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">176  </td>
 163             <td class="snns plane cyan">characters</td>
 164             <td class="snnn number cyan">373293</td>
 165             <td class="snns plane cyan">nodes</td>
 166             <td class="ssnn number cyan">1085467</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">76</td>
 172             <td class="snns plane green">lemmas</td>
 173             <td class="snnn number green">780</td>
 174             <td class="snns plane green">total</td>
 175             <td class="ssnn number green">856</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">71</td>
 183             <td class="snss plane yellow">total</td>
 184             <td class="sssn number yellow">114</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">context-sensitive extended computation</td>
 406             <td class="snns file cyan">cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?] ? )</td>
 407             <td class="snnn file cyan">cpxs_lift</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">weakly normalizing computation</td>
 420             <td class="snns file cyan">cpe ( ? ⊢ ➡* 𝐍⦃?⦄ )</td>
 421             <td class="snnn file cyan">cpe_cpe</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="snns plane cyan">strongly normalizing computation</td>
 434             <td class="snns file cyan">csn_vector ( ? ⊢ ⬊* ? )</td>
 435             <td class="snnn file cyan">csn_tstc_vector csn_aaa</td>
 436             <td class="snnn file cyan">
 437               <br />
 438             </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="nnns plane cyan">
 448               <br />
 449             </td>
 450             <td class="snns file cyan">csn ( ? ⊢ ⬊* ? )</td>
 451             <td class="snnn file cyan">csn_alt ( ? ⊢ ⬊⬊* ? )</td>
 452             <td class="snnn file cyan">csn_lift csn_lpr</td>
 453             <td class="ssnn file cyan">
 454               <br />
 455             </td>
 456           </tr>
 457           <tr>
 458             <td class="nnns component cyan">
 459               <br />
 460             </td>
 461             <td class="snns plane cyan">context-sensitive computation</td>
 462             <td class="snns file cyan">lprs ( ? ⊢ ➡* ? )</td>
 463             <td class="snnn file cyan">lprs_alt ( ? ⊢ ➡➡* ? )</td>
 464             <td class="snnn file cyan">lprs_ldrop lprs_lpss lprs_aaa lprs_cprs lprs_lprs</td>
 465             <td class="ssnn file cyan">
 466               <br />
 467             </td>
 468           </tr>
 469           <tr>
 470             <td class="nnns component cyan">
 471               <br />
 472             </td>
 473             <td class="nnns plane cyan">
 474               <br />
 475             </td>
 476             <td class="snns file cyan">cprs ( ? ⊢ ? ➡* ?)</td>
 477             <td class="snnn file cyan">cprs_tstc cprs_tstc_vector cprs_lift cprs_lpss cprs_aaa cprs_cprs</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">local env. ref. for abstract candidates of reducibility</td>
 490             <td class="snns file cyan">lsubc ( ? ⊑[?] ? )</td>
 491             <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
 492             <td class="snnn file cyan">
 493               <br />
 494             </td>
 495             <td class="ssnn file cyan">
 496               <br />
 497             </td>
 498           </tr>
 499           <tr>
 500             <td class="nnns component cyan">
 501               <br />
 502             </td>
 503             <td class="snns plane cyan">support for abstract computation properties</td>
 504             <td class="snns file cyan">acp</td>
 505             <td class="snnn file cyan">acp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )</td>
 506             <td class="snnn file cyan">acp_aaa</td>
 507             <td class="ssnn file cyan">
 508               <br />
 509             </td>
 510           </tr>
 511           <tr>
 512             <td class="snns component water">reduction</td>
 513             <td class="snns plane water">context-sensitive extended reduction</td>
 514             <td class="snns file water">lpx ( ⦃?,?⦄ ⊢ ➡[?] ? )</td>
 515             <td class="snnn file water">lpx_ldrop lpx_aaa</td>
 516             <td class="snnn file water">
 517               <br />
 518             </td>
 519             <td class="ssnn file water">
 520               <br />
 521             </td>
 522           </tr>
 523           <tr>
 524             <td class="nnns component water">
 525               <br />
 526             </td>
 527             <td class="nnns plane water">
 528               <br />
 529             </td>
 530             <td class="snns file water">cpx ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
 531             <td class="snnn file water">cpx_lift</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 normal forms</td>
 544             <td class="snns file water">cnf ( ? ⊢ 𝐍⦃?⦄ )</td>
 545             <td class="snnn file water">cnf_liftt cnf_crf cnf_cif</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="snns plane water">context-sensitive reduction</td>
 558             <td class="snns file water">lpr ( ? ⊢ ➡ ? )</td>
 559             <td class="snnn file water">lpr_ldrop lpr_lpss lpr_lpr</td>
 560             <td class="snnn file water">
 561               <br />
 562             </td>
 563             <td class="ssnn file water">
 564               <br />
 565             </td>
 566           </tr>
 567           <tr>
 568             <td class="nnns component water">
 569               <br />
 570             </td>
 571             <td class="nnns plane water">
 572               <br />
 573             </td>
 574             <td class="snns file water">cpr ( ? ⊢ ? ➡ ? )</td>
 575             <td class="snnn file water">cpr_lift cpr_cif</td>
 576             <td class="snnn file water">
 577               <br />
 578             </td>
 579             <td class="ssnn file water">
 580               <br />
 581             </td>
 582           </tr>
 583           <tr>
 584             <td class="nnns component water">
 585               <br />
 586             </td>
 587             <td class="snns plane water">context-sensitive reducible forms</td>
 588             <td class="snns file water">crf ( ? ⊢ 𝐑⦃?⦄ )</td>
 589             <td class="snnn file water">crf_append</td>
 590             <td class="snnn file water">cif ( ? ⊢ 𝐈⦃?⦄ )</td>
 591             <td class="ssnn file water">cif_append</td>
 592           </tr>
 593           <tr>
 594             <td class="snns component green">unfold</td>
 595             <td class="snns plane green">restricted parallel computation</td>
 596             <td class="snns file green">lpqs ( ? ⊢ ➤* ? )</td>
 597             <td class="snnn file green">lpqs_ldrop lpqs_cpqs lpqs_lpqs</td>
 598             <td class="snnn file green">
 599               <br />
 600             </td>
 601             <td class="ssnn file green">
 602               <br />
 603             </td>
 604           </tr>
 605           <tr>
 606             <td class="nnns component green">
 607               <br />
 608             </td>
 609             <td class="nnns plane green">
 610               <br />
 611             </td>
 612             <td class="snns file green">cpqs ( ? ⊢ ? ➤* ? )</td>
 613             <td class="snnn file green">cpqs_lift</td>
 614             <td class="snnn file green">
 615               <br />
 616             </td>
 617             <td class="ssnn file green">
 618               <br />
 619             </td>
 620           </tr>
 621           <tr>
 622             <td class="nnns component green">
 623               <br />
 624             </td>
 625             <td class="snns plane green">unfold</td>
 626             <td class="snns file green">unfold ( ? ⊢ ? ⧫* ? )</td>
 627             <td class="snnn file green">
 628               <br />
 629             </td>
 630             <td class="snnn file green">
 631               <br />
 632             </td>
 633             <td class="ssnn file green">
 634               <br />
 635             </td>
 636           </tr>
 637           <tr>
 638             <td class="nnns component green">
 639               <br />
 640             </td>
 641             <td class="snns plane green">iterated stratified static type assignment</td>
 642             <td class="snns file green">sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )</td>
 643             <td class="snnn file green">sstas_lift sstas_lpss sstas_aaa sstas_sstas</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="snns component grass">static typing</td>
 653             <td class="snns plane grass">stratified static type assignment</td>
 654             <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
 655             <td class="snnn file grass">ssta_lift ssta_lpss ssta_aaa ssta_ssta</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">local env. ref. for atomic arity assignment</td>
 668             <td class="snns file grass">lsuba ( ? ⁝⊑ ? )</td>
 669             <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</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">atomic arity assignment</td>
 682             <td class="snns file grass">aaa ( ? ⊢ ? ⁝ ? )</td>
 683             <td class="snnn file grass">aaa_lift aaa_lifts aaa_lpss aaa_aaa</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="nnns component grass">
 693               <br />
 694             </td>
 695             <td class="snns plane grass">parameters</td>
 696             <td class="snns file grass">sh</td>
 697             <td class="snnn file grass">sd</td>
 698             <td class="snnn file grass">
 699               <br />
 700             </td>
 701             <td class="ssnn file grass">
 702               <br />
 703             </td>
 704           </tr>
 705           <tr>
 706             <td class="snns component yellow">substitution</td>
 707             <td class="snns plane yellow">parallel substitution</td>
 708             <td class="snns file yellow">lpss ( ? ⊢ ▶* ? )</td>
 709             <td class="snnn file yellow">lpss_ldrop lpss_cpss lpss_lpss</td>
 710             <td class="snnn file yellow">
 711               <br />
 712             </td>
 713             <td class="ssnn file yellow">
 714               <br />
 715             </td>
 716           </tr>
 717           <tr>
 718             <td class="nnns component yellow">
 719               <br />
 720             </td>
 721             <td class="nnns plane yellow">
 722               <br />
 723             </td>
 724             <td class="snns file yellow">cpss ( ? ⊢ ? ▶* ? )</td>
 725             <td class="snnn file yellow">cpss_lift</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">local env. ref. for substitution</td>
 738             <td class="snns file yellow">lsubr ( ? ⊑ ? )</td>
 739             <td class="snnn file yellow">lsubr_lsubr</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="snns plane yellow">iterated structural successor for closures</td>
 752             <td class="snns file yellow">fsups ( ⦃?,?⦄ ⊃* ⦃?,?⦄ )</td>
 753             <td class="snnn file yellow">fsups_fsups</td>
 754             <td class="snnn file yellow">
 755               <br />
 756             </td>
 757             <td class="ssnn file yellow">
 758               <br />
 759             </td>
 760           </tr>
 761           <tr>
 762             <td class="nnns component yellow">
 763               <br />
 764             </td>
 765             <td class="nnns plane yellow">
 766               <br />
 767             </td>
 768             <td class="snns file yellow">fsupp ( ⦃?,?⦄ ⊃+ ⦃?,?⦄ )</td>
 769             <td class="snnn file yellow">fsupp_fsupp</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 local env. slicing</td>
 782             <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
 783             <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</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="snns plane yellow">generic term relocation</td>
 796             <td class="snns file yellow">lifts_vector ( ⇧*[?] ? ≡ ? )</td>
 797             <td class="snnn file yellow">lifts_lift_vector</td>
 798             <td class="snnn file yellow">
 799               <br />
 800             </td>
 801             <td class="ssnn file yellow">
 802               <br />
 803             </td>
 804           </tr>
 805           <tr>
 806             <td class="nnns component yellow">
 807               <br />
 808             </td>
 809             <td class="nnns plane yellow">
 810               <br />
 811             </td>
 812             <td class="snns file yellow">lifts ( ⇧*[?] ? ≡ ? )</td>
 813             <td class="snnn file yellow">lifts_lift lifts_lifts</td>
 814             <td class="snnn file yellow">
 815               <br />
 816             </td>
 817             <td class="ssnn file yellow">
 818               <br />
 819             </td>
 820           </tr>
 821           <tr>
 822             <td class="nnns component yellow">
 823               <br />
 824             </td>
 825             <td class="snns plane yellow">support for generic relocation</td>
 826             <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
 827             <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
 828             <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
 829             <td class="ssnn file yellow">gr2_gr2</td>
 830           </tr>
 831           <tr>
 832             <td class="snns component orange">relocation</td>
 833             <td class="snns plane orange">structural successor for closures</td>
 834             <td class="snns file orange">fsup ( ⦃?,?⦄ ⊃ ⦃?,?⦄ )</td>
 835             <td class="snnn file orange">fsupq ( ⦃?,?⦄ ⊃⸮ ⦃?,?⦄ )</td>
 836             <td class="snnn file orange">fsupq_alt</td>
 837             <td class="ssnn file orange">
 838               <br />
 839             </td>
 840           </tr>
 841           <tr>
 842             <td class="nnns component orange">
 843               <br />
 844             </td>
 845             <td class="snns plane orange">global env. slicing</td>
 846             <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
 847             <td class="snnn file orange">gdrop_gdrop</td>
 848             <td class="snnn file orange">
 849               <br />
 850             </td>
 851             <td class="ssnn file orange">
 852               <br />
 853             </td>
 854           </tr>
 855           <tr>
 856             <td class="nnns component orange">
 857               <br />
 858             </td>
 859             <td class="snns plane orange">basic local env. slicing</td>
 860             <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
 861             <td class="snnn file orange">ldrop_append ldrop_lpx_sn ldrop_ldrop</td>
 862             <td class="snnn file orange">
 863               <br />
 864             </td>
 865             <td class="ssnn file orange">
 866               <br />
 867             </td>
 868           </tr>
 869           <tr>
 870             <td class="nnns component orange">
 871               <br />
 872             </td>
 873             <td class="snns plane orange">basic term relocation</td>
 874             <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
 875             <td class="snnn file orange">lift_lift_vector</td>
 876             <td class="snnn file orange">
 877               <br />
 878             </td>
 879             <td class="ssnn file orange">
 880               <br />
 881             </td>
 882           </tr>
 883           <tr>
 884             <td class="nnns component orange">
 885               <br />
 886             </td>
 887             <td class="nnns plane orange">
 888               <br />
 889             </td>
 890             <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
 891             <td class="snnn file orange">lift_lift</td>
 892             <td class="snnn file orange">
 893               <br />
 894             </td>
 895             <td class="ssnn file orange">
 896               <br />
 897             </td>
 898           </tr>
 899           <tr>
 900             <td class="snns component red">grammar</td>
 901             <td class="snns plane red">pointwise extension of a relation</td>
 902             <td class="snns file red">lpx_sn</td>
 903             <td class="snnn file red">lpx_sn_tc lpx_sn_lpx_sn</td>
 904             <td class="snnn file red">
 905               <br />
 906             </td>
 907             <td class="ssnn file red">
 908               <br />
 909             </td>
 910           </tr>
 911           <tr>
 912             <td class="nnns component red">
 913               <br />
 914             </td>
 915             <td class="snns plane red">same top term constructor</td>
 916             <td class="snns file red">tstc ( ? ≃ ? )</td>
 917             <td class="snnn file red">tstc_tstc tstc_vector</td>
 918             <td class="snnn file red">
 919               <br />
 920             </td>
 921             <td class="ssnn file red">
 922               <br />
 923             </td>
 924           </tr>
 925           <tr>
 926             <td class="nnns component red">
 927               <br />
 928             </td>
 929             <td class="snns plane red">closures</td>
 930             <td class="snns file red">cl_shift ( ? @@ ? )</td>
 931             <td class="snnn file red">cl_weight ( ♯{?,?} )</td>
 932             <td class="snnn file red">
 933               <br />
 934             </td>
 935             <td class="ssnn file red">
 936               <br />
 937             </td>
 938           </tr>
 939           <tr>
 940             <td class="nnns component red">
 941               <br />
 942             </td>
 943             <td class="snns plane red">internal syntax</td>
 944             <td class="snns file red">genv</td>
 945             <td class="snnn file red">
 946               <br />
 947             </td>
 948             <td class="snnn file red">
 949               <br />
 950             </td>
 951             <td class="ssnn file red">
 952               <br />
 953             </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">lenv</td>
 963             <td class="snnn file red">lenv_weight ( ♯{?} )</td>
 964             <td class="snnn file red">lenv_length ( |?| )</td>
 965             <td class="ssnn file red">lenv_append ( ? @@ ? )</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">term</td>
 975             <td class="snnn file red">term_weight ( ♯{?} )</td>
 976             <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
 977             <td class="ssnn file red">term_vector</td>
 978           </tr>
 979           <tr>
 980             <td class="nnns component red">
 981               <br />
 982             </td>
 983             <td class="nnns plane red">
 984               <br />
 985             </td>
 986             <td class="snns file red">item</td>
 987             <td class="snnn file red">
 988               <br />
 989             </td>
 990             <td class="snnn file red">
 991               <br />
 992             </td>
 993             <td class="ssnn file red">
 994               <br />
 995             </td>
 996           </tr>
 997           <tr>
 998             <td class="nnss component red">
 999               <br />
1000             </td>
1001             <td class="snss plane red">external syntax</td>
1002             <td class="snss file red">aarity</td>
1003             <td class="snsn file red">
1004               <br />
1005             </td>
1006             <td class="snsn file red">
1007               <br />
1008             </td>
1009             <td class="sssn file red">
1010               <br />
1011             </td>
1012           </tr>
1013         </tbody>
1014       </table>
1015     </div>
1016
1017    <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
1018    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
1019          one for each component.
1020    </div>
1021    <div class="spacer">
1022       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
1023     </div>
1024     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1025       <br />
1026     </div>
1027     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1028       <a href="http://validator.w3.org/check?uri=referer">
1029         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
1030       </a>
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1033       </a>
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1035         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
1036       </a>
1037       <a href="http://www.w3.org/Graphics/PNG/">
1038         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
1039       </a>
1040       <a href="http://www.anybrowser.org/campaign/">
1041         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
1042       </a>
1043     </div>
1044     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1045       <br />
1046     </div>
1047     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Thu, 20 Jun 2013 19:25:05 +0200</div>
1048 </body>
1049 </html>