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- <img class="icon32" alt="[\lambda\delta home]" title="\lambda\delta home" src="http://lambdadelta.info/images/crux_32.png" />
- </a>
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- <div class="head1">cic:/matita/lambdadelta/basic_2/ (core λδ version 2)</div>
- <div class="spacer">
- <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
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- <div xmlns:ld="http://lambdadelta.info/" class="spacer">
- <br />
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="text">
- <table cellpadding="4" cellspacing="0">
- <tbody>
- <tr>
- <td class="snns capitalize italic sky">
- <a href="http://lambdadelta.info/home.html">home</a>
- </td>
- <td class="snns capitalize italic magenta">
- <a href="http://lambdadelta.info/news.html">news</a>
- </td>
- <td class="snns capitalize italic white">
- <a href="http://lambdadelta.info/specification.html">specification</a>
- </td>
- <td class="snnn capitalize italic white">
- <br />
- </td>
- <td class="snnn capitalize italic white">
- <br />
- </td>
- <td class="snns capitalize italic orange">
- <a href="http://lambdadelta.info/documentation.html">documentation</a>
- </td>
- <td class="snns capitalize italic green">
- <a href="http://lambdadelta.info/implementation.html">implementation</a>
- </td>
- <td class="ssnn capitalize italic green">
- <br />
- </td>
- </tr>
- <tr>
- <td class="snns capitalize sky">
- <a href="http://lambdadelta.info/home.html#foreword">foreword</a>
- </td>
- <td class="snns capitalize magenta">
- <a href="http://lambdadelta.info/news.html#milestones">milestones</a>
- </td>
- <td class="snns capitalize white">
- <a href="http://lambdadelta.info/specification.html#v2">version 2</a>
- </td>
- <td class="snnn capitalize white">(<a href="http://lambdadelta.info/ground_2.html">background</a> - <a href="http://lambdadelta.info/basic_2.html">core</a> - <a href="http://lambdadelta.info/apps_2.html">applications</a>)</td>
- <td class="snnn capitalize white">
- <br />
- </td>
- <td class="snns capitalize orange">
- <a href="http://lambdadelta.info/documentation.html#v2">version 2</a>
- </td>
- <td class="snns capitalize green">
- <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
- </td>
- <td class="ssnn capitalize green">
- <a href="http://lambdadelta.info/osn/">Open Symbolic Notation (OSN)</a>
- </td>
- </tr>
- <tr>
- <td class="snss capitalize sky">
- <a href="http://lambdadelta.info/home.html#citations">citations</a>
- </td>
- <td class="snss capitalize magenta">
- <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
- </td>
- <td class="snss capitalize white">
- <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
- </td>
- <td class="snsn capitalize white">(<a href="http://lambdadelta.info/ground_1.html">background</a> - <a href="http://lambdadelta.info/basic_1.html">core</a>)</td>
- <td class="snsn capitalize white">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
- <td class="snss capitalize orange">
- <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
- </td>
- <td class="snss capitalize green">
- <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
- </td>
- <td class="sssn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
- </tr>
- </tbody>
- </table>
- </div>
- <!--
- <section>System's Syntax and Behavior</section>
- <body>This is a summary of the "block structure"
- of the System's syntactic items and reductions.
- </body>
- <table name="basic_2_blk"/>
- <body>* In terms only.
- ** In terms and local environments only.
- *** In global environments only.
- **** Sort level k in terms only.
- </body>
--->
- <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="summary">Summary of the Specification <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b4.png" />
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="text">Here is a numerical account of the specification's contents
- and its timeline.
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="text">
- <table cellpadding="4" cellspacing="0">
- <tbody>
- <tr>
- <td class="snns capitalize italic gray">category</td>
- <td class="snns italic gray">units</td>
- <td class="snnn right italic gray">
- <br />
- </td>
- <td class="snnn italic gray">
- <br />
- </td>
- <td class="snnn right italic gray">
- <br />
- </td>
- <td class="snnn italic gray">
- <br />
- </td>
- <td class="ssnn right italic gray">
- <br />
- </td>
- </tr>
- <tr>
- <td class="snns capitalize italic water">sizes</td>
- <td class="snns italic water">characters (files)</td>
- <td class="snnn right italic water">315581 (309)</td>
- <td class="snns italic water">nodes (objects)</td>
- <td class="snnn right italic water">1458870 (1431)</td>
- <td class="snns italic water">intrinsic loss factor</td>
- <td class="ssnn right italic water">4.6</td>
- </tr>
- <tr>
- <td class="snns capitalize italic green">propositions</td>
- <td class="snns italic green">theorems</td>
- <td class="snnn right italic green">92</td>
- <td class="snns italic green">lemmas</td>
- <td class="snnn right italic green">1085</td>
- <td class="snns italic green">total</td>
- <td class="ssnn right italic green">1177</td>
- </tr>
- <tr>
- <td class="snss capitalize italic grass">concepts</td>
- <td class="snss italic grass">declared</td>
- <td class="snsn right italic grass">34</td>
- <td class="snss italic grass">defined</td>
- <td class="snsn right italic grass">93</td>
- <td class="snss italic grass">total</td>
- <td class="sssn right italic grass">127</td>
- </tr>
- </tbody>
- </table>
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="B">Stage "B"</div>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">Ongoing.</span>
- Context-sensitive subject equivalence
- for native type assignment.
- </li>
- </ul>
- <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A2">Stage "A2": "Extending the Applicability Condition"</div>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2017 October 17.</span>
- Exclusion binder in local environments.
- Syntactic component updated:
- syntax, relocation, s_transition, s_computation, static, i_static.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2017 April 16.</span>
- Strong rt-normalization
- for simply typed terms
- (anniversary milestone).
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2017 March 16.</span>
- First behavioral component reconstructed:
- rt_transition.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2017 February 19.</span>
- Generic candidates of reducibility.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2017 January 17.</span>
- Confluence for parallel r-transition on referred entries of local environments.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2016 September 15.</span>
- Confluence for context-sensitive parallel r-transition on terms.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2016 April 16.</span>
- Syntactic component reconstructed:
- syntax, relocation, s_transition, s_computation, static
- (anniversary milestone).
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2016 March 25.</span>
- Relocation with reference transforming maps (rtmap).
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2015 October 9.</span>
- λδ version 2A2 is started.
- </li>
- </ul>
- <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A1">Stage "A1": "Extending the Applicability Condition"</div>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph delta">2015 August 27.</span>
- λδ version 2A1 appears too complex and is dismissed.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph gamma">2014 October 28.</span>
- λδ version 2A1 is released.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph beta">2014 September 9.</span>
- Iterated static type assignment defined (more elegantly)
- as a primitive notion.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph beta">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="emph alpha">2014 June 9.</span>
- Strong qrst-normalization
- for simply typed terms.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2014 April 16.</span>
- Lazy equivalence on local environments
- added as q-step to rst-computation on closures
- (anniversary milestone).
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2014 January 20.</span>
- Parametrized slicing on 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/">
- <li>
- <span class="emph alpha">2013 August 7.</span>
- Passive support for global environments.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2013 July 27.</span>
- Reaxiomatized β-reductum as in rt-reduction.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2013 July 20.</span>
- Context-sensitive strong rt-normalization
- for simply typed terms.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2013 April 16.</span>
- Reaxiomatized substitution and reduction
- commute with respect to subclosure
- (anniversary milestone).
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2013 March 16.</span>
- Mutual recursive preservation of stratified native validity
- for rst-computation on closures.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2012 October 16.</span>
- Confluence for context-free parallel reduction on closures.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2012 July 26.</span>
- Term binders polarized to control ζ-reduction (not released).
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2012 April 16.</span>
- Context-sensitive subject equivalence
- for atomic arity assignment
- (anniversary milestone).
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2012 March 15.</span>
- Context-sensitive strong normalization
- for simply typed terms.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2012 January 27.</span>
- Generic candidates of reducibility.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2011 September 21.</span>
- Confluence for context-sensitive parallel reduction on terms.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2011 September 6.</span>
- Confluence for context-free parallel reduction on terms.
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/">
- <li>
- <span class="emph alpha">2011 April 17.</span>
- λδ version 2 is started.
- </li>
- </ul>
- <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="structure">Logical Structure of the Specification <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b4.png" />
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="text">This table reports the specification's components and their planes.
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="text">
- <table cellpadding="4" cellspacing="0">
- <tbody>
- <tr>
- <td class="snns top capitalize italic gray">component</td>
- <td class="snns top capitalize italic gray">section</td>
- <td class="snns top italic gray">plane</td>
- <td class="snns top gray">files</td>
- <td class="ssnn top gray">
- <br />
- </td>
- </tr>
- <tr>
- <td class="snns top capitalize italic blue">rt-conversion</td>
- <td class="snns top capitalize italic blue">context-sensitive parallel r-conversion</td>
- <td class="snns top italic blue">for terms</td>
- <td class="snns top blue">cpc ( ⦃?,?⦄ ⊢ ? ⬌[?] ? )</td>
- <td class="ssnn top blue">cpc_cpc</td>
- </tr>
- <tr>
- <td class="snns top capitalize italic sky">rt-computation</td>
- <td class="snns top capitalize italic sky">uncounted context-sensitive parallel rt-computation</td>
- <td class="snns top italic sky">refinement for lenvs</td>
- <td class="snns top sky">lsubsx ( ? ⊢ ? ⊆ⓧ[?,?,?] ? )</td>
- <td class="ssnn top sky">lsubsx_lfsx lsubsx_lsubsx</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic sky">
- <br />
- </td>
- <td class="nnns top capitalize italic sky">
- <br />
- </td>
- <td class="snns top italic sky">strongly normalizing for lenvs on referred entries</td>
- <td class="snns top sky">lfsx ( ? ⊢ ⬈*[?,?,?] 𝐒⦃?⦄ )</td>
- <td class="ssnn top sky">lfsx_drops lfsx_fqup lfsx_lfpxs lfsx_lfsx</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic sky">
- <br />
- </td>
- <td class="nnns top capitalize italic sky">
- <br />
- </td>
- <td class="snns top italic sky">strongly normalizing for term vectors</td>
- <td class="snns top sky">csx_vector ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )</td>
- <td class="ssnn top sky">csx_cnx_vector csx_csx_vector</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic sky">
- <br />
- </td>
- <td class="nnns top capitalize italic sky">
- <br />
- </td>
- <td class="snns top italic sky">strongly normalizing for terms</td>
- <td class="snns top sky">csx ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )</td>
- <td class="ssnn top sky">csx_simple csx_simple_theq csx_drops csx_lsubr csx_lfdeq csx_aaa csx_gcp csx_gcr csx_lfpx csx_cnx csx_cpxs csx_lfpxs csx_csx</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic sky">
- <br />
- </td>
- <td class="nnns top capitalize italic sky">
- <br />
- </td>
- <td class="snns top italic sky">for lenvs on referred entries</td>
- <td class="snns top sky">lfpxs ( ⦃?,?⦄ ⊢ ⬈*[?,?] ? )</td>
- <td class="ssnn top sky">lfpxs_length lfpxs_drops lfpxs_fqup lfpxs_lfdeq lfpxs_aaa lfpxs_cpxs lfpxs_lpxs lfpxs_lfpxs</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic sky">
- <br />
- </td>
- <td class="nnns top capitalize italic sky">
- <br />
- </td>
- <td class="snns top italic sky">for lenvs on all entries</td>
- <td class="snns top sky">lpxs ( ⦃?,?⦄ ⊢ ⬈*[?] ? )</td>
- <td class="ssnn top sky">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic sky">
- <br />
- </td>
- <td class="nnns top capitalize italic sky">
- <br />
- </td>
- <td class="snns top italic sky">for terms</td>
- <td class="snns top sky">cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )</td>
- <td class="ssnn top sky">cpxs_tdeq cpxs_theq cpxs_theq_vector cpxs_drops cpxs_fqus cpxs_lsubr cpxs_lfdeq cpxs_aaa cpxs_lpx cpxs_lfpx cpxs_cnx cpxs_cpxs</td>
- </tr>
- <tr>
- <td class="snns top capitalize italic cyan">rt-transition</td>
- <td class="snns top capitalize italic cyan">uncounted parallel rst-transition</td>
- <td class="snns top italic cyan">for closures</td>
- <td class="snns top cyan">fpbq ( ⦃?,?,?⦄ ≽[?] ⦃?,?,?⦄ )</td>
- <td class="ssnn top cyan">fpbq_aaa</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="snns top italic cyan">proper for closures</td>
- <td class="snns top cyan">fpb ( ⦃?,?,?⦄ ≻[?] ⦃?,?,?⦄ )</td>
- <td class="ssnn top cyan">fpb_lfdeq</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="snns top capitalize italic cyan">context-sensitive parallel r-transition</td>
- <td class="snns top italic cyan">for lenvs on referred entries</td>
- <td class="snns top cyan">lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
- <td class="ssnn top cyan">lfpr_length lfpr_drops lfpr_fquq lfpr_fqup lfpr_frees lfpr_aaa lfpr_lfpx lfpr_lfpr</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="snns top italic cyan">for binders</td>
- <td class="snns top cyan">cpr_ext ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
- <td class="ssnn top cyan">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="snns top italic cyan">for terms</td>
- <td class="snns top cyan">cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
- <td class="ssnn top cyan">cpr_drops</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="snns top capitalize italic cyan">t-bound context-sensitive parallel rt-transition</td>
- <td class="snns top italic cyan">for terms</td>
- <td class="snns top cyan">cpm ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
- <td class="ssnn top cyan">cpm_simple cpm_drops cpm_lsubr cpm_lfxs cpm_cpx</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="snns top capitalize italic cyan">uncounted context-sensitive parallel rt-transition</td>
- <td class="snns top italic cyan">normal form for terms</td>
- <td class="snns top cyan">cnx ( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )</td>
- <td class="ssnn top cyan">cnx_simple cnx_drops cnx_cnx</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="snns top italic cyan">for lenvs on referred entries</td>
- <td class="snns top cyan">lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )</td>
- <td class="ssnn top cyan">lfpx_length lfpx_drops lfpx_fqup lfpx_frees lfpx_lfdeq lfpx_aaa lfpx_cpx lfpx_lfpx</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="snns top italic cyan">for lenvs on all entries</td>
- <td class="snns top cyan">lpx ( ⦃?,?⦄ ⊢ ⬈[?] ? )</td>
- <td class="ssnn top cyan">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="snns top italic cyan">for binders</td>
- <td class="snns top cyan">cpx_ext ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
- <td class="ssnn top cyan">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="snns top italic cyan">for terms</td>
- <td class="snns top cyan">cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
- <td class="ssnn top cyan">cpx_simple cpx_drops cpx_fqus cpx_lsubr cpx_lfxs cpx_lfeq</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic cyan">
- <br />
- </td>
- <td class="snns top capitalize italic cyan">counted context-sensitive parallel rt-transition</td>
- <td class="snns top italic cyan">for terms</td>
- <td class="snns top cyan">cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )</td>
- <td class="ssnn top cyan">cpg_simple cpg_drops cpg_lsubr</td>
- </tr>
- <tr>
- <td class="snns top capitalize italic water">iterated static typing</td>
- <td class="snns top capitalize italic water">iterated generic extension of a context-sensitive relation</td>
- <td class="snns top italic water">for lenvs on referred entries</td>
- <td class="snns top water">tc_lfxs ( ? ⦻**[?,?] ? )</td>
- <td class="ssnn top water">tc_lfxs_length tc_lfxs_lex tc_lfxs_drops tc_lfxs_fqup tc_lfxs_tc_lfxs</td>
- </tr>
- <tr>
- <td class="snns top capitalize italic green">static typing</td>
- <td class="snns top capitalize italic green">generic reducibility</td>
- <td class="snns top italic green">restricted refinement for lenvs</td>
- <td class="snns top green">lsubc ( ? ⊢ ? ⫃[?] ? )</td>
- <td class="ssnn top green">lsubc_drops lsubc_lsubr lsubc_lsuba</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic green">
- <br />
- </td>
- <td class="nnns top capitalize italic green">
- <br />
- </td>
- <td class="snns top italic green">candidates</td>
- <td class="snns top green">gcp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
- <td class="ssnn top green">gcp_aaa</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic green">
- <br />
- </td>
- <td class="nnns top capitalize italic green">
- <br />
- </td>
- <td class="snns top italic green">computation properties</td>
- <td class="snns top green">gcp</td>
- <td class="ssnn top green">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic green">
- <br />
- </td>
- <td class="snns top capitalize italic green">atomic arity assignment</td>
- <td class="snns top italic green">restricted refinement for lenvs</td>
- <td class="snns top green">lsuba ( ? ⊢ ? ⫃⁝ ? )</td>
- <td class="ssnn top green">lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic green">
- <br />
- </td>
- <td class="nnns top capitalize italic green">
- <br />
- </td>
- <td class="snns top italic green">for terms</td>
- <td class="snns top green">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
- <td class="ssnn top green">aaa_drops aaa_fqus aaa_lfdeq aaa_aaa</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic green">
- <br />
- </td>
- <td class="snns top capitalize italic green">degree-based equivalence</td>
- <td class="snns top italic green">for closures on referred entries</td>
- <td class="snns top green">ffdeq ( ⦃?,?,?⦄ ≛[?,?] ⦃?,?,?⦄ )</td>
- <td class="ssnn top green">ffdeq_fqup ffdeq_ffdeq</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic green">
- <br />
- </td>
- <td class="nnns top capitalize italic green">
- <br />
- </td>
- <td class="snns top italic green">for lenvs on referred entries</td>
- <td class="snns top green">lfdeq ( ? ≛[?,?,?] ? )</td>
- <td class="ssnn top green">lfdeq_length lfdeq_drops lfdeq_fqup lfdeq_fqus lfdeq_lfdeq</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic green">
- <br />
- </td>
- <td class="snns top capitalize italic green">syntactic equivalence</td>
- <td class="snns top italic green">for lenvs on referred entries</td>
- <td class="snns top green">lfeq ( ? ≡[?] ? )</td>
- <td class="ssnn top green">lfeq_fqup lfeq_lfeq</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic green">
- <br />
- </td>
- <td class="snns top capitalize italic green">generic extension of a context-sensitive relation</td>
- <td class="snns top italic green">for lenvs on referred entries</td>
- <td class="snns top green">lfxs ( ? ⦻*[?,?] ? )</td>
- <td class="ssnn top green">lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic green">
- <br />
- </td>
- <td class="snns top capitalize italic green">context-sensitive free variables</td>
- <td class="snns top italic green">restricted refinement for lenvs</td>
- <td class="snns top green">lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )</td>
- <td class="ssnn top green">lsubf_lsubr lsubf_frees lsubf_lsubf</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic green">
- <br />
- </td>
- <td class="nnns top capitalize italic green">
- <br />
- </td>
- <td class="snns top italic green">for terms</td>
- <td class="snns top green">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
- <td class="ssnn top green">frees_drops frees_fqup frees_frees</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic green">
- <br />
- </td>
- <td class="snns top capitalize italic green">local environments</td>
- <td class="snns top italic green">restricted refinement</td>
- <td class="snns top green">lsubr ( ? ⫃ ? )</td>
- <td class="ssnn top green">lsubr_length lsubr_drops lsubr_lsubr</td>
- </tr>
- <tr>
- <td class="snns top capitalize italic grass">s-computation</td>
- <td class="snns top capitalize italic grass">iterated structural successor</td>
- <td class="snns top italic grass">for closures</td>
- <td class="snns top grass">fqus ( ⦃?,?,?⦄ ⊐*[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
- <td class="ssnn top grass">fqus_weight fqus_drops fqus_fqup fqus_fqus</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic grass">
- <br />
- </td>
- <td class="nnns top capitalize italic grass">
- <br />
- </td>
- <td class="snns top italic grass">proper for closures</td>
- <td class="snns top grass">fqup ( ⦃?,?,?⦄ ⊐+[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
- <td class="ssnn top grass">fqup_weight fqup_drops fqup_fqup</td>
- </tr>
- <tr>
- <td class="snns top capitalize italic yellow">s-transition</td>
- <td class="snns top capitalize italic yellow">structural successor</td>
- <td class="snns top italic yellow">for closures</td>
- <td class="snns top yellow">fquq ( ⦃?,?,?⦄ ⊐⸮[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
- <td class="ssnn top yellow">fquq_length fquq_weight</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic yellow">
- <br />
- </td>
- <td class="nnns top capitalize italic yellow">
- <br />
- </td>
- <td class="snns top italic yellow">proper for closures</td>
- <td class="snns top yellow">fqu ( ⦃?,?,?⦄ ⊐[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
- <td class="ssnn top yellow">fqu_length fqu_weight</td>
- </tr>
- <tr>
- <td class="snns top capitalize italic orange">relocation</td>
- <td class="snns top capitalize italic orange">generic slicing</td>
- <td class="snns top italic orange">for lenvs</td>
- <td class="snns top orange">drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
- <td class="ssnn top orange">drops_lstar drops_weight drops_length drops_cext2 drops_lexs drops_lreq drops_drops drops_vector</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic orange">
- <br />
- </td>
- <td class="snns top capitalize italic orange">generic relocation</td>
- <td class="snns top italic orange">for binders</td>
- <td class="snns top orange">lifts_bind ( ⬆*[?] ? ≡ ? )</td>
- <td class="ssnn top orange">lifts_weight_bind lifts_lifts_bind</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic orange">
- <br />
- </td>
- <td class="nnns top capitalize italic orange">
- <br />
- </td>
- <td class="snns top italic orange">for term vectors</td>
- <td class="snns top orange">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
- <td class="ssnn top orange">lifts_lifts_vector</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic orange">
- <br />
- </td>
- <td class="nnns top capitalize italic orange">
- <br />
- </td>
- <td class="snns top italic orange">for terms</td>
- <td class="snns top orange">lifts ( ⬆*[?] ? ≡ ? )</td>
- <td class="ssnn top orange">lifts_simple lifts_weight lifts_tdeq lifts_lifts</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic orange">
- <br />
- </td>
- <td class="snns top capitalize italic orange">syntactic equivalence</td>
- <td class="snns top italic orange">for lenvs on selected entries</td>
- <td class="snns top orange">lreq ( ? ≡[?] ? )</td>
- <td class="ssnn top orange">lreq_length lreq_lreq</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic orange">
- <br />
- </td>
- <td class="snns top capitalize italic orange">generic entrywise extension</td>
- <td class="snns top italic orange">for lenvs of one contex-sensitive relation</td>
- <td class="snns top orange">lex ( ? ⦻[?] ? )</td>
- <td class="ssnn top orange">lex_tc</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic orange">
- <br />
- </td>
- <td class="nnns top capitalize italic orange">
- <br />
- </td>
- <td class="snns top italic orange">for lenvs of two contex-sensitive relations</td>
- <td class="snns top orange">lexs ( ? ⦻*[?,?,?] ? )</td>
- <td class="ssnn top orange">lexs_tc lexs_length lexs_lexs</td>
- </tr>
- <tr>
- <td class="snns top capitalize italic red">syntax</td>
- <td class="snns top capitalize italic red">append for local environments</td>
- <td class="snns top italic red" />
- <td class="snns top red">append ( ? @@ ? )</td>
- <td class="ssnn top red">append_length</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top capitalize italic red">head equivalence for terms</td>
- <td class="snns top italic red" />
- <td class="snns top red">theq ( ? ⩳[?,?] ? )</td>
- <td class="ssnn top red">theq_simple theq_tdeq theq_theq theq_simple_vector</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top capitalize italic red">degree-based equivalence</td>
- <td class="snns top italic red" />
- <td class="snns top red">tdeq_ext ( ? ≛[?,?] ? ) ( ? ⊢ ? ≛[?,?] ? )</td>
- <td class="ssnn top red">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top italic red" />
- <td class="snns top red">tdeq ( ? ≛[?,?] ? )</td>
- <td class="ssnn top red">tdeq_tdeq</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top capitalize italic red">closures</td>
- <td class="snns top italic red" />
- <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
- <td class="ssnn top red">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top italic red" />
- <td class="snns top red">cl_restricted_weight ( ♯{?,?} )</td>
- <td class="ssnn top red">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top capitalize italic red">global environments</td>
- <td class="snns top italic red" />
- <td class="snns top red">genv</td>
- <td class="ssnn top red">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top capitalize italic red">local environments</td>
- <td class="snns top italic red" />
- <td class="snns top red">ceq_ext</td>
- <td class="ssnn top red">ceq_ext_ceq_ext</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top italic red" />
- <td class="snns top red">cext2</td>
- <td class="ssnn top red">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top italic red" />
- <td class="snns top red">lenv_length ( |?| )</td>
- <td class="ssnn top red">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top italic red" />
- <td class="snns top red">lenv_weight ( ♯{?} )</td>
- <td class="ssnn top red">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top italic red" />
- <td class="snns top red">lenv</td>
- <td class="ssnn top red">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top capitalize italic red">binders for local environments</td>
- <td class="snns top italic red" />
- <td class="snns top red">ext2</td>
- <td class="ssnn top red">ext2_tc ext2_ext2</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top italic red" />
- <td class="snns top red">bind</td>
- <td class="ssnn top red">bind_weight</td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top capitalize italic red">terms</td>
- <td class="snns top italic red" />
- <td class="snns top red">term_vector ( Ⓐ?.? )</td>
- <td class="ssnn top red">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top italic red" />
- <td class="snns top red">term_simple ( 𝐒⦃?⦄ )</td>
- <td class="ssnn top red">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top italic red" />
- <td class="snns top red">term_weight ( ♯{?} )</td>
- <td class="ssnn top red">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top italic red" />
- <td class="snns top red">term</td>
- <td class="ssnn top red">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top capitalize italic red">items</td>
- <td class="snns top italic red" />
- <td class="snns top red">item_sd</td>
- <td class="ssnn top red">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top italic red" />
- <td class="snns top red">item_sh</td>
- <td class="ssnn top red">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="nnns top capitalize italic red">
- <br />
- </td>
- <td class="snns top italic red" />
- <td class="snns top red">item</td>
- <td class="ssnn top red">
- <br />
- </td>
- </tr>
- <tr>
- <td class="nnss top capitalize italic red">
- <br />
- </td>
- <td class="snss top capitalize italic red">atomic arities</td>
- <td class="snss top italic red" />
- <td class="snss top red">aarity</td>
- <td class="sssn top red">
- <br />
- </td>
- </tr>
- </tbody>
- </table>
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projects / helm.git / blobdiff