update in basic_2

[helm.git] / helm / www / lambdadelta / basic_2.html

diff --git a/helm/www/lambdadelta/basic_2.html b/helm/www/lambdadelta/basic_2.html
index a14edca6753bdae6d108492f3507682bd9deb73d..1d89601876e0a0265bd633aa204801c0feeb1b17 100644 (file)
--- a/helm/www/lambdadelta/basic_2.html
+++ b/helm/www/lambdadelta/basic_2.html
@@ -133,10 +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"
+         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].
+         pp. 53-78].
    </div>
    <div xmlns:ld="http://lambdadelta.info/" class="text">
       <table cellpadding="4" cellspacing="0">
@@ -163,29 +163,29 @@
           <tr>
             <td class="snns component cyan">sizes</td>
             <td class="snns plane cyan">files</td>
-            <td class="snnn number cyan">247  </td>
+            <td class="snnn number cyan">307  </td>
             <td class="snns plane cyan">characters</td>
-            <td class="snnn number cyan">350287</td>
+            <td class="snnn number cyan">488137</td>
             <td class="snns plane cyan">nodes</td>
-            <td class="ssnn number cyan">1035865</td>
+            <td class="ssnn number cyan">1416510</td>
           </tr>
           <tr>
             <td class="snns component green">propositions</td>
             <td class="snns plane green">theorems</td>
-            <td class="snnn number green">76</td>
+            <td class="snnn number green">90</td>
             <td class="snns plane green">lemmas</td>
-            <td class="snnn number green">748</td>
+            <td class="snnn number green">956</td>
             <td class="snns plane green">total</td>
-            <td class="ssnn number green">824</td>
+            <td class="ssnn number green">1046</td>
           </tr>
           <tr>
             <td class="snss component yellow">concepts</td>
             <td class="snss plane yellow">declared</td>
-            <td class="snsn number yellow">41</td>
+            <td class="snsn number yellow">48</td>
             <td class="snss plane yellow">defined</td>
-            <td class="snsn number yellow">77</td>
+            <td class="snsn number yellow">75</td>
             <td class="snss plane yellow">total</td>
-            <td class="sssn number yellow">118</td>
+            <td class="sssn number yellow">123</td>
           </tr>
         </tbody>
       </table>
@@ -206,10 +206,10 @@
     </ul>
    <ul xmlns:ld="http://lambdadelta.info/">
       <li>
-        <span class="date">In progress.</span>
+        <span class="date">2013 August 7.</span>
          Passive support for global environments.
    </li>
-    </ul>   
+    </ul>
    <ul xmlns:ld="http://lambdadelta.info/">
       <li>
         <span class="date">2013 July 27.</span>
@@ -226,7 +226,7 @@
    <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>
@@ -235,7 +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/">
@@ -293,7 +293,7 @@
    <div xmlns:ld="http://lambdadelta.info/" class="head2">Logical Structure of the Specification</div>
    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in planes and components
          according to the following table.
-         A notation file covering the whole specification is provided.
+         Notation files covering the whole specification are provided.
          The notation for the relations or functions introduced in each file
          is shown in parentheses (? are placeholders).
    </div>
@@ -316,19 +316,9 @@
           </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="ssnn file prune">ygt_ygt</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="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_lsubd lsubsv_lsuba lsubsv_lsstas lsubsv_cpds lsubsv_cpcs lsubsv_snv</td>
             <td class="snnn file prune">
               <br />
             </td>
@@ -340,9 +330,9 @@
             <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="snns plane prune">stratified native validity</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>
@@ -351,23 +341,23 @@
             </td>
           </tr>
           <tr>
-            <td class="nnns component prune">
-              <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_aaa snv_ssta snv_sstas snv_ssta_lpr snv_lpr snv_cpcs</td>
-            <td class="snnn file prune">
+            <td class="snns component blue">equivalence</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>
-            <td class="ssnn file prune">
+            <td class="ssnn file blue">
               <br />
             </td>
           </tr>
           <tr>
-            <td class="snns component blue">equivalence</td>
+            <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="snns file blue">cpcs ( ⦃?,?⦄ ⊢ ? ⬌* ? )</td>
             <td class="snnn file blue">cpcs_aaa cpcs_cprs cpcs_cpcs</td>
             <td class="snnn file blue">
               <br />
@@ -379,7 +369,7 @@
           <tr>
             <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="snns file sky">cpc ( ⦃?,?⦄ ⊢ ? ⬌ ? )</td>
             <td class="snnn file sky">cpc_cpc</td>
             <td class="snnn file sky">
               <br />
@@ -391,7 +381,7 @@
           <tr>
             <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="snns file cyan">cpxe ( ⦃?,?⦄ ⊢ ➡*[?,?] 𝐍⦃?⦄ )</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -407,7 +397,7 @@
               <br />
             </td>
             <td class="snns plane cyan">context-sensitive evaluation</td>
-            <td class="snns file cyan">cpre ( ? ⊢ ➡* 𝐍⦃?⦄ )</td>
+            <td class="snns file cyan">cpre ( ⦃?,?⦄ ⊢ ➡* 𝐍⦃?⦄ )</td>
             <td class="snnn file cyan">cpre_cpre</td>
             <td class="snnn file cyan">
               <br />
@@ -420,9 +410,97 @@
             <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_tstc_vector csn_aaa</td>
+            <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_aaa fsb_csx</td>
+            <td class="ssnn file cyan">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <td class="nnns component cyan">
+              <br />
+            </td>
+            <td class="snns plane cyan">strongly normalizing extended computation</td>
+            <td class="snns file cyan">lsx ( ? ⊢ ⬊*[?,?,?] ? )</td>
+            <td class="snnn file cyan">lsx_cpxs lsx_csx</td>
+            <td class="snnn file cyan">
+              <br />
+            </td>
+            <td class="ssnn file cyan">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <td class="nnns component cyan">
+              <br />
+            </td>
+            <td class="nnns plane cyan">
+              <br />
+            </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 cyan">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <td class="nnns component cyan">
+              <br />
+            </td>
+            <td class="nnns plane cyan">
+              <br />
+            </td>
+            <td class="snns file cyan">csx ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )</td>
+            <td class="snnn file cyan">csx_alt ( ⦃?,?⦄ ⊢ ⬊⬊*[?,?] ? )</td>
+            <td class="snnn file cyan">csx_lift csx_lpx csx_fpbs</td>
+            <td class="ssnn file cyan">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <td class="nnns component cyan">
+              <br />
+            </td>
+            <td class="snns plane cyan">"big tree" parallel computation</td>
+            <td class="snns file cyan">fpbg ( ⦃?,?,?⦄ &gt;⋕[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file cyan">fpbg_lift fpbg_fpns fpbg_fpbg</td>
+            <td class="snnn file cyan">
+              <br />
+            </td>
+            <td class="ssnn file cyan">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <td class="nnns component cyan">
+              <br />
+            </td>
+            <td class="nnns plane cyan">
+              <br />
+            </td>
+            <td class="snns file cyan">fpbc ( ⦃?,?,?⦄ ≻⋕[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file cyan">fpbc_fpns fpbc_fpbs</td>
+            <td class="snnn file cyan">
+              <br />
+            </td>
+            <td class="ssnn file cyan">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <td class="nnns component cyan">
+              <br />
+            </td>
+            <td class="nnns plane cyan">
+              <br />
+            </td>
+            <td class="snns file cyan">fpbu ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file cyan">fpbu_lift fpbu_fpns</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -437,9 +515,23 @@
             <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_lpx</td>
+            <td class="snns file cyan">fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file cyan">fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file cyan">fpbs_lift fpbs_fpns fpbs_fpbs</td>
+            <td class="ssnn file cyan">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <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>
             <td class="ssnn file cyan">
               <br />
             </td>
@@ -449,8 +541,8 @@
               <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_aaa dxprs_dxprs</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>
@@ -463,9 +555,9 @@
               <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="snns file cyan">lpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? )</td>
+            <td class="snnn file cyan">lpxs_alt ( ⦃?,?⦄ ⊢ ➡➡*[?,?] ? )</td>
+            <td class="snnn file cyan">lpxs_ldrop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs</td>
             <td class="ssnn file cyan">
               <br />
             </td>
@@ -477,8 +569,8 @@
             <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="snns file cyan">cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )</td>
+            <td class="snnn file cyan">cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -491,8 +583,8 @@
               <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="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 />
@@ -505,7 +597,7 @@
             <td class="nnns plane cyan">
               <br />
             </td>
-            <td class="snns file cyan">cprs ( ? ⊢ ? ➡* ?)</td>
+            <td class="snns file cyan">cprs ( ⦃?,?⦄ ⊢ ? ➡* ?)</td>
             <td class="snnn file cyan">cprs_lift cprs_cprs</td>
             <td class="snnn file cyan">
               <br />
@@ -519,7 +611,7 @@
               <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 ( ? â\8a¢ ? â\8a\91[?] ? )</td>
             <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
             <td class="snnn file cyan">
               <br />
@@ -534,7 +626,7 @@
             </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="ssnn file cyan">
               <br />
@@ -542,8 +634,22 @@
           </tr>
           <tr>
             <td class="snns component water">reduction</td>
+            <td class="snns plane water">"big tree" parallel reduction</td>
+            <td class="snns file water">fpb ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file water">fpb_lift</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-sensitive extended normal forms</td>
-            <td class="snns file water">cnx ( ⦃?,?⦄ ⊢ 𝐍[?]⦃?⦄ )</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 />
@@ -557,8 +663,8 @@
               <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</td>
+            <td class="snns file water">lpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
+            <td class="snnn file water">lpx_leq lpx_ldrop lpx_lleq lpx_aaa</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -573,8 +679,8 @@
             <td class="nnns plane water">
               <br />
             </td>
-            <td class="snns file water">cpx ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
-            <td class="snnn file water">cpx_lift cpx_cix</td>
+            <td class="snns file water">cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
+            <td class="snnn file water">cpx_leq cpx_lift cpx_cix</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -587,7 +693,7 @@
               <br />
             </td>
             <td class="snns plane water">context-sensitive extended irreducible forms</td>
-            <td class="snns file water">cix ( ⦃?,?⦄ ⊢ 𝐈[?]⦃?⦄ )</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 />
@@ -601,7 +707,7 @@
               <br />
             </td>
             <td class="snns plane water">context-sensitive extended reducible forms</td>
-            <td class="snns file water">crx ( ⦃?,?⦄ ⊢ 𝐑[?]⦃?⦄ )</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 />
@@ -615,7 +721,7 @@
               <br />
             </td>
             <td class="snns plane water">context-sensitive normal forms</td>
-            <td class="snns file water">cnr ( ? ⊢ 𝐍⦃?⦄ )</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 />
@@ -629,7 +735,7 @@
               <br />
             </td>
             <td class="snns plane water">context-sensitive reduction</td>
-            <td class="snns file water">lpr ( ? ⊢ ➡ ? )</td>
+            <td class="snns file water">lpr ( ⦃?,?⦄ ⊢ ➡ ? )</td>
             <td class="snnn file water">lpr_ldrop lpr_lpr</td>
             <td class="snnn file water">
               <br />
@@ -645,7 +751,7 @@
             <td class="nnns plane water">
               <br />
             </td>
-            <td class="snns file water">cpr ( ? ⊢ ? ➡ ? )</td>
+            <td class="snns file water">cpr ( ⦃?,?⦄ ⊢ ? ➡ ? )</td>
             <td class="snnn file water">cpr_lift cpr_cir</td>
             <td class="snnn file water">
               <br />
@@ -659,7 +765,7 @@
               <br />
             </td>
             <td class="snns plane water">context-sensitive irreducible forms</td>
-            <td class="snns file water">cir ( ? ⊢ 𝐈⦃?⦄ )</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 />
@@ -673,7 +779,7 @@
               <br />
             </td>
             <td class="snns plane water">context-sensitive reducible forms</td>
-            <td class="snns file water">crr ( ? ⊢ 𝐑⦃?⦄ )</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 />
@@ -685,7 +791,7 @@
           <tr>
             <td class="snns component green">unfold</td>
             <td class="snns plane green">unfold</td>
-            <td class="snns file green">unfold ( ? ⊢ ? ⧫* ? )</td>
+            <td class="snns file green">unfold ( ⦃?,?⦄ ⊢ ? ⧫* ? )</td>
             <td class="snnn file green">
               <br />
             </td>
@@ -700,21 +806,47 @@
             <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_aaa sstas_sstas</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">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="ssnn file grass">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <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_da aaa_ssta aaa_aaa</td>
+            <td class="snnn file grass">
+              <br />
+            </td>
+            <td class="ssnn file grass">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <td class="nnns component 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_aaa ssta_ssta</td>
+            <td class="snnn file grass">ssta_lift ssta_ssta</td>
             <td class="snnn file grass">
               <br />
             </td>
@@ -726,9 +858,9 @@
             <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="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>
@@ -740,9 +872,9 @@
             <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_aaa</td>
+            <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>
@@ -781,8 +913,8 @@
               <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="snns file yellow">fqus ( ⦃?,?,?⦄ ⊃* ⦃?,?,?⦄ )</td>
+            <td class="snnn file yellow">fqus_alt fqus_lleq fqus_fqus</td>
             <td class="snnn file yellow">
               <br />
             </td>
@@ -797,8 +929,8 @@
             <td class="nnns plane yellow">
               <br />
             </td>
-            <td class="snns file yellow">fsupp ( ⦃?,?⦄ ⊃+ ⦃?,?⦄ )</td>
-            <td class="snnn file yellow">fsupp_fsupp</td>
+            <td class="snns file yellow">fqup ( ⦃?,?,?⦄ ⊃+ ⦃?,?,?⦄ )</td>
+            <td class="snnn file yellow">fqup_lleq fqup_fqup</td>
             <td class="snnn file yellow">
               <br />
             </td>
@@ -863,9 +995,39 @@
           <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">fsupq ( ⦃?,?⦄ ⊃⸮ ⦃?,?⦄ )</td>
-            <td class="snnn file orange">fsupq_alt</td>
+            <td class="snns file orange">fquq ( ⦃?,?,?⦄ ⊃⸮ ⦃?,?,?⦄ )</td>
+            <td class="snnn file orange">fquq_alt ( ⦃?,?,?⦄ ⊃⊃⸮ ⦃?,?,?⦄ )</td>
+            <td class="snnn file orange">fquq_lleq</td>
+            <td class="ssnn file orange">
+              <br />
+            </td>
+          </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_lleq</td>
+            <td class="snnn file orange">
+              <br />
+            </td>
+            <td class="ssnn file orange">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <td class="nnns component 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_lleq</td>
+            <td class="snnn file orange">
+              <br />
+            </td>
             <td class="ssnn file orange">
               <br />
             </td>
@@ -890,7 +1052,7 @@
             </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">ldrop_append ldrop_lpx_sn ldrop_leq ldrop_ldrop</td>
             <td class="snnn file orange">
               <br />
             </td>
@@ -930,6 +1092,22 @@
           </tr>
           <tr>
             <td class="snns component red">grammar</td>
+            <td class="snns plane red">equivalence for local environments</td>
+            <td class="snns file red">leq ( ? ≃[?,?] ? ) </td>
+            <td class="snnn file red">
+              <br />
+            </td>
+            <td class="snnn file red">
+              <br />
+            </td>
+            <td class="ssnn file red">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <td class="nnns component 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>
@@ -960,7 +1138,7 @@
             </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">cl_weight ( ♯{?,?,?} )</td>
             <td class="snnn file red">
               <br />
             </td>
@@ -1076,6 +1254,6 @@
     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
       <br />
     </div>
-    <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sat, 27 Jul 2013 18:22:47 +0200</div>
+    <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sat, 14 Dec 2013 23:22:14 +0100</div>
 </body>
 </html>