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<html xmlns="http://www.w3.org/1999/xhtml"><head><title>Biabduction__Predicates (infer.Biabduction__Predicates)</title><link rel="stylesheet" href="../../odoc.css"/><meta charset="utf-8"/><meta name="generator" content="odoc 1.5.0"/><meta name="viewport" content="width=device-width,initial-scale=1.0"/><script src="../../highlight.pack.js"></script><script>hljs.initHighlightingOnLoad();</script></head><body><div class="content"><header><nav><a href="../index.html">Up</a> – <a href="../index.html">infer</a> » Biabduction__Predicates</nav><h1>Module <code>Biabduction__Predicates</code></h1><nav class="toc"><ul><li><a href="#components-of-propositions">Components of Propositions</a></li><li><a href="#compaction">Compaction</a></li><li><a href="#comparision-and-inspection-functions">Comparision And Inspection Functions</a></li><li><a href="#functions-for-traversing-sil-data-types">Functions for traversing SIL data types</a></li><li><a href="#substitution">Substitution</a></li><li><a href="#functions-for-replacing-occurrences-of-expressions.">Functions for replacing occurrences of expressions.</a></li><li><a href="#functions-for-constructing-or-destructing-entities-in-this-module">Functions for constructing or destructing entities in this module</a></li></ul></nav></header><div class="spec module" id="module-F"><a href="#module-F" class="anchor"></a><code><span class="keyword">module</span> F = Stdlib.Format</code></div><dl><dt class="spec type" id="type-offset"><a href="#type-offset" class="anchor"></a><code><span class="keyword">type</span> offset</code><code> = </code><table class="variant"><tr id="type-offset.Off_fld" class="anchored"><td class="def constructor"><a href="#type-offset.Off_fld" class="anchor"></a><code>| </code><code><span class="constructor">Off_fld</span> <span class="keyword">of</span> <a href="../IR/Fieldname/index.html#type-t">IR.Fieldname.t</a> * <a href="../IR/Typ/index.html#type-t">IR.Typ.t</a></code></td></tr><tr id="type-offset.Off_index" class="anchored"><td class="def constructor"><a href="#type-offset.Off_index" class="anchor"></a><code>| </code><code><span class="constructor">Off_index</span> <span class="keyword">of</span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a></code></td></tr></table></dt><dd><p>Offset for an lvalue.</p></dd></dl><section><header><h3 id="components-of-propositions"><a href="#components-of-propositions" class="anchor"></a>Components of Propositions</h3></header><dl><dt class="spec type" id="type-atom"><a href="#type-atom" class="anchor"></a><code><span class="keyword">type</span> atom</code><code> = </code><table class="variant"><tr id="type-atom.Aeq" class="anchored"><td class="def constructor"><a href="#type-atom.Aeq" class="anchor"></a><code>| </code><code><span class="constructor">Aeq</span> <span class="keyword">of</span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a></code></td><td class="doc"><p>equality</p></td></tr><tr id="type-atom.Aneq" class="anchored"><td class="def constructor"><a href="#type-atom.Aneq" class="anchor"></a><code>| </code><code><span class="constructor">Aneq</span> <span class="keyword">of</span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a></code></td><td class="doc"><p>disequality</p></td></tr><tr id="type-atom.Apred" class="anchored"><td class="def constructor"><a href="#type-atom.Apred" class="anchor"></a><code>| </code><code><span class="constructor">Apred</span> <span class="keyword">of</span> <a href="../IR/PredSymb/index.html#type-t">IR.PredSymb.t</a> * <span><a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> list</span></code></td><td class="doc"><p>predicate symbol applied to exps</p></td></tr><tr id="type-atom.Anpred" class="anchored"><td class="def constructor"><a href="#type-atom.Anpred" class="anchor"></a><code>| </code><code><span class="constructor">Anpred</span> <span class="keyword">of</span> <a href="../IR/PredSymb/index.html#type-t">IR.PredSymb.t</a> * <span><a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> list</span></code></td><td class="doc"><p>negated predicate symbol applied to exps</p></td></tr></table></dt><dd><p>an atom is a pure atomic formula</p></dd></dl><div><div class="spec include"><div class="doc"><dl><dt class="spec value" id="val-compare_atom"><a href="#val-compare_atom" class="anchor"></a><code><span class="keyword">val</span> compare_atom : <a href="index.html#type-atom">atom</a> <span>-></span> <a href="index.html#type-atom">atom</a> <span>-></span> int</code></dt></dl></div></div></div><dl><dt class="spec value" id="val-equal_atom"><a href="#val-equal_atom" class="anchor"></a><code><span class="keyword">val</span> equal_atom : <a href="index.html#type-atom">atom</a> <span>-></span> <a href="index.html#type-atom">atom</a> <span>-></span> bool</code></dt><dt class="spec value" id="val-atom_has_local_addr"><a href="#val-atom_has_local_addr" class="anchor"></a><code><span class="keyword">val</span> atom_has_local_addr : <a href="index.html#type-atom">atom</a> <span>-></span> bool</code></dt></dl><dl><dt class="spec type" id="type-lseg_kind"><a href="#type-lseg_kind" class="anchor"></a><code><span class="keyword">type</span> lseg_kind</code><code> = </code><table class="variant"><tr id="type-lseg_kind.Lseg_NE" class="anchored"><td class="def constructor"><a href="#type-lseg_kind.Lseg_NE" class="anchor"></a><code>| </code><code><span class="constructor">Lseg_NE</span></code></td><td class="doc"><p>nonempty (possibly circular) listseg</p></td></tr><tr id="type-lseg_kind.Lseg_PE" class="anchored"><td class="def constructor"><a href="#type-lseg_kind.Lseg_PE" class="anchor"></a><code>| </code><code><span class="constructor">Lseg_PE</span></code></td><td class="doc"><p>possibly empty (possibly circular) listseg</p></td></tr></table></dt><dd><p>kind of lseg or dllseg predicates</p></dd></dl><div><div class="spec include"><div class="doc"><dl><dt class="spec value" id="val-compare_lseg_kind"><a href="#val-compare_lseg_kind" class="anchor"></a><code><span class="keyword">val</span> compare_lseg_kind : <a href="index.html#type-lseg_kind">lseg_kind</a> <span>-></span> <a href="index.html#type-lseg_kind">lseg_kind</a> <span>-></span> int</code></dt></dl></div></div></div><dl><dt class="spec value" id="val-equal_lseg_kind"><a href="#val-equal_lseg_kind" class="anchor"></a><code><span class="keyword">val</span> equal_lseg_kind : <a href="index.html#type-lseg_kind">lseg_kind</a> <span>-></span> <a href="index.html#type-lseg_kind">lseg_kind</a> <span>-></span> bool</code></dt></dl><dl><dt class="spec type" id="type-zero_flag"><a href="#type-zero_flag" class="anchor"></a><code><span class="keyword">type</span> zero_flag</code><code> = <span>bool option</span></code></dt><dd><p>The boolean is true when the pointer was dereferenced without testing for zero.</p></dd></dl><dl><dt class="spec type" id="type-null_case_flag"><a href="#type-null_case_flag" class="anchor"></a><code><span class="keyword">type</span> null_case_flag</code><code> = bool</code></dt><dd><p>True when the value was obtained by doing case analysis on null in a procedure call.</p></dd></dl><dl><dt class="spec type" id="type-inst"><a href="#type-inst" class="anchor"></a><code><span class="keyword">type</span> inst</code><code> = </code><table class="variant"><tr id="type-inst.Iabstraction" class="anchored"><td class="def constructor"><a href="#type-inst.Iabstraction" class="anchor"></a><code>| </code><code><span class="constructor">Iabstraction</span></code></td></tr><tr id="type-inst.Iactual_precondition" class="anchored"><td class="def constructor"><a href="#type-inst.Iactual_precondition" class="anchor"></a><code>| </code><code><span class="constructor">Iactual_precondition</span></code></td></tr><tr id="type-inst.Ialloc" class="anchored"><td class="def constructor"><a href="#type-inst.Ialloc" class="anchor"></a><code>| </code><code><span class="constructor">Ialloc</span></code></td></tr><tr id="type-inst.Iformal" class="anchored"><td class="def constructor"><a href="#type-inst.Iformal" class="anchor"></a><code>| </code><code><span class="constructor">Iformal</span> <span class="keyword">of</span> <a href="index.html#type-zero_flag">zero_flag</a> * <a href="index.html#type-null_case_flag">null_case_flag</a></code></td></tr><tr id="type-inst.Iinitial" class="anchored"><td class="def constructor"><a href="#type-inst.Iinitial" class="anchor"></a><code>| </code><code><span class="constructor">Iinitial</span></code></td></tr><tr id="type-inst.Ilookup" class="anchored"><td class="def constructor"><a href="#type-inst.Ilookup" class="anchor"></a><code>| </code><code><span class="constructor">Ilookup</span></code></td></tr><tr id="type-inst.Inone" class="anchored"><td class="def constructor"><a href="#type-inst.Inone" class="anchor"></a><code>| </code><code><span class="constructor">Inone</span></code></td></tr><tr id="type-inst.Inullify" class="anchored"><td class="def constructor"><a href="#type-inst.Inullify" class="anchor"></a><code>| </code><code><span class="constructor">Inullify</span></code></td></tr><tr id="type-inst.Irearrange" class="anchored"><td class="def constructor"><a href="#type-inst.Irearrange" class="anchor"></a><code>| </code><code><span class="constructor">Irearrange</span> <span class="keyword">of</span> <a href="index.html#type-zero_flag">zero_flag</a> * <a href="index.html#type-null_case_flag">null_case_flag</a> * int * <a href="../IR/PredSymb/index.html#type-path_pos">IR.PredSymb.path_pos</a></code></td></tr><tr id="type-inst.Itaint" class="anchored"><td class="def constructor"><a href="#type-inst.Itaint" class="anchor"></a><code>| </code><code><span class="constructor">Itaint</span></code></td></tr><tr id="type-inst.Iupdate" class="anchored"><td class="def constructor"><a href="#type-inst.Iupdate" class="anchor"></a><code>| </code><code><span class="constructor">Iupdate</span> <span class="keyword">of</span> <a href="index.html#type-zero_flag">zero_flag</a> * <a href="index.html#type-null_case_flag">null_case_flag</a> * int * <a href="../IR/PredSymb/index.html#type-path_pos">IR.PredSymb.path_pos</a></code></td></tr><tr id="type-inst.Ireturn_from_call" class="anchored"><td class="def constructor"><a href="#type-inst.Ireturn_from_call" class="anchor"></a><code>| </code><code><span class="constructor">Ireturn_from_call</span> <span class="keyword">of</span> int</code></td></tr></table></dt><dd><p>instrumentation of heap values</p></dd></dl><div><div class="spec include"><div class="doc"><dl><dt class="spec value" id="val-compare_inst"><a href="#val-compare_inst" class="anchor"></a><code><span class="keyword">val</span> compare_inst : <a href="index.html#type-inst">inst</a> <span>-></span> <a href="index.html#type-inst">inst</a> <span>-></span> int</code></dt></dl></div></div></div><dl><dt class="spec value" id="val-equal_inst"><a href="#val-equal_inst" class="anchor"></a><code><span class="keyword">val</span> equal_inst : <a href="index.html#type-inst">inst</a> <span>-></span> <a href="index.html#type-inst">inst</a> <span>-></span> bool</code></dt><dt class="spec value" id="val-inst_actual_precondition"><a href="#val-inst_actual_precondition" class="anchor"></a><code><span class="keyword">val</span> inst_actual_precondition : <a href="index.html#type-inst">inst</a></code></dt><dt class="spec value" id="val-inst_formal"><a href="#val-inst_formal" class="anchor"></a><code><span class="keyword">val</span> inst_formal : <a href="index.html#type-inst">inst</a></code></dt><dt class="spec value" id="val-inst_initial"><a href="#val-inst_initial" class="anchor"></a><code><span class="keyword">val</span> inst_initial : <a href="index.html#type-inst">inst</a></code></dt><dd><p>for formal parameters and heap values at the beginning of the function</p></dd></dl><dl><dt class="spec value" id="val-inst_lookup"><a href="#val-inst_lookup" class="anchor"></a><code><span class="keyword">val</span> inst_lookup : <a href="index.html#type-inst">inst</a></code></dt><dd><p>for initial values</p></dd></dl><dl><dt class="spec value" id="val-inst_none"><a href="#val-inst_none" class="anchor"></a><code><span class="keyword">val</span> inst_none : <a href="index.html#type-inst">inst</a></code></dt><dt class="spec value" id="val-inst_nullify"><a href="#val-inst_nullify" class="anchor"></a><code><span class="keyword">val</span> inst_nullify : <a href="index.html#type-inst">inst</a></code></dt><dt class="spec value" id="val-inst_rearrange"><a href="#val-inst_rearrange" class="anchor"></a><code><span class="keyword">val</span> inst_rearrange : bool <span>-></span> <a href="../IBase/Location/index.html#type-t">IBase.Location.t</a> <span>-></span> <a href="../IR/PredSymb/index.html#type-path_pos">IR.PredSymb.path_pos</a> <span>-></span> <a href="index.html#type-inst">inst</a></code></dt><dd><p>the boolean indicates whether the pointer is known nonzero</p></dd></dl><dl><dt class="spec value" id="val-inst_update"><a href="#val-inst_update" class="anchor"></a><code><span class="keyword">val</span> inst_update : <a href="../IBase/Location/index.html#type-t">IBase.Location.t</a> <span>-></span> <a href="../IR/PredSymb/index.html#type-path_pos">IR.PredSymb.path_pos</a> <span>-></span> <a href="index.html#type-inst">inst</a></code></dt><dt class="spec value" id="val-inst_set_null_case_flag"><a href="#val-inst_set_null_case_flag" class="anchor"></a><code><span class="keyword">val</span> inst_set_null_case_flag : <a href="index.html#type-inst">inst</a> <span>-></span> <a href="index.html#type-inst">inst</a></code></dt><dd><p>Set the null case flag of the inst.</p></dd></dl><dl><dt class="spec value" id="val-inst_new_loc"><a href="#val-inst_new_loc" class="anchor"></a><code><span class="keyword">val</span> inst_new_loc : <a href="../IBase/Location/index.html#type-t">IBase.Location.t</a> <span>-></span> <a href="index.html#type-inst">inst</a> <span>-></span> <a href="index.html#type-inst">inst</a></code></dt><dd><p>update the location of the instrumentation</p></dd></dl><dl><dt class="spec value" id="val-update_inst"><a href="#val-update_inst" class="anchor"></a><code><span class="keyword">val</span> update_inst : <a href="index.html#type-inst">inst</a> <span>-></span> <a href="index.html#type-inst">inst</a> <span>-></span> <a href="index.html#type-inst">inst</a></code></dt><dd><p>Update <code>inst_old</code> to <code>inst_new</code> preserving the zero flag</p></dd></dl><dl><dt class="spec exception" id="exception-JoinFail"><a href="#exception-JoinFail" class="anchor"></a><code><span class="keyword">exception</span> </code><code><span class="exception">JoinFail</span></code></dt></dl><dl><dt class="spec value" id="val-inst_partial_join"><a href="#val-inst_partial_join" class="anchor"></a><code><span class="keyword">val</span> inst_partial_join : <a href="index.html#type-inst">inst</a> <span>-></span> <a href="index.html#type-inst">inst</a> <span>-></span> <a href="index.html#type-inst">inst</a></code></dt><dd><p>join of instrumentations, can raise JoinFail</p></dd></dl><dl><dt class="spec value" id="val-inst_partial_meet"><a href="#val-inst_partial_meet" class="anchor"></a><code><span class="keyword">val</span> inst_partial_meet : <a href="index.html#type-inst">inst</a> <span>-></span> <a href="index.html#type-inst">inst</a> <span>-></span> <a href="index.html#type-inst">inst</a></code></dt><dd><p>meet of instrumentations</p></dd></dl><dl><dt class="spec type" id="type-strexp0"><a href="#type-strexp0" class="anchor"></a><code><span class="keyword">type</span> <span>'inst strexp0</span></code><code> = </code><table class="variant"><tr id="type-strexp0.Eexp" class="anchored"><td class="def constructor"><a href="#type-strexp0.Eexp" class="anchor"></a><code>| </code><code><span class="constructor">Eexp</span> <span class="keyword">of</span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <span class="type-var">'inst</span></code></td><td class="doc"><p>Base case: expression with instrumentation</p></td></tr><tr id="type-strexp0.Estruct" class="anchored"><td class="def constructor"><a href="#type-strexp0.Estruct" class="anchor"></a><code>| </code><code><span class="constructor">Estruct</span> <span class="keyword">of</span> <span><span>(<a href="../IR/Fieldname/index.html#type-t">IR.Fieldname.t</a> * <span><span class="type-var">'inst</span> <a href="index.html#type-strexp0">strexp0</a></span>)</span> list</span> * <span class="type-var">'inst</span></code></td><td class="doc"><p>C structure</p></td></tr><tr id="type-strexp0.Earray" class="anchored"><td class="def constructor"><a href="#type-strexp0.Earray" class="anchor"></a><code>| </code><code><span class="constructor">Earray</span> <span class="keyword">of</span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <span><span>(<a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <span><span class="type-var">'inst</span> <a href="index.html#type-strexp0">strexp0</a></span>)</span> list</span> * <span class="type-var">'inst</span></code></td><td class="doc"><p>Array of given length There are two conditions imposed / used in the array case. First, if some index and value pair appears inside an array in a strexp, then the index is less than the length of the array. For instance, <code>x |->[10 | e1: v1]</code> implies that <code>e1 <= 9</code>. Second, if two indices appear in an array, they should be different. For instance, <code>x |->[10 | e1: v1, e2: v2]</code> implies that <code>e1 != e2</code>.</p></td></tr></table></dt><dd><p>structured expressions represent a value of structured type, such as an array or a struct.</p></dd></dl><div><div class="spec include"><div class="doc"><dl><dt class="spec value" id="val-compare_strexp0"><a href="#val-compare_strexp0" class="anchor"></a><code><span class="keyword">val</span> compare_strexp0 : <span>(<span class="type-var">'inst</span> <span>-></span> <span class="type-var">'inst</span> <span>-></span> int)</span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-strexp0">strexp0</a></span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-strexp0">strexp0</a></span> <span>-></span> int</code></dt></dl></div></div></div><dl><dt class="spec type" id="type-strexp"><a href="#type-strexp" class="anchor"></a><code><span class="keyword">type</span> strexp</code><code> = <span><a href="index.html#type-inst">inst</a> <a href="index.html#type-strexp0">strexp0</a></span></code></dt></dl><dl><dt class="spec value" id="val-compare_strexp"><a href="#val-compare_strexp" class="anchor"></a><code><span class="keyword">val</span> compare_strexp : <span>?⁠inst:bool</span> <span>-></span> <a href="index.html#type-strexp">strexp</a> <span>-></span> <a href="index.html#type-strexp">strexp</a> <span>-></span> int</code></dt><dd><p>Comparison function for strexp. The inst:: parameter specifies whether instumentations should also be considered (false by default).</p></dd></dl><dl><dt class="spec value" id="val-equal_strexp"><a href="#val-equal_strexp" class="anchor"></a><code><span class="keyword">val</span> equal_strexp : <span>?⁠inst:bool</span> <span>-></span> <a href="index.html#type-strexp">strexp</a> <span>-></span> <a href="index.html#type-strexp">strexp</a> <span>-></span> bool</code></dt><dd><p>Equality function for strexp. The inst:: parameter specifies whether instumentations should also be considered (false by default).</p></dd></dl><dl><dt class="spec type" id="type-hpred0"><a href="#type-hpred0" class="anchor"></a><code><span class="keyword">type</span> <span>'inst hpred0</span></code><code> = </code><table class="variant"><tr id="type-hpred0.Hpointsto" class="anchored"><td class="def constructor"><a href="#type-hpred0.Hpointsto" class="anchor"></a><code>| </code><code><span class="constructor">Hpointsto</span> <span class="keyword">of</span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <span><span class="type-var">'inst</span> <a href="index.html#type-strexp0">strexp0</a></span> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a></code></td><td class="doc"><p>represents <code>exp|->strexp:typexp</code> where <code>typexp</code> is an expression representing a type, e.h. <code>sizeof(t)</code>.</p></td></tr><tr id="type-hpred0.Hlseg" class="anchored"><td class="def constructor"><a href="#type-hpred0.Hlseg" class="anchor"></a><code>| </code><code><span class="constructor">Hlseg</span> <span class="keyword">of</span> <a href="index.html#type-lseg_kind">lseg_kind</a> * <span><span class="type-var">'inst</span> <a href="index.html#type-hpara0">hpara0</a></span> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <span><a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> list</span></code></td><td class="doc"><p>higher - order predicate for singly - linked lists. Should ensure that exp1!= exp2 implies that exp1 is allocated. This assumption is used in the rearrangement. The last <code>exp list</code> parameter is used to denote the shared links by all the nodes in the list.</p></td></tr><tr id="type-hpred0.Hdllseg" class="anchored"><td class="def constructor"><a href="#type-hpred0.Hdllseg" class="anchor"></a><code>| </code><code><span class="constructor">Hdllseg</span> <span class="keyword">of</span> <a href="index.html#type-lseg_kind">lseg_kind</a> * <span><span class="type-var">'inst</span> <a href="index.html#type-hpara_dll0">hpara_dll0</a></span> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <span><a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> list</span></code></td><td class="doc"><p>higher-order predicate for doubly-linked lists. Parameter for the higher-order singly-linked list predicate. Means "lambda (root,next,svars). Exists evars. body". Assume that root, next, svars, evars are disjoint sets of primed identifiers, and include all the free primed identifiers in body. body should not contain any non - primed identifiers or program variables (i.e. pvars).</p></td></tr></table></dt><dd><p>an atomic heap predicate</p></dd></dl><dl><dt class="spec type" id="type-hpara0"><a href="#type-hpara0" class="anchor"></a><code><span class="keyword">and</span> <span>'inst hpara0</span></code><code> = </code><code>{</code><table class="record"><tr id="type-hpara0.root" class="anchored"><td class="def field"><a href="#type-hpara0.root" class="anchor"></a><code>root : <a href="../IR/Ident/index.html#type-t">IR.Ident.t</a>;</code></td></tr><tr id="type-hpara0.next" class="anchored"><td class="def field"><a href="#type-hpara0.next" class="anchor"></a><code>next : <a href="../IR/Ident/index.html#type-t">IR.Ident.t</a>;</code></td></tr><tr id="type-hpara0.svars" class="anchored"><td class="def field"><a href="#type-hpara0.svars" class="anchor"></a><code>svars : <span><a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> list</span>;</code></td></tr><tr id="type-hpara0.evars" class="anchored"><td class="def field"><a href="#type-hpara0.evars" class="anchor"></a><code>evars : <span><a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> list</span>;</code></td></tr><tr id="type-hpara0.body" class="anchored"><td class="def field"><a href="#type-hpara0.body" class="anchor"></a><code>body : <span><span><span class="type-var">'inst</span> <a href="index.html#type-hpred0">hpred0</a></span> list</span>;</code></td></tr></table><code>}</code></dt><dt class="spec type" id="type-hpara_dll0"><a href="#type-hpara_dll0" class="anchor"></a><code><span class="keyword">and</span> <span>'inst hpara_dll0</span></code><code> = </code><code>{</code><table class="record"><tr id="type-hpara_dll0.cell" class="anchored"><td class="def field"><a href="#type-hpara_dll0.cell" class="anchor"></a><code>cell : <a href="../IR/Ident/index.html#type-t">IR.Ident.t</a>;</code></td><td class="doc"><p>address cell</p></td></tr><tr id="type-hpara_dll0.blink" class="anchored"><td class="def field"><a href="#type-hpara_dll0.blink" class="anchor"></a><code>blink : <a href="../IR/Ident/index.html#type-t">IR.Ident.t</a>;</code></td><td class="doc"><p>backward link</p></td></tr><tr id="type-hpara_dll0.flink" class="anchored"><td class="def field"><a href="#type-hpara_dll0.flink" class="anchor"></a><code>flink : <a href="../IR/Ident/index.html#type-t">IR.Ident.t</a>;</code></td><td class="doc"><p>forward link</p></td></tr><tr id="type-hpara_dll0.svars_dll" class="anchored"><td class="def field"><a href="#type-hpara_dll0.svars_dll" class="anchor"></a><code>svars_dll : <span><a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> list</span>;</code></td></tr><tr id="type-hpara_dll0.evars_dll" class="anchored"><td class="def field"><a href="#type-hpara_dll0.evars_dll" class="anchor"></a><code>evars_dll : <span><a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> list</span>;</code></td></tr><tr id="type-hpara_dll0.body_dll" class="anchored"><td class="def field"><a href="#type-hpara_dll0.body_dll" class="anchor"></a><code>body_dll : <span><span><span class="type-var">'inst</span> <a href="index.html#type-hpred0">hpred0</a></span> list</span>;</code></td></tr></table><code>}</code></dt><dd><p>parameter for the higher-order doubly-linked list predicates. Assume that all the free identifiers in body_dll should belong to cell, blink, flink, svars_dll, evars_dll.</p></dd></dl><div><div class="spec include"><div class="doc"><dl><dt class="spec value" id="val-compare_hpred0"><a href="#val-compare_hpred0" class="anchor"></a><code><span class="keyword">val</span> compare_hpred0 : <span>(<span class="type-var">'inst</span> <span>-></span> <span class="type-var">'inst</span> <span>-></span> int)</span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpred0">hpred0</a></span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpred0">hpred0</a></span> <span>-></span> int</code></dt><dt class="spec value" id="val-compare_hpara0"><a href="#val-compare_hpara0" class="anchor"></a><code><span class="keyword">val</span> compare_hpara0 : <span>(<span class="type-var">'inst</span> <span>-></span> <span class="type-var">'inst</span> <span>-></span> int)</span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpara0">hpara0</a></span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpara0">hpara0</a></span> <span>-></span> int</code></dt><dt class="spec value" id="val-compare_hpara_dll0"><a href="#val-compare_hpara_dll0" class="anchor"></a><code><span class="keyword">val</span> compare_hpara_dll0 : <span>(<span class="type-var">'inst</span> <span>-></span> <span class="type-var">'inst</span> <span>-></span> int)</span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpara_dll0">hpara_dll0</a></span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpara_dll0">hpara_dll0</a></span> <span>-></span> int</code></dt><dt class="spec value" id="val-compare_hpred0"><a href="#val-compare_hpred0" class="anchor"></a><code><span class="keyword">val</span> compare_hpred0 : <span>(<span class="type-var">'inst</span> <span>-></span> <span class="type-var">'inst</span> <span>-></span> int)</span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpred0">hpred0</a></span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpred0">hpred0</a></span> <span>-></span> int</code></dt><dt class="spec value" id="val-compare_hpara0"><a href="#val-compare_hpara0" class="anchor"></a><code><span class="keyword">val</span> compare_hpara0 : <span>(<span class="type-var">'inst</span> <span>-></span> <span class="type-var">'inst</span> <span>-></span> int)</span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpara0">hpara0</a></span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpara0">hpara0</a></span> <span>-></span> int</code></dt><dt class="spec value" id="val-compare_hpara_dll0"><a href="#val-compare_hpara_dll0" class="anchor"></a><code><span class="keyword">val</span> compare_hpara_dll0 : <span>(<span class="type-var">'inst</span> <span>-></span> <span class="type-var">'inst</span> <span>-></span> int)</span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpara_dll0">hpara_dll0</a></span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpara_dll0">hpara_dll0</a></span> <span>-></span> int</code></dt><dt class="spec value" id="val-compare_hpred0"><a href="#val-compare_hpred0" class="anchor"></a><code><span class="keyword">val</span> compare_hpred0 : <span>(<span class="type-var">'inst</span> <span>-></span> <span class="type-var">'inst</span> <span>-></span> int)</span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpred0">hpred0</a></span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpred0">hpred0</a></span> <span>-></span> int</code></dt><dt class="spec value" id="val-compare_hpara0"><a href="#val-compare_hpara0" class="anchor"></a><code><span class="keyword">val</span> compare_hpara0 : <span>(<span class="type-var">'inst</span> <span>-></span> <span class="type-var">'inst</span> <span>-></span> int)</span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpara0">hpara0</a></span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpara0">hpara0</a></span> <span>-></span> int</code></dt><dt class="spec value" id="val-compare_hpara_dll0"><a href="#val-compare_hpara_dll0" class="anchor"></a><code><span class="keyword">val</span> compare_hpara_dll0 : <span>(<span class="type-var">'inst</span> <span>-></span> <span class="type-var">'inst</span> <span>-></span> int)</span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpara_dll0">hpara_dll0</a></span> <span>-></span> <span><span class="type-var">'inst</span> <a href="index.html#type-hpara_dll0">hpara_dll0</a></span> <span>-></span> int</code></dt></dl></div></div></div><dl><dt class="spec type" id="type-hpred"><a href="#type-hpred" class="anchor"></a><code><span class="keyword">type</span> hpred</code><code> = <span><a href="index.html#type-inst">inst</a> <a href="index.html#type-hpred0">hpred0</a></span></code></dt><dt class="spec type" id="type-hpara"><a href="#type-hpara" class="anchor"></a><code><span class="keyword">type</span> hpara</code><code> = <span><a href="index.html#type-inst">inst</a> <a href="index.html#type-hpara0">hpara0</a></span></code></dt><dt class="spec type" id="type-hpara_dll"><a href="#type-hpara_dll" class="anchor"></a><code><span class="keyword">type</span> hpara_dll</code><code> = <span><a href="index.html#type-inst">inst</a> <a href="index.html#type-hpara_dll0">hpara_dll0</a></span></code></dt></dl><dl><dt class="spec value" id="val-compare_hpred"><a href="#val-compare_hpred" class="anchor"></a><code><span class="keyword">val</span> compare_hpred : <span>?⁠inst:bool</span> <span>-></span> <a href="index.html#type-hpred">hpred</a> <span>-></span> <a href="index.html#type-hpred">hpred</a> <span>-></span> int</code></dt><dd><p>Comparison function for hpred. The inst:: parameter specifies whether instumentations should also be considered (false by default).</p></dd></dl><dl><dt class="spec value" id="val-equal_hpred"><a href="#val-equal_hpred" class="anchor"></a><code><span class="keyword">val</span> equal_hpred : <span>?⁠inst:bool</span> <span>-></span> <a href="index.html#type-hpred">hpred</a> <span>-></span> <a href="index.html#type-hpred">hpred</a> <span>-></span> bool</code></dt><dd><p>Equality function for hpred. The inst:: parameter specifies whether instumentations should also be considered (false by default).</p></dd></dl><dl><dt class="spec module" id="module-HpredSet"><a href="#module-HpredSet" class="anchor"></a><code><span class="keyword">module</span> HpredSet : <a href="../IStdlib/index.html#module-IStd">IStdlib.IStd</a>.Caml.Set.S <span class="keyword">with</span> <span class="keyword">type</span> <a href="index.html#module-HpredSet">HpredSet</a>.elt = <a href="index.html#type-hpred">hpred</a></code></dt><dd><p>Sets of heap predicates</p></dd></dl></section><section><header><h3 id="compaction"><a href="#compaction" class="anchor"></a>Compaction</h3></header><dl><dt class="spec type" id="type-sharing_env"><a href="#type-sharing_env" class="anchor"></a><code><span class="keyword">type</span> sharing_env</code></dt></dl><dl><dt class="spec value" id="val-create_sharing_env"><a href="#val-create_sharing_env" class="anchor"></a><code><span class="keyword">val</span> create_sharing_env : unit <span>-></span> <a href="index.html#type-sharing_env">sharing_env</a></code></dt><dd><p>Create a sharing env to store canonical representations</p></dd></dl><dl><dt class="spec value" id="val-hpred_compact"><a href="#val-hpred_compact" class="anchor"></a><code><span class="keyword">val</span> hpred_compact : <a href="index.html#type-sharing_env">sharing_env</a> <span>-></span> <a href="index.html#type-hpred">hpred</a> <span>-></span> <a href="index.html#type-hpred">hpred</a></code></dt><dd><p>Return a compact representation of the exp</p></dd></dl><dl><dt class="spec value" id="val-is_objc_object"><a href="#val-is_objc_object" class="anchor"></a><code><span class="keyword">val</span> is_objc_object : <a href="index.html#type-hpred">hpred</a> <span>-></span> bool</code></dt></dl></section><section><header><h3 id="comparision-and-inspection-functions"><a href="#comparision-and-inspection-functions" class="anchor"></a>Comparision And Inspection Functions</h3></header><dl><dt class="spec value" id="val-pp_offset"><a href="#val-pp_offset" class="anchor"></a><code><span class="keyword">val</span> pp_offset : <a href="../IStdlib/Pp/index.html#type-env">IStdlib.Pp.env</a> <span>-></span> <a href="index.html#module-F">F</a>.formatter <span>-></span> <a href="index.html#type-offset">offset</a> <span>-></span> unit</code></dt><dt class="spec value" id="val-d_offset_list"><a href="#val-d_offset_list" class="anchor"></a><code><span class="keyword">val</span> d_offset_list : <span><a href="index.html#type-offset">offset</a> list</span> <span>-></span> unit</code></dt><dd><p>Dump a list of offsets</p></dd></dl><dl><dt class="spec value" id="val-pp_atom"><a href="#val-pp_atom" class="anchor"></a><code><span class="keyword">val</span> pp_atom : <a href="../IStdlib/Pp/index.html#type-env">IStdlib.Pp.env</a> <span>-></span> <a href="index.html#module-F">F</a>.formatter <span>-></span> <a href="index.html#type-atom">atom</a> <span>-></span> unit</code></dt><dd><p>Pretty print an atom.</p></dd></dl><dl><dt class="spec value" id="val-d_atom"><a href="#val-d_atom" class="anchor"></a><code><span class="keyword">val</span> d_atom : <a href="index.html#type-atom">atom</a> <span>-></span> unit</code></dt><dd><p>Dump an atom.</p></dd></dl><dl><dt class="spec value" id="val-pp_inst"><a href="#val-pp_inst" class="anchor"></a><code><span class="keyword">val</span> pp_inst : <a href="index.html#module-F">F</a>.formatter <span>-></span> <a href="index.html#type-inst">inst</a> <span>-></span> unit</code></dt><dd><p>pretty-print an inst</p></dd></dl><dl><dt class="spec value" id="val-pp_sexp"><a href="#val-pp_sexp" class="anchor"></a><code><span class="keyword">val</span> pp_sexp : <a href="../IStdlib/Pp/index.html#type-env">IStdlib.Pp.env</a> <span>-></span> <a href="index.html#module-F">F</a>.formatter <span>-></span> <a href="index.html#type-strexp">strexp</a> <span>-></span> unit</code></dt><dd><p>Pretty print a strexp.</p></dd></dl><dl><dt class="spec value" id="val-d_sexp"><a href="#val-d_sexp" class="anchor"></a><code><span class="keyword">val</span> d_sexp : <a href="index.html#type-strexp">strexp</a> <span>-></span> unit</code></dt><dd><p>Dump a strexp.</p></dd></dl><dl><dt class="spec value" id="val-pp_hpred"><a href="#val-pp_hpred" class="anchor"></a><code><span class="keyword">val</span> pp_hpred : <a href="../IStdlib/Pp/index.html#type-env">IStdlib.Pp.env</a> <span>-></span> <a href="index.html#module-F">F</a>.formatter <span>-></span> <a href="index.html#type-hpred">hpred</a> <span>-></span> unit</code></dt><dd><p>Pretty print a hpred.</p></dd></dl><dl><dt class="spec value" id="val-d_hpred"><a href="#val-d_hpred" class="anchor"></a><code><span class="keyword">val</span> d_hpred : <a href="index.html#type-hpred">hpred</a> <span>-></span> unit</code></dt><dd><p>Dump a hpred.</p></dd></dl><dl><dt class="spec value" id="val-pp_hpara"><a href="#val-pp_hpara" class="anchor"></a><code><span class="keyword">val</span> pp_hpara : <a href="../IStdlib/Pp/index.html#type-env">IStdlib.Pp.env</a> <span>-></span> <a href="index.html#module-F">F</a>.formatter <span>-></span> <a href="index.html#type-hpara">hpara</a> <span>-></span> unit</code></dt><dd><p>Pretty print a hpara.</p></dd></dl><dl><dt class="spec value" id="val-pp_hpara_dll"><a href="#val-pp_hpara_dll" class="anchor"></a><code><span class="keyword">val</span> pp_hpara_dll : <a href="../IStdlib/Pp/index.html#type-env">IStdlib.Pp.env</a> <span>-></span> <a href="index.html#module-F">F</a>.formatter <span>-></span> <a href="index.html#type-hpara_dll">hpara_dll</a> <span>-></span> unit</code></dt><dd><p>Pretty print a hpara_dll.</p></dd></dl><dl><dt class="spec module" id="module-Env"><a href="#module-Env" class="anchor"></a><code><span class="keyword">module</span> <a href="Env/index.html">Env</a> : <span class="keyword">sig</span> ... <span class="keyword">end</span></code></dt><dd><p>record the occurrences of predicates as parameters of (doubly -)linked lists and Epara. Provides unique numbering for predicates and an iterator.</p></dd></dl><dl><dt class="spec value" id="val-pp_hpred_env"><a href="#val-pp_hpred_env" class="anchor"></a><code><span class="keyword">val</span> pp_hpred_env : <a href="../IStdlib/Pp/index.html#type-env">IStdlib.Pp.env</a> <span>-></span> <span><a href="Env/index.html#type-t">Env.t</a> option</span> <span>-></span> <a href="index.html#module-F">F</a>.formatter <span>-></span> <a href="index.html#type-hpred">hpred</a> <span>-></span> unit</code></dt><dd><p>Pretty print a hpred with optional predicate env</p></dd></dl></section><section><header><h3 id="functions-for-traversing-sil-data-types"><a href="#functions-for-traversing-sil-data-types" class="anchor"></a>Functions for traversing SIL data types</h3></header><dl><dt class="spec value" id="val-strexp_expmap"><a href="#val-strexp_expmap" class="anchor"></a><code><span class="keyword">val</span> strexp_expmap : <span>(<span>(<a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <span><a href="index.html#type-inst">inst</a> option</span>)</span> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <span><a href="index.html#type-inst">inst</a> option</span>)</span> <span>-></span> <a href="index.html#type-strexp">strexp</a> <span>-></span> <a href="index.html#type-strexp">strexp</a></code></dt><dd><p>Change exps in strexp using <code>f</code>. WARNING: the result might not be normalized.</p></dd></dl><dl><dt class="spec value" id="val-hpred_expmap"><a href="#val-hpred_expmap" class="anchor"></a><code><span class="keyword">val</span> hpred_expmap : <span>(<span>(<a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <span><a href="index.html#type-inst">inst</a> option</span>)</span> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <span><a href="index.html#type-inst">inst</a> option</span>)</span> <span>-></span> <a href="index.html#type-hpred">hpred</a> <span>-></span> <a href="index.html#type-hpred">hpred</a></code></dt><dd><p>Change exps in hpred by <code>f</code>. WARNING: the result might not be normalized.</p></dd></dl><dl><dt class="spec value" id="val-hpred_instmap"><a href="#val-hpred_instmap" class="anchor"></a><code><span class="keyword">val</span> hpred_instmap : <span>(<a href="index.html#type-inst">inst</a> <span>-></span> <a href="index.html#type-inst">inst</a>)</span> <span>-></span> <a href="index.html#type-hpred">hpred</a> <span>-></span> <a href="index.html#type-hpred">hpred</a></code></dt><dd><p>Change instrumentations in hpred using <code>f</code>.</p></dd></dl><dl><dt class="spec value" id="val-hpred_list_expmap"><a href="#val-hpred_list_expmap" class="anchor"></a><code><span class="keyword">val</span> hpred_list_expmap : <span>(<span>(<a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <span><a href="index.html#type-inst">inst</a> option</span>)</span> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <span><a href="index.html#type-inst">inst</a> option</span>)</span> <span>-></span> <span><a href="index.html#type-hpred">hpred</a> list</span> <span>-></span> <span><a href="index.html#type-hpred">hpred</a> list</span></code></dt><dd><p>Change exps in hpred list by <code>f</code>. WARNING: the result might not be normalized.</p></dd></dl><dl><dt class="spec value" id="val-atom_expmap"><a href="#val-atom_expmap" class="anchor"></a><code><span class="keyword">val</span> atom_expmap : <span>(<a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a>)</span> <span>-></span> <a href="index.html#type-atom">atom</a> <span>-></span> <a href="index.html#type-atom">atom</a></code></dt><dd><p>Change exps in atom by <code>f</code>. WARNING: the result might not be normalized.</p></dd></dl><dl><dt class="spec value" id="val-hpred_list_get_lexps"><a href="#val-hpred_list_get_lexps" class="anchor"></a><code><span class="keyword">val</span> hpred_list_get_lexps : <span>(<a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> <span>-></span> bool)</span> <span>-></span> <span><a href="index.html#type-hpred">hpred</a> list</span> <span>-></span> <span><a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> list</span></code></dt><dt class="spec value" id="val-hpred_entries"><a href="#val-hpred_entries" class="anchor"></a><code><span class="keyword">val</span> hpred_entries : <a href="index.html#type-hpred">hpred</a> <span>-></span> <span><a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> list</span></code></dt><dt class="spec value" id="val-atom_free_vars"><a href="#val-atom_free_vars" class="anchor"></a><code><span class="keyword">val</span> atom_free_vars : <a href="index.html#type-atom">atom</a> <span>-></span> <span><a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> <a href="../IStdlib/index.html#module-IStd">IStdlib.IStd</a>.Sequence.t</span></code></dt><dt class="spec value" id="val-atom_gen_free_vars"><a href="#val-atom_gen_free_vars" class="anchor"></a><code><span class="keyword">val</span> atom_gen_free_vars : <a href="index.html#type-atom">atom</a> <span>-></span> <span><span>(unit, <a href="../IR/Ident/index.html#type-t">IR.Ident.t</a>)</span> <a href="../IStdlib/index.html#module-IStd">IStdlib.IStd</a>.Sequence.Generator.t</span></code></dt><dt class="spec value" id="val-hpred_free_vars"><a href="#val-hpred_free_vars" class="anchor"></a><code><span class="keyword">val</span> hpred_free_vars : <a href="index.html#type-hpred">hpred</a> <span>-></span> <span><a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> <a href="../IStdlib/index.html#module-IStd">IStdlib.IStd</a>.Sequence.t</span></code></dt><dt class="spec value" id="val-hpred_gen_free_vars"><a href="#val-hpred_gen_free_vars" class="anchor"></a><code><span class="keyword">val</span> hpred_gen_free_vars : <a href="index.html#type-hpred">hpred</a> <span>-></span> <span><span>(unit, <a href="../IR/Ident/index.html#type-t">IR.Ident.t</a>)</span> <a href="../IStdlib/index.html#module-IStd">IStdlib.IStd</a>.Sequence.Generator.t</span></code></dt><dt class="spec value" id="val-hpara_shallow_free_vars"><a href="#val-hpara_shallow_free_vars" class="anchor"></a><code><span class="keyword">val</span> hpara_shallow_free_vars : <a href="index.html#type-hpara">hpara</a> <span>-></span> <span><a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> <a href="../IStdlib/index.html#module-IStd">IStdlib.IStd</a>.Sequence.t</span></code></dt><dt class="spec value" id="val-hpara_dll_shallow_free_vars"><a href="#val-hpara_dll_shallow_free_vars" class="anchor"></a><code><span class="keyword">val</span> hpara_dll_shallow_free_vars : <a href="index.html#type-hpara_dll">hpara_dll</a> <span>-></span> <span><a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> <a href="../IStdlib/index.html#module-IStd">IStdlib.IStd</a>.Sequence.t</span></code></dt><dd><p>Variables in hpara_dll, excluding bound vars in the body</p></dd></dl></section><section><header><h3 id="substitution"><a href="#substitution" class="anchor"></a>Substitution</h3></header><dl><dt class="spec type" id="type-subst"><a href="#type-subst" class="anchor"></a><code><span class="keyword">type</span> subst</code><code> = <span class="keyword">private</span> <span><span>(<a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a>)</span> list</span></code></dt></dl><div><div class="spec include"><div class="doc"><dl><dt class="spec value" id="val-compare_subst"><a href="#val-compare_subst" class="anchor"></a><code><span class="keyword">val</span> compare_subst : <a href="index.html#type-subst">subst</a> <span>-></span> <a href="index.html#type-subst">subst</a> <span>-></span> int</code></dt></dl></div></div></div><dl><dt class="spec value" id="val-equal_subst"><a href="#val-equal_subst" class="anchor"></a><code><span class="keyword">val</span> equal_subst : <a href="index.html#type-subst">subst</a> <span>-></span> <a href="index.html#type-subst">subst</a> <span>-></span> bool</code></dt><dd><p>Equality for substitutions.</p></dd></dl><dl><dt class="spec value" id="val-subst_of_list"><a href="#val-subst_of_list" class="anchor"></a><code><span class="keyword">val</span> subst_of_list : <span><span>(<a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a>)</span> list</span> <span>-></span> <a href="index.html#type-subst">subst</a></code></dt><dd><p>Create a substitution from a list of pairs. For all (id1, e1), (id2, e2) in the input list, if id1 = id2, then e1 = e2.</p></dd></dl><dl><dt class="spec value" id="val-subst_of_list_duplicates"><a href="#val-subst_of_list_duplicates" class="anchor"></a><code><span class="keyword">val</span> subst_of_list_duplicates : <span><span>(<a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a>)</span> list</span> <span>-></span> <a href="index.html#type-subst">subst</a></code></dt><dd><p>like subst_of_list, but allow duplicate ids and only keep the first occurrence</p></dd></dl><dl><dt class="spec value" id="val-sub_to_list"><a href="#val-sub_to_list" class="anchor"></a><code><span class="keyword">val</span> sub_to_list : <a href="index.html#type-subst">subst</a> <span>-></span> <span><span>(<a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a>)</span> list</span></code></dt><dd><p>Convert a subst to a list of pairs.</p></dd></dl><dl><dt class="spec value" id="val-sub_empty"><a href="#val-sub_empty" class="anchor"></a><code><span class="keyword">val</span> sub_empty : <a href="index.html#type-subst">subst</a></code></dt><dd><p>The empty substitution.</p></dd></dl><dl><dt class="spec value" id="val-is_sub_empty"><a href="#val-is_sub_empty" class="anchor"></a><code><span class="keyword">val</span> is_sub_empty : <a href="index.html#type-subst">subst</a> <span>-></span> bool</code></dt><dt class="spec value" id="val-sub_join"><a href="#val-sub_join" class="anchor"></a><code><span class="keyword">val</span> sub_join : <a href="index.html#type-subst">subst</a> <span>-></span> <a href="index.html#type-subst">subst</a> <span>-></span> <a href="index.html#type-subst">subst</a></code></dt><dd><p>Compute the common id-exp part of two inputs <code>subst1</code> and <code>subst2</code>. The first component of the output is this common part. The second and third components are the remainder of <code>subst1</code> and <code>subst2</code>, respectively.</p></dd></dl><dl><dt class="spec value" id="val-sub_symmetric_difference"><a href="#val-sub_symmetric_difference" class="anchor"></a><code><span class="keyword">val</span> sub_symmetric_difference : <a href="index.html#type-subst">subst</a> <span>-></span> <a href="index.html#type-subst">subst</a> <span>-></span> <a href="index.html#type-subst">subst</a> * <a href="index.html#type-subst">subst</a> * <a href="index.html#type-subst">subst</a></code></dt><dd><p>Compute the common id-exp part of two inputs <code>subst1</code> and <code>subst2</code>. The first component of the output is this common part. The second and third components are the remainder of <code>subst1</code> and <code>subst2</code>, respectively.</p></dd></dl><dl><dt class="spec value" id="val-sub_find"><a href="#val-sub_find" class="anchor"></a><code><span class="keyword">val</span> sub_find : <span>(<a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> <span>-></span> bool)</span> <span>-></span> <a href="index.html#type-subst">subst</a> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a></code></dt><dd><p><code>sub_find filter sub</code> returns the expression associated to the first identifier that satisfies <code>filter</code>. Raise <code>Not_found_s/Caml.Not_found</code> if there isn't one.</p></dd></dl><dl><dt class="spec value" id="val-sub_filter"><a href="#val-sub_filter" class="anchor"></a><code><span class="keyword">val</span> sub_filter : <span>(<a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> <span>-></span> bool)</span> <span>-></span> <a href="index.html#type-subst">subst</a> <span>-></span> <a href="index.html#type-subst">subst</a></code></dt><dd><p><code>sub_filter filter sub</code> restricts the domain of <code>sub</code> to the identifiers satisfying <code>filter</code>.</p></dd></dl><dl><dt class="spec value" id="val-sub_filter_pair"><a href="#val-sub_filter_pair" class="anchor"></a><code><span class="keyword">val</span> sub_filter_pair : <a href="index.html#type-subst">subst</a> <span>-></span> <span>f:<span>(<span>(<a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a>)</span> <span>-></span> bool)</span></span> <span>-></span> <a href="index.html#type-subst">subst</a></code></dt><dd><p><code>sub_filter_exp filter sub</code> restricts the domain of <code>sub</code> to the identifiers satisfying <code>filter(id, sub(id))</code>.</p></dd></dl><dl><dt class="spec value" id="val-sub_range_partition"><a href="#val-sub_range_partition" class="anchor"></a><code><span class="keyword">val</span> sub_range_partition : <span>(<a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> <span>-></span> bool)</span> <span>-></span> <a href="index.html#type-subst">subst</a> <span>-></span> <a href="index.html#type-subst">subst</a> * <a href="index.html#type-subst">subst</a></code></dt><dd><p><code>sub_range_partition filter sub</code> partitions <code>sub</code> according to whether range expressions satisfy <code>filter</code>.</p></dd></dl><dl><dt class="spec value" id="val-sub_domain_partition"><a href="#val-sub_domain_partition" class="anchor"></a><code><span class="keyword">val</span> sub_domain_partition : <span>(<a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> <span>-></span> bool)</span> <span>-></span> <a href="index.html#type-subst">subst</a> <span>-></span> <a href="index.html#type-subst">subst</a> * <a href="index.html#type-subst">subst</a></code></dt><dd><p><code>sub_domain_partition filter sub</code> partitions <code>sub</code> according to whether domain identifiers satisfy <code>filter</code>.</p></dd></dl><dl><dt class="spec value" id="val-sub_domain"><a href="#val-sub_domain" class="anchor"></a><code><span class="keyword">val</span> sub_domain : <a href="index.html#type-subst">subst</a> <span>-></span> <span><a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> list</span></code></dt><dd><p>Return the list of identifiers in the domain of the substitution.</p></dd></dl><dl><dt class="spec value" id="val-sub_range"><a href="#val-sub_range" class="anchor"></a><code><span class="keyword">val</span> sub_range : <a href="index.html#type-subst">subst</a> <span>-></span> <span><a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> list</span></code></dt><dd><p>Return the list of expressions in the range of the substitution.</p></dd></dl><dl><dt class="spec value" id="val-sub_range_map"><a href="#val-sub_range_map" class="anchor"></a><code><span class="keyword">val</span> sub_range_map : <span>(<a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a>)</span> <span>-></span> <a href="index.html#type-subst">subst</a> <span>-></span> <a href="index.html#type-subst">subst</a></code></dt><dd><p><code>sub_range_map f sub</code> applies <code>f</code> to the expressions in the range of <code>sub</code>.</p></dd></dl><dl><dt class="spec value" id="val-sub_map"><a href="#val-sub_map" class="anchor"></a><code><span class="keyword">val</span> sub_map : <span>(<a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> <span>-></span> <a href="../IR/Ident/index.html#type-t">IR.Ident.t</a>)</span> <span>-></span> <span>(<a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a>)</span> <span>-></span> <a href="index.html#type-subst">subst</a> <span>-></span> <a href="index.html#type-subst">subst</a></code></dt><dd><p><code>sub_map f g sub</code> applies the renaming <code>f</code> to identifiers in the domain of <code>sub</code> and the substitution <code>g</code> to the expressions in the range of <code>sub</code>.</p></dd></dl><dl><dt class="spec value" id="val-extend_sub"><a href="#val-extend_sub" class="anchor"></a><code><span class="keyword">val</span> extend_sub : <a href="index.html#type-subst">subst</a> <span>-></span> <a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> <span>-></span> <span><a href="index.html#type-subst">subst</a> option</span></code></dt><dd><p>Extend substitution and return <code>None</code> if not possible.</p></dd></dl><dl><dt class="spec value" id="val-subst_free_vars"><a href="#val-subst_free_vars" class="anchor"></a><code><span class="keyword">val</span> subst_free_vars : <a href="index.html#type-subst">subst</a> <span>-></span> <span><a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> <a href="../IStdlib/index.html#module-IStd">IStdlib.IStd</a>.Sequence.t</span></code></dt><dt class="spec value" id="val-subst_gen_free_vars"><a href="#val-subst_gen_free_vars" class="anchor"></a><code><span class="keyword">val</span> subst_gen_free_vars : <a href="index.html#type-subst">subst</a> <span>-></span> <span><span>(unit, <a href="../IR/Ident/index.html#type-t">IR.Ident.t</a>)</span> <a href="../IStdlib/index.html#module-IStd">IStdlib.IStd</a>.Sequence.Generator.t</span></code></dt></dl><aside><p>substitution functions WARNING: these functions do not ensure that the results are normalized.</p></aside><dl><dt class="spec value" id="val-exp_sub"><a href="#val-exp_sub" class="anchor"></a><code><span class="keyword">val</span> exp_sub : <a href="index.html#type-subst">subst</a> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a></code></dt><dt class="spec value" id="val-atom_sub"><a href="#val-atom_sub" class="anchor"></a><code><span class="keyword">val</span> atom_sub : <a href="index.html#type-subst">subst</a> <span>-></span> <a href="index.html#type-atom">atom</a> <span>-></span> <a href="index.html#type-atom">atom</a></code></dt><dt class="spec value" id="val-instr_sub"><a href="#val-instr_sub" class="anchor"></a><code><span class="keyword">val</span> instr_sub : <a href="index.html#type-subst">subst</a> <span>-></span> <a href="../IR/Sil/index.html#type-instr">IR.Sil.instr</a> <span>-></span> <a href="../IR/Sil/index.html#type-instr">IR.Sil.instr</a></code></dt><dd><p>apply <code>subst</code> to all id's in <code>instr</code>, including LHS id's</p></dd></dl><dl><dt class="spec value" id="val-hpred_sub"><a href="#val-hpred_sub" class="anchor"></a><code><span class="keyword">val</span> hpred_sub : <a href="index.html#type-subst">subst</a> <span>-></span> <a href="index.html#type-hpred">hpred</a> <span>-></span> <a href="index.html#type-hpred">hpred</a></code></dt></dl></section><section><header><h3 id="functions-for-replacing-occurrences-of-expressions."><a href="#functions-for-replacing-occurrences-of-expressions." class="anchor"></a>Functions for replacing occurrences of expressions.</h3></header><dl><dt class="spec value" id="val-exp_replace_exp"><a href="#val-exp_replace_exp" class="anchor"></a><code><span class="keyword">val</span> exp_replace_exp : <span><span>(<a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a>)</span> list</span> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a></code></dt><dt class="spec value" id="val-atom_replace_exp"><a href="#val-atom_replace_exp" class="anchor"></a><code><span class="keyword">val</span> atom_replace_exp : <span><span>(<a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a>)</span> list</span> <span>-></span> <a href="index.html#type-atom">atom</a> <span>-></span> <a href="index.html#type-atom">atom</a></code></dt><dt class="spec value" id="val-hpred_replace_exp"><a href="#val-hpred_replace_exp" class="anchor"></a><code><span class="keyword">val</span> hpred_replace_exp : <span><span>(<a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> * <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a>)</span> list</span> <span>-></span> <a href="index.html#type-hpred">hpred</a> <span>-></span> <a href="index.html#type-hpred">hpred</a></code></dt></dl></section><section><header><h3 id="functions-for-constructing-or-destructing-entities-in-this-module"><a href="#functions-for-constructing-or-destructing-entities-in-this-module" class="anchor"></a>Functions for constructing or destructing entities in this module</h3></header><dl><dt class="spec value" id="val-exp_get_offsets"><a href="#val-exp_get_offsets" class="anchor"></a><code><span class="keyword">val</span> exp_get_offsets : <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> <span>-></span> <span><a href="index.html#type-offset">offset</a> list</span></code></dt><dd><p>Compute the offset list of an expression</p></dd></dl><dl><dt class="spec value" id="val-exp_add_offsets"><a href="#val-exp_add_offsets" class="anchor"></a><code><span class="keyword">val</span> exp_add_offsets : <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> <span>-></span> <span><a href="index.html#type-offset">offset</a> list</span> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a></code></dt><dd><p>Add the offset list to an expression</p></dd></dl><dl><dt class="spec value" id="val-sigma_to_sigma_ne"><a href="#val-sigma_to_sigma_ne" class="anchor"></a><code><span class="keyword">val</span> sigma_to_sigma_ne : <span><a href="index.html#type-hpred">hpred</a> list</span> <span>-></span> <span><span>(<span><a href="index.html#type-atom">atom</a> list</span> * <span><a href="index.html#type-hpred">hpred</a> list</span>)</span> list</span></code></dt><dt class="spec value" id="val-hpara_instantiate"><a href="#val-hpara_instantiate" class="anchor"></a><code><span class="keyword">val</span> hpara_instantiate : <a href="index.html#type-hpara">hpara</a> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> <span>-></span> <span><a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> list</span> <span>-></span> <span><a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> list</span> * <span><a href="index.html#type-hpred">hpred</a> list</span></code></dt><dd><p><code>hpara_instantiate para e1 e2 elist</code> instantiates <code>para</code> with <code>e1</code>, <code>e2</code> and <code>elist</code>. If <code>para = lambda (x, y, xs). exists zs. b</code>, then the result of the instantiation is <code>b[e1 / x, e2 / y, elist / xs, _zs'/ zs]</code> for some fresh <code>_zs'</code>.</p></dd></dl><dl><dt class="spec value" id="val-hpara_dll_instantiate"><a href="#val-hpara_dll_instantiate" class="anchor"></a><code><span class="keyword">val</span> hpara_dll_instantiate : <a href="index.html#type-hpara_dll">hpara_dll</a> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> <span>-></span> <a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> <span>-></span> <span><a href="../IR/Exp/index.html#type-t">IR.Exp.t</a> list</span> <span>-></span> <span><a href="../IR/Ident/index.html#type-t">IR.Ident.t</a> list</span> * <span><a href="index.html#type-hpred">hpred</a> list</span></code></dt><dd><p><code>hpara_dll_instantiate para cell blink flink elist</code> instantiates <code>para</code> with <code>cell</code>, <code>blink</code>, <code>flink</code>, and <code>elist</code>. If <code>para = lambda (x, y, z, xs). exists zs. b</code>, then the result of the instantiation is <code>b[cell / x, blink / y, flink / z, elist / xs, _zs'/ zs]</code> for some fresh <code>_zs'</code>.</p></dd></dl><dl><dt class="spec value" id="val-custom_error"><a href="#val-custom_error" class="anchor"></a><code><span class="keyword">val</span> custom_error : <a href="../IR/Pvar/index.html#type-t">IR.Pvar.t</a></code></dt></dl></section></div></body></html>