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">173  </td>
 163             <td class="snns plane cyan">characters</td>
 164             <td class="snnn number cyan">363812</td>
 165             <td class="snns plane cyan">nodes</td>
 166             <td class="ssnn number cyan">1057233</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">75</td>
 172             <td class="snns plane green">lemmas</td>
 173             <td class="snnn number green">750</td>
 174             <td class="snns plane green">total</td>
 175             <td class="ssnn number green">825</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">43</td>
 181             <td class="snss plane yellow">defined</td>
 182             <td class="snsn number yellow">68</td>
 183             <td class="snss plane yellow">total</td>
 184             <td class="sssn number yellow">111</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_lpss snv_aaa snv_ssta snv_sstas snv_ssta_lpr snv_lpr 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">local env. ref. for stratified static type assignment</td>
 354             <td class="snns file blue">lsubss ( ? •⊑[?] ? )</td>
 355             <td class="snnn file blue">lsubss_ldrop lsubss_ssta lsubss_cpcs</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="snns plane blue">context-sensitive equivalence</td>
 368             <td class="snns file blue">cpcs ( ? ⊢ ? ⬌* ? )</td>
 369             <td class="snnn file blue">cpcs_lpss cpcs_aaa cpcs_cprs cpcs_cpcs</td>
 370             <td class="snnn file blue">
 371               <br />
 372             </td>
 373             <td class="ssnn file blue">
 374               <br />
 375             </td>
 376           </tr>
 377           <tr>
 378             <td class="snns component sky">conversion</td>
 379             <td class="snns plane sky">context-sensitive conversion</td>
 380             <td class="snns file sky">cpc ( ? ⊢ ? ⬌ ? )</td>
 381             <td class="snnn file sky">cpc_cpc</td>
 382             <td class="snnn file sky">
 383               <br />
 384             </td>
 385             <td class="ssnn file sky">
 386               <br />
 387             </td>
 388           </tr>
 389           <tr>
 390             <td class="snns component cyan">computation</td>
 391             <td class="snns plane cyan">decomposed extended computation</td>
 392             <td class="snns file cyan">dxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )</td>
 393             <td class="snnn file cyan">dxprs_lift dxprs_lpss dxprs_aaa dxprs_dxprs</td>
 394             <td class="snnn file cyan">
 395               <br />
 396             </td>
 397             <td class="ssnn file cyan">
 398               <br />
 399             </td>
 400           </tr>
 401           <tr>
 402             <td class="nnns component cyan">
 403               <br />
 404             </td>
 405             <td class="snns plane cyan">weakly normalizing computation</td>
 406             <td class="snns file cyan">cpe ( ? ⊢ ➡* 𝐍⦃?⦄ )</td>
 407             <td class="snnn file cyan">cpe_cpe</td>
 408             <td class="snnn file cyan">
 409               <br />
 410             </td>
 411             <td class="ssnn file cyan">
 412               <br />
 413             </td>
 414           </tr>
 415           <tr>
 416             <td class="nnns component cyan">
 417               <br />
 418             </td>
 419             <td class="snns plane cyan">strongly normalizing computation</td>
 420             <td class="snns file cyan">csn_vector ( ? ⊢ ⬊* ? )</td>
 421             <td class="snnn file cyan">csn_tstc_vector csn_aaa</td>
 422             <td class="snnn file cyan">
 423               <br />
 424             </td>
 425             <td class="ssnn file cyan">
 426               <br />
 427             </td>
 428           </tr>
 429           <tr>
 430             <td class="nnns component cyan">
 431               <br />
 432             </td>
 433             <td class="nnns plane cyan">
 434               <br />
 435             </td>
 436             <td class="snns file cyan">csn ( ? ⊢ ⬊* ? )</td>
 437             <td class="snnn file cyan">csn_alt ( ? ⊢ ⬊⬊* ? )</td>
 438             <td class="snnn file cyan">csn_lift csn_lpr</td>
 439             <td class="ssnn file cyan">
 440               <br />
 441             </td>
 442           </tr>
 443           <tr>
 444             <td class="nnns component cyan">
 445               <br />
 446             </td>
 447             <td class="snns plane cyan">context-sensitive computation</td>
 448             <td class="snns file cyan">lprs ( ? ⊢ ➡* ? )</td>
 449             <td class="snnn file cyan">lprs_alt ( ? ⊢ ➡➡* ? )</td>
 450             <td class="snnn file cyan">lprs_ldrop lprs_lpss lprs_aaa lprs_cprs lprs_lprs</td>
 451             <td class="ssnn file cyan">
 452               <br />
 453             </td>
 454           </tr>
 455           <tr>
 456             <td class="nnns component cyan">
 457               <br />
 458             </td>
 459             <td class="nnns plane cyan">
 460               <br />
 461             </td>
 462             <td class="snns file cyan">cprs ( ? ⊢ ? ➡* ?)</td>
 463             <td class="snnn file cyan">cprs_tstc cprs_tstc_vector cprs_lift cprs_lpss cprs_aaa cprs_cprs</td>
 464             <td class="snnn file cyan">
 465               <br />
 466             </td>
 467             <td class="ssnn file cyan">
 468               <br />
 469             </td>
 470           </tr>
 471           <tr>
 472             <td class="nnns component cyan">
 473               <br />
 474             </td>
 475             <td class="snns plane cyan">local env. ref. for abstract candidates of reducibility</td>
 476             <td class="snns file cyan">lsubc ( ? ⊑[?] ? )</td>
 477             <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</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="snns plane cyan">support for abstract computation properties</td>
 490             <td class="snns file cyan">acp</td>
 491             <td class="snnn file cyan">acp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )</td>
 492             <td class="snnn file cyan">acp_aaa</td>
 493             <td class="ssnn file cyan">
 494               <br />
 495             </td>
 496           </tr>
 497           <tr>
 498             <td class="snns component water">reduction</td>
 499             <td class="snns plane water">context-sensitive extended reduction</td>
 500             <td class="snns file water">lpx ( ⦃?,?⦄ ⊢ ➡[?] ? )</td>
 501             <td class="snnn file water">lpx_ldrop lpx_aaa</td>
 502             <td class="snnn file water">
 503               <br />
 504             </td>
 505             <td class="ssnn file water">
 506               <br />
 507             </td>
 508           </tr>
 509           <tr>
 510             <td class="nnns component water">
 511               <br />
 512             </td>
 513             <td class="nnns plane water">
 514               <br />
 515             </td>
 516             <td class="snns file water">cpx ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
 517             <td class="snnn file water">cpx_lift</td>
 518             <td class="snnn file water">
 519               <br />
 520             </td>
 521             <td class="ssnn file water">
 522               <br />
 523             </td>
 524           </tr>
 525           <tr>
 526             <td class="nnns component water">
 527               <br />
 528             </td>
 529             <td class="snns plane water">context-sensitive normal forms</td>
 530             <td class="snns file water">cnf ( ? ⊢ 𝐍⦃?⦄ )</td>
 531             <td class="snnn file water">cnf_liftt cnf_crf cnf_cif</td>
 532             <td class="snnn file water">
 533               <br />
 534             </td>
 535             <td class="ssnn file water">
 536               <br />
 537             </td>
 538           </tr>
 539           <tr>
 540             <td class="nnns component water">
 541               <br />
 542             </td>
 543             <td class="snns plane water">context-sensitive reduction</td>
 544             <td class="snns file water">lpr ( ? ⊢ ➡ ? )</td>
 545             <td class="snnn file water">lpr_ldrop lpr_lpss lpr_lpr</td>
 546             <td class="snnn file water">
 547               <br />
 548             </td>
 549             <td class="ssnn file water">
 550               <br />
 551             </td>
 552           </tr>
 553           <tr>
 554             <td class="nnns component water">
 555               <br />
 556             </td>
 557             <td class="nnns plane water">
 558               <br />
 559             </td>
 560             <td class="snns file water">cpr ( ? ⊢ ? ➡ ? )</td>
 561             <td class="snnn file water">cpr_lift cpr_cif</td>
 562             <td class="snnn file water">
 563               <br />
 564             </td>
 565             <td class="ssnn file water">
 566               <br />
 567             </td>
 568           </tr>
 569           <tr>
 570             <td class="nnns component water">
 571               <br />
 572             </td>
 573             <td class="snns plane water">context-sensitive reducible forms</td>
 574             <td class="snns file water">crf ( ? ⊢ 𝐑⦃?⦄ )</td>
 575             <td class="snnn file water">crf_append</td>
 576             <td class="snnn file water">cif ( ? ⊢ 𝐈⦃?⦄ )</td>
 577             <td class="ssnn file water">cif_append</td>
 578           </tr>
 579           <tr>
 580             <td class="snns component green">unfold</td>
 581             <td class="snns plane green">restricted parallel computation</td>
 582             <td class="snns file green">lpqs ( ? ⊢ ➤* ? )</td>
 583             <td class="snnn file green">lpqs_ldrop lpqs_cpqs lpqs_lpqs</td>
 584             <td class="snnn file green">
 585               <br />
 586             </td>
 587             <td class="ssnn file green">
 588               <br />
 589             </td>
 590           </tr>
 591           <tr>
 592             <td class="nnns component green">
 593               <br />
 594             </td>
 595             <td class="nnns plane green">
 596               <br />
 597             </td>
 598             <td class="snns file green">cpqs ( ? ⊢ ? ➤* ? )</td>
 599             <td class="snnn file green">cpqs_lift</td>
 600             <td class="snnn file green">
 601               <br />
 602             </td>
 603             <td class="ssnn file green">
 604               <br />
 605             </td>
 606           </tr>
 607           <tr>
 608             <td class="nnns component green">
 609               <br />
 610             </td>
 611             <td class="snns plane green">unfold</td>
 612             <td class="snns file green">unfold ( ? ⊢ ? ⧫* ? )</td>
 613             <td class="snnn file green">
 614               <br />
 615             </td>
 616             <td class="snnn file green">
 617               <br />
 618             </td>
 619             <td class="ssnn file green">
 620               <br />
 621             </td>
 622           </tr>
 623           <tr>
 624             <td class="nnns component green">
 625               <br />
 626             </td>
 627             <td class="snns plane green">iterated stratified static type assignment</td>
 628             <td class="snns file green">sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )</td>
 629             <td class="snnn file green">sstas_lift sstas_lpss sstas_aaa sstas_sstas</td>
 630             <td class="snnn file green">
 631               <br />
 632             </td>
 633             <td class="ssnn file green">
 634               <br />
 635             </td>
 636           </tr>
 637           <tr>
 638             <td class="snns component grass">static typing</td>
 639             <td class="snns plane grass">stratified static type assignment</td>
 640             <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
 641             <td class="snnn file grass">ssta_lift ssta_lpss ssta_aaa ssta_ssta</td>
 642             <td class="snnn file grass">
 643               <br />
 644             </td>
 645             <td class="ssnn file grass">
 646               <br />
 647             </td>
 648           </tr>
 649           <tr>
 650             <td class="nnns component grass">
 651               <br />
 652             </td>
 653             <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
 654             <td class="snns file grass">lsuba ( ? ⁝⊑ ? )</td>
 655             <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
 656             <td class="snnn file grass">
 657               <br />
 658             </td>
 659             <td class="ssnn file grass">
 660               <br />
 661             </td>
 662           </tr>
 663           <tr>
 664             <td class="nnns component grass">
 665               <br />
 666             </td>
 667             <td class="snns plane grass">atomic arity assignment</td>
 668             <td class="snns file grass">aaa ( ? ⊢ ? ⁝ ? )</td>
 669             <td class="snnn file grass">aaa_lift aaa_lifts aaa_lpss aaa_aaa</td>
 670             <td class="snnn file grass">
 671               <br />
 672             </td>
 673             <td class="ssnn file grass">
 674               <br />
 675             </td>
 676           </tr>
 677           <tr>
 678             <td class="nnns component grass">
 679               <br />
 680             </td>
 681             <td class="snns plane grass">parameters</td>
 682             <td class="snns file grass">sh</td>
 683             <td class="snnn file grass">sd</td>
 684             <td class="snnn file grass">
 685               <br />
 686             </td>
 687             <td class="ssnn file grass">
 688               <br />
 689             </td>
 690           </tr>
 691           <tr>
 692             <td class="snns component yellow">substitution</td>
 693             <td class="snns plane yellow">parallel substitution</td>
 694             <td class="snns file yellow">lpss ( ? ⊢ ▶* ? )</td>
 695             <td class="snnn file yellow">lpss_ldrop lpss_cpss lpss_lpss</td>
 696             <td class="snnn file yellow">
 697               <br />
 698             </td>
 699             <td class="ssnn file yellow">
 700               <br />
 701             </td>
 702           </tr>
 703           <tr>
 704             <td class="nnns component yellow">
 705               <br />
 706             </td>
 707             <td class="nnns plane yellow">
 708               <br />
 709             </td>
 710             <td class="snns file yellow">cpss ( ? ⊢ ? ▶* ? )</td>
 711             <td class="snnn file yellow">cpss_lift</td>
 712             <td class="snnn file yellow">
 713               <br />
 714             </td>
 715             <td class="ssnn file yellow">
 716               <br />
 717             </td>
 718           </tr>
 719           <tr>
 720             <td class="nnns component yellow">
 721               <br />
 722             </td>
 723             <td class="snns plane yellow">local env. ref. for substitution</td>
 724             <td class="snns file yellow">lsubr ( ? ⊑ ? )</td>
 725             <td class="snnn file yellow">lsubr_lsubr</td>
 726             <td class="snnn file yellow">
 727               <br />
 728             </td>
 729             <td class="ssnn file yellow">
 730               <br />
 731             </td>
 732           </tr>
 733           <tr>
 734             <td class="nnns component yellow">
 735               <br />
 736             </td>
 737             <td class="snns plane yellow">iterated structural successor for closures</td>
 738             <td class="snns file yellow">fsups ( ⦃?,?⦄ ⊃* ⦃?,?⦄ )</td>
 739             <td class="snnn file yellow">fsups_fsups</td>
 740             <td class="snnn file yellow">
 741               <br />
 742             </td>
 743             <td class="ssnn file yellow">
 744               <br />
 745             </td>
 746           </tr>
 747           <tr>
 748             <td class="nnns component yellow">
 749               <br />
 750             </td>
 751             <td class="nnns plane yellow">
 752               <br />
 753             </td>
 754             <td class="snns file yellow">fsupp ( ⦃?,?⦄ ⊃+ ⦃?,?⦄ )</td>
 755             <td class="snnn file yellow">fsupp_fsupp</td>
 756             <td class="snnn file yellow">
 757               <br />
 758             </td>
 759             <td class="ssnn file yellow">
 760               <br />
 761             </td>
 762           </tr>
 763           <tr>
 764             <td class="nnns component yellow">
 765               <br />
 766             </td>
 767             <td class="snns plane yellow">generic local env. slicing</td>
 768             <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
 769             <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</td>
 770             <td class="snnn file yellow">
 771               <br />
 772             </td>
 773             <td class="ssnn file yellow">
 774               <br />
 775             </td>
 776           </tr>
 777           <tr>
 778             <td class="nnns component yellow">
 779               <br />
 780             </td>
 781             <td class="snns plane yellow">generic term relocation</td>
 782             <td class="snns file yellow">lifts_vector ( ⇧*[?] ? ≡ ? )</td>
 783             <td class="snnn file yellow">lifts_lift_vector</td>
 784             <td class="snnn file yellow">
 785               <br />
 786             </td>
 787             <td class="ssnn file yellow">
 788               <br />
 789             </td>
 790           </tr>
 791           <tr>
 792             <td class="nnns component yellow">
 793               <br />
 794             </td>
 795             <td class="nnns plane yellow">
 796               <br />
 797             </td>
 798             <td class="snns file yellow">lifts ( ⇧*[?] ? ≡ ? )</td>
 799             <td class="snnn file yellow">lifts_lift lifts_lifts</td>
 800             <td class="snnn file yellow">
 801               <br />
 802             </td>
 803             <td class="ssnn file yellow">
 804               <br />
 805             </td>
 806           </tr>
 807           <tr>
 808             <td class="nnns component yellow">
 809               <br />
 810             </td>
 811             <td class="snns plane yellow">support for generic relocation</td>
 812             <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
 813             <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
 814             <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
 815             <td class="ssnn file yellow">gr2_gr2</td>
 816           </tr>
 817           <tr>
 818             <td class="snns component orange">relocation</td>
 819             <td class="snns plane orange">structural successor for closures</td>
 820             <td class="snns file orange">fsup ( ⦃?,?⦄ ⊃ ⦃?,?⦄ )</td>
 821             <td class="snnn file orange">fsupq ( ⦃?,?⦄ ⊃⸮ ⦃?,?⦄ )</td>
 822             <td class="snnn file orange">
 823               <br />
 824             </td>
 825             <td class="ssnn file orange">
 826               <br />
 827             </td>
 828           </tr>
 829           <tr>
 830             <td class="nnns component orange">
 831               <br />
 832             </td>
 833             <td class="snns plane orange">global env. slicing</td>
 834             <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
 835             <td class="snnn file orange">gdrop_gdrop</td>
 836             <td class="snnn file orange">
 837               <br />
 838             </td>
 839             <td class="ssnn file orange">
 840               <br />
 841             </td>
 842           </tr>
 843           <tr>
 844             <td class="nnns component orange">
 845               <br />
 846             </td>
 847             <td class="snns plane orange">basic local env. slicing</td>
 848             <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
 849             <td class="snnn file orange">ldrop_append ldrop_lpx_sn ldrop_ldrop</td>
 850             <td class="snnn file orange">
 851               <br />
 852             </td>
 853             <td class="ssnn file orange">
 854               <br />
 855             </td>
 856           </tr>
 857           <tr>
 858             <td class="nnns component orange">
 859               <br />
 860             </td>
 861             <td class="snns plane orange">basic term relocation</td>
 862             <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
 863             <td class="snnn file orange">lift_lift_vector</td>
 864             <td class="snnn file orange">
 865               <br />
 866             </td>
 867             <td class="ssnn file orange">
 868               <br />
 869             </td>
 870           </tr>
 871           <tr>
 872             <td class="nnns component orange">
 873               <br />
 874             </td>
 875             <td class="nnns plane orange">
 876               <br />
 877             </td>
 878             <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
 879             <td class="snnn file orange">lift_lift</td>
 880             <td class="snnn file orange">
 881               <br />
 882             </td>
 883             <td class="ssnn file orange">
 884               <br />
 885             </td>
 886           </tr>
 887           <tr>
 888             <td class="snns component red">grammar</td>
 889             <td class="snns plane red">pointwise extension of a relation</td>
 890             <td class="snns file red">lpx_sn</td>
 891             <td class="snnn file red">lpx_sn_tc lpx_sn_lpx_sn</td>
 892             <td class="snnn file red">
 893               <br />
 894             </td>
 895             <td class="ssnn file red">
 896               <br />
 897             </td>
 898           </tr>
 899           <tr>
 900             <td class="nnns component red">
 901               <br />
 902             </td>
 903             <td class="snns plane red">same top term constructor</td>
 904             <td class="snns file red">tstc ( ? ≃ ? )</td>
 905             <td class="snnn file red">tstc_tstc tstc_vector</td>
 906             <td class="snnn file red">
 907               <br />
 908             </td>
 909             <td class="ssnn file red">
 910               <br />
 911             </td>
 912           </tr>
 913           <tr>
 914             <td class="nnns component red">
 915               <br />
 916             </td>
 917             <td class="snns plane red">closures</td>
 918             <td class="snns file red">cl_shift ( ? @@ ? )</td>
 919             <td class="snnn file red">cl_weight ( ♯{?,?} )</td>
 920             <td class="snnn file red">
 921               <br />
 922             </td>
 923             <td class="ssnn file red">
 924               <br />
 925             </td>
 926           </tr>
 927           <tr>
 928             <td class="nnns component red">
 929               <br />
 930             </td>
 931             <td class="snns plane red">internal syntax</td>
 932             <td class="snns file red">genv</td>
 933             <td class="snnn file red">
 934               <br />
 935             </td>
 936             <td class="snnn file red">
 937               <br />
 938             </td>
 939             <td class="ssnn file red">
 940               <br />
 941             </td>
 942           </tr>
 943           <tr>
 944             <td class="nnns component red">
 945               <br />
 946             </td>
 947             <td class="nnns plane red">
 948               <br />
 949             </td>
 950             <td class="snns file red">lenv</td>
 951             <td class="snnn file red">lenv_weight ( ♯{?} )</td>
 952             <td class="snnn file red">lenv_length ( |?| )</td>
 953             <td class="ssnn file red">lenv_append ( ? @@ ? )</td>
 954           </tr>
 955           <tr>
 956             <td class="nnns component red">
 957               <br />
 958             </td>
 959             <td class="nnns plane red">
 960               <br />
 961             </td>
 962             <td class="snns file red">term</td>
 963             <td class="snnn file red">term_weight ( ♯{?} )</td>
 964             <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
 965             <td class="ssnn file red">term_vector</td>
 966           </tr>
 967           <tr>
 968             <td class="nnns component red">
 969               <br />
 970             </td>
 971             <td class="nnns plane red">
 972               <br />
 973             </td>
 974             <td class="snns file red">item</td>
 975             <td class="snnn file red">
 976               <br />
 977             </td>
 978             <td class="snnn file red">
 979               <br />
 980             </td>
 981             <td class="ssnn file red">
 982               <br />
 983             </td>
 984           </tr>
 985           <tr>
 986             <td class="nnss component red">
 987               <br />
 988             </td>
 989             <td class="snss plane red">external syntax</td>
 990             <td class="snss file red">aarity</td>
 991             <td class="snsn file red">
 992               <br />
 993             </td>
 994             <td class="snsn file red">
 995               <br />
 996             </td>
 997             <td class="sssn file red">
 998               <br />
 999             </td>
1000           </tr>
1001         </tbody>
1002       </table>
1003     </div>
1004
1005    <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
1006    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
1007          one for each component.
1008    </div>
1009    <div class="spacer">
1010       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
1011     </div>
1012     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1013       <br />
1014     </div>
1015     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1016       <a href="http://validator.w3.org/check?uri=referer">
1017         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
1018       </a>
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1021       </a>
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1023         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
1024       </a>
1025       <a href="http://www.w3.org/Graphics/PNG/">
1026         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
1027       </a>
1028       <a href="http://www.anybrowser.org/campaign/">
1029         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
1030       </a>
1031     </div>
1032     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1033       <br />
1034     </div>
1035     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sat, 08 Jun 2013 22:22:33 +0200</div>
1036 </body>
1037 </html>