidates of reducibility.
 256    </li>
 257     </ul>
 258    <ul xmlns:ld="http://lambdadelta.info/">
 259       <li>
 260         <span class="date">2011 September 21.</span>
 261          Confluence for context-sensitive parallel reduction on terms.
 262    </li>
 263     </ul>
 264    <ul xmlns:ld="http://lambdadelta.info/">
 265       <li>
 266         <span class="date">2011 September 6.</span>
 267          Confluence for context-free parallel reduction on terms.
 268    </li>
 269     </ul>
 270    <ul xmlns:ld="http://lambdadelta.info/">
 271       <li>
 272         <span class="date">2011 April 17.</span>
 273          Specification starts.
 274    </li>
 275     </ul>
 276
 277    <div xmlns:ld="http://lambdadelta.info/" class="head2">Logical Structure of the Specification</div>
 278    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in planes and components
 279          according to the following table.
 280          A notation file covering the whole specification is provided.
 281          The notation for the relations or functions introduced in each file
 282          is shown in parentheses (? are placeholders).
 283    </div>
 284    <div xmlns:ld="http://lambdadelta.info/" class="text">
 285       <table cellpadding="4" cellspacing="0">
 286         <tbody>
 287           <tr>
 288             <td class="snns component grey">component</td>
 289             <td class="snns plane grey">plane</td>
 290             <td class="snns file grey">files</td>
 291             <td class="snnn file grey">
 292               <br />
 293             </td>
 294             <td class="snnn file grey">
 295               <br />
 296             </td>
 297             <td class="ssnn file grey">
 298               <br />
 299             </td>
 300           </tr>
 301           <tr>
 302             <td class="snns component prune">dynamic typing</td>
 303             <td class="snns plane prune">"big tree" parallel computation</td>
 304             <td class="snns file prune">yprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )</td>
 305             <td class="snnn file prune">yprs_yprs</td>
 306             <td class="snnn file prune">ygt ( ? ⊢ ⦃?,?⦄ &gt;[g] ⦃?,?⦄ )</td>
 307             <td class="ssnn file prune">ygt_ygt</td>
 308           </tr>
 309           <tr>
 310             <td class="nnns component prune">
 311               <br />
 312             </td>
 313             <td class="snns plane prune">"big tree" parallel reduction</td>
 314             <td class="snns file prune">ypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )</td>
 315             <td class="snnn file prune">ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ )</td>
 316             <td class="snnn file prune">
 317               <br />
 318             </td>
 319             <td class="ssnn file prune">
 320               <br />
 321             </td>
 322           </tr>
 323           <tr>
 324             <td class="nnns component prune">
 325               <br />
 326             </td>
 327             <td class="snns plane prune">local env. ref. for stratified native validity</td>
 328             <td class="snns file prune">lsubsv ( ? ⊢ ? ¡⊑[?] ? )</td>
 329             <td class="snnn file prune">lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv</td>
 330             <td class="snnn file prune">
 331               <br />
 332             </td>
 333             <td class="ssnn file prune">
 334               <br />
 335             </td>
 336           </tr>
 337           <tr>
 338             <td class="nnns component prune">
 339               <br />
 340             </td>
 341             <td class="snns plane prune">stratified native validity</td>
 342             <td class="snns file prune">snv ( ⦃?,?⦄ ⊢ ? ¡[?] )</td>
 343             <td class="snnn file prune">snv_lift snv_ltpss_dx snv_ltpss_sn snv_aaa snv_ssta snv_sstas snv_ssta_ltpr snv_ltpr snv_cpcs</td>
 344             <td class="snnn file prune">
 345               <br />
 346             </td>
 347             <td class="ssnn file prune">
 348               <br />
 349             </td>
 350           </tr>
 351           <tr>
 352             <td class="snns component blue">equivalence</td>
 353             <td class="snns plane blue">focalized equivalence</td>
 354             <td class="snns file blue">lfpcs ( ⦃?⦄ ⬌* ⦃?⦄ )</td>
 355             <td class="snnn file blue">lfpcs_aaa lfpcs_fpcs lfpcs_lfprs lfpcs_lfpcs</td>
 356             <td class="snnn file blue">
 357               <br />
 358             </td>
 359             <td class="ssnn file blue">
 360               <br />
 361             </td>
 362           </tr>
 363           <tr>
 364             <td class="nnns component blue">
 365               <br />
 366             </td>
 367             <td class="nnns plane blue">
 368               <br />
 369             </td>
 370             <td class="snns file blue">fpcs ( ⦃?,?⦄ ⬌* ⦃?,?⦄ )</td>
 371             <td class="snnn file blue">fpcs_aaa fpcs_cpcs fpcs_fprs fpcs_fpcs</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="nnns component blue">
 381               <br />
 382             </td>
 383             <td class="snns plane blue">local env. ref. for stratified static type assignment</td>
 384             <td class="snns file blue">lsubss ( ? •⊑[?] ? )</td>
 385             <td class="snnn file blue">lsubss_ldrop lsubss_ssta lsubss_cpcs</td>
 386             <td class="snnn file blue">
 387               <br />
 388             </td>
 389             <td class="ssnn file blue">
 390               <br />
 391             </td>
 392           </tr>
 393           <tr>
 394             <td class="nnns component blue">
 395               <br />
 396             </td>
 397             <td class="snns plane blue">context-sensitive equivalence</td>
 398             <td class="snns file blue">cpcs ( ? ⊢ ? ⬌* ? )</td>
 399             <td class="snnn file blue">cpcs_ltpss_dx cpcs_ltpss_sn cpcs_delift cpcs_aaa cpcs_ltpr cpcs_cprs cpcs_cpcs</td>
 400             <td class="snnn file blue">
 401               <br />
 402             </td>
 403             <td class="ssnn file blue">
 404               <br />
 405             </td>
 406           </tr>
 407           <tr>
 408             <td class="snns component sky">conversion</td>
 409             <td class="snns plane sky">focalized conversion</td>
 410             <td class="snns file sky">lfpc ( ⦃?⦄ ⬌ ⦃?⦄ )</td>
 411             <td class="snnn file sky">lfpc_lfpc</td>
 412             <td class="snnn file sky">
 413               <br />
 414             </td>
 415             <td class="ssnn file sky">
 416               <br />
 417             </td>
 418           </tr>
 419           <tr>
 420             <td class="nnns component sky">
 421               <br />
 422             </td>
 423             <td class="nnns plane sky">
 424               <br />
 425             </td>
 426             <td class="snns file sky">fpc ( ⦃?,?⦄ ⬌ ⦃?,?⦄ )</td>
 427             <td class="snnn file sky">fpc_fpc</td>
 428             <td class="snnn file sky">
 429               <br />
 430             </td>
 431             <td class="ssnn file sky">
 432               <br />
 433             </td>
 434           </tr>
 435           <tr>
 436             <td class="nnns component sky">
 437               <br />
 438             </td>
 439             <td class="snns plane sky">context-sensitive conversion</td>
 440             <td class="snns file sky">cpc ( ? ⊢ ? ⬌ ? )</td>
 441             <td class="snnn file sky">cpc_cpc</td>
 442             <td class="snnn file sky">
 443               <br />
 444             </td>
 445             <td class="ssnn file sky">
 446               <br />
 447             </td>
 448           </tr>
 449           <tr>
 450             <td class="snns component cyan">computation</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_lpss 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">weakly normalizing computation</td>
 466             <td class="snns file cyan">cpe ( ? ⊢ ➡* 𝐍⦃?⦄ )</td>
 467             <td class="snnn file cyan">cpe_cpe</td>
 468             <td class="snnn file cyan">
 469               <br />
 470             </td>
 471             <td class="ssnn file cyan">
 472               <br />
 473             </td>
 474           </tr>
 475           <tr>
 476             <td class="nnns component cyan">
 477               <br />
 478             </td>
 479             <td class="snns plane cyan">strongly normalizing computation</td>
 480             <td class="snns file cyan">csn_vector ( ? ⊢ ⬊* ? )</td>
 481             <td class="snnn file cyan">csn_tstc_vector csn_aaa</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="nnns plane cyan">
 494               <br />
 495             </td>
 496             <td class="snns file cyan">csn ( ? ⊢ ⬊* ? )</td>
 497             <td class="snnn file cyan">csn_alt ( ? ⊢ ⬊⬊* ? )</td>
 498             <td class="snnn file cyan">csn_lift csn_lpr</td>
 499             <td class="ssnn file cyan">
 500               <br />
 501             </td>
 502           </tr>
 503           <tr>
 504             <td class="nnns component cyan">
 505               <br />
 506             </td>
 507             <td class="snns plane cyan">context-sensitive computation</td>
 508             <td class="snns file cyan">lprs ( ? ⊢ ➡* ? )</td>
 509             <td class="snnn file cyan">lprs_alt ( ? ⊢ ➡➡* ? )</td>
 510             <td class="snnn file cyan">lprs_ldrop lprs_lpss lprs_aaa lprs_cprs lprs_lprs</td>
 511             <td class="ssnn file cyan">
 512               <br />
 513             </td>
 514           </tr>
 515           <tr>
 516             <td class="nnns component cyan">
 517               <br />
 518             </td>
 519             <td class="nnns plane cyan">
 520               <br />
 521             </td>
 522             <td class="snns file cyan">cprs ( ? ⊢ ? ➡* ?)</td>
 523             <td class="snnn file cyan">cprs_tstc cprs_tstc_vector cprs_lift cprs_lpss cprs_aaa cprs_cprs</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">local env. ref. for abstract candidates of reducibility</td>
 536             <td class="snns file cyan">lsubc ( ? ⊑[?] ? )</td>
 537             <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
 538             <td class="snnn file cyan">
 539               <br />
 540             </td>
 541             <td class="ssnn file cyan">
 542               <br />
 543             </td>
 544           </tr>
 545           <tr>
 546             <td class="nnns component cyan">
 547               <br />
 548             </td>
 549             <td class="snns plane cyan">support for abstract computation properties</td>
 550             <td class="snns file cyan">acp</td>
 551             <td class="snnn file cyan">acp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )</td>
 552             <td class="snnn file cyan">acp_aaa</td>
 553             <td class="ssnn file cyan">
 554               <br />
 555             </td>
 556           </tr>
 557           <tr>
 558             <td class="snns component water">reduction</td>
 559             <td class="snns plane water">context-sensitive normal forms</td>
 560             <td class="snns file water">cnf ( ? ⊢ 𝐍⦃?⦄ )</td>
 561             <td class="snnn file water">cnf_liftt cnf_crf cnf_cif</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="snns plane water">context-sensitive reduction</td>
 574             <td class="snns file water">lpr ( ? ⊢ ➡ ? )</td>
 575             <td class="snnn file water">lpr_ldrop lpr_lpss lpr_aaa lpr_lpr</td>
 576             <td class="snnn file water">
 577               <br />
 578             </td>
 579             <td class="ssnn file water">
 580               <br />
 581             </td>
 582           </tr>
 583           <tr>
 584             <td class="nnns component water">
 585               <br />
 586             </td>
 587             <td class="nnns plane water">
 588               <br />
 589             </td>
 590             <td class="snns file water">cpr ( ? ⊢ ? ➡ ? )</td>
 591             <td class="snnn file water">cpr_lift cpr_cif</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 reducible forms</td>
 604             <td class="snns file water">crf ( ? ⊢ 𝐑⦃?⦄ )</td>
 605             <td class="snnn file water">crf_append</td>
 606             <td class="snnn file water">cif ( ? ⊢ 𝐈⦃?⦄ )</td>
 607             <td class="ssnn file water">cif_append</td>
 608           </tr>
 609           <tr>
 610             <td class="snns component green">unfold</td>
 611             <td class="snns plane green">restricted parallel computation</td>
 612             <td class="snns file green">lpqs ( ? ⊢ ➤* ? )</td>
 613             <td class="snnn file green">lpqs_ldrop lpqs_cpqs lpqs_lpqs</td>
 614             <td class="snnn file green">
 615               <br />
 616             </td>
 617             <td class="ssnn file green">
 618               <br />
 619             </td>
 620           </tr>
 621           <tr>
 622             <td class="nnns component green">
 623               <br />
 624             </td>
 625             <td class="nnns plane green">
 626               <br />
 627             </td>
 628             <td class="snns file green">cpqs ( ? ⊢ ? ➤* ? )</td>
 629             <td class="snnn file green">cpqs_lift</td>
 630             <td class="snnn file green">
 631               <br />
 632             </td>
 633             <td class="ssnn file green">
 634               <br />
 635             </td>
 636           </tr>
 637           <tr>
 638             <td class="nnns component green">
 639               <br />
 640             </td>
 641             <td class="snns plane green">unfold</td>
 642             <td class="snns file green">unfold ( ? ⊢ ? ⧫* ? )</td>
 643             <td class="snnn file green">
 644               <br />
 645             </td>
 646             <td class="snnn file green">
 647               <br />
 648             </td>
 649             <td class="ssnn file green">
 650               <br />
 651             </td>
 652           </tr>
 653           <tr>
 654             <td class="nnns component green">
 655               <br />
 656             </td>
 657             <td class="snns plane green">iterated stratified static type assignment</td>
 658             <td class="snns file green">sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )</td>
 659             <td class="snnn file green">sstas_lift sstas_lpss sstas_aaa sstas_sstas</td>
 660             <td class="snnn file green">
 661               <br />
 662             </td>
 663             <td class="ssnn file green">
 664               <br />
 665             </td>
 666           </tr>
 667           <tr>
 668             <td class="snns component grass">static typing</td>
 669             <td class="snns plane grass">stratified static type assignment</td>
 670             <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
 671             <td class="snnn file grass">ssta_lift ssta_lpss ssta_aaa ssta_ssta</td>
 672             <td class="snnn file grass">
 673               <br />
 674             </td>
 675             <td class="ssnn file grass">
 676               <br />
 677             </td>
 678           </tr>
 679           <tr>
 680             <td class="nnns component grass">
 681               <br />
 682             </td>
 683             <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
 684             <td class="snns file grass">lsuba ( ? ⁝⊑ ? )</td>
 685             <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
 686             <td class="snnn file grass">
 687               <br />
 688             </td>
 689             <td class="ssnn file grass">
 690               <br />
 691             </td>
 692           </tr>
 693           <tr>
 694             <td class="nnns component grass">
 695               <br />
 696             </td>
 697             <td class="snns plane grass">atomic arity assignment</td>
 698             <td class="snns file grass">aaa ( ? ⊢ ? ⁝ ? )</td>
 699             <td class="snnn file grass">aaa_lift aaa_lifts aaa_lpss aaa_aaa</td>
 700             <td class="snnn file grass">
 701               <br />
 702             </td>
 703             <td class="ssnn file grass">
 704               <br />
 705             </td>
 706           </tr>
 707           <tr>
 708             <td class="nnns component grass">
 709               <br />
 710             </td>
 711             <td class="snns plane grass">parameters</td>
 712             <td class="snns file grass">sh</td>
 713             <td class="snnn file grass">sd</td>
 714             <td class="snnn file grass">
 715               <br />
 716             </td>
 717             <td class="ssnn file grass">
 718               <br />
 719             </td>
 720           </tr>
 721           <tr>
 722             <td class="snns component yellow">substitution</td>
 723             <td class="snns plane yellow">parallel substitution</td>
 724             <td class="snns file yellow">lpss ( ? ⊢ ▶* ? )</td>
 725             <td class="snnn file yellow">lpss_ldrop lpss_cpss lpss_lpss</td>
 726             <td class="snnn file yellow">
 727               <br />
 728             </td>
 729             <td class="ssnn file yellow">
 730               <br />
 731             </td>
 732           </tr>
 733           <tr>
 734             <td class="nnns component yellow">
 735               <br />
 736             </td>
 737             <td class="nnns plane yellow">
 738               <br />
 739             </td>
 740             <td class="snns file yellow">cpss ( ? ⊢ ? ▶* ? )</td>
 741             <td class="snnn file yellow">cpss_lift</td>
 742             <td class="snnn file yellow">
 743               <br />
 744             </td>
 745             <td class="ssnn file yellow">
 746               <br />
 747             </td>
 748           </tr>
 749           <tr>
 750             <td class="nnns component yellow">
 751               <br />
 752             </td>
 753             <td class="snns plane yellow">local env. ref. for substitution</td>
 754             <td class="snns file yellow">lsubr ( ? ⊑ ? )</td>
 755             <td class="snnn file yellow">lsubr_lsubr</td>
 756             <td class="snnn file yellow">
 757               <br />
 758             </td>
 759             <td class="ssnn file yellow">
 760               <br />
 761             </td>
 762           </tr>
 763           <tr>
 764             <td class="nnns component yellow">
 765               <br />
 766             </td>
 767             <td class="snns plane yellow">iterated structural successor for closures</td>
 768             <td class="snns file yellow">fsups ( ⦃?,?⦄ ⊃* ⦃?,?⦄ )</td>
 769             <td class="snnn file yellow">fsups_fsups</td>
 770             <td class="snnn file yellow">
 771               <br />
 772             </td>
 773             <td class="ssnn file yellow">
 774               <br />
 775             </td>
 776           </tr>
 777           <tr>
 778             <td class="nnns component yellow">
 779               <br />
 780             </td>
 781             <td class="nnns plane yellow">
 782               <br />
 783             </td>
 784             <td class="snns file yellow">fsupp ( ⦃?,?⦄ ⊃+ ⦃?,?⦄ )</td>
 785             <td class="snnn file yellow">fsupp_fsupp</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="snns plane yellow">generic local env. slicing</td>
 798             <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
 799             <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</td>
 800             <td class="snnn file yellow">
 801               <br />
 802             </td>
 803             <td class="ssnn file yellow">
 804               <br />
 805             </td>
 806           </tr>
 807           <tr>
 808             <td class="nnns component yellow">
 809               <br />
 810             </td>
 811             <td class="snns plane yellow">generic term relocation</td>
 812             <td class="snns file yellow">lifts_vector ( ⇧*[?] ? ≡ ? )</td>
 813             <td class="snnn file yellow">lifts_lift_vector</td>
 814             <td class="snnn file yellow">
 815               <br />
 816             </td>
 817             <td class="ssnn file yellow">
 818               <br />
 819             </td>
 820           </tr>
 821           <tr>
 822             <td class="nnns component yellow">
 823               <br />
 824             </td>
 825             <td class="nnns plane yellow">
 826               <br />
 827             </td>
 828             <td class="snns file yellow">lifts ( ⇧*[?] ? ≡ ? )</td>
 829             <td class="snnn file yellow">lifts_lift lifts_lifts</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="snns plane yellow">support for generic relocation</td>
 842             <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
 843             <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
 844             <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
 845             <td class="ssnn file yellow">gr2_gr2</td>
 846           </tr>
 847           <tr>
 848             <td class="snns component orange">relocation</td>
 849             <td class="snns plane orange">structural successor for closures</td>
 850             <td class="snns file orange">fsup ( ⦃?,?⦄ ⊃ ⦃?,?⦄ )</td>
 851             <td class="snnn file orange">
 852               <br />
 853             </td>
 854             <td class="snnn file orange">
 855               <br />
 856             </td>
 857             <td class="ssnn file orange">
 858               <br />
 859             </td>
 860           </tr>
 861           <tr>
 862             <td class="nnns component orange">
 863               <br />
 864             </td>
 865             <td class="snns plane orange">global env. slicing</td>
 866             <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
 867             <td class="snnn file orange">gdrop_gdrop</td>
 868             <td class="snnn file orange">
 869               <br />
 870             </td>
 871             <td class="ssnn file orange">
 872               <br />
 873             </td>
 874           </tr>
 875           <tr>
 876             <td class="nnns component orange">
 877               <br />
 878             </td>
 879             <td class="snns plane orange">basic local env. slicing</td>
 880             <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
 881             <td class="snnn file orange">ldrop_append ldrop_lpx_sn ldrop_ldrop</td>
 882             <td class="snnn file orange">
 883               <br />
 884             </td>
 885             <td class="ssnn file orange">
 886               <br />
 887             </td>
 888           </tr>
 889           <tr>
 890             <td class="nnns component orange">
 891               <br />
 892             </td>
 893             <td class="snns plane orange">basic term relocation</td>
 894             <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
 895             <td class="snnn file orange">lift_lift_vector</td>
 896             <td class="snnn file orange">
 897               <br />
 898             </td>
 899             <td class="ssnn file orange">
 900               <br />
 901             </td>
 902           </tr>
 903           <tr>
 904             <td class="nnns component orange">
 905               <br />
 906             </td>
 907             <td class="nnns plane orange">
 908               <br />
 909             </td>
 910             <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
 911             <td class="snnn file orange">lift_lift</td>
 912             <td class="snnn file orange">
 913               <br />
 914             </td>
 915             <td class="ssnn file orange">
 916               <br />
 917             </td>
 918           </tr>
 919           <tr>
 920             <td class="snns component red">grammar</td>
 921             <td class="snns plane red">pointwise extension of a relation</td>
 922             <td class="snns file red">lpx_sn</td>
 923             <td class="snnn file red">lpx_sn_tc lpx_sn_lpx_sn</td>
 924             <td class="snnn file red">
 925               <br />
 926             </td>
 927             <td class="ssnn file red">
 928               <br />
 929             </td>
 930           </tr>
 931           <tr>
 932             <td class="nnns component red">
 933               <br />
 934             </td>
 935             <td class="snns plane red">same top term constructor</td>
 936             <td class="snns file red">tstc ( ? ≃ ? )</td>
 937             <td class="snnn file red">tstc_tstc tstc_vector</td>
 938             <td class="snnn file red">
 939               <br />
 940             </td>
 941             <td class="ssnn file red">
 942               <br />
 943             </td>
 944           </tr>
 945           <tr>
 946             <td class="nnns component red">
 947               <br />
 948             </td>
 949             <td class="snns plane red">closures</td>
 950             <td class="snns file red">cl_shift ( ? @@ ? )</td>
 951             <td class="snnn file red">cl_weight ( ♯{?,?} )</td>
 952             <td class="snnn file red">
 953               <br />
 954             </td>
 955             <td class="ssnn file red">
 956               <br />
 957             </td>
 958           </tr>
 959           <tr>
 960             <td class="nnns component red">
 961               <br />
 962             </td>
 963             <td class="snns plane red">internal syntax</td>
 964             <td class="snns file red">genv</td>
 965             <td class="snnn file red">
 966               <br />
 967             </td>
 968             <td class="snnn file red">
 969               <br />
 970             </td>
 971             <td class="ssnn file red">
 972               <br />
 973             </td>
 974           </tr>
 975           <tr>
 976             <td class="nnns component red">
 977               <br />
 978             </td>
 979             <td class="nnns plane red">
 980               <br />
 981             </td>
 982             <td class="snns file red">lenv</td>
 983             <td class="snnn file red">lenv_weight ( ♯{?} )</td>
 984             <td class="snnn file red">lenv_length ( |?| )</td>
 985             <td class="ssnn file red">lenv_append ( ? @@ ? )</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">term</td>
 995             <td class="snnn file red">term_weight ( ♯{?} )</td>
 996             <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
 997             <td class="ssnn file red">term_vector</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">item</td>
1007             <td class="snnn file red">
1008               <br />
1009             </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="nnss component red">
1019               <br />
1020             </td>
1021             <td class="snss plane red">external syntax</td>
1022             <td class="snss file red">aarity</td>
1023             <td class="snsn file red">
1024               <br />
1025             </td>
1026             <td class="snsn file red">
1027               <br />
1028             </td>
1029             <td class="sssn file red">
1030               <br />
1031             </td>
1032           </tr>
1033         </tbody>
1034       </table>
1035     </div>
1036
1037    <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
1038    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
1039          one for each component.
1040    </div>
1041    <div class="spacer">
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1045       <br />
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1057       <a href="http://www.w3.org/Graphics/PNG/">
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1061         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
1062       </a>
1063     </div>
1064     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1065       <br />
1066     </div>
1067     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Thu, 09 May 2013 22:55:12 +0200</div>
1068 </body>
1069 </html>