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[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 ba3b40d4a62c890d0b83ced0d3d4cd35a13028eb..b858c6cc31e74b632574d0acef6c6eda7e228ac4 100644 (file)
--- 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" />
@@ -23,114 +23,9 @@
     <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="head2sn" id="">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"
@@ -142,50 +37,50 @@
       <table cellpadding="4" cellspacing="0">
         <tbody>
           <tr>
-            <td class="snns component grey">category</td>
-            <td class="snns plane grey">objects</td>
-            <td class="snnn number grey">
+            <td class="snns component gray">category</td>
+            <td class="snns plane gray">objects</td>
+            <td class="snnn number gray">
               <br />
             </td>
-            <td class="snnn plane grey">
+            <td class="snnn plane gray">
               <br />
             </td>
-            <td class="snnn number grey">
+            <td class="snnn number gray">
               <br />
             </td>
-            <td class="snnn plane grey">
+            <td class="snnn plane gray">
               <br />
             </td>
-            <td class="ssnn number grey">
+            <td class="ssnn number gray">
               <br />
             </td>
           </tr>
           <tr>
             <td class="snns component cyan">sizes</td>
             <td class="snns plane cyan">files</td>
-            <td class="snnn number cyan">310  </td>
+            <td class="snnn number cyan">362</td>
             <td class="snns plane cyan">characters</td>
-            <td class="snnn number cyan">491788</td>
+            <td class="snnn number cyan">431125</td>
             <td class="snns plane cyan">nodes</td>
-            <td class="ssnn number cyan">1422888</td>
+            <td class="ssnn number cyan">1829252</td>
           </tr>
           <tr>
             <td class="snns component green">propositions</td>
             <td class="snns plane green">theorems</td>
-            <td class="snnn number green">90</td>
+            <td class="snnn number green">123</td>
             <td class="snns plane green">lemmas</td>
-            <td class="snnn number green">964</td>
+            <td class="snnn number green">1300</td>
             <td class="snns plane green">total</td>
-            <td class="ssnn number green">1054</td>
+            <td class="ssnn number green">1423</td>
           </tr>
           <tr>
             <td class="snss component yellow">concepts</td>
             <td class="snss plane yellow">declared</td>
-            <td class="snsn number yellow">48</td>
+            <td class="snsn number yellow">54</td>
             <td class="snss plane yellow">defined</td>
-            <td class="snsn number yellow">75</td>
+            <td class="snsn number yellow">84</td>
             <td class="snss plane yellow">total</td>
-            <td class="sssn number yellow">123</td>
+            <td class="sssn number yellow">138</td>
           </tr>
         </tbody>
       </table>
@@ -199,9 +94,32 @@
     </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/">
+      <li>
+        <span class="date">2014 January 20.</span>
+         Parametrized slicing for local environments
+        comprises both versions of this operation
+        (one from basic_1, the other used in basic_2 till now).
    </li>
     </ul>
    <ul xmlns:ld="http://lambdadelta.info/">
@@ -247,7 +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/">
@@ -290,7 +208,7 @@
    </li>
     </ul>
 
-   <div xmlns:ld="http://lambdadelta.info/" class="head2">Logical Structure of the Specification</div>
+   <div xmlns:ld="http://lambdadelta.info/" class="head2sn" id="">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.
          Notation files covering the whole specification are provided.
@@ -301,24 +219,52 @@
       <table cellpadding="4" cellspacing="0">
         <tbody>
           <tr>
-            <td class="snns component grey">component</td>
-            <td class="snns plane grey">plane</td>
-            <td class="snns file grey">files</td>
-            <td class="snnn file grey">
+            <td class="snns component gray">component</td>
+            <td class="snns plane gray">plane</td>
+            <td class="snns file gray">files</td>
+            <td class="snnn file gray">
+              <br />
+            </td>
+            <td class="snnn file gray">
+              <br />
+            </td>
+            <td class="ssnn file gray">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <td class="snns component wine">examples</td>
+            <td class="snns plane wine">terms with special features</td>
+            <td class="snns file wine">ex_cpr_omega</td>
+            <td class="snnn file wine">
               <br />
             </td>
-            <td class="snnn file grey">
+            <td class="snnn file wine">
               <br />
             </td>
-            <td class="ssnn file grey">
+            <td class="ssnn file wine">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <td class="snns component magenta" />
+            <td class="snns plane magenta" />
+            <td class="snns file magenta" />
+            <td class="snnn file magenta">
+              <br />
+            </td>
+            <td class="snnn file magenta">
+              <br />
+            </td>
+            <td class="ssnn file magenta">
               <br />
             </td>
           </tr>
           <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 ( ? â\8a¢ ? ¡â\8a\91[?,?] ? )</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 ( ? â\8a¢ ? ¡â«\83[?,?] ? )</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>
@@ -332,7 +278,7 @@
             </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>
@@ -380,7 +326,7 @@
           </tr>
           <tr>
             <td class="snns component cyan">computation</td>
-            <td class="snns plane cyan">context-sensitive extended evaluation</td>
+            <td class="snns plane cyan">evaluation for context-sensitive extended reduction</td>
             <td class="snns file cyan">cpxe ( ⦃?,?⦄ ⊢ ➡*[?,?] 𝐍⦃?⦄ )</td>
             <td class="snnn file cyan">
               <br />
@@ -396,7 +342,7 @@
             <td class="nnns component cyan">
               <br />
             </td>
-            <td class="snns plane cyan">context-sensitive evaluation</td>
+            <td class="snns plane cyan">evaluation for context-sensitive reduction</td>
             <td class="snns file cyan">cpre ( ⦃?,?⦄ ⊢ ➡* 𝐍⦃?⦄ )</td>
             <td class="snnn file cyan">cpre_cpre</td>
             <td class="snnn file cyan">
@@ -423,8 +369,8 @@
               <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="snns file cyan">lcosx ( ? ⊢ ~⬊*[?,?,?] ? )</td>
+            <td class="snnn file cyan">lcosx_cpx</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -432,6 +378,20 @@
               <br />
             </td>
           </tr>
+          <tr>
+            <td class="nnns component cyan">
+              <br />
+            </td>
+            <td class="nnns plane cyan">
+              <br />
+            </td>
+            <td class="snns file cyan">lsx ( ? ⊢ ⬊*[?,?,?,?] ? )</td>
+            <td class="snnn file cyan">lsx_alt ( ? ⊢ ⬊⬊*[?,?,?,?] ? )</td>
+            <td class="snnn file cyan">lsx_drop lsx_lpx lsx_lpxs llsx_csx</td>
+            <td class="ssnn file cyan">
+              <br />
+            </td>
+          </tr>
           <tr>
             <td class="nnns component cyan">
               <br />
@@ -457,7 +417,7 @@
             </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>
@@ -467,8 +427,8 @@
               <br />
             </td>
             <td class="snns plane cyan">"big tree" parallel computation</td>
-            <td class="snns file cyan">fpbg ( â¦\83?,?,?â¦\84 &gt;â\8b\95[?,?] ⦃?,?,?⦄ )</td>
-            <td class="snnn file cyan">fpbg_lift fpbg_fpns fpbg_fpbg</td>
+            <td class="snns file cyan">fpbg ( â¦\83?,?,?â¦\84 &gt;â\89¡[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file cyan">fpbg_lift fpbg_fleq fpbg_fpbg</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -483,8 +443,8 @@
             <td class="nnns plane cyan">
               <br />
             </td>
-            <td class="snns file cyan">fpbc ( â¦\83?,?,?â¦\84 â\89»â\8b\95[?,?] ⦃?,?,?⦄ )</td>
-            <td class="snnn file cyan">fpbc_fpns fpbc_fpbs</td>
+            <td class="snns file cyan">fpbc ( â¦\83?,?,?â¦\84 â\89»â\89¡[?,?] ⦃?,?,?⦄ )</td>
+            <td class="snnn file cyan">fpbc_fleq fpbc_fpbs</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -500,10 +460,8 @@
               <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>
@@ -517,21 +475,7 @@
             </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>
@@ -556,8 +500,10 @@
             </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">lpxs_drop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs</td>
+            <td class="snnn file cyan">
+              <br />
+            </td>
             <td class="ssnn file cyan">
               <br />
             </td>
@@ -570,7 +516,7 @@
               <br />
             </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">cpxs_tstc cpxs_tstc_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -584,8 +530,10 @@
             </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">lprs_drop lprs_cprs lprs_lprs</td>
+            <td class="snnn file cyan">
+              <br />
+            </td>
             <td class="ssnn file cyan">
               <br />
             </td>
@@ -611,8 +559,8 @@
               <br />
             </td>
             <td class="snns plane cyan">local env. ref. for abstract candidates of reducibility</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="snns file cyan">lsubc ( ? â\8a¢ ? â«\83[?] ? )</td>
+            <td class="snnn file cyan">lsubc_drop lsubc_drops lsubc_lsuba</td>
             <td class="snnn file cyan">
               <br />
             </td>
@@ -648,8 +596,8 @@
             <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 plane water">normal forms for context-sensitive extended reduction</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 />
@@ -664,10 +612,8 @@
             </td>
             <td class="snns plane water">context-sensitive extended reduction</td>
             <td class="snns file water">lpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
-            <td class="snnn file water">lpx_leq lpx_ldrop lpx_lleq lpx_aaa</td>
-            <td class="snnn file water">
-              <br />
-            </td>
+            <td class="snnn file water">lpx_drop lpx_frees</td>
+            <td class="snnn file water">lpx_lleq lpx_aaa</td>
             <td class="ssnn file water">
               <br />
             </td>
@@ -680,7 +626,7 @@
               <br />
             </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">cpx_leq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -692,9 +638,9 @@
             <td class="nnns component 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="snns plane water">irreducible forms for context-sensitive extended reduction</td>
+            <td class="snns file water">cix ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐈⦃?⦄ )</td>
+            <td class="snnn file water">cix_lift</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -706,9 +652,9 @@
             <td class="nnns component water">
               <br />
             </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="snns plane water">reducible forms for context-sensitive extended reduction</td>
+            <td class="snns file water">crx ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐑⦃?⦄ )</td>
+            <td class="snnn file water">crx_lift</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -720,8 +666,8 @@
             <td class="nnns component water">
               <br />
             </td>
-            <td class="snns plane water">context-sensitive normal forms</td>
-            <td class="snns file water">cnr ( ⦃?,?⦄ ⊢ 𝐍⦃?⦄ )</td>
+            <td class="snns plane water">normal forms for context-sensitive reduction</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 />
@@ -736,7 +682,7 @@
             </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">lpr_drop lpr_lpr</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -752,7 +698,7 @@
               <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>
@@ -764,9 +710,9 @@
             <td class="nnns component water">
               <br />
             </td>
-            <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="snns plane water">irreducible forms for context-sensitive reduction</td>
+            <td class="snns file water">cir ( ⦃?,?⦄ ⊢ ➡ 𝐈⦃?⦄ )</td>
+            <td class="snnn file water">cir_lift</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -778,9 +724,9 @@
             <td class="nnns component water">
               <br />
             </td>
-            <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="snns plane water">reducible forms for context-sensitive reduction</td>
+            <td class="snns file water">crr ( ⦃?,?⦄ ⊢ ➡ 𝐑⦃?⦄ )</td>
+            <td class="snnn file water">crr_lift</td>
             <td class="snnn file water">
               <br />
             </td>
@@ -807,18 +753,18 @@
               <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>
@@ -830,9 +776,9 @@
             <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>
@@ -844,9 +790,9 @@
             <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>
@@ -858,9 +804,9 @@
             <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>
@@ -872,9 +818,9 @@
             <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>
@@ -886,9 +832,9 @@
             <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="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>
@@ -897,10 +843,82 @@
             </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="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>
+            <td class="ssnn file grass">
+              <br />
+            </td>
+          </tr>
+          <tr>
+            <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_drop 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_drop 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_drop</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>
@@ -908,13 +926,25 @@
               <br />
             </td>
           </tr>
+          <tr>
+            <td class="nnns component yellow">
+              <br />
+            </td>
+            <td class="snns plane yellow">contxt-sensitive extended multiple substitution</td>
+            <td class="snns file yellow">cpys ( ⦃?,?⦄ ⊢ ? ▶*[?,?] ? )</td>
+            <td class="snnn file yellow">cpys_alt ( ⦃?,?⦄ ⊢ ? ▶▶*[?,?] ? )</td>
+            <td class="snnn file yellow">cpys_lift cpys_cpys</td>
+            <td class="ssnn file yellow">
+              <br />
+            </td>
+          </tr>
           <tr>
             <td class="nnns component yellow">
               <br />
             </td>
             <td class="snns plane yellow">iterated structural successor for closures</td>
-            <td class="snns file yellow">fqus ( â¦\83?,?,?â¦\84 â\8a\83* ⦃?,?,?⦄ )</td>
-            <td class="snnn file yellow">fqus_alt fqus_lleq fqus_fqus</td>
+            <td class="snns file yellow">fqus ( â¦\83?,?,?â¦\84 â\8a\90* ⦃?,?,?⦄ )</td>
+            <td class="snnn file yellow">fqus_alt fqus_fqus</td>
             <td class="snnn file yellow">
               <br />
             </td>
@@ -929,8 +959,8 @@
             <td class="nnns plane yellow">
               <br />
             </td>
-            <td class="snns file yellow">fqup ( â¦\83?,?,?â¦\84 â\8a\83+ ⦃?,?,?⦄ )</td>
-            <td class="snnn file yellow">fqup_lleq fqup_fqup</td>
+            <td class="snns file yellow">fqup ( â¦\83?,?,?â¦\84 â\8a\90+ ⦃?,?,?⦄ )</td>
+            <td class="snnn file yellow">fqup_fqup</td>
             <td class="snnn file yellow">
               <br />
             </td>
@@ -942,9 +972,9 @@
             <td class="nnns component yellow">
               <br />
             </td>
-            <td class="snns plane yellow">generic local env. slicing</td>
-            <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
-            <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</td>
+            <td class="snns plane yellow">iterated local env. slicing</td>
+            <td class="snns file yellow">drops ( ⇩*[?,?] ? ≡ ? )</td>
+            <td class="snnn file yellow">drops_drop drops_drops</td>
             <td class="snnn file yellow">
               <br />
             </td>
@@ -993,11 +1023,13 @@
             <td class="ssnn file yellow">gr2_gr2</td>
           </tr>
           <tr>
-            <td class="snns component orange">relocation</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">fquq_lleq</td>
+            <td class="snns file orange">fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
+            <td class="snnn file orange">fquq_alt ( ⦃?,?,?⦄ ⊐⊐⸮ ⦃?,?,?⦄ )</td>
+            <td class="snnn file orange">
+              <br />
+            </td>
             <td class="ssnn file orange">
               <br />
             </td>
@@ -1009,8 +1041,10 @@
             <td class="nnns plane orange">
               <br />
             </td>
-            <td class="snns file orange">fqu ( ⦃?,?,?⦄ ⊃ ⦃?,?,?⦄ )</td>
-            <td class="snnn file orange">fqu_lleq</td>
+            <td class="snns file orange">fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
+            <td class="snnn file orange">
+              <br />
+            </td>
             <td class="snnn file orange">
               <br />
             </td>
@@ -1022,9 +1056,9 @@
             <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="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>
@@ -1036,9 +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">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>
@@ -1050,9 +1084,9 @@
             <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_sn ldrop_leq ldrop_ldrop</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>
@@ -1064,9 +1098,9 @@
             <td class="nnns component orange">
               <br />
             </td>
-            <td class="snns plane orange">basic term relocation</td>
-            <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
-            <td class="snnn file orange">lift_lift_vector</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_drop lpx_sn_lpx_sn</td>
             <td class="snnn file orange">
               <br />
             </td>
@@ -1078,11 +1112,9 @@
             <td class="nnns component orange">
               <br />
             </td>
-            <td class="nnns plane orange">
-              <br />
-            </td>
-            <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
-            <td class="snnn file orange">lift_lift</td>
+            <td class="snns plane orange">basic local env. slicing</td>
+            <td class="snns file orange">drop ( ⇩[?,?,?] ? ≡ ? )</td>
+            <td class="snnn file orange">drop_append drop_leq drop_drop</td>
             <td class="snnn file orange">
               <br />
             </td>
@@ -1091,26 +1123,40 @@
             </td>
           </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">
+            <td class="nnns component orange">
               <br />
             </td>
-            <td class="snnn file red">
+            <td class="snns plane orange">basic term relocation</td>
+            <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
+            <td class="snnn file orange">lift_lift_vector</td>
+            <td class="snnn file orange">
               <br />
             </td>
-            <td class="ssnn file red">
+            <td class="ssnn file orange">
               <br />
             </td>
           </tr>
           <tr>
-            <td class="nnns component red">
+            <td class="nnns component orange">
               <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="nnns plane orange">
+              <br />
+            </td>
+            <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
+            <td class="snnn file orange">lift_neq lift_lift</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">equivalence for local environments</td>
+            <td class="snns file red">leq ( ? ⩬[?,?] ? )</td>
+            <td class="snnn file red">leq_leq</td>
             <td class="snnn file red">
               <br />
             </td>
@@ -1123,7 +1169,7 @@
               <br />
             </td>
             <td class="snns plane red">same top term constructor</td>
-            <td class="snns file red">tstc ( ? â\89\83 ? )</td>
+            <td class="snns file red">tstc ( ? â\89\82 ? )</td>
             <td class="snnn file red">tstc_tstc tstc_vector</td>
             <td class="snnn file red">
               <br />
@@ -1137,8 +1183,8 @@
               <br />
             </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="snns file red">cl_weight ( ♯{?,?,?} )</td>
+            <td class="snnn file red">cl_restricted_weight ( ♯{?,?} )</td>
             <td class="snnn file red">
               <br />
             </td>
@@ -1224,7 +1270,7 @@
       </table>
     </div>
 
-   <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
+   <div xmlns:ld="http://lambdadelta.info/" class="head2sn" id="">Physical Structure of the Specification</div>
    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
          one for each component.
    </div>
@@ -1254,6 +1300,6 @@
     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
       <br />
     </div>
-    <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sun, 15 Dec 2013 16:51:14 +0100</div>
+    <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sun, 13 Jul 2014 15:47:14 +0200</div>
 </body>
 </html>