X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fwww%2Flambdadelta%2Fbasic_2.html;h=007aded03ab5ea453de4ad46f28b87679602e84c;hb=3a47f3e553f17690908dfcacfdfa58c0da378a9b;hp=cd756f629a03988a1c1d8f02cc8894a8acd341d6;hpb=640716b0624d2a7cd9f339b9ab975e85b3288a50;p=helm.git

diff --git a/helm/www/lambdadelta/basic_2.html b/helm/www/lambdadelta/basic_2.html
index cd756f629..007aded03 100644
--- a/helm/www/lambdadelta/basic_2.html
+++ b/helm/www/lambdadelta/basic_2.html
@@ -133,6 +133,10 @@
    <div xmlns:ld="http://lambdadelta.info/" class="head2">Summary of the Specification</div>
    <div xmlns:ld="http://lambdadelta.info/" class="text">Here is a numerical acount of the specification's contents
          and its timeline.
+         Nodes are counted according to the "intrinsinc complexity measure"
+         [F. Guidi: "Procedural Representation of CIC Proof Terms"
+         Journal of Automated Reasoning 44(1-2), Springer (February 2010),
+         pp. 53-78].
    </div>
    <div xmlns:ld="http://lambdadelta.info/" class="text">
       <table cellpadding="4" cellspacing="0">
@@ -159,29 +163,29 @@
           <tr>
             <td class="snns component cyan">sizes</td>
             <td class="snns plane cyan">files</td>
-            <td class="snnn number cyan">237  </td>
+            <td class="snnn number cyan">293  </td>
             <td class="snns plane cyan">characters</td>
-            <td class="snnn number cyan">420425</td>
+            <td class="snnn number cyan">439998</td>
             <td class="snns plane cyan">nodes</td>
-            <td class="ssnn number cyan">1063117</td>
+            <td class="ssnn number cyan">1286813</td>
           </tr>
           <tr>
             <td class="snns component green">propositions</td>
             <td class="snns plane green">theorems</td>
-            <td class="snnn number green">85</td>
+            <td class="snnn number green">91</td>
             <td class="snns plane green">lemmas</td>
-            <td class="snnn number green">946</td>
+            <td class="snnn number green">888</td>
             <td class="snns plane green">total</td>
-            <td class="ssnn number green">1031</td>
+            <td class="ssnn number green">979</td>
           </tr>
           <tr>
             <td class="snss component yellow">concepts</td>
             <td class="snss plane yellow">declared</td>
-            <td class="snsn number yellow">45</td>
+            <td class="snsn number yellow">49</td>
             <td class="snss plane yellow">defined</td>
-            <td class="snsn number yellow">80</td>
+            <td class="snsn number yellow">85</td>
             <td class="snss plane yellow">total</td>
-            <td class="sssn number yellow">125</td>
+            <td class="sssn number yellow">134</td>
           </tr>
         </tbody>
       </table>
@@ -196,21 +200,33 @@
    <ul xmlns:ld="http://lambdadelta.info/">
       <li>
         <span class="date">In progress.</span>
-         Closure of extended context-sensitive computation
+         Closure of context-sensitive extended computation
          for native validity.
    </li>
     </ul>
    <ul xmlns:ld="http://lambdadelta.info/">
       <li>
-        <span class="date">In progress.</span>
-         Extended context-sensitive strong normalization
+        <span class="date">2013 August 7.</span>
+         Passive support for global environments.
+   </li>
+    </ul>
+   <ul xmlns:ld="http://lambdadelta.info/">
+      <li>
+        <span class="date">2013 July 27.</span>
+         Reaxiomatized β-reductum as in extended β-reduction
+   </li>
+    </ul>
+   <ul xmlns:ld="http://lambdadelta.info/">
+      <li>
+        <span class="date">2013 July 20.</span>
+         Context-sensitive extended strong normalization
          for simply typed terms.
    </li>
     </ul>
    <ul xmlns:ld="http://lambdadelta.info/">
       <li>
         <span class="date">2013 April 16.</span>
-         Reaxiomatized substitution and reduction 
+         Reaxiomatized substitution and reduction
          commute with respect to subclosure
          (anniversary milestone).
    </li>
@@ -219,7 +235,7 @@
       <li>
         <span class="date">2013 March 16.</span>
          Mutual recursive preservation of stratified native validity
-	 for hyper computation on closures.
+         for "big tree" computation on closures.
    </li>
     </ul>
    <ul xmlns:ld="http://lambdadelta.info/">
@@ -231,7 +247,7 @@
    <ul xmlns:ld="http://lambdadelta.info/">
       <li>
         <span class="date">2012 July 26.</span>
-         Term binders polarized to control ζ reduction.
+         Term binders polarized to control ζ-reduction.
    </li>
     </ul>
    <ul xmlns:ld="http://lambdadelta.info/">
@@ -294,51 +310,15 @@
             <td class="snnn file grey">
               <br />
             </td>
-            <td class="snnn file grey">
-              <br />
-            </td>
             <td class="ssnn file grey">
               <br />
             </td>
           </tr>
           <tr>
             <td class="snns component prune">dynamic typing</td>
-            <td class="snns plane prune">"big tree" parallel computation</td>
-            <td class="snns file prune">yprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )</td>
-            <td class="snnn file prune">yprs_yprs</td>
-            <td class="snnn file prune">ygt ( ? ⊢ ⦃?,?⦄ &gt;[g] ⦃?,?⦄ )</td>
-            <td class="snnn file prune">ygt_ygt</td>
-            <td class="ssnn file prune">
-              <br />
-            </td>
-          </tr>
-          <tr>
-            <td class="nnns component prune">
-              <br />
-            </td>
-            <td class="snns plane prune">"big tree" parallel reduction</td>
-            <td class="snns file prune">ypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )</td>
-            <td class="snnn file prune">ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ )</td>
-            <td class="snnn file prune">
-              <br />
-            </td>
-            <td class="snnn file prune">
-              <br />
-            </td>
-            <td class="ssnn file prune">
-              <br />
-            </td>
-          </tr>
-          <tr>
-            <td class="nnns component prune">
-              <br />
-            </td>
             <td class="snns plane prune">local env. ref. for stratified native validity</td>
-            <td class="snns file prune">lsubsv ( ? ⊢ ? ¡⊑[?] ? )</td>
-            <td class="snnn file prune">lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv</td>
-            <td class="snnn file prune">
-              <br />
-            </td>
+            <td class="snns file prune">lsubsv ( ? ⊢ ? ¡⊑[?,?] ? )</td>
+            <td class="snnn file prune">lsubsv_ldrop lsubsv_lsubd lsubsv_lsuba lsubsv_lsstas lsubsv_cpds lsubsv_cpcs lsubsv_snv</td>
             <td class="snnn file prune">
               <br />
             </td>
@@ -351,11 +331,8 @@
               <br />
             </td>
             <td class="snns plane prune">stratified native validity</td>
-            <td class="snns file prune">snv ( ⦃?,?⦄ ⊢ ? ¡[?] )</td>
-            <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>
-            <td class="snnn file prune">
-              <br />
-            </td>
+            <td class="snns file prune">snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )</td>
+            <td class="snnn file prune">snv_lift snv_da_lpr snv_aaa snv_lsstas snv_lsstas_lpr snv_lpr snv_cpcs</td>
             <td class="snnn file prune">
               <br />
             </td>
@@ -365,12 +342,9 @@
           </tr>
           <tr>
             <td class="snns component blue">equivalence</td>
-            <td class="snns plane blue">focalized equivalence</td>
-            <td class="snns file blue">lfpcs ( ⦃?⦄ ⬌* ⦃?⦄ )</td>
-            <td class="snnn file blue">lfpcs_aaa lfpcs_fpcs lfpcs_lfprs lfpcs_lfpcs</td>
-            <td class="snnn file blue">
-              <br />
-            </td>
+            <td class="snns plane blue">decomposed extended equivalence</td>
+            <td class="snns file blue">cpes ( ⦃?,?⦄ ⊢ ? •*⬌*[?,?] ? )</td>
+            <td class="snnn file blue">cpes_cpds</td>
             <td class="snnn file blue">
               <br />
             </td>
@@ -382,14 +356,9 @@
             <td class="nnns component blue">
               <br />
             </td>
-            <td class="nnns plane blue">
-              <br />
-            </td>
-            <td class="snns file blue">fpcs ( ⦃?,?⦄ ⬌* ⦃?,?⦄ )</td>
-            <td class="snnn file blue">fpcs_aaa fpcs_cpcs fpcs_fprs fpcs_fpcs</td>
-            <td class="snnn file blue">
-              <br />
-            </td>
+            <td class="snns plane blue">context-sensitive equivalence</td>
+            <td class="snns file blue">cpcs ( ⦃?,?⦄ ⊢ ? ⬌* ? )</td>
+            <td class="snnn file blue">cpcs_aaa cpcs_cprs cpcs_cpcs</td>
             <td class="snnn file blue">
               <br />
             </td>
@@ -398,98 +367,92 @@
             </td>
           </tr>
           <tr>
-            <td class="nnns component blue">
-              <br />
-            </td>
-            <td class="snns plane blue">local env. ref. for stratified static type assignment</td>
-            <td class="snns file blue">lsubss ( ? •⊑[?] ? )</td>
-            <td class="snnn file blue">lsubss_ldrop lsubss_ssta lsubss_cpcs</td>
-            <td class="snnn file blue">
-              <br />
-            </td>
-            <td class="snnn file blue">
+            <td class="snns component sky">conversion</td>
+            <td class="snns plane sky">context-sensitive conversion</td>
+            <td class="snns file sky">cpc ( ⦃?,?⦄ ⊢ ? ⬌ ? )</td>
+            <td class="snnn file sky">cpc_cpc</td>
+            <td class="snnn file sky">
               <br />
             </td>
-            <td class="ssnn file blue">
+            <td class="ssnn file sky">
               <br />
             </td>
           </tr>
           <tr>
-            <td class="nnns component blue">
-              <br />
-            </td>
-            <td class="snns plane blue">context-sensitive equivalence</td>
-            <td class="snns file blue">cpcs ( ? ⊢ ? ⬌* ? )</td>
-            <td class="snnn file blue">cpcs_ltpss_dx cpcs_ltpss_sn cpcs_delift cpcs_aaa cpcs_ltpr cpcs_cprs cpcs_cpcs</td>
-            <td class="snnn file blue">
+            <td class="snns component cyan">computation</td>
+            <td class="snns plane cyan">context-sensitive extended evaluation</td>
+            <td class="snns file cyan">cpxe ( ⦃?,?⦄ ⊢ ➡*[?,?] 𝐍⦃?⦄ )</td>
+            <td class="snnn file cyan">
               <br />
             </td>
-            <td class="snnn file blue">
+            <td class="snnn file cyan">
               <br />
             </td>
-            <td class="ssnn file blue">
+            <td class="ssnn file cyan">
               <br />
             </td>
           </tr>
           <tr>
-            <td class="snns component sky">conversion</td>
-            <td class="snns plane sky">focalized conversion</td>
-            <td class="snns file sky">lfpc ( ⦃?⦄ ⬌ ⦃?⦄ )</td>
-            <td class="snnn file sky">lfpc_lfpc</td>
-            <td class="snnn file sky">
+            <td class="nnns component cyan">
               <br />
             </td>
-            <td class="snnn file sky">
+            <td class="snns plane cyan">context-sensitive evaluation</td>
+            <td class="snns file cyan">cpre ( ⦃?,?⦄ ⊢ ➡* 𝐍⦃?⦄ )</td>
+            <td class="snnn file cyan">cpre_cpre</td>
+            <td class="snnn file cyan">
               <br />
             </td>
-            <td class="ssnn file sky">
+            <td class="ssnn file cyan">
               <br />
             </td>
           </tr>
           <tr>
-            <td class="nnns component sky">
+            <td class="nnns component cyan">
               <br />
             </td>
-            <td class="nnns plane sky">
+            <td class="snns plane cyan">strongly normalizing "big tree" computation</td>
+            <td class="snns file cyan">fsb ( ⦃?,?⦄ ⊢ ⦥[?,?] ? )</td>
+            <td class="snnn file cyan">fsb_alt ( ⦃?,?⦄ ⊢ ⦥⦥[?,?] ? )</td>
+            <td class="snnn file cyan">fsb_fleq fsb_csx</td>
+            <td class="ssnn file cyan">
               <br />
             </td>
-            <td class="snns file sky">fpc ( ⦃?,?⦄ ⬌ ⦃?,?⦄ )</td>
-            <td class="snnn file sky">fpc_fpc</td>
-            <td class="snnn file sky">
+          </tr>
+          <tr>
+            <td class="nnns component cyan">
               <br />
             </td>
-            <td class="snnn file sky">
+            <td class="snns plane cyan">strongly normalizing extended computation</td>
+            <td class="snns file cyan">csx_vector ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )</td>
+            <td class="snnn file cyan">csx_tstc_vector csx_aaa</td>
+            <td class="snnn file cyan">
               <br />
             </td>
-            <td class="ssnn file sky">
+            <td class="ssnn file cyan">
               <br />
             </td>
           </tr>
           <tr>
-            <td class="nnns component sky">
-              <br />
-            </td>
-            <td class="snns plane sky">context-sensitive conversion</td>
-            <td class="snns file sky">cpc ( ? ⊢ ? ⬌ ? )</td>
-            <td class="snnn file sky">cpc_cpc</td>
-            <td class="snnn file sky">
+            <td class="nnns component cyan">
               <br />
             </td>
-            <td class="snnn file sky">
+            <td class="nnns plane cyan">
               <br />
             </td>
-            <td class="ssnn file sky">
+            <td class="snns file cyan">csx ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )</td>
+            <td class="snnn file cyan">csx_alt ( ⦃?,?⦄ ⊢ ⬊⬊*[?,?] ? )</td>
+            <td class="snnn file cyan">csx_lift csx_lpx</td>
+            <td class="ssnn file cyan">
               <br />
             </td>
           </tr>
           <tr>
-            <td class="snns component cyan">computation</td>
-            <td class="snns plane cyan">focalized computation</td>
-            <td class="snns file cyan">lfprs ( ⦃?⦄ ➡* ⦃?⦄ )</td>
-            <td class="snnn file cyan">lfprs_aaa lfprs_ltprs lfprs_cprs lfprs_fprs lfprs_lfprs</td>
-            <td class="snnn file cyan">
+            <td class="nnns component cyan">
               <br />
             </td>
+            <td class="snns plane cyan">parallel computation for "big tree" normal forms</td>
+            <td class="snns file cyan">fpns ( ⦃?,?,?⦄ ⊢ ⋕➡*[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file cyan">fpns_fpns</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -501,14 +464,9 @@
             <td class="nnns component cyan">
               <br />
             </td>
-            <td class="nnns plane cyan">
-              <br />
-            </td>
-            <td class="snns file cyan">fprs ( ⦃?,?⦄ ➡* ⦃?,?⦄ )</td>
-            <td class="snnn file cyan">fprs_aaa fprs_fprs</td>
-            <td class="snnn file cyan">
-              <br />
-            </td>
+            <td class="snns plane cyan">"big tree" parallel computation</td>
+            <td class="snns file cyan">fpbr ( ⦃?,?,?⦄ ⊃≥[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file cyan">fpbr_fpbr</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -520,12 +478,11 @@
             <td class="nnns component cyan">
               <br />
             </td>
-            <td class="snns plane cyan">decomposed extended computation</td>
-            <td class="snns file cyan">dxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )</td>
-            <td class="snnn file cyan">dxprs_lift dxprs_ltpss_dx dxprs_ltpss_sn dxprs_aaa dxprs_dxprs</td>
-            <td class="snnn file cyan">
+            <td class="nnns plane cyan">
               <br />
             </td>
+            <td class="snns file cyan">fpbg ( ⦃?,?,?⦄ &gt;[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file cyan">fpbg_lift fpbg_fpbg</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -537,15 +494,12 @@
             <td class="nnns component cyan">
               <br />
             </td>
-            <td class="snns plane cyan">weakly normalizing computation</td>
-            <td class="snns file cyan">cpe ( ? ⊢ ➡* 𝐍⦃?⦄ )</td>
-            <td class="snnn file cyan">cpe_cpe</td>
-            <td class="snnn file cyan">
-              <br />
-            </td>
-            <td class="snnn file cyan">
+            <td class="nnns plane cyan">
               <br />
             </td>
+            <td class="snns file cyan">fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file cyan">fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file cyan">fpbs_lift fpbs_fleq fpbs_fpbs</td>
             <td class="ssnn file cyan">
               <br />
             </td>
@@ -554,12 +508,9 @@
             <td class="nnns component cyan">
               <br />
             </td>
-            <td class="snns plane cyan">strongly normalizing computation</td>
-            <td class="snns file cyan">csn_vector ( ? ⊢ ⬊* ? )</td>
-            <td class="snnn file cyan">csn_cpr_vector csn_tstc_vector csn_aaa</td>
-            <td class="snnn file cyan">
-              <br />
-            </td>
+            <td class="snns plane cyan">decomposed extended computation</td>
+            <td class="snns file cyan">cpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?] ? )</td>
+            <td class="snnn file cyan">cpds_lift cpds_aaa cpds_cpds</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -571,15 +522,10 @@
             <td class="nnns component cyan">
               <br />
             </td>
-            <td class="nnns plane cyan">
-              <br />
-            </td>
-            <td class="snns file cyan">csn ( ? ⊢ ⬊* ? )</td>
-            <td class="snnn file cyan">csn_alt ( ? ⊢ ⬊⬊* ? )</td>
-            <td class="snnn file cyan">csn_lift csn_cpr csn_lfpr</td>
-            <td class="snnn file cyan">
-              <br />
-            </td>
+            <td class="snns plane cyan">context-sensitive extended computation</td>
+            <td class="snns file cyan">lpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? )</td>
+            <td class="snnn file cyan">lpxs_alt ( ⦃?,?⦄ ⊢ ➡➡*[?,?] ? )</td>
+            <td class="snnn file cyan">lpxs_ldrop lpxs_aaa lpxs_cpxs lpxs_lpxs</td>
             <td class="ssnn file cyan">
               <br />
             </td>
@@ -588,12 +534,11 @@
             <td class="nnns component cyan">
               <br />
             </td>
-            <td class="snns plane cyan">context-sensitive computation</td>
-            <td class="snns file cyan">cprs (? ⊢ ? ➡* ?)</td>
-            <td class="snnn file cyan">cprs_lift cprs_tpss cprs_ltpss_dx cprs_ltpss_sn cprs_delift cprs_aaa cprs_ltpr cprs_lfpr cprs_cprs cprs_lfprs cprs_tstc cprs_tstc_vector</td>
-            <td class="snnn file cyan">
+            <td class="nnns plane cyan">
               <br />
             </td>
+            <td class="snns file cyan">cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )</td>
+            <td class="snnn file cyan">cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_aaa cpxs_cpxs</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -605,13 +550,10 @@
             <td class="nnns component cyan">
               <br />
             </td>
-            <td class="snns plane cyan">context-free computation</td>
-            <td class="snns file cyan">ltprs ( ? ➡* ? )</td>
-            <td class="snnn file cyan">ltprs_alt ( ? ➡➡* ? )</td>
-            <td class="snnn file cyan">ltprs_ldrop ltprs_ltprs</td>
-            <td class="snnn file cyan">
-              <br />
-            </td>
+            <td class="snns plane cyan">context-sensitive computation</td>
+            <td class="snns file cyan">lprs ( ⦃?,?⦄ ⊢ ➡* ? )</td>
+            <td class="snnn file cyan">lprs_alt ( ⦃?,?⦄ ⊢ ➡➡* ? )</td>
+            <td class="snnn file cyan">lprs_ldrop lprs_cprs lprs_lprs</td>
             <td class="ssnn file cyan">
               <br />
             </td>
@@ -623,11 +565,8 @@
             <td class="nnns plane cyan">
               <br />
             </td>
-            <td class="snns file cyan">tprs ( ? ➡* ?)</td>
-            <td class="snnn file cyan">tprs_lift tprs_tprs</td>
-            <td class="snnn file cyan">
-              <br />
-            </td>
+            <td class="snns file cyan">cprs ( ⦃?,?⦄ ⊢ ? ➡* ?)</td>
+            <td class="snnn file cyan">cprs_lift cprs_cprs</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -640,14 +579,11 @@
               <br />
             </td>
             <td class="snns plane cyan">local env. ref. for abstract candidates of reducibility</td>
-            <td class="snns file cyan">lsubc ( ? ⊑[?] ? )</td>
+            <td class="snns file cyan">lsubc ( ? ⊢ ? ⊑[?] ? )</td>
             <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
             <td class="snnn file cyan">
               <br />
             </td>
-            <td class="snnn file cyan">
-              <br />
-            </td>
             <td class="ssnn file cyan">
               <br />
             </td>
@@ -658,38 +594,17 @@
             </td>
             <td class="snns plane cyan">support for abstract computation properties</td>
             <td class="snns file cyan">acp</td>
-            <td class="snnn file cyan">acp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )</td>
+            <td class="snnn file cyan">acp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
             <td class="snnn file cyan">acp_aaa</td>
-            <td class="snnn file cyan">
-              <br />
-            </td>
             <td class="ssnn file cyan">
               <br />
             </td>
           </tr>
           <tr>
-            <td class="snns component water">reducibility</td>
-            <td class="snns plane water">context-sensitive focalized reduction</td>
-            <td class="snns file water">cfpr ( ? ⊢ ⦃?,?⦄ ➡ ⦃?,?⦄ )</td>
-            <td class="snnn file water">cnfpr_ltpss cfpr_aaa cfpr_cpr cfpr_cfpr</td>
-            <td class="snnn file water">
-              <br />
-            </td>
-            <td class="snnn file water">
-              <br />
-            </td>
-            <td class="ssnn file water">
-              <br />
-            </td>
-          </tr>
-          <tr>
-            <td class="nnns component water">
-              <br />
-            </td>
-            <td class="snns plane water">context-free focalized reduction</td>
-            <td class="snns file water">lfpr ( ⦃?⦄ ➡ ⦃?⦄ )</td>
-            <td class="snnn file water">lfpr_alt ( ⦃?⦄ ➡➡ ⦃?⦄ )</td>
-            <td class="snnn file water">lfpr_aaa lfpr_cpr lfpr_fpr lfpr_lfpr</td>
+            <td class="snns component water">reduction</td>
+            <td class="snns plane water">"big tree" parallel reduction</td>
+            <td class="snns file water">fpbc ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file water">fpbc_lift</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -704,11 +619,8 @@
             <td class="nnns plane water">
               <br />
             </td>
-            <td class="snns file water">fpr ( ⦃?,?⦄ ➡ ⦃?,?⦄ )</td>
-            <td class="snnn file water">fpr_cpr fpr_fpr</td>
-            <td class="snnn file water">
-              <br />
-            </td>
+            <td class="snns file water">fpb ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file water">fpb_lift</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -720,12 +632,9 @@
             <td class="nnns component water">
               <br />
             </td>
-            <td class="snns plane water">context-sensitive normal forms</td>
-            <td class="snns file water">cnf ( ? ⊢ 𝐍⦃?⦄ )</td>
-            <td class="snnn file water">cnf_lift cnf_cif</td>
-            <td class="snnn file water">
-              <br />
-            </td>
+            <td class="snns plane water">context-sensitive extended normal forms</td>
+            <td class="snns file water">cnx ( ⦃?,?⦄ ⊢ 𝐍[?,?]⦃?⦄ )</td>
+            <td class="snnn file water">cnx_lift cnx_crx cnx_cix</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -737,12 +646,9 @@
             <td class="nnns component water">
               <br />
             </td>
-            <td class="snns plane water">revised context-sensitive reduction</td>
-            <td class="snns file water">lpr ( ? ⊢ ➡ ? )</td>
-            <td class="snnn file water">lpr_ldrop lpr_cpr lpr_lpr</td>
-            <td class="snnn file water">
-              <br />
-            </td>
+            <td class="snns plane water">context-sensitive extended reduction</td>
+            <td class="snns file water">lpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
+            <td class="snnn file water">lpx_ldrop lpx_aaa lpx_lpx</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -757,11 +663,8 @@
             <td class="nnns plane water">
               <br />
             </td>
-            <td class="snns file water">cpr ( ? ⊢ ? ➡ ? )</td>
-            <td class="snnn file water">cpr_lift</td>
-            <td class="snnn file water">
-              <br />
-            </td>
+            <td class="snns file water">cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
+            <td class="snnn file water">cpx_lift cpx_cix cpx_cpx</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -773,12 +676,9 @@
             <td class="nnns component water">
               <br />
             </td>
-            <td class="snns plane water">context-sensitive reduction</td>
-            <td class="snns file water">cpr ( ? ⊢ ? ➡ ? )</td>
-            <td class="snnn file water">cpr_lift cpr_tpss cpr_ltpss_dx cpr_ltpss_sn cpr_delift cpr_aaa cpr_ltpr cpr_cpr</td>
-            <td class="snnn file water">
-              <br />
-            </td>
+            <td class="snns plane water">context-sensitive extended irreducible forms</td>
+            <td class="snns file water">cix ( ⦃?,?⦄ ⊢ 𝐈[?,?]⦃?⦄ )</td>
+            <td class="snnn file water">cix_append cix_lift</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -790,11 +690,12 @@
             <td class="nnns component water">
               <br />
             </td>
-            <td class="snns plane water">context-sensitive reducible forms</td>
-            <td class="snns file water">crf ( ? ⊢ 𝐑⦃?⦄ )</td>
-            <td class="snnn file water">crf_append</td>
-            <td class="snnn file water">cif ( ? ⊢ 𝐈⦃?⦄ )</td>
-            <td class="snnn file water">cif_append</td>
+            <td class="snns plane water">context-sensitive extended reducible forms</td>
+            <td class="snns file water">crx ( ⦃?,?⦄ ⊢ 𝐑[?,?]⦃?⦄ )</td>
+            <td class="snnn file water">crx_append crx_lift</td>
+            <td class="snnn file water">
+              <br />
+            </td>
             <td class="ssnn file water">
               <br />
             </td>
@@ -803,14 +704,9 @@
             <td class="nnns component water">
               <br />
             </td>
-            <td class="snns plane water">context-free normal forms</td>
-            <td class="snns file water">thnf ( 𝐇𝐍⦃?⦄ )</td>
-            <td class="snnn file water">
-              <br />
-            </td>
-            <td class="snnn file water">
-              <br />
-            </td>
+            <td class="snns plane water">context-sensitive normal forms</td>
+            <td class="snns file water">cnr ( ⦃?,?⦄ ⊢ 𝐍⦃?⦄ )</td>
+            <td class="snnn file water">cnr_lift cnr_crr cnr_cir</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -822,12 +718,9 @@
             <td class="nnns component water">
               <br />
             </td>
-            <td class="snns plane water">context-free reduction</td>
-            <td class="snns file water">ltpr ( ? ➡ ? )</td>
-            <td class="snnn file water">ltpr_ldrop ltpr_tps ltpr_tpss ltpr_ltpss_dx ltpr_ltpss_sn ltpr_aaa ltpr_ltpr</td>
-            <td class="snnn file water">
-              <br />
-            </td>
+            <td class="snns plane water">context-sensitive reduction</td>
+            <td class="snns file water">lpr ( ⦃?,?⦄ ⊢ ➡ ? )</td>
+            <td class="snnn file water">lpr_ldrop lpr_lpr</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -842,11 +735,8 @@
             <td class="nnns plane water">
               <br />
             </td>
-            <td class="snns file water">tpr ( ? ➡ ? )</td>
-            <td class="snnn file water">tpr_lift tpr_delift tpr_tpr</td>
-            <td class="snnn file water">
-              <br />
-            </td>
+            <td class="snns file water">cpr ( ⦃?,?⦄ ⊢ ? ➡ ? )</td>
+            <td class="snnn file water">cpr_lift cpr_cir</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -855,48 +745,37 @@
             </td>
           </tr>
           <tr>
-            <td class="snns component green">unfold</td>
-            <td class="snns plane green">restricted parallel computation</td>
-            <td class="snns file green">lpqs ( ? ⊢ ➤* ? )</td>
-            <td class="snnn file green">lpqs_ldrop lpqs_cpqs lpqs_lpqs</td>
-            <td class="snnn file green">
+            <td class="nnns component water">
               <br />
             </td>
-            <td class="snnn file green">
+            <td class="snns plane water">context-sensitive irreducible forms</td>
+            <td class="snns file water">cir ( ⦃?,?⦄ ⊢ 𝐈⦃?⦄ )</td>
+            <td class="snnn file water">cir_append cir_lift</td>
+            <td class="snnn file water">
               <br />
             </td>
-            <td class="ssnn file green">
+            <td class="ssnn file water">
               <br />
             </td>
           </tr>
           <tr>
-            <td class="nnns component green">
-              <br />
-            </td>
-            <td class="nnns plane green">
-              <br />
-            </td>
-            <td class="snns file green">cpqs ( ? ⊢ ? ➤* ? )</td>
-            <td class="snnn file green">cpqs_lift</td>
-            <td class="snnn file green">
+            <td class="nnns component water">
               <br />
             </td>
-            <td class="snnn file green">
+            <td class="snns plane water">context-sensitive reducible forms</td>
+            <td class="snns file water">crr ( ⦃?,?⦄ ⊢ 𝐑⦃?⦄ )</td>
+            <td class="snnn file water">crr_append crr_lift</td>
+            <td class="snnn file water">
               <br />
             </td>
-            <td class="ssnn file green">
+            <td class="ssnn file water">
               <br />
             </td>
           </tr>
           <tr>
-            <td class="nnns component green">
-              <br />
-            </td>
+            <td class="snns component green">unfold</td>
             <td class="snns plane green">unfold</td>
-            <td class="snns file green">unfold ( ? ⊢ ? ⧫* ? )</td>
-            <td class="snnn file green">
-              <br />
-            </td>
+            <td class="snns file green">unfold ( ⦃?,?⦄ ⊢ ? ⧫* ? )</td>
             <td class="snnn file green">
               <br />
             </td>
@@ -911,27 +790,19 @@
             <td class="nnns component green">
               <br />
             </td>
-            <td class="snns plane green">iterated stratified static type assignment</td>
-            <td class="snns file green">sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )</td>
-            <td class="snnn file green">sstas_lift sstas_lpss sstas_aaa sstas_sstas</td>
-            <td class="snnn file green">
-              <br />
-            </td>
-            <td class="snnn file green">
-              <br />
-            </td>
+            <td class="snns plane green">iterated static type assignment</td>
+            <td class="snns file green">lsstas ( ⦃?,?⦄ ⊢ ? •*[?,?,?] ? )</td>
+            <td class="snnn file green">lsstas_alt ( ⦃?,?⦄ ⊢ ? ••*[?,?,?] ? )</td>
+            <td class="snnn file green">lsstas_lift lsstas_aaa lsstas_lsstas</td>
             <td class="ssnn file green">
               <br />
             </td>
           </tr>
           <tr>
             <td class="snns component grass">static typing</td>
-            <td class="snns plane grass">stratified static type assignment</td>
-            <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
-            <td class="snnn file grass">ssta_lift ssta_lpss ssta_aaa ssta_ssta</td>
-            <td class="snnn file grass">
-              <br />
-            </td>
+            <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
+            <td class="snns file grass">lsuba ( ? ⊢ ? ⁝⊑ ? )</td>
+            <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
             <td class="snnn file grass">
               <br />
             </td>
@@ -943,12 +814,9 @@
             <td class="nnns component grass">
               <br />
             </td>
-            <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
-            <td class="snns file grass">lsuba ( ? ⁝⊑ ? )</td>
-            <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
-            <td class="snnn file grass">
-              <br />
-            </td>
+            <td class="snns plane grass">atomic arity assignment</td>
+            <td class="snns file grass">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
+            <td class="snnn file grass">aaa_lift aaa_lifts aaa_da aaa_ssta aaa_aaa</td>
             <td class="snnn file grass">
               <br />
             </td>
@@ -960,12 +828,9 @@
             <td class="nnns component grass">
               <br />
             </td>
-            <td class="snns plane grass">atomic arity assignment</td>
-            <td class="snns file grass">aaa ( ? ⊢ ? ⁝ ? )</td>
-            <td class="snnn file grass">aaa_lift aaa_lifts aaa_lpss aaa_aaa</td>
-            <td class="snnn file grass">
-              <br />
-            </td>
+            <td class="snns plane grass">stratified static type assignment</td>
+            <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
+            <td class="snnn file grass">ssta_lift ssta_ssta</td>
             <td class="snnn file grass">
               <br />
             </td>
@@ -977,12 +842,9 @@
             <td class="nnns component grass">
               <br />
             </td>
-            <td class="snns plane grass">parameters</td>
-            <td class="snns file grass">sh</td>
-            <td class="snnn file grass">sd</td>
-            <td class="snnn file grass">
-              <br />
-            </td>
+            <td class="snns plane grass">local env. ref. for degree assignment</td>
+            <td class="snns file grass">lsubd ( ? ⊢ ? ▪⊑ ? )</td>
+            <td class="snnn file grass">lsubd_da lsubd_lsubd</td>
             <td class="snnn file grass">
               <br />
             </td>
@@ -991,32 +853,38 @@
             </td>
           </tr>
           <tr>
-            <td class="snns component yellow">substitution</td>
-            <td class="snns plane yellow">parallel substitution</td>
-            <td class="snns file yellow">lpss ( ? ⊢ ▶* ? )</td>
-            <td class="snnn file yellow">lpss_ldrop lpss_cpss lpss_lpss</td>
-            <td class="snnn file yellow">
+            <td class="nnns component grass">
               <br />
             </td>
-            <td class="snnn file yellow">
+            <td class="snns plane grass">degree assignment</td>
+            <td class="snns file grass">da ( ⦃?,?⦄ ⊢ ? ▪[?,?] ? )</td>
+            <td class="snnn file grass">da_lift da_da</td>
+            <td class="snnn file grass">
               <br />
             </td>
-            <td class="ssnn file yellow">
+            <td class="ssnn file grass">
               <br />
             </td>
           </tr>
           <tr>
-            <td class="nnns component yellow">
+            <td class="nnns component grass">
               <br />
             </td>
-            <td class="nnns plane yellow">
+            <td class="snns plane grass">parameters</td>
+            <td class="snns file grass">sh</td>
+            <td class="snnn file grass">sd</td>
+            <td class="snnn file grass">
               <br />
             </td>
-            <td class="snns file yellow">cpss ( ? ⊢ ? ▶* ? )</td>
-            <td class="snnn file yellow">cpss_lift</td>
-            <td class="snnn file yellow">
+            <td class="ssnn file grass">
               <br />
             </td>
+          </tr>
+          <tr>
+            <td class="snns component yellow">substitution</td>
+            <td class="snns plane yellow">restricted local env. ref.</td>
+            <td class="snns file yellow">lsubr ( ? ⊑ ? )</td>
+            <td class="snnn file yellow">lsubr_lsubr</td>
             <td class="snnn file yellow">
               <br />
             </td>
@@ -1029,11 +897,8 @@
               <br />
             </td>
             <td class="snns plane yellow">iterated structural successor for closures</td>
-            <td class="snns file yellow">fsups ( ⦃?,?⦄ ⊃* ⦃?,?⦄ )</td>
-            <td class="snnn file yellow">fsups_fsups</td>
-            <td class="snnn file yellow">
-              <br />
-            </td>
+            <td class="snns file yellow">fqus ( ⦃?,?,?⦄ ⊃* ⦃?,?,?⦄ )</td>
+            <td class="snnn file yellow">fqus_alt fqus_fqus</td>
             <td class="snnn file yellow">
               <br />
             </td>
@@ -1048,11 +913,8 @@
             <td class="nnns plane yellow">
               <br />
             </td>
-            <td class="snns file yellow">fsupp ( ⦃?,?⦄ ⊃+ ⦃?,?⦄ )</td>
-            <td class="snnn file yellow">fsupp_fsupp</td>
-            <td class="snnn file yellow">
-              <br />
-            </td>
+            <td class="snns file yellow">fqup ( ⦃?,?,?⦄ ⊃+ ⦃?,?,?⦄ )</td>
+            <td class="snnn file yellow">fqup_fqup</td>
             <td class="snnn file yellow">
               <br />
             </td>
@@ -1070,9 +932,6 @@
             <td class="snnn file yellow">
               <br />
             </td>
-            <td class="snnn file yellow">
-              <br />
-            </td>
             <td class="ssnn file yellow">
               <br />
             </td>
@@ -1087,9 +946,6 @@
             <td class="snnn file yellow">
               <br />
             </td>
-            <td class="snnn file yellow">
-              <br />
-            </td>
             <td class="ssnn file yellow">
               <br />
             </td>
@@ -1106,9 +962,6 @@
             <td class="snnn file yellow">
               <br />
             </td>
-            <td class="snnn file yellow">
-              <br />
-            </td>
             <td class="ssnn file yellow">
               <br />
             </td>
@@ -1121,21 +974,27 @@
             <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
             <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
             <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
-            <td class="snnn file yellow">gr2_gr2</td>
-            <td class="ssnn file yellow">
-              <br />
-            </td>
+            <td class="ssnn file yellow">gr2_gr2</td>
           </tr>
           <tr>
             <td class="snns component orange">relocation</td>
             <td class="snns plane orange">structural successor for closures</td>
-            <td class="snns file orange">fsup ( ⦃?,?⦄ ⊃ ⦃?,?⦄ )</td>
-            <td class="snnn file orange">
+            <td class="snns file orange">fquq ( ⦃?,?,?⦄ ⊃⸮ ⦃?,?,?⦄ )</td>
+            <td class="snnn file orange">fquq_alt ( ⦃?,?,?⦄ ⊃⊃⸮ ⦃?,?,?⦄ )</td>
+            <td class="snnn file orange">fquq_fquq</td>
+            <td class="ssnn file orange">
               <br />
             </td>
-            <td class="snnn file orange">
+          </tr>
+          <tr>
+            <td class="nnns component orange">
               <br />
             </td>
+            <td class="nnns plane orange">
+              <br />
+            </td>
+            <td class="snns file orange">fqu ( ⦃?,?,?⦄ ⊃ ⦃?,?,?⦄ )</td>
+            <td class="snnn file orange">fqu_fqu</td>
             <td class="snnn file orange">
               <br />
             </td>
@@ -1147,12 +1006,9 @@
             <td class="nnns component orange">
               <br />
             </td>
-            <td class="snns plane orange">global env. slicing</td>
-            <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
-            <td class="snnn file orange">gdrop_gdrop</td>
-            <td class="snnn file orange">
-              <br />
-            </td>
+            <td class="snns plane orange">lazy equivalence for local environments</td>
+            <td class="snns file orange">lleq ( ? ⋕[?] ? )</td>
+            <td class="snnn file orange">lleq_fleq</td>
             <td class="snnn file orange">
               <br />
             </td>
@@ -1164,12 +1020,9 @@
             <td class="nnns component orange">
               <br />
             </td>
-            <td class="snns plane orange">basic local env. slicing</td>
-            <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
-            <td class="snnn file orange">ldrop_append ldrop_lpx ldrop_lpx_sn ldrop_lbotr ldrop_ldrop</td>
-            <td class="snnn file orange">
-              <br />
-            </td>
+            <td class="snns plane orange">global env. slicing</td>
+            <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
+            <td class="snnn file orange">gdrop_gdrop</td>
             <td class="snnn file orange">
               <br />
             </td>
@@ -1181,10 +1034,9 @@
             <td class="nnns component orange">
               <br />
             </td>
-            <td class="snns plane orange">local env. ref. for substitution</td>
-            <td class="snns file orange">lsubr ( ? ⊑[?,?] ? )</td>
-            <td class="snnn file orange">(lsubr_lsubr)</td>
-            <td class="snnn file orange">lsubr_lbotr ( ⊒[?,?] ? )</td>
+            <td class="snns plane orange">basic local env. slicing</td>
+            <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
+            <td class="snnn file orange">ldrop_append ldrop_lpx_sn ldrop_ldrop</td>
             <td class="snnn file orange">
               <br />
             </td>
@@ -1202,9 +1054,6 @@
             <td class="snnn file orange">
               <br />
             </td>
-            <td class="snnn file orange">
-              <br />
-            </td>
             <td class="ssnn file orange">
               <br />
             </td>
@@ -1221,21 +1070,15 @@
             <td class="snnn file orange">
               <br />
             </td>
-            <td class="snnn file orange">
-              <br />
-            </td>
             <td class="ssnn file orange">
               <br />
             </td>
           </tr>
           <tr>
             <td class="snns component red">grammar</td>
-            <td class="snns plane red">same head term form</td>
-            <td class="snns file red">tshf ( ? ≈ ? )</td>
-            <td class="snnn file red">(tshf_tshf)</td>
-            <td class="snnn file red">
-              <br />
-            </td>
+            <td class="snns plane red">pointwise extension of a relation</td>
+            <td class="snns file red">lpx_sn</td>
+            <td class="snnn file red">lpx_sn_tc lpx_sn_lpx_sn</td>
             <td class="snnn file red">
               <br />
             </td>
@@ -1253,9 +1096,6 @@
             <td class="snnn file red">
               <br />
             </td>
-            <td class="snnn file red">
-              <br />
-            </td>
             <td class="ssnn file red">
               <br />
             </td>
@@ -1266,10 +1106,7 @@
             </td>
             <td class="snns plane red">closures</td>
             <td class="snns file red">cl_shift ( ? @@ ? )</td>
-            <td class="snnn file red">cl_weight ( ♯{?,?} )</td>
-            <td class="snnn file red">
-              <br />
-            </td>
+            <td class="snnn file red">cl_weight ( ♯{?,?,?} )</td>
             <td class="snnn file red">
               <br />
             </td>
@@ -1289,9 +1126,6 @@
             <td class="snnn file red">
               <br />
             </td>
-            <td class="snnn file red">
-              <br />
-            </td>
             <td class="ssnn file red">
               <br />
             </td>
@@ -1306,8 +1140,7 @@
             <td class="snns file red">lenv</td>
             <td class="snnn file red">lenv_weight ( ♯{?} )</td>
             <td class="snnn file red">lenv_length ( |?| )</td>
-            <td class="snnn file red">lenv_append ( ? @@ ? )</td>
-            <td class="ssnn file red">lenv_px lenv_px_sn lenv_px_bi</td>
+            <td class="ssnn file red">lenv_append ( ? @@ ? )</td>
           </tr>
           <tr>
             <td class="nnns component red">
@@ -1319,10 +1152,7 @@
             <td class="snns file red">term</td>
             <td class="snnn file red">term_weight ( ♯{?} )</td>
             <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
-            <td class="snnn file red">term_vector</td>
-            <td class="ssnn file red">
-              <br />
-            </td>
+            <td class="ssnn file red">term_vector</td>
           </tr>
           <tr>
             <td class="nnns component red">
@@ -1338,9 +1168,6 @@
             <td class="snnn file red">
               <br />
             </td>
-            <td class="snnn file red">
-              <br />
-            </td>
             <td class="ssnn file red">
               <br />
             </td>
@@ -1357,9 +1184,6 @@
             <td class="snsn file red">
               <br />
             </td>
-            <td class="snsn file red">
-              <br />
-            </td>
             <td class="sssn file red">
               <br />
             </td>
@@ -1398,6 +1222,6 @@
     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
       <br />
     </div>
-    <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sat, 20 Apr 2013 21:34:40 +0200</div>
+    <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sun, 03 Nov 2013 13:06:26 +0100</div>
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