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">256  </td>
 163             <td class="snns plane cyan">characters</td>
 164             <td class="snnn number cyan">489336</td>
 165             <td class="snns plane cyan">nodes</td>
 166             <td class="ssnn number cyan">1309021</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">1125</td>
 174             <td class="snns plane green">total</td>
 175             <td class="ssnn number green">1210</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">46</td>
 181             <td class="snss plane yellow">defined</td>
 182             <td class="snsn number yellow">83</td>
 183             <td class="snss plane yellow">total</td>
 184             <td class="sssn number yellow">129</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">2012 October 16.</span>
 213          Confluence for context-free parallel reduction on closures.
 214    </li>
 215     </ul>
 216    <ul xmlns:ld="http://lambdadelta.info/">
 217       <li>
 218         <span class="date">2012 July 26.</span>
 219          Term binders polarized to control ζ reduction.
 220    </li>
 221     </ul>
 222    <ul xmlns:ld="http://lambdadelta.info/">
 223       <li>
 224         <span class="date">2012 April 16.</span>
 225          Context-sensitive subject equivalence
 226          for atomic arity assignment
 227          (anniversary milestone).
 228    </li>
 229     </ul>
 230    <ul xmlns:ld="http://lambdadelta.info/">
 231       <li>
 232         <span class="date">2012 March 15.</span>
 233          Context-sensitive strong normalization
 234          for simply typed terms.
 235    </li>
 236     </ul>
 237    <ul xmlns:ld="http://lambdadelta.info/">
 238       <li>
 239         <span class="date">2012 January 27.</span>
 240          Support for abstract candidates of reducibility.
 241    </li>
 242     </ul>
 243    <ul xmlns:ld="http://lambdadelta.info/">
 244       <li>
 245         <span class="date">2011 September 21.</span>
 246          Confluence for context-sensitive parallel reduction on terms.
 247    </li>
 248     </ul>
 249    <ul xmlns:ld="http://lambdadelta.info/">
 250       <li>
 251         <span class="date">2011 September 6.</span>
 252          Confluence for context-free parallel reduction on terms.
 253    </li>
 254     </ul>
 255    <ul xmlns:ld="http://lambdadelta.info/">
 256       <li>
 257         <span class="date">2011 April 17.</span>
 258          Specification starts.
 259    </li>
 260     </ul>
 261
 262    <div xmlns:ld="http://lambdadelta.info/" class="head2">Logical Structure of the Specification</div>
 263    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in planes and components
 264          according to the following table.
 265          A notation file covering the whole specification is provided.
 266          The notation for the relations or functions introduced in each file
 267          is shown in parentheses (? are placeholders).
 268    </div>
 269    <div xmlns:ld="http://lambdadelta.info/" class="text">
 270       <table cellpadding="4" cellspacing="0">
 271         <tbody>
 272           <tr>
 273             <td class="snns component grey">component</td>
 274             <td class="snns plane grey">plane</td>
 275             <td class="snns file grey">files</td>
 276             <td class="snnn file grey">
 277               <br />
 278             </td>
 279             <td class="snnn file grey">
 280               <br />
 281             </td>
 282             <td class="snnn file grey">
 283               <br />
 284             </td>
 285             <td class="ssnn file grey">
 286               <br />
 287             </td>
 288           </tr>
 289           <tr>
 290             <td class="snns component prune">dynamic typing</td>
 291             <td class="snns plane prune">"big tree" parallel computation</td>
 292             <td class="snns file prune">yprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )</td>
 293             <td class="snnn file prune">yprs_yprs</td>
 294             <td class="snnn file prune">ygt ( ? ⊢ ⦃?,?⦄ &gt;[g] ⦃?,?⦄ )</td>
 295             <td class="snnn file prune">ygt_ygt</td>
 296             <td class="ssnn file prune">
 297               <br />
 298             </td>
 299           </tr>
 300           <tr>
 301             <td class="nnns component prune">
 302               <br />
 303             </td>
 304             <td class="snns plane prune">"big tree" parallel reduction</td>
 305             <td class="snns file prune">ypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )</td>
 306             <td class="snnn file prune">ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ )</td>
 307             <td class="snnn file prune">
 308               <br />
 309             </td>
 310             <td class="snnn file prune">
 311               <br />
 312             </td>
 313             <td class="ssnn file prune">
 314               <br />
 315             </td>
 316           </tr>
 317           <tr>
 318             <td class="nnns component prune">
 319               <br />
 320             </td>
 321             <td class="snns plane prune">local env. ref. for stratified native validity</td>
 322             <td class="snns file prune">lsubsv ( ? ⊢ ? ⊩:⊑[?] ? )</td>
 323             <td class="snnn file prune">lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv</td>
 324             <td class="snnn file prune">
 325               <br />
 326             </td>
 327             <td class="snnn file prune">
 328               <br />
 329             </td>
 330             <td class="ssnn file prune">
 331               <br />
 332             </td>
 333           </tr>
 334           <tr>
 335             <td class="nnns component prune">
 336               <br />
 337             </td>
 338             <td class="snns plane prune">stratified native validity</td>
 339             <td class="snns file prune">snv ( ⦃?,?⦄ ⊩ ? :[?] )</td>
 340             <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>
 341             <td class="snnn file prune">
 342               <br />
 343             </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="snnn file blue">
 360               <br />
 361             </td>
 362             <td class="ssnn file blue">
 363               <br />
 364             </td>
 365           </tr>
 366           <tr>
 367             <td class="nnns component blue">
 368               <br />
 369             </td>
 370             <td class="nnns plane blue">
 371               <br />
 372             </td>
 373             <td class="snns file blue">fpcs ( ⦃?,?⦄ ⬌* ⦃?,?⦄ )</td>
 374             <td class="snnn file blue">fpcs_aaa fpcs_cpcs fpcs_fprs fpcs_fpcs</td>
 375             <td class="snnn file blue">
 376               <br />
 377             </td>
 378             <td class="snnn file blue">
 379               <br />
 380             </td>
 381             <td class="ssnn file blue">
 382               <br />
 383             </td>
 384           </tr>
 385           <tr>
 386             <td class="nnns component blue">
 387               <br />
 388             </td>
 389             <td class="snns plane blue">local env. ref. for context-sensitive equivalence</td>
 390             <td class="snns file blue">lsubse ( ? ⊢•⊑[?] ? )</td>
 391             <td class="snnn file blue">lsubse_ldrop lsubse_ssta lsubse_cpcs</td>
 392             <td class="snnn file blue">
 393               <br />
 394             </td>
 395             <td class="snnn file blue">
 396               <br />
 397             </td>
 398             <td class="ssnn file blue">
 399               <br />
 400             </td>
 401           </tr>
 402           <tr>
 403             <td class="nnns component blue">
 404               <br />
 405             </td>
 406             <td class="snns plane blue">context-sensitive equivalence</td>
 407             <td class="snns file blue">cpcs ( ? ⊢ ? ⬌* ? )</td>
 408             <td class="snnn file blue">cpcs_ltpss_dx cpcs_ltpss_sn cpcs_delift cpcs_aaa cpcs_ltpr cpcs_cprs cpcs_cpcs</td>
 409             <td class="snnn file blue">
 410               <br />
 411             </td>
 412             <td class="snnn file blue">
 413               <br />
 414             </td>
 415             <td class="ssnn file blue">
 416               <br />
 417             </td>
 418           </tr>
 419           <tr>
 420             <td class="snns component sky">conversion</td>
 421             <td class="snns plane sky">focalized conversion</td>
 422             <td class="snns file sky">lfpc ( ⦃?⦄ ⬌ ⦃?⦄ )</td>
 423             <td class="snnn file sky">lfpc_lfpc</td>
 424             <td class="snnn file sky">
 425               <br />
 426             </td>
 427             <td class="snnn file sky">
 428               <br />
 429             </td>
 430             <td class="ssnn file sky">
 431               <br />
 432             </td>
 433           </tr>
 434           <tr>
 435             <td class="nnns component sky">
 436               <br />
 437             </td>
 438             <td class="nnns plane sky">
 439               <br />
 440             </td>
 441             <td class="snns file sky">fpc ( ⦃?,?⦄ ⬌ ⦃?,?⦄ )</td>
 442             <td class="snnn file sky">fpc_fpc</td>
 443             <td class="snnn file sky">
 444               <br />
 445             </td>
 446             <td class="snnn file sky">
 447               <br />
 448             </td>
 449             <td class="ssnn file sky">
 450               <br />
 451             </td>
 452           </tr>
 453           <tr>
 454             <td class="nnns component sky">
 455               <br />
 456             </td>
 457             <td class="snns plane sky">context-sensitive conversion</td>
 458             <td class="snns file sky">cpc ( ? ⊢ ? ⬌ ? )</td>
 459             <td class="snnn file sky">cpc_cpc</td>
 460             <td class="snnn file sky">
 461               <br />
 462             </td>
 463             <td class="snnn file sky">
 464               <br />
 465             </td>
 466             <td class="ssnn file sky">
 467               <br />
 468             </td>
 469           </tr>
 470           <tr>
 471             <td class="snns component cyan">computation</td>
 472             <td class="snns plane cyan">focalized computation</td>
 473             <td class="snns file cyan">lfprs ( ⦃?⦄ ➡* ⦃?⦄ )</td>
 474             <td class="snnn file cyan">lfprs_aaa lfprs_ltprs lfprs_cprs lfprs_fprs lfprs_lfprs</td>
 475             <td class="snnn file cyan">
 476               <br />
 477             </td>
 478             <td class="snnn file cyan">
 479               <br />
 480             </td>
 481             <td class="ssnn file cyan">
 482               <br />
 483             </td>
 484           </tr>
 485           <tr>
 486             <td class="nnns component cyan">
 487               <br />
 488             </td>
 489             <td class="nnns plane cyan">
 490               <br />
 491             </td>
 492             <td class="snns file cyan">fprs ( ⦃?,?⦄ ➡* ⦃?,?⦄ )</td>
 493             <td class="snnn file cyan">fprs_aaa fprs_fprs</td>
 494             <td class="snnn file cyan">
 495               <br />
 496             </td>
 497             <td class="snnn file cyan">
 498               <br />
 499             </td>
 500             <td class="ssnn file cyan">
 501               <br />
 502             </td>
 503           </tr>
 504           <tr>
 505             <td class="nnns component cyan">
 506               <br />
 507             </td>
 508             <td class="snns plane cyan">decomposed extended computation</td>
 509             <td class="snns file cyan">dxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )</td>
 510             <td class="snnn file cyan">dxprs_lift dxprs_ltpss_dx dxprs_ltpss_sn dxprs_aaa dxprs_dxprs</td>
 511             <td class="snnn file cyan">
 512               <br />
 513             </td>
 514             <td class="snnn file cyan">
 515               <br />
 516             </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="snns plane cyan">weakly normalizing computation</td>
 526             <td class="snns file cyan">cpe ( ? ⊢ ➡* 𝐍⦃?⦄ )</td>
 527             <td class="snnn file cyan">cpe_cpe</td>
 528             <td class="snnn file cyan">
 529               <br />
 530             </td>
 531             <td class="snnn file cyan">
 532               <br />
 533             </td>
 534             <td class="ssnn file cyan">
 535               <br />
 536             </td>
 537           </tr>
 538           <tr>
 539             <td class="nnns component cyan">
 540               <br />
 541             </td>
 542             <td class="snns plane cyan">strongly normalizing computation</td>
 543             <td class="snns file cyan">csn_vector ( ? ⊢ ⬊* ? )</td>
 544             <td class="snnn file cyan">csn_cpr_vector csn_tstc_vector csn_aaa</td>
 545             <td class="snnn file cyan">
 546               <br />
 547             </td>
 548             <td class="snnn file cyan">
 549               <br />
 550             </td>
 551             <td class="ssnn file cyan">
 552               <br />
 553             </td>
 554           </tr>
 555           <tr>
 556             <td class="nnns component cyan">
 557               <br />
 558             </td>
 559             <td class="nnns plane cyan">
 560               <br />
 561             </td>
 562             <td class="snns file cyan">csn ( ? ⊢ ⬊* ? )</td>
 563             <td class="snnn file cyan">csn_alt ( ? ⊢ ⬊⬊* ? )</td>
 564             <td class="snnn file cyan">csn_lift csn_cpr csn_lfpr</td>
 565             <td class="snnn file cyan">
 566               <br />
 567             </td>
 568             <td class="ssnn file cyan">
 569               <br />
 570             </td>
 571           </tr>
 572           <tr>
 573             <td class="nnns component cyan">
 574               <br />
 575             </td>
 576             <td class="snns plane cyan">context-sensitive computation</td>
 577             <td class="snns file cyan">cprs (? ⊢ ? ➡* ?)</td>
 578             <td class="snnn file cyan">cprs_lift cprs_tpss cprs_ltpss_dx cprs_ltpss_sn cprs_delift cprs_aaa cprs_ltpr cprs_lfpr cprs_cprs cprs_lfprs cprs_tstc cprs_tstc_vector</td>
 579             <td class="snnn file cyan">
 580               <br />
 581             </td>
 582             <td class="snnn file cyan">
 583               <br />
 584             </td>
 585             <td class="ssnn file cyan">
 586               <br />
 587             </td>
 588           </tr>
 589           <tr>
 590             <td class="nnns component cyan">
 591               <br />
 592             </td>
 593             <td class="snns plane cyan">context-free computation</td>
 594             <td class="snns file cyan">ltprs ( ? ➡* ? )</td>
 595             <td class="snnn file cyan">ltprs_alt ( ? ➡➡* ? )</td>
 596             <td class="snnn file cyan">ltprs_ldrop ltprs_ltprs</td>
 597             <td class="snnn file cyan">
 598               <br />
 599             </td>
 600             <td class="ssnn file cyan">
 601               <br />
 602             </td>
 603           </tr>
 604           <tr>
 605             <td class="nnns component cyan">
 606               <br />
 607             </td>
 608             <td class="nnns plane cyan">
 609               <br />
 610             </td>
 611             <td class="snns file cyan">tprs ( ? ➡* ?)</td>
 612             <td class="snnn file cyan">tprs_lift tprs_tprs</td>
 613             <td class="snnn file cyan">
 614               <br />
 615             </td>
 616             <td class="snnn file cyan">
 617               <br />
 618             </td>
 619             <td class="ssnn file cyan">
 620               <br />
 621             </td>
 622           </tr>
 623           <tr>
 624             <td class="nnns component cyan">
 625               <br />
 626             </td>
 627             <td class="snns plane cyan">local env. ref. for abstract candidates of reducibility</td>
 628             <td class="snns file cyan">lsubc ( ? ⊑[?] ? )</td>
 629             <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
 630             <td class="snnn file cyan">
 631               <br />
 632             </td>
 633             <td class="snnn file cyan">
 634               <br />
 635             </td>
 636             <td class="ssnn file cyan">
 637               <br />
 638             </td>
 639           </tr>
 640           <tr>
 641             <td class="nnns component cyan">
 642               <br />
 643             </td>
 644             <td class="snns plane cyan">support for abstract computation properties</td>
 645             <td class="snns file cyan">acp</td>
 646             <td class="snnn file cyan">acp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )</td>
 647             <td class="snnn file cyan">acp_aaa</td>
 648             <td class="snnn file cyan">
 649               <br />
 650             </td>
 651             <td class="ssnn file cyan">
 652               <br />
 653             </td>
 654           </tr>
 655           <tr>
 656             <td class="snns component water">reducibility</td>
 657             <td class="snns plane water">context-sensitive focalized reduction</td>
 658             <td class="snns file water">cfpr ( ? ⊢ ⦃?,?⦄ ➡ ⦃?,?⦄ )</td>
 659             <td class="snnn file water">cnfpr_ltpss cfpr_aaa cfpr_cpr cfpr_cfpr</td>
 660             <td class="snnn file water">
 661               <br />
 662             </td>
 663             <td class="snnn file water">
 664               <br />
 665             </td>
 666             <td class="ssnn file water">
 667               <br />
 668             </td>
 669           </tr>
 670           <tr>
 671             <td class="nnns component water">
 672               <br />
 673             </td>
 674             <td class="snns plane water">context-free focalized reduction</td>
 675             <td class="snns file water">lfpr ( ⦃?⦄ ➡ ⦃?⦄ )</td>
 676             <td class="snnn file water">lfpr_alt ( ⦃?⦄ ➡➡ ⦃?⦄ )</td>
 677             <td class="snnn file water">lfpr_aaa lfpr_cpr lfpr_fpr lfpr_lfpr</td>
 678             <td class="snnn file water">
 679               <br />
 680             </td>
 681             <td class="ssnn file water">
 682               <br />
 683             </td>
 684           </tr>
 685           <tr>
 686             <td class="nnns component water">
 687               <br />
 688             </td>
 689             <td class="nnns plane water">
 690               <br />
 691             </td>
 692             <td class="snns file water">fpr ( ⦃?,?⦄ ➡ ⦃?,?⦄ )</td>
 693             <td class="snnn file water">fpr_cpr fpr_fpr</td>
 694             <td class="snnn file water">
 695               <br />
 696             </td>
 697             <td class="snnn file water">
 698               <br />
 699             </td>
 700             <td class="ssnn file water">
 701               <br />
 702             </td>
 703           </tr>
 704           <tr>
 705             <td class="nnns component water">
 706               <br />
 707             </td>
 708             <td class="snns plane water">context-sensitive normal forms</td>
 709             <td class="snns file water">cnf ( ? ⊢ 𝐍⦃?⦄ )</td>
 710             <td class="snnn file water">cnf_lift cnf_cif</td>
 711             <td class="snnn file water">
 712               <br />
 713             </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 reduction</td>
 726             <td class="snns file water">cpr ( ? ⊢ ? ➡ ? )</td>
 727             <td class="snnn file water">cpr_lift cpr_tpss cpr_ltpss_dx cpr_ltpss_sn cpr_delift cpr_aaa cpr_ltpr cpr_cpr</td>
 728             <td class="snnn file water">
 729               <br />
 730             </td>
 731             <td class="snnn file water">
 732               <br />
 733             </td>
 734             <td class="ssnn file water">
 735               <br />
 736             </td>
 737           </tr>
 738           <tr>
 739             <td class="nnns component water">
 740               <br />
 741             </td>
 742             <td class="snns plane water">context-sensitive reducible forms</td>
 743             <td class="snns file water">crf ( ? ⊢ 𝐑⦃?⦄ )</td>
 744             <td class="snnn file water">crf_append</td>
 745             <td class="snnn file water">cif ( ? ⊢ 𝐈⦃?⦄ )</td>
 746             <td class="snnn file water">cif_append</td>
 747             <td class="ssnn file water">
 748               <br />
 749             </td>
 750           </tr>
 751           <tr>
 752             <td class="nnns component water">
 753               <br />
 754             </td>
 755             <td class="snns plane water">context-free normal forms</td>
 756             <td class="snns file water">thnf ( 𝐇𝐍⦃?⦄ )</td>
 757             <td class="snnn file water">
 758               <br />
 759             </td>
 760             <td class="snnn file water">
 761               <br />
 762             </td>
 763             <td class="snnn file water">
 764               <br />
 765             </td>
 766             <td class="ssnn file water">
 767               <br />
 768             </td>
 769           </tr>
 770           <tr>
 771             <td class="nnns component water">
 772               <br />
 773             </td>
 774             <td class="snns plane water">context-free reduction</td>
 775             <td class="snns file water">ltpr ( ? ➡ ? )</td>
 776             <td class="snnn file water">ltpr_ldrop ltpr_tps ltpr_ltpss_dx ltpr_ltpss_sn ltpr_aaa ltpr_ltpr</td>
 777             <td class="snnn file water">
 778               <br />
 779             </td>
 780             <td class="snnn file water">
 781               <br />
 782             </td>
 783             <td class="ssnn file water">
 784               <br />
 785             </td>
 786           </tr>
 787           <tr>
 788             <td class="nnns component water">
 789               <br />
 790             </td>
 791             <td class="nnns plane water">
 792               <br />
 793             </td>
 794             <td class="snns file water">tpr ( ? ➡ ? )</td>
 795             <td class="snnn file water">tpr_lift tpr_tps tpr_tpss tpr_delift tpr_tpr</td>
 796             <td class="snnn file water">
 797               <br />
 798             </td>
 799             <td class="snnn file water">
 800               <br />
 801             </td>
 802             <td class="ssnn file water">
 803               <br />
 804             </td>
 805           </tr>
 806           <tr>
 807             <td class="snns component green">unwind</td>
 808             <td class="snns plane green">iterated stratified static type assignment</td>
 809             <td class="snns file green">sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )</td>
 810             <td class="snnn file green">sstas_lift sstas_ltpss_dx sstas_ltpss_sn sstas_aaa sstas_sstas</td>
 811             <td class="snnn file green">
 812               <br />
 813             </td>
 814             <td class="snnn file green">
 815               <br />
 816             </td>
 817             <td class="ssnn file green">
 818               <br />
 819             </td>
 820           </tr>
 821           <tr>
 822             <td class="snns component grass">static typing</td>
 823             <td class="snns plane grass">stratified static type assignment</td>
 824             <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
 825             <td class="snnn file grass">ssta_lift ssta_ltpss_dx ssta_ltpss_sn ssta_aaa ssta_ssta</td>
 826             <td class="snnn file grass">
 827               <br />
 828             </td>
 829             <td class="snnn file grass">
 830               <br />
 831             </td>
 832             <td class="ssnn file grass">
 833               <br />
 834             </td>
 835           </tr>
 836           <tr>
 837             <td class="nnns component grass">
 838               <br />
 839             </td>
 840             <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
 841             <td class="snns file grass">lsuba ( ? ⁝⊑ ? )</td>
 842             <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
 843             <td class="snnn file grass">
 844               <br />
 845             </td>
 846             <td class="snnn file grass">
 847               <br />
 848             </td>
 849             <td class="ssnn file grass">
 850               <br />
 851             </td>
 852           </tr>
 853           <tr>
 854             <td class="nnns component grass">
 855               <br />
 856             </td>
 857             <td class="snns plane grass">atomic arity assignment</td>
 858             <td class="snns file grass">aaa ( ? ⊢ ? ⁝ ? )</td>
 859             <td class="snnn file grass">aaa_lift aaa_lifts aaa_ltpss_dx aaa_ltpss_sn aaa_aaa</td>
 860             <td class="snnn file grass">
 861               <br />
 862             </td>
 863             <td class="snnn file grass">
 864               <br />
 865             </td>
 866             <td class="ssnn file grass">
 867               <br />
 868             </td>
 869           </tr>
 870           <tr>
 871             <td class="nnns component grass">
 872               <br />
 873             </td>
 874             <td class="snns plane grass">parameters</td>
 875             <td class="snns file grass">sh</td>
 876             <td class="snnn file grass">sd</td>
 877             <td class="snnn file grass">
 878               <br />
 879             </td>
 880             <td class="snnn file grass">
 881               <br />
 882             </td>
 883             <td class="ssnn file grass">
 884               <br />
 885             </td>
 886           </tr>
 887           <tr>
 888             <td class="snns component yellow">unfold</td>
 889             <td class="snns plane yellow">basic local env. thinning</td>
 890             <td class="snns file yellow">thin ( ? ▼*[?,?] ≡ ? )</td>
 891             <td class="snnn file yellow">thin_ldrop thin_delift</td>
 892             <td class="snnn file yellow">
 893               <br />
 894             </td>
 895             <td class="snnn file yellow">
 896               <br />
 897             </td>
 898             <td class="ssnn file yellow">
 899               <br />
 900             </td>
 901           </tr>
 902           <tr>
 903             <td class="nnns component yellow">
 904               <br />
 905             </td>
 906             <td class="snns plane yellow">inverse basic term relocation</td>
 907             <td class="snns file yellow">delift ( ? ⊢ ? ▼*[?,?] ≡ ? )</td>
 908             <td class="snnn file yellow">delift_alt ( ? ⊢ ? ▼▼*[?,?] ≡ ? )</td>
 909             <td class="snnn file yellow">delift_lift delift_tpss delift_ltpss delift_delift</td>
 910             <td class="snnn file yellow">
 911               <br />
 912             </td>
 913             <td class="ssnn file yellow">
 914               <br />
 915             </td>
 916           </tr>
 917           <tr>
 918             <td class="nnns component yellow">
 919               <br />
 920             </td>
 921             <td class="snns plane yellow">partial unfold</td>
 922             <td class="snns file yellow">ltpss_sn ( ? ⊢ ▶*[?,?] ? )</td>
 923             <td class="snnn file yellow">ltpss_sn_alt ( ? ⊢ ▶▶*[?,?] ? )</td>
 924             <td class="snnn file yellow">ltpss_sn_ldrop ltpss_sn_tps ltpss_sn_tpss ltpss_sn_ltpss_sn</td>
 925             <td class="snnn file yellow">
 926               <br />
 927             </td>
 928             <td class="ssnn file yellow">
 929               <br />
 930             </td>
 931           </tr>
 932           <tr>
 933             <td class="nnns component yellow">
 934               <br />
 935             </td>
 936             <td class="nnns plane yellow">
 937               <br />
 938             </td>
 939             <td class="snns file yellow">ltpss_dx ( ? ▶*[?,?] ? )</td>
 940             <td class="snnn file yellow">ltpss_dx_ldrop ltpss_dx_tps ltpss_dx_tpss ltpss_dx_ltpss_dx</td>
 941             <td class="snnn file yellow">
 942               <br />
 943             </td>
 944             <td class="snnn file yellow">
 945               <br />
 946             </td>
 947             <td class="ssnn file yellow">
 948               <br />
 949             </td>
 950           </tr>
 951           <tr>
 952             <td class="nnns component yellow">
 953               <br />
 954             </td>
 955             <td class="nnns plane yellow">
 956               <br />
 957             </td>
 958             <td class="snns file yellow">tpss ( ? ⊢ ? ▶*[?,?] ? )</td>
 959             <td class="snnn file yellow">tpss_alt ( ? ⊢ ? ▶▶*[?,?] ? )</td>
 960             <td class="snnn file yellow">tpss_lift</td>
 961             <td class="snnn file yellow">tpss_tpss</td>
 962             <td class="ssnn file yellow">
 963               <br />
 964             </td>
 965           </tr>
 966           <tr>
 967             <td class="nnns component yellow">
 968               <br />
 969             </td>
 970             <td class="snns plane yellow">generic local env. slicing</td>
 971             <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
 972             <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</td>
 973             <td class="snnn file yellow">
 974               <br />
 975             </td>
 976             <td class="snnn file yellow">
 977               <br />
 978             </td>
 979             <td class="ssnn file yellow">
 980               <br />
 981             </td>
 982           </tr>
 983           <tr>
 984             <td class="nnns component yellow">
 985               <br />
 986             </td>
 987             <td class="snns plane yellow">iterated restricted structural predecessor for closures</td>
 988             <td class="snns file yellow">frsups ( ⦃?,?⦄ ⧁* ⦃?,?⦄ )</td>
 989             <td class="snnn file yellow">frsups_frsups</td>
 990             <td class="snnn file yellow">
 991               <br />
 992             </td>
 993             <td class="snnn file yellow">
 994               <br />
 995             </td>
 996             <td class="ssnn file yellow">
 997               <br />
 998             </td>
 999           </tr>
1000           <tr>
1001             <td class="nnns component yellow">
1002               <br />
1003             </td>
1004             <td class="nnns plane yellow">
1005               <br />
1006             </td>
1007             <td class="snns file yellow">frsupp ( ⦃?,?⦄ ⧁+ ⦃?,?⦄ )</td>
1008             <td class="snnn file yellow">frsupp_frsupp</td>
1009             <td class="snnn file yellow">
1010               <br />
1011             </td>
1012             <td class="snnn file yellow">
1013               <br />
1014             </td>
1015             <td class="ssnn file yellow">
1016               <br />
1017             </td>
1018           </tr>
1019           <tr>
1020             <td class="nnns component yellow">
1021               <br />
1022             </td>
1023             <td class="snns plane yellow">generic term relocation</td>
1024             <td class="snns file yellow">lifts_vector ( ⇧*[?] ? ≡ ? )</td>
1025             <td class="snnn file yellow">lifts_lift_vector</td>
1026             <td class="snnn file yellow">
1027               <br />
1028             </td>
1029             <td class="snnn file yellow">
1030               <br />
1031             </td>
1032             <td class="ssnn file yellow">
1033               <br />
1034             </td>
1035           </tr>
1036           <tr>
1037             <td class="nnns component yellow">
1038               <br />
1039             </td>
1040             <td class="nnns plane yellow">
1041               <br />
1042             </td>
1043             <td class="snns file yellow">lifts ( ⇧*[?] ? ≡ ? )</td>
1044             <td class="snnn file yellow">lifts_lift lifts_lifts</td>
1045             <td class="snnn file yellow">
1046               <br />
1047             </td>
1048             <td class="snnn file yellow">
1049               <br />
1050             </td>
1051             <td class="ssnn file yellow">
1052               <br />
1053             </td>
1054           </tr>
1055           <tr>
1056             <td class="nnns component yellow">
1057               <br />
1058             </td>
1059             <td class="snns plane yellow">support for generic relocation</td>
1060             <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
1061             <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
1062             <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
1063             <td class="snnn file yellow">gr2_gr2</td>
1064             <td class="ssnn file yellow">
1065               <br />
1066             </td>
1067           </tr>
1068           <tr>
1069             <td class="snns component orange">substitution</td>
1070             <td class="snns plane orange">parallel substitution</td>
1071             <td class="snns file orange">tps ( ? ⊢ ? ▶[?,?] ? )</td>
1072             <td class="snnn file orange">tps_lift tps_tps</td>
1073             <td class="snnn file orange">
1074               <br />
1075             </td>
1076             <td class="snnn file orange">
1077               <br />
1078             </td>
1079             <td class="ssnn file orange">
1080               <br />
1081             </td>
1082           </tr>
1083           <tr>
1084             <td class="nnns component orange">
1085               <br />
1086             </td>
1087             <td class="snns plane orange">global env. slicing</td>
1088             <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
1089             <td class="snnn file orange">gdrop_gdrop</td>
1090             <td class="snnn file orange">
1091               <br />
1092             </td>
1093             <td class="snnn file orange">
1094               <br />
1095             </td>
1096             <td class="ssnn file orange">
1097               <br />
1098             </td>
1099           </tr>
1100           <tr>
1101             <td class="nnns component orange">
1102               <br />
1103             </td>
1104             <td class="snns plane orange">basic local env. slicing</td>
1105             <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
1106             <td class="snnn file orange">ldrop_append ldrop_lpx ldrop_sfr ldrop_ldrop</td>
1107             <td class="snnn file orange">
1108               <br />
1109             </td>
1110             <td class="snnn file orange">
1111               <br />
1112             </td>
1113             <td class="ssnn file orange">
1114               <br />
1115             </td>
1116           </tr>
1117           <tr>
1118             <td class="nnns component orange">
1119               <br />
1120             </td>
1121             <td class="snns plane orange">local env. ref. for substitution</td>
1122             <td class="snns file orange">lsubs ( ? ≼[?,?] ? )</td>
1123             <td class="snnn file orange">(lsubs_lsubs)</td>
1124             <td class="snnn file orange">lsubs_sfr ( ≽[?,?] ? )</td>
1125             <td class="snnn file orange">
1126               <br />
1127             </td>
1128             <td class="ssnn file orange">
1129               <br />
1130             </td>
1131           </tr>
1132           <tr>
1133             <td class="nnns component orange">
1134               <br />
1135             </td>
1136             <td class="snns plane orange">restricted structural predecessor for closures</td>
1137             <td class="snns file orange">frsup ( ⦃?,?⦄ ⧁ ⦃?,?⦄ )</td>
1138             <td class="snnn file orange">
1139               <br />
1140             </td>
1141             <td class="snnn file orange">
1142               <br />
1143             </td>
1144             <td class="snnn file orange">
1145               <br />
1146             </td>
1147             <td class="ssnn file orange">
1148               <br />
1149             </td>
1150           </tr>
1151           <tr>
1152             <td class="nnns component orange">
1153               <br />
1154             </td>
1155             <td class="snns plane orange">basic term relocation</td>
1156             <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
1157             <td class="snnn file orange">lift_lift_vector</td>
1158             <td class="snnn file orange">
1159               <br />
1160             </td>
1161             <td class="snnn file orange">
1162               <br />
1163             </td>
1164             <td class="ssnn file orange">
1165               <br />
1166             </td>
1167           </tr>
1168           <tr>
1169             <td class="nnns component orange">
1170               <br />
1171             </td>
1172             <td class="nnns plane orange">
1173               <br />
1174             </td>
1175             <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
1176             <td class="snnn file orange">lift_lift</td>
1177             <td class="snnn file orange">
1178               <br />
1179             </td>
1180             <td class="snnn file orange">
1181               <br />
1182             </td>
1183             <td class="ssnn file orange">
1184               <br />
1185             </td>
1186           </tr>
1187           <tr>
1188             <td class="snns component red">grammar</td>
1189             <td class="snns plane red">same head term form</td>
1190             <td class="snns file red">tshf ( ? ≈ ? )</td>
1191             <td class="snnn file red">(tshf_tshf)</td>
1192             <td class="snnn file red">
1193               <br />
1194             </td>
1195             <td class="snnn file red">
1196               <br />
1197             </td>
1198             <td class="ssnn file red">
1199               <br />
1200             </td>
1201           </tr>
1202           <tr>
1203             <td class="nnns component red">
1204               <br />
1205             </td>
1206             <td class="snns plane red">same top term constructor</td>
1207             <td class="snns file red">tstc ( ? ≃ ? )</td>
1208             <td class="snnn file red">tstc_tstc tstc_vector</td>
1209             <td class="snnn file red">
1210               <br />
1211             </td>
1212             <td class="snnn file red">
1213               <br />
1214             </td>
1215             <td class="ssnn file red">
1216               <br />
1217             </td>
1218           </tr>
1219           <tr>
1220             <td class="nnns component red">
1221               <br />
1222             </td>
1223             <td class="snns plane red">closures</td>
1224             <td class="snns file red">cl_shift ( ? @@ ? )</td>
1225             <td class="snnn file red">cl_weight ( ♯{?,?} )</td>
1226             <td class="snnn file red">
1227               <br />
1228             </td>
1229             <td class="snnn file red">
1230               <br />
1231             </td>
1232             <td class="ssnn file red">
1233               <br />
1234             </td>
1235           </tr>
1236           <tr>
1237             <td class="nnns component red">
1238               <br />
1239             </td>
1240             <td class="snns plane red">internal syntax</td>
1241             <td class="snns file red">genv</td>
1242             <td class="snnn file red">
1243               <br />
1244             </td>
1245             <td class="snnn file red">
1246               <br />
1247             </td>
1248             <td class="snnn file red">
1249               <br />
1250             </td>
1251             <td class="ssnn file red">
1252               <br />
1253             </td>
1254           </tr>
1255           <tr>
1256             <td class="nnns component red">
1257               <br />
1258             </td>
1259             <td class="nnns plane red">
1260               <br />
1261             </td>
1262             <td class="snns file red">lenv</td>
1263             <td class="snnn file red">lenv_weight ( ♯{?} )</td>
1264             <td class="snnn file red">lenv_length ( |?| )</td>
1265             <td class="snnn file red">lenv_append ( ? @@ ? )</td>
1266             <td class="ssnn file red">lenv_px lenv_px_bi</td>
1267           </tr>
1268           <tr>
1269             <td class="nnns component red">
1270               <br />
1271             </td>
1272             <td class="nnns plane red">
1273               <br />
1274             </td>
1275             <td class="snns file red">term</td>
1276             <td class="snnn file red">term_weight ( ♯{?} )</td>
1277             <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
1278             <td class="snnn file red">term_vector</td>
1279             <td class="ssnn file red">
1280               <br />
1281             </td>
1282           </tr>
1283           <tr>
1284             <td class="nnns component red">
1285               <br />
1286             </td>
1287             <td class="nnns plane red">
1288               <br />
1289             </td>
1290             <td class="snns file red">item</td>
1291             <td class="snnn file red">
1292               <br />
1293             </td>
1294             <td class="snnn file red">
1295               <br />
1296             </td>
1297             <td class="snnn file red">
1298               <br />
1299             </td>
1300             <td class="ssnn file red">
1301               <br />
1302             </td>
1303           </tr>
1304           <tr>
1305             <td class="nnss component red">
1306               <br />
1307             </td>
1308             <td class="snss plane red">external syntax</td>
1309             <td class="snss file red">aarity</td>
1310             <td class="snsn file red">
1311               <br />
1312             </td>
1313             <td class="snsn file red">
1314               <br />
1315             </td>
1316             <td class="snsn file red">
1317               <br />
1318             </td>
1319             <td class="sssn file red">
1320               <br />
1321             </td>
1322           </tr>
1323         </tbody>
1324       </table>
1325     </div>
1326
1327    <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
1328    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
1329          one for each component.
1330    </div>
1331    <div class="spacer">
1332       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
1333     </div>
1334     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1335       <br />
1336     </div>
1337     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1338       <a href="http://validator.w3.org/check?uri=referer">
1339         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
1340       </a>
1341       <a href="http://jigsaw.w3.org/css-validator/check/referer">
1342         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
1343       </a>
1344       <a href="http://www.w3.org/XML/">
1345         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
1346       </a>
1347       <a href="http://www.w3.org/Graphics/PNG/">
1348         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
1349       </a>
1350       <a href="http://www.anybrowser.org/campaign/">
1351         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
1352       </a>
1353     </div>
1354     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1355       <br />
1356     </div>
1357     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Fri, 15 Mar 2013 00:07:00 +0100</div>
1358 </body>
1359 </html>