X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fwww%2Flambdadelta%2Fbasic_2.html;h=60a48ff5db4adadf5bd95040c2bcd9228ded67f3;hb=47293eadb6240cdfa50cc9571aeddcc85b229b51;hp=b6ba4f2bef310ac3c810e447efcbb2350b58d18b;hpb=c713c14cb3c69b1e9a4c693aed382eedc04512c1;p=helm.git

diff --git a/helm/www/lambdadelta/basic_2.html b/helm/www/lambdadelta/basic_2.html
index b6ba4f2be..60a48ff5d 100644
--- a/helm/www/lambdadelta/basic_2.html
+++ b/helm/www/lambdadelta/basic_2.html
@@ -6,8 +6,8 @@
     <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
     <meta http-equiv="Content-Style-Type" content="text/css" />
     <meta name="author" content="Ferruccio Guidi" />
-    <meta name="description" content="lambdadelta version 2" />
-    <title>lambdadelta version 2</title>
+    <meta name="description" content="\lambda\delta version 2" />
+    <title>\lambda\delta version 2</title>
     <link rel="stylesheet" type="text/css" href="http://lambdadelta.info/css/ld_web.css" />
     <link rel="stylesheet" type="text/css" href="http://lambdadelta.info/css/lddl.css" />
     <link rel="stylesheet" type="text/css" href="http://lambdadelta.info/css/xhtbl.css" />
@@ -23,112 +23,7 @@
     <div class="spacer">
       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
     </div>
-   <div xmlns:ld="http://lambdadelta.info/" class="head2">System's Syntax and Behavior</div>
-   <div xmlns:ld="http://lambdadelta.info/" class="text">This is a summary of the "block structure"
-         of the System's syntactic items and reductions.
-   </div>
-   <div xmlns:ld="http://lambdadelta.info/" class="text">
-      <table cellpadding="4" cellspacing="0">
-        <tbody>
-          <tr>
-            <td class="snns text grey">domain</td>
-            <td class="snns plane grey">block</td>
-            <td class="snns text grey">leader</td>
-            <td class="snns text grey">applicator (with →θ)*</td>
-            <td class="snns text grey">reduction</td>
-            <td class="snns text grey">→ζ *</td>
-            <td class="ssns text grey">reference *</td>
-          </tr>
-          <tr>
-            <td class="snns text">{X | Γ ⊢ X : W}</td>
-            <td class="snns plane wine">local typed abstraction *</td>
-            <td class="snns text wine">Γ ⊢ +λW</td>
-            <td class="snns text wine">ⓐV</td>
-            <td class="snns text wine">→β</td>
-            <td class="snns text wine">no</td>
-            <td class="ssns text wine">#i</td>
-          </tr>
-          <tr>
-            <td class="nnns text">
-              <br />
-            </td>
-            <td class="snns plane magenta">local typed declaration **</td>
-            <td class="snns text magenta">Γ ⊢ -λW</td>
-            <td class="snns text magenta">ⓐV</td>
-            <td class="snns text magenta">→β</td>
-            <td class="snns text magenta">no</td>
-            <td class="ssns text magenta">#i</td>
-          </tr>
-          <tr>
-            <td class="nnns text">
-              <br />
-            </td>
-            <td class="snns plane prune">global typed declaration ***</td>
-            <td class="snns text prune">Γ ⊢ pλW</td>
-            <td class="snns text prune">no</td>
-            <td class="snns text prune">no</td>
-            <td class="snns text prune">no</td>
-            <td class="ssns text prune">$p</td>
-          </tr>
-          <tr>
-            <td class="nnns text">
-              <br />
-            </td>
-            <td class="snns plane blue">native type annotation *</td>
-            <td class="snns text blue">Γ ⊢ ⓝW</td>
-            <td class="snns text blue">no</td>
-            <td class="snns text blue">no</td>
-            <td class="snns text blue">yes</td>
-            <td class="ssns text blue">no</td>
-          </tr>
-          <tr>
-            <td class="snns text">{X | Γ ⊢ X = V}</td>
-            <td class="snns plane sky">local abbreviation *</td>
-            <td class="snns text sky">Γ ⊢ +δV</td>
-            <td class="snns text sky">no</td>
-            <td class="snns text sky">local →δ</td>
-            <td class="snns text sky">yes</td>
-            <td class="ssns text sky">#i</td>
-          </tr>
-          <tr>
-            <td class="nnns text">
-              <br />
-            </td>
-            <td class="snns plane cyan">local definition **</td>
-            <td class="snns text cyan">Γ ⊢ -δV</td>
-            <td class="snns text cyan">no</td>
-            <td class="snns text cyan">local →δ</td>
-            <td class="snns text cyan">no</td>
-            <td class="ssns text cyan">#i</td>
-          </tr>
-          <tr>
-            <td class="nnns text">
-              <br />
-            </td>
-            <td class="snns plane water">global definition ***</td>
-            <td class="snns text water">Γ ⊢ pδV</td>
-            <td class="snns text water">no</td>
-            <td class="snns text water">global →δ</td>
-            <td class="snns text water">no</td>
-            <td class="ssns text water">$p</td>
-          </tr>
-          <tr>
-            <td class="snss text">no</td>
-            <td class="snss plane green">sort ****</td>
-            <td class="snss text green">Γ ⊢ ⋆k</td>
-            <td class="snss text green">no</td>
-            <td class="snss text green">no</td>
-            <td class="snss text green">no</td>
-            <td class="ssss text green">no</td>
-          </tr>
-        </tbody>
-      </table>
-    </div>
-   <div xmlns:ld="http://lambdadelta.info/" class="text">* In terms only.
-         ** In terms and local environments only.
-         *** In global environments only.
-         **** Sort level k in terms only.
-   </div>
+
 
    <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
@@ -163,29 +58,29 @@
           <tr>
             <td class="snns component cyan">sizes</td>
             <td class="snns plane cyan">files</td>
-            <td class="snnn number cyan">327  </td>
+            <td class="snnn number cyan">361</td>
             <td class="snns plane cyan">characters</td>
-            <td class="snnn number cyan">564871</td>
+            <td class="snnn number cyan">653633</td>
             <td class="snns plane cyan">nodes</td>
-            <td class="ssnn number cyan">1606196</td>
+            <td class="ssnn number cyan">1828417</td>
           </tr>
           <tr>
             <td class="snns component green">propositions</td>
             <td class="snns plane green">theorems</td>
-            <td class="snnn number green">105</td>
+            <td class="snnn number green">121</td>
             <td class="snns plane green">lemmas</td>
-            <td class="snnn number green">1107</td>
+            <td class="snnn number green">1299</td>
             <td class="snns plane green">total</td>
-            <td class="ssnn number green">1212</td>
+            <td class="ssnn number green">1420</td>
           </tr>
           <tr>
             <td class="snss component yellow">concepts</td>
             <td class="snss plane yellow">declared</td>
-            <td class="snsn number yellow">52</td>
+            <td class="snsn number yellow">54</td>
             <td class="snss plane yellow">defined</td>
-            <td class="snsn number yellow">76</td>
+            <td class="snsn number yellow">81</td>
             <td class="snss plane yellow">total</td>
-            <td class="sssn number yellow">128</td>
+            <td class="sssn number yellow">135</td>
           </tr>
         </tbody>
       </table>
@@ -199,9 +94,24 @@
     </ul>
    <ul xmlns:ld="http://lambdadelta.info/">
       <li>
-        <span class="date">In progress.</span>
-         Closure of context-sensitive extended computation
-         for native validity.
+        <span class="date">2014 June 18.</span>
+         Preservation of stratified native validity
+         for context-sensitive computation on terms.
+   </li>
+    </ul>
+   <ul xmlns:ld="http://lambdadelta.info/">
+      <li>
+        <span class="date">2014 June 9.</span>
+         "Big tree" strong normalization
+         for simply typed terms.
+   </li>
+    </ul>
+   <ul xmlns:ld="http://lambdadelta.info/">
+      <li>
+        <span class="date">2014 April 16.</span>
+         lazy equivalence on local environments
+	 serves as irrelevant step in "big tree" computation on closures
+         (anniversary milestone).
    </li>
     </ul>
    <ul xmlns:ld="http://lambdadelta.info/">
@@ -255,7 +165,7 @@
    <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 (not released).
    </li>
     </ul>
    <ul xmlns:ld="http://lambdadelta.info/">
@@ -325,8 +235,8 @@
           <tr>
             <td class="snns component prune">dynamic typing</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="snns file prune">lsubsv ( ? ⊢ ? ¡⫃[?,?] ? )</td>
+            <td class="snnn file prune">lsubsv_lsuba lsubsv_lsubd lsubsv_lstas lsubsv_cpds lsubsv_cpcs lsubsv_snv</td>
             <td class="snnn file prune">
               <br />
             </td>
@@ -340,7 +250,7 @@
             </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">snv_lift snv_aaa snv_da_lpr snv_lstas snv_lstas_lpr snv_lpr snv_cpcs snv_preserve</td>
             <td class="snnn file prune">
               <br />
             </td>
@@ -431,8 +341,8 @@
               <br />
             </td>
             <td class="snns plane cyan">strongly normalizing extended computation</td>
-            <td class="snns file cyan">lcosx ( ? ⊢ ⧤⬊*[?,?,?] ? )</td>
-            <td class="snnn file cyan">lcosx_cpxs</td>
+            <td class="snns file cyan">lcosx ( ? ⊢ ~⬊*[?,?,?] ? )</td>
+            <td class="snnn file cyan">lcosx_cpx</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -447,11 +357,9 @@
             <td class="nnns plane cyan">
               <br />
             </td>
-            <td class="snns file cyan">lsx ( ? ⊢ ⋕⬊*[?,?,?,?] ? )</td>
-            <td class="snnn file cyan">lsx_ldrop lsx_cpxs lsx_csx</td>
-            <td class="snnn file cyan">
-              <br />
-            </td>
+            <td class="snns file cyan">lsx ( ? ⊢ ⬊*[?,?,?,?] ? )</td>
+            <td class="snnn file cyan">lsx_alt ( ? ⊢ ⬊⬊*[?,?,?,?] ? )</td>
+            <td class="snnn file cyan">lsx_ldrop lsx_lpx lsx_lpxs llsx_csx</td>
             <td class="ssnn file cyan">
               <br />
             </td>
@@ -481,7 +389,7 @@
             </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="snnn file cyan">csx_lift csx_lleq csx_lpx csx_lpxs csx_fpbs</td>
             <td class="ssnn file cyan">
               <br />
             </td>
@@ -491,8 +399,8 @@
               <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="snns file cyan">fpbg ( ⦃?,?,?⦄ &gt;≡[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file cyan">fpbg_lift fpbg_fleq fpbg_fpbg</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -507,8 +415,8 @@
             <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="snns file cyan">fpbc ( ⦃?,?,?⦄ ≻≡[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file cyan">fpbc_fleq fpbc_fpbs</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -524,10 +432,8 @@
               <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>
+            <td class="snnn file cyan">fpbu_lift fpbu_lleq</td>
+            <td class="snnn file cyan">fpbu_fleq</td>
             <td class="ssnn file cyan">
               <br />
             </td>
@@ -541,21 +447,7 @@
             </td>
             <td class="snns file cyan">fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )</td>
             <td class="snnn file cyan">fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ )</td>
-            <td class="snnn file cyan">fpbs_lift fpbs_aaa 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="snnn file cyan">fpbs_lift fpbs_fleq fpbs_aaa fpbs_fpbs fpbs_ext</td>
             <td class="ssnn file cyan">
               <br />
             </td>
@@ -580,8 +472,10 @@
             </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_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs</td>
+            <td class="snnn file cyan">
+              <br />
+            </td>
             <td class="ssnn file cyan">
               <br />
             </td>
@@ -594,7 +488,7 @@
               <br />
             </td>
             <td class="snns file cyan">cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )</td>
-            <td class="snnn file cyan">cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_cpys cpxs_lleq cpxs_aaa cpxs_cpxs</td>
+            <td class="snnn file cyan">cpxs_tstc cpxs_tstc_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -608,8 +502,10 @@
             </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="snnn file cyan">
+              <br />
+            </td>
             <td class="ssnn file cyan">
               <br />
             </td>
@@ -635,7 +531,7 @@
               <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 ( ? ⊢ ? ⫃[?] ? )</td>
             <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
             <td class="snnn file cyan">
               <br />
@@ -688,10 +584,8 @@
             </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_cpys lpx_lleq lpx_aaa</td>
-            <td class="snnn file water">
-              <br />
-            </td>
+            <td class="snnn file water">lpx_ldrop lpx_frees</td>
+            <td class="snnn file water">lpx_lleq lpx_aaa</td>
             <td class="ssnn file water">
               <br />
             </td>
@@ -704,7 +598,7 @@
               <br />
             </td>
             <td class="snns file water">cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
-            <td class="snnn file water">cpx_lift cpx_cpys cpx_lleq cpx_cix</td>
+            <td class="snnn file water">cpx_leq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -776,7 +670,7 @@
               <br />
             </td>
             <td class="snns file water">cpr ( ⦃?,?⦄ ⊢ ? ➡ ? )</td>
-            <td class="snnn file water">cpr_lift cpr_cir</td>
+            <td class="snnn file water">cpr_lift cpr_llpx_sn cpr_cir</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -831,18 +725,18 @@
               <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="snns file green">lstas ( ⦃?,?⦄ ⊢ ? •*[?,?] ? )</td>
+            <td class="snnn file green">lstas_alt ( ⦃?,?⦄ ⊢ ? ••*[?,?] ? )</td>
+            <td class="snnn file green">lstas_lift lstas_aaa lstas_da lstas_lstas</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="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>
@@ -854,9 +748,9 @@
             <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_fqus aaa_da aaa_ssta 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_aaa da_sta da_da</td>
             <td class="snnn file grass">
               <br />
             </td>
@@ -868,9 +762,9 @@
             <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_ssta</td>
+            <td class="snns plane grass">static type assignment</td>
+            <td class="snns file grass">sta ( ⦃?,?⦄ ⊢ ? •[?] ? )</td>
+            <td class="snnn file grass">sta_lift sta_lpx_sn sta_aaa sta_sta</td>
             <td class="snnn file grass">
               <br />
             </td>
@@ -882,9 +776,9 @@
             <td class="nnns component 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="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>
@@ -896,9 +790,9 @@
             <td class="nnns component grass">
               <br />
             </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="snns plane grass">local env. ref. for atomic arity assignment</td>
+            <td class="snns file grass">lsuba ( ? ⊢ ? ⁝⫃ ? )</td>
+            <td class="snnn file grass">lsuba_aaa lsuba_lsuba</td>
             <td class="snnn file grass">
               <br />
             </td>
@@ -910,9 +804,23 @@
             <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="snns plane grass">atomic arity assignment</td>
+            <td class="snns file grass">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
+            <td class="snnn file grass">aaa_lift aaa_lifts aaa_fqus aaa_lleq 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">restricted local env. ref.</td>
+            <td class="snns file grass">lsubr ( ? ⫃ ? )</td>
+            <td class="snnn file grass">lsubr_lsubr</td>
             <td class="snnn file grass">
               <br />
             </td>
@@ -921,11 +829,71 @@
             </td>
           </tr>
           <tr>
-            <td class="snns component yellow">substitution</td>
-            <td class="snns plane yellow">lazy equivalence for local environments</td>
-            <td class="snns file yellow">lleq ( ? ⋕[?,?] ? )</td>
-            <td class="snnn file yellow">lleq_alt ( ? ⋕⋕[?,?] ? )</td>
-            <td class="snnn file yellow">lleq_ldrop lleq_fqus lleq_lleq lleq_ext</td>
+            <td class="snns component yellow">multiple substitution</td>
+            <td class="snns plane yellow">lazy equivalence</td>
+            <td class="snns file yellow">fleq ( ⦃?,?,?⦄ ≡[?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file yellow">fleq_fleq</td>
+            <td class="snnn file yellow">
+              <br />
+            </td>
+            <td class="ssnn file yellow">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <td class="nnns component yellow">
+              <br />
+            </td>
+            <td class="nnns plane yellow">
+              <br />
+            </td>
+            <td class="snns file yellow">lleq ( ? ≡[?,?] ? )</td>
+            <td class="snnn file yellow">lleq_alt lleq_alt_rec lleq_leq lleq_ldrop lleq_fqus lleq_llor lleq_lleq</td>
+            <td class="snnn file yellow">
+              <br />
+            </td>
+            <td class="ssnn file yellow">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <td class="nnns component yellow">
+              <br />
+            </td>
+            <td class="snns plane yellow">lazy pointwise extension of a relation</td>
+            <td class="snns file yellow">llpx_sn</td>
+            <td class="snnn file yellow">llpx_sn_alt llpx_sn_alt_rec llpx_sn_tc llpx_sn_leq llpx_sn_ldrop llpx_sn_lpx_sn llpx_sn_frees llpx_sn_llor</td>
+            <td class="snnn file yellow">
+              <br />
+            </td>
+            <td class="ssnn file yellow">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <td class="nnns component yellow">
+              <br />
+            </td>
+            <td class="snns plane yellow">pointwise union for local environments</td>
+            <td class="snns file yellow">llor ( ? ⩖[?,?] ? ≡ ? )</td>
+            <td class="snnn file yellow">llor_alt llor_ldrop</td>
+            <td class="snnn file yellow">
+              <br />
+            </td>
+            <td class="ssnn file yellow">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <td class="nnns component yellow">
+              <br />
+            </td>
+            <td class="snns plane yellow">context-sensitive exclusion from free variables</td>
+            <td class="snns file yellow">frees ( ? ⊢ ? ϵ 𝐅*[?]⦃?⦄ )</td>
+            <td class="snnn file yellow">frees_append frees_leq frees_lift</td>
+            <td class="snnn file yellow">
+              <br />
+            </td>
             <td class="ssnn file yellow">
               <br />
             </td>
@@ -947,7 +915,7 @@
               <br />
             </td>
             <td class="snns plane yellow">iterated structural successor for closures</td>
-            <td class="snns file yellow">fqus ( ⦃?,?,?⦄ ⊃* ⦃?,?,?⦄ )</td>
+            <td class="snns file yellow">fqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
             <td class="snnn file yellow">fqus_alt fqus_fqus</td>
             <td class="snnn file yellow">
               <br />
@@ -963,7 +931,7 @@
             <td class="nnns plane yellow">
               <br />
             </td>
-            <td class="snns file yellow">fqup ( ⦃?,?,?⦄ ⊃+ ⦃?,?,?⦄ )</td>
+            <td class="snns file yellow">fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
             <td class="snnn file yellow">fqup_fqup</td>
             <td class="snnn file yellow">
               <br />
@@ -1027,10 +995,10 @@
             <td class="ssnn file yellow">gr2_gr2</td>
           </tr>
           <tr>
-            <td class="snns component orange">relocation</td>
-            <td class="snns plane orange">contxt-sensitive extended ordinary substitution</td>
-            <td class="snns file orange">cpy ( ⦃?,?⦄ ⊢ ? ▶[?,?] ? )</td>
-            <td class="snnn file orange">cpy_lift cpy_cpy</td>
+            <td class="snns component orange">substitution</td>
+            <td class="snns plane orange">structural successor for closures</td>
+            <td class="snns file orange">fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
+            <td class="snnn file orange">fquq_alt ( ⦃?,?,?⦄ ⊐⊐⸮ ⦃?,?,?⦄ )</td>
             <td class="snnn file orange">
               <br />
             </td>
@@ -1042,9 +1010,13 @@
             <td class="nnns component orange">
               <br />
             </td>
-            <td class="snns plane orange">restricted local env. ref.</td>
-            <td class="snns file orange">lsubr ( ? ⊑ ? )</td>
-            <td class="snnn file orange">lsubr_lsubr</td>
+            <td class="nnns plane orange">
+              <br />
+            </td>
+            <td class="snns file orange">fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
+            <td class="snnn file orange">
+              <br />
+            </td>
             <td class="snnn file orange">
               <br />
             </td>
@@ -1056,9 +1028,9 @@
             <td class="nnns component orange">
               <br />
             </td>
-            <td class="snns plane orange">local env. ref. for extended substitution</td>
-            <td class="snns file orange">lsuby ( ? ⊑×[?,?] ? )</td>
-            <td class="snnn file orange">lsuby_lsuby</td>
+            <td class="snns plane orange">global env. slicing</td>
+            <td class="snns file orange">gget ( ⇩[?] ? ≡ ? )</td>
+            <td class="snnn file orange">gget_gget</td>
             <td class="snnn file orange">
               <br />
             </td>
@@ -1070,9 +1042,9 @@
             <td class="nnns component orange">
               <br />
             </td>
-            <td class="snns plane orange">structural successor for closures</td>
-            <td class="snns file orange">fquq ( ⦃?,?,?⦄ ⊃⸮ ⦃?,?,?⦄ )</td>
-            <td class="snnn file orange">fquq_alt ( ⦃?,?,?⦄ ⊃⊃⸮ ⦃?,?,?⦄ )</td>
+            <td class="snns plane orange">contxt-sensitive extended ordinary substitution</td>
+            <td class="snns file orange">cpy ( ⦃?,?⦄ ⊢ ? ▶[?,?] ? )</td>
+            <td class="snnn file orange">cpy_lift cpy_nlift cpy_cpy</td>
             <td class="snnn file orange">
               <br />
             </td>
@@ -1084,13 +1056,9 @@
             <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">
-              <br />
-            </td>
+            <td class="snns plane orange">local env. ref. for extended substitution</td>
+            <td class="snns file orange">lsuby ( ? ⊑×[?,?] ? )</td>
+            <td class="snnn file orange">lsuby_lsuby</td>
             <td class="snnn file orange">
               <br />
             </td>
@@ -1102,9 +1070,9 @@
             <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="snns plane orange">pointwise extension of a relation</td>
+            <td class="snns file orange">lpx_sn</td>
+            <td class="snnn file orange">lpx_sn_alt lpx_sn_tc lpx_sn_ldrop lpx_sn_lpx_sn</td>
             <td class="snnn file orange">
               <br />
             </td>
@@ -1118,7 +1086,7 @@
             </td>
             <td class="snns plane orange">basic local env. slicing</td>
             <td class="snns file orange">ldrop ( ⇩[?,?,?] ? ≡ ? )</td>
-            <td class="snnn file orange">ldrop_lpx_sn ldrop_leq ldrop_ldrop</td>
+            <td class="snnn file orange">ldrop_append ldrop_leq ldrop_ldrop</td>
             <td class="snnn file orange">
               <br />
             </td>
@@ -1148,7 +1116,7 @@
               <br />
             </td>
             <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
-            <td class="snnn file orange">lift_lift</td>
+            <td class="snnn file orange">lift_neq lift_lift</td>
             <td class="snnn file orange">
               <br />
             </td>
@@ -1168,20 +1136,6 @@
               <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>
-            <td class="snnn file red">
-              <br />
-            </td>
-            <td class="ssnn file red">
-              <br />
-            </td>
-          </tr>
           <tr>
             <td class="nnns component red">
               <br />
@@ -1318,6 +1272,6 @@
     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
       <br />
     </div>
-    <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Fri, 21 Feb 2014 17:37:37 +0100</div>
+    <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Thu, 19 Jun 2014 15:37:14 +0200</div>
 </body>
 </html>