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| <a href="./../..">Project Website</a> | ||
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| <a href="./toc.html">Table of Contents</a> | ||
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| <div id="content" tabindex="-1" onblur="document.getElementById('content').focus()"> | ||
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| <div class="code"> | ||
| <span class="id" title="keyword">From</span> <span class="id" title="var">ABS</span> <span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="ABS.abs_defs.html#"><span class="id" title="library">abs_defs</span></a>.<br/> | ||
| <span class="id" title="keyword">From</span> <span class="id" title="var">stdpp</span> <span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <span class="id" title="library">prelude</span> <span class="id" title="library">base</span>.<br/> | ||
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| </div> | ||
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| <div class="doc"> | ||
| <a id="lab2"></a><h1 class="section">ABS Examples</h1> | ||
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| </div> | ||
| <div class="code"> | ||
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| <br/> | ||
| <span class="id" title="keyword">Definition</span> <a id="e_const_5" class="idref" href="#e_const_5"><span class="id" title="definition">e_const_5</span></a> : <a class="idref" href="ABS.abs_defs.html#e"><span class="id" title="inductive">e</span></a> := <br/> | ||
| <a class="idref" href="ABS.abs_defs.html#e_t"><span class="id" title="constructor">e_t</span></a> (<a class="idref" href="ABS.abs_defs.html#t_int"><span class="id" title="constructor">t_int</span></a> 5%<span class="id" title="var">Z</span>).<br/> | ||
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| <span class="id" title="keyword">Definition</span> <a id="func_const_5" class="idref" href="#func_const_5"><span class="id" title="definition">func_const_5</span></a> : <a class="idref" href="ABS.abs_defs.html#F"><span class="id" title="inductive">F</span></a> := <br/> | ||
| <a class="idref" href="ABS.abs_defs.html#F_fn"><span class="id" title="constructor">F_fn</span></a> <a class="idref" href="ABS.abs_defs.html#T_int"><span class="id" title="constructor">T_int</span></a> "const_5"%<span class="id" title="var">string</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.18.0/stdlib//Coq.Lists.List.html#ae9a5e1034e143b218b09d8e454472bd"><span class="id" title="notation">[]</span></a> <a class="idref" href="ABS.abs_examples.html#e_const_5"><span class="id" title="definition">e_const_5</span></a>.<br/> | ||
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| <span class="id" title="keyword">Definition</span> <a id="e_call_const_5" class="idref" href="#e_call_const_5"><span class="id" title="definition">e_call_const_5</span></a> : <a class="idref" href="ABS.abs_defs.html#e"><span class="id" title="inductive">e</span></a> :=<br/> | ||
| <a class="idref" href="ABS.abs_defs.html#e_fn_call"><span class="id" title="constructor">e_fn_call</span></a> "const_5"%<span class="id" title="var">string</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.18.0/stdlib//Coq.Lists.List.html#ae9a5e1034e143b218b09d8e454472bd"><span class="id" title="notation">[]</span></a>.<br/> | ||
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| <span class="id" title="keyword">Definition</span> <a id="Ctx" class="idref" href="#Ctx"><span class="id" title="definition">Ctx</span></a> : <a class="idref" href="ABS.abs_defs.html#G"><span class="id" title="definition">G</span></a> :=<br/> | ||
| <a class="idref" href="ABS.abs_defs.html#Map.add"><span class="id" title="definition">Map.add</span></a> ("const_5"%<span class="id" title="var">string</span>) (<a class="idref" href="ABS.abs_defs.html#ctxv_sig"><span class="id" title="constructor">ctxv_sig</span></a> (<a class="idref" href="ABS.abs_defs.html#sig_sig"><span class="id" title="constructor">sig_sig</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.18.0/stdlib//Coq.Lists.List.html#ae9a5e1034e143b218b09d8e454472bd"><span class="id" title="notation">[]</span></a> <a class="idref" href="ABS.abs_defs.html#T_int"><span class="id" title="constructor">T_int</span></a>)) (<a class="idref" href="ABS.abs_defs.html#Map.empty"><span class="id" title="definition">Map.empty</span></a> <a class="idref" href="ABS.abs_defs.html#ctxv"><span class="id" title="inductive">ctxv</span></a>).<br/> | ||
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| <span class="id" title="keyword">Lemma</span> <a id="e_const_5_T_int" class="idref" href="#e_const_5_T_int"><span class="id" title="lemma">e_const_5_T_int</span></a> :<br/> | ||
| <a class="idref" href="ABS.abs_defs.html#typ_e"><span class="id" title="inductive">typ_e</span></a> <a class="idref" href="ABS.abs_examples.html#Ctx"><span class="id" title="definition">Ctx</span></a> <a class="idref" href="ABS.abs_examples.html#e_const_5"><span class="id" title="definition">e_const_5</span></a> <a class="idref" href="ABS.abs_defs.html#T_int"><span class="id" title="constructor">T_int</span></a>.<br/> | ||
| <span class="id" title="keyword">Proof</span>. <span class="id" title="tactic">by</span> <span class="id" title="tactic">apply</span> <a class="idref" href="ABS.abs_defs.html#typ_int"><span class="id" title="constructor">typ_int</span></a>. <span class="id" title="keyword">Qed</span>.<br/> | ||
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| <span class="id" title="keyword">Lemma</span> <a id="e_call_const_typ_F" class="idref" href="#e_call_const_typ_F"><span class="id" title="lemma">e_call_const_typ_F</span></a> :<br/> | ||
| <a class="idref" href="ABS.abs_defs.html#typ_F"><span class="id" title="inductive">typ_F</span></a> <a class="idref" href="ABS.abs_examples.html#Ctx"><span class="id" title="definition">Ctx</span></a> <a class="idref" href="ABS.abs_examples.html#func_const_5"><span class="id" title="definition">func_const_5</span></a>.<br/> | ||
| <span class="id" title="keyword">Proof</span>.<br/> | ||
| <span class="id" title="tactic">apply</span> <a class="idref" href="ABS.abs_defs.html#typ_func_decl"><span class="id" title="constructor">typ_func_decl</span></a>.<br/> | ||
| - <span class="id" title="var">easy</span>.<br/> | ||
| - <span class="id" title="tactic">apply</span> <a class="idref" href="ABS.abs_examples.html#e_const_5_T_int"><span class="id" title="lemma">e_const_5_T_int</span></a>.<br/> | ||
| - <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">constructor</span>.<br/> | ||
| <span class="id" title="keyword">Qed</span>.<br/> | ||
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| <br/> | ||
| <span class="id" title="keyword">Lemma</span> <a id="e_call_const_5_T_int" class="idref" href="#e_call_const_5_T_int"><span class="id" title="lemma">e_call_const_5_T_int</span></a> :<br/> | ||
| <a class="idref" href="ABS.abs_defs.html#typ_e"><span class="id" title="inductive">typ_e</span></a> <a class="idref" href="ABS.abs_examples.html#Ctx"><span class="id" title="definition">Ctx</span></a> <a class="idref" href="ABS.abs_examples.html#e_call_const_5"><span class="id" title="definition">e_call_const_5</span></a> <a class="idref" href="ABS.abs_defs.html#T_int"><span class="id" title="constructor">T_int</span></a>.<br/> | ||
| <span class="id" title="keyword">Proof</span>.<br/> | ||
| <span class="id" title="tactic">unfold</span> <a class="idref" href="ABS.abs_examples.html#e_call_const_5"><span class="id" title="definition">e_call_const_5</span></a>.<br/> | ||
| <span class="id" title="tactic">replace</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.18.0/stdlib//Coq.Lists.List.html#ae9a5e1034e143b218b09d8e454472bd"><span class="id" title="notation">[]</span></a> <span class="id" title="keyword">with</span> (<a class="idref" href="http://coq.inria.fr/distrib/V8.18.0/stdlib//Coq.Lists.List.html#map"><span class="id" title="definition">map</span></a> (<span class="id" title="keyword">fun</span> (<a id="pat_:1" class="idref" href="#pat_:1"><span class="id" title="binder"><span id="pat_:3" class="id">pat_</span></span></a>:(<a class="idref" href="ABS.abs_defs.html#e"><span class="id" title="inductive">e</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.18.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">*</span></a><a class="idref" href="ABS.abs_defs.html#T"><span class="id" title="inductive">T</span></a>)) => <span class="id" title="keyword">match</span> <a class="idref" href="ABS.abs_examples.html#pat_:1"><span class="id" title="variable">pat_</span></a> <span class="id" title="keyword">with</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.18.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><span class="id" title="var">e_</span><a class="idref" href="http://coq.inria.fr/distrib/V8.18.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a><span class="id" title="var">T_</span><a class="idref" href="http://coq.inria.fr/distrib/V8.18.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">)</span></a> => <span class="id" title="var">e_</span> <span class="id" title="keyword">end</span> ) <a class="idref" href="http://coq.inria.fr/distrib/V8.18.0/stdlib//Coq.Lists.List.html#ae9a5e1034e143b218b09d8e454472bd"><span class="id" title="notation">[]</span></a>)<br/> | ||
| <span class="id" title="tactic">by</span> <span class="id" title="tactic">auto</span>.<br/> | ||
| <span class="id" title="tactic">by</span> <span class="id" title="tactic">apply</span> <a class="idref" href="ABS.abs_defs.html#typ_func_expr"><span class="id" title="constructor">typ_func_expr</span></a>.<br/> | ||
| <span class="id" title="keyword">Qed</span>.<br/> | ||
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