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">195  </td>
 163             <td class="snns plane cyan">characters</td>
 164             <td class="snnn number cyan">365052</td>
 165             <td class="snns plane cyan">nodes</td>
 166             <td class="ssnn number cyan">984918</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">84</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">865</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">focalized computation</td>
 452             <td class="snns file cyan">lfprs ( ⦃?⦄ ➡* ⦃?⦄ )</td>
 453             <td class="snnn file cyan">lfprs_aaa lfprs_ltprs lfprs_cprs lfprs_fprs lfprs_lfprs</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="nnns plane cyan">
 466               <br />
 467             </td>
 468             <td class="snns file cyan">fprs ( ⦃?,?⦄ ➡* ⦃?,?⦄ )</td>
 469             <td class="snnn file cyan">fprs_aaa fprs_fprs</td>
 470             <td class="snnn file cyan">
 471               <br />
 472             </td>
 473             <td class="ssnn file cyan">
 474               <br />
 475             </td>
 476           </tr>
 477           <tr>
 478             <td class="nnns component cyan">
 479               <br />
 480             </td>
 481             <td class="snns plane cyan">decomposed extended computation</td>
 482             <td class="snns file cyan">dxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )</td>
 483             <td class="snnn file cyan">dxprs_lift dxprs_ltpss_dx dxprs_ltpss_sn dxprs_aaa dxprs_dxprs</td>
 484             <td class="snnn file cyan">
 485               <br />
 486             </td>
 487             <td class="ssnn file cyan">
 488               <br />
 489             </td>
 490           </tr>
 491           <tr>
 492             <td class="nnns component cyan">
 493               <br />
 494             </td>
 495             <td class="snns plane cyan">weakly normalizing computation</td>
 496             <td class="snns file cyan">cpe ( ? ⊢ ➡* 𝐍⦃?⦄ )</td>
 497             <td class="snnn file cyan">cpe_cpe</td>
 498             <td class="snnn file cyan">
 499               <br />
 500             </td>
 501             <td class="ssnn file cyan">
 502               <br />
 503             </td>
 504           </tr>
 505           <tr>
 506             <td class="nnns component cyan">
 507               <br />
 508             </td>
 509             <td class="snns plane cyan">strongly normalizing computation</td>
 510             <td class="snns file cyan">csn_vector ( ? ⊢ ⬊* ? )</td>
 511             <td class="snnn file cyan">csn_cpr_vector csn_tstc_vector csn_aaa</td>
 512             <td class="snnn file cyan">
 513               <br />
 514             </td>
 515             <td class="ssnn file cyan">
 516               <br />
 517             </td>
 518           </tr>
 519           <tr>
 520             <td class="nnns component cyan">
 521               <br />
 522             </td>
 523             <td class="nnns plane cyan">
 524               <br />
 525             </td>
 526             <td class="snns file cyan">csn ( ? ⊢ ⬊* ? )</td>
 527             <td class="snnn file cyan">csn_alt ( ? ⊢ ⬊⬊* ? )</td>
 528             <td class="snnn file cyan">csn_lift csn_cpr csn_lfpr</td>
 529             <td class="ssnn file cyan">
 530               <br />
 531             </td>
 532           </tr>
 533           <tr>
 534             <td class="nnns component cyan">
 535               <br />
 536             </td>
 537             <td class="snns plane cyan">context-sensitive computation</td>
 538             <td class="snns file cyan">lprs ( ? ⊢ ➡* ? )</td>
 539             <td class="snnn file cyan">lprs_alt ( ? ⊢ ➡➡* ? )</td>
 540             <td class="snnn file cyan">lprs_ldrop lprs_aaa lprs_cprs lprs_lprs</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="nnns plane cyan">
 550               <br />
 551             </td>
 552             <td class="snns file cyan">cprs ( ? ⊢ ? ➡* ?)</td>
 553             <td class="snnn file cyan">cprs_lift cprs_tpss cprs_ltpss_dx cprs_ltpss_sn cprs_aaa cprs_lpr cprs_cprs cprs_tstc cprs_tstc_vector</td>
 554             <td class="snnn file cyan">
 555               <br />
 556             </td>
 557             <td class="ssnn file cyan">
 558               <br />
 559             </td>
 560           </tr>
 561           <tr>
 562             <td class="nnns component cyan">
 563               <br />
 564             </td>
 565             <td class="snns plane cyan">local env. ref. for abstract candidates of reducibility</td>
 566             <td class="snns file cyan">lsubc ( ? ⊑[?] ? )</td>
 567             <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
 568             <td class="snnn file cyan">
 569               <br />
 570             </td>
 571             <td class="ssnn file cyan">
 572               <br />
 573             </td>
 574           </tr>
 575           <tr>
 576             <td class="nnns component cyan">
 577               <br />
 578             </td>
 579             <td class="snns plane cyan">support for abstract computation properties</td>
 580             <td class="snns file cyan">acp</td>
 581             <td class="snnn file cyan">acp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )</td>
 582             <td class="snnn file cyan">acp_aaa</td>
 583             <td class="ssnn file cyan">
 584               <br />
 585             </td>
 586           </tr>
 587           <tr>
 588             <td class="snns component water">reduction</td>
 589             <td class="snns plane water">context-sensitive normal forms</td>
 590             <td class="snns file water">cnf ( ? ⊢ 𝐍⦃?⦄ )</td>
 591             <td class="snnn file water">cnf_liftt cnf_crf cnf_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 reduction</td>
 604             <td class="snns file water">lpr ( ? ⊢ ➡ ? )</td>
 605             <td class="snnn file water">lpr_ldrop lpr_cpss lpr_lpss lpr_aaa lpr_cpr lpr_lpr</td>
 606             <td class="snnn file water">
 607               <br />
 608             </td>
 609             <td class="ssnn file water">
 610               <br />
 611             </td>
 612           </tr>
 613           <tr>
 614             <td class="nnns component water">
 615               <br />
 616             </td>
 617             <td class="nnns plane water">
 618               <br />
 619             </td>
 620             <td class="snns file water">cpr ( ? ⊢ ? ➡ ? )</td>
 621             <td class="snnn file water">cpr_lift cpr_cif</td>
 622             <td class="snnn file water">
 623               <br />
 624             </td>
 625             <td class="ssnn file water">
 626               <br />
 627             </td>
 628           </tr>
 629           <tr>
 630             <td class="nnns component water">
 631               <br />
 632             </td>
 633             <td class="snns plane water">context-sensitive reducible forms</td>
 634             <td class="snns file water">crf ( ? ⊢ 𝐑⦃?⦄ )</td>
 635             <td class="snnn file water">crf_append</td>
 636             <td class="snnn file water">cif ( ? ⊢ 𝐈⦃?⦄ )</td>
 637             <td class="ssnn file water">cif_append</td>
 638           </tr>
 639           <tr>
 640             <td class="snns component green">unfold</td>
 641             <td class="snns plane green">restricted parallel computation</td>
 642             <td class="snns file green">lpqs ( ? ⊢ ➤* ? )</td>
 643             <td class="snnn file green">lpqs_ldrop lpqs_cpqs lpqs_lpqs</td>
 644             <td class="snnn file green">
 645               <br />
 646             </td>
 647             <td class="ssnn file green">
 648               <br />
 649             </td>
 650           </tr>
 651           <tr>
 652             <td class="nnns component green">
 653               <br />
 654             </td>
 655             <td class="nnns plane green">
 656               <br />
 657             </td>
 658             <td class="snns file green">cpqs ( ? ⊢ ? ➤* ? )</td>
 659             <td class="snnn file green">cpqs_lift</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="nnns component green">
 669               <br />
 670             </td>
 671             <td class="snns plane green">unfold</td>
 672             <td class="snns file green">unfold ( ? ⊢ ? ⧫* ? )</td>
 673             <td class="snnn file green">
 674               <br />
 675             </td>
 676             <td class="snnn file green">
 677               <br />
 678             </td>
 679             <td class="ssnn file green">
 680               <br />
 681             </td>
 682           </tr>
 683           <tr>
 684             <td class="nnns component green">
 685               <br />
 686             </td>
 687             <td class="snns plane green">iterated stratified static type assignment</td>
 688             <td class="snns file green">sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )</td>
 689             <td class="snnn file green">sstas_lift sstas_lpss sstas_aaa sstas_sstas</td>
 690             <td class="snnn file green">
 691               <br />
 692             </td>
 693             <td class="ssnn file green">
 694               <br />
 695             </td>
 696           </tr>
 697           <tr>
 698             <td class="snns component grass">static typing</td>
 699             <td class="snns plane grass">stratified static type assignment</td>
 700             <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
 701             <td class="snnn file grass">ssta_lift ssta_lpss ssta_aaa ssta_ssta</td>
 702             <td class="snnn file grass">
 703               <br />
 704             </td>
 705             <td class="ssnn file grass">
 706               <br />
 707             </td>
 708           </tr>
 709           <tr>
 710             <td class="nnns component grass">
 711               <br />
 712             </td>
 713             <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
 714             <td class="snns file grass">lsuba ( ? ⁝⊑ ? )</td>
 715             <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
 716             <td class="snnn file grass">
 717               <br />
 718             </td>
 719             <td class="ssnn file grass">
 720               <br />
 721             </td>
 722           </tr>
 723           <tr>
 724             <td class="nnns component grass">
 725               <br />
 726             </td>
 727             <td class="snns plane grass">atomic arity assignment</td>
 728             <td class="snns file grass">aaa ( ? ⊢ ? ⁝ ? )</td>
 729             <td class="snnn file grass">aaa_lift aaa_lifts aaa_lpss aaa_aaa</td>
 730             <td class="snnn file grass">
 731               <br />
 732             </td>
 733             <td class="ssnn file grass">
 734               <br />
 735             </td>
 736           </tr>
 737           <tr>
 738             <td class="nnns component grass">
 739               <br />
 740             </td>
 741             <td class="snns plane grass">parameters</td>
 742             <td class="snns file grass">sh</td>
 743             <td class="snnn file grass">sd</td>
 744             <td class="snnn file grass">
 745               <br />
 746             </td>
 747             <td class="ssnn file grass">
 748               <br />
 749             </td>
 750           </tr>
 751           <tr>
 752             <td class="snns component yellow">substitution</td>
 753             <td class="snns plane yellow">parallel substitution</td>
 754             <td class="snns file yellow">lpss ( ? ⊢ ▶* ? )</td>
 755             <td class="snnn file yellow">lpss_ldrop lpss_cpss lpss_lpss</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="nnns plane yellow">
 768               <br />
 769             </td>
 770             <td class="snns file yellow">cpss ( ? ⊢ ? ▶* ? )</td>
 771             <td class="snnn file yellow">cpss_lift</td>
 772             <td class="snnn file yellow">
 773               <br />
 774             </td>
 775             <td class="ssnn file yellow">
 776               <br />
 777             </td>
 778           </tr>
 779           <tr>
 780             <td class="nnns component yellow">
 781               <br />
 782             </td>
 783             <td class="snns plane yellow">local env. ref. for substitution</td>
 784             <td class="snns file yellow">lsubr ( ? ⊑ ? )</td>
 785             <td class="snnn file yellow">lsubr_lsubr</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">iterated structural successor for closures</td>
 798             <td class="snns file yellow">fsups ( ⦃?,?⦄ ⊃* ⦃?,?⦄ )</td>
 799             <td class="snnn file yellow">fsups_fsups</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="nnns plane yellow">
 812               <br />
 813             </td>
 814             <td class="snns file yellow">fsupp ( ⦃?,?⦄ ⊃+ ⦃?,?⦄ )</td>
 815             <td class="snnn file yellow">fsupp_fsupp</td>
 816             <td class="snnn file yellow">
 817               <br />
 818             </td>
 819             <td class="ssnn file yellow">
 820               <br />
 821             </td>
 822           </tr>
 823           <tr>
 824             <td class="nnns component yellow">
 825               <br />
 826             </td>
 827             <td class="snns plane yellow">generic local env. slicing</td>
 828             <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
 829             <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</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">generic term relocation</td>
 842             <td class="snns file yellow">lifts_vector ( ⇧*[?] ? ≡ ? )</td>
 843             <td class="snnn file yellow">lifts_lift_vector</td>
 844             <td class="snnn file yellow">
 845               <br />
 846             </td>
 847             <td class="ssnn file yellow">
 848               <br />
 849             </td>
 850           </tr>
 851           <tr>
 852             <td class="nnns component yellow">
 853               <br />
 854             </td>
 855             <td class="nnns plane yellow">
 856               <br />
 857             </td>
 858             <td class="snns file yellow">lifts ( ⇧*[?] ? ≡ ? )</td>
 859             <td class="snnn file yellow">lifts_lift lifts_lifts</td>
 860             <td class="snnn file yellow">
 861               <br />
 862             </td>
 863             <td class="ssnn file yellow">
 864               <br />
 865             </td>
 866           </tr>
 867           <tr>
 868             <td class="nnns component yellow">
 869               <br />
 870             </td>
 871             <td class="snns plane yellow">support for generic relocation</td>
 872             <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
 873             <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
 874             <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
 875             <td class="ssnn file yellow">gr2_gr2</td>
 876           </tr>
 877           <tr>
 878             <td class="snns component orange">relocation</td>
 879             <td class="snns plane orange">structural successor for closures</td>
 880             <td class="snns file orange">fsup ( ⦃?,?⦄ ⊃ ⦃?,?⦄ )</td>
 881             <td class="snnn file orange">
 882               <br />
 883             </td>
 884             <td class="snnn file orange">
 885               <br />
 886             </td>
 887             <td class="ssnn file orange">
 888               <br />
 889             </td>
 890           </tr>
 891           <tr>
 892             <td class="nnns component orange">
 893               <br />
 894             </td>
 895             <td class="snns plane orange">global env. slicing</td>
 896             <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
 897             <td class="snnn file orange">gdrop_gdrop</td>
 898             <td class="snnn file orange">
 899               <br />
 900             </td>
 901             <td class="ssnn file orange">
 902               <br />
 903             </td>
 904           </tr>
 905           <tr>
 906             <td class="nnns component orange">
 907               <br />
 908             </td>
 909             <td class="snns plane orange">basic local env. slicing</td>
 910             <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
 911             <td class="snnn file orange">ldrop_append ldrop_lpx_sn ldrop_ldrop</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="nnns component orange">
 921               <br />
 922             </td>
 923             <td class="snns plane orange">basic term relocation</td>
 924             <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
 925             <td class="snnn file orange">lift_lift_vector</td>
 926             <td class="snnn file orange">
 927               <br />
 928             </td>
 929             <td class="ssnn file orange">
 930               <br />
 931             </td>
 932           </tr>
 933           <tr>
 934             <td class="nnns component orange">
 935               <br />
 936             </td>
 937             <td class="nnns plane orange">
 938               <br />
 939             </td>
 940             <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
 941             <td class="snnn file orange">lift_lift</td>
 942             <td class="snnn file orange">
 943               <br />
 944             </td>
 945             <td class="ssnn file orange">
 946               <br />
 947             </td>
 948           </tr>
 949           <tr>
 950             <td class="snns component red">grammar</td>
 951             <td class="snns plane red">pointwise extension of a relation</td>
 952             <td class="snns file red">lpx_sn</td>
 953             <td class="snnn file red">lpx_sn_tc lpx_sn_lpx_sn</td>
 954             <td class="snnn file red">
 955               <br />
 956             </td>
 957             <td class="ssnn file red">
 958               <br />
 959             </td>
 960           </tr>
 961           <tr>
 962             <td class="nnns component red">
 963               <br />
 964             </td>
 965             <td class="snns plane red">same top term constructor</td>
 966             <td class="snns file red">tstc ( ? ≃ ? )</td>
 967             <td class="snnn file red">tstc_tstc tstc_vector</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="snns plane red">closures</td>
 980             <td class="snns file red">cl_shift ( ? @@ ? )</td>
 981             <td class="snnn file red">cl_weight ( ♯{?,?} )</td>
 982             <td class="snnn file red">
 983               <br />
 984             </td>
 985             <td class="ssnn file red">
 986               <br />
 987             </td>
 988           </tr>
 989           <tr>
 990             <td class="nnns component red">
 991               <br />
 992             </td>
 993             <td class="snns plane red">internal syntax</td>
 994             <td class="snns file red">genv</td>
 995             <td class="snnn file red">
 996               <br />
 997             </td>
 998             <td class="snnn file red">
 999               <br />
1000             </td>
1001             <td class="ssnn file red">
1002               <br />
1003             </td>
1004           </tr>
1005           <tr>
1006             <td class="nnns component red">
1007               <br />
1008             </td>
1009             <td class="nnns plane red">
1010               <br />
1011             </td>
1012             <td class="snns file red">lenv</td>
1013             <td class="snnn file red">lenv_weight ( ♯{?} )</td>
1014             <td class="snnn file red">lenv_length ( |?| )</td>
1015             <td class="ssnn file red">lenv_append ( ? @@ ? )</td>
1016           </tr>
1017           <tr>
1018             <td class="nnns component red">
1019               <br />
1020             </td>
1021             <td class="nnns plane red">
1022               <br />
1023             </td>
1024             <td class="snns file red">term</td>
1025             <td class="snnn file red">term_weight ( ♯{?} )</td>
1026             <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
1027             <td class="ssnn file red">term_vector</td>
1028           </tr>
1029           <tr>
1030             <td class="nnns component red">
1031               <br />
1032             </td>
1033             <td class="nnns plane red">
1034               <br />
1035             </td>
1036             <td class="snns file red">item</td>
1037             <td class="snnn file red">
1038               <br />
1039             </td>
1040             <td class="snnn file red">
1041               <br />
1042             </td>
1043             <td class="ssnn file red">
1044               <br />
1045             </td>
1046           </tr>
1047           <tr>
1048             <td class="nnss component red">
1049               <br />
1050             </td>
1051             <td class="snss plane red">external syntax</td>
1052             <td class="snss file red">aarity</td>
1053             <td class="snsn file red">
1054               <br />
1055             </td>
1056             <td class="snsn file red">
1057               <br />
1058             </td>
1059             <td class="sssn file red">
1060               <br />
1061             </td>
1062           </tr>
1063         </tbody>
1064       </table>
1065     </div>
1066
1067    <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
1068    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
1069          one for each component.
1070    </div>
1071    <div class="spacer">
1072       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
1073     </div>
1074     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1075       <br />
1076     </div>
1077     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1078       <a href="http://validator.w3.org/check?uri=referer">
1079         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
1080       </a>
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1086       </a>
1087       <a href="http://www.w3.org/Graphics/PNG/">
1088         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
1089       </a>
1090       <a href="http://www.anybrowser.org/campaign/">
1091         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
1092       </a>
1093     </div>
1094     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1095       <br />
1096     </div>
1097     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sun, 05 May 2013 20:24:24 +0200</div>
1098 </body>
1099 </html>