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GCC Code Coverage Report

Directory:	.		Exec	Total	Coverage
File:	src/theory/quantifiers/skolemize.cpp	Lines:	184	206	89.3 %
Date:	2021-09-16	Branches:	417	992	42.0 %


/******************************************************************************
 * Top contributors (to current version):
 *   Andrew Reynolds, Mathias Preiner, Andres Noetzli
 *
 * This file is part of the cvc5 project.
 *
 * Copyright (c) 2009-2021 by the authors listed in the file AUTHORS
 * in the top-level source directory and their institutional affiliations.
 * All rights reserved.  See the file COPYING in the top-level source
 * directory for licensing information.
 * ****************************************************************************
 *
 * Implementation of skolemization utility.
 */

#include "theory/quantifiers/skolemize.h"

#include "expr/dtype.h"
#include "expr/dtype_cons.h"
#include "expr/skolem_manager.h"
#include "options/quantifiers_options.h"
#include "options/smt_options.h"
#include "proof/proof.h"
#include "proof/proof_node_manager.h"
#include "theory/quantifiers/quantifiers_attributes.h"
#include "theory/quantifiers/quantifiers_state.h"
#include "theory/quantifiers/term_registry.h"
#include "theory/quantifiers/term_util.h"
#include "theory/rewriter.h"
#include "theory/sort_inference.h"

using namespace cvc5::kind;

namespace cvc5 {
namespace theory {
namespace quantifiers {

Skolemize::Skolemize(Env& env,
                     QuantifiersState& qs,
                     TermRegistry& tr,
                     ProofNodeManager* pnm)
    : EnvObj(env),
      d_qstate(qs),
      d_treg(tr),
      d_skolemized(userContext()),
      d_pnm(pnm),
      d_epg(pnm == nullptr
                ? nullptr
                : new EagerProofGenerator(pnm, userContext(), "Skolemize::epg"))
{
}

TrustNode Skolemize::process(Node q)
{
  Assert(q.getKind() == FORALL);
  // do skolemization
  if (d_skolemized.find(q) != d_skolemized.end())
  {
    return TrustNode::null();
  }
  Node lem;
  ProofGenerator* pg = nullptr;
  if (isProofEnabled() && !options::dtStcInduction()
      && !options::intWfInduction())
  {
    // if using proofs and not using induction, we use the justified
    // skolemization
    NodeManager* nm = NodeManager::currentNM();
    SkolemManager* skm = nm->getSkolemManager();
    std::vector<Node> echildren(q.begin(), q.end());
    echildren[1] = echildren[1].notNode();
    Node existsq = nm->mkNode(EXISTS, echildren);
    Node res = skm->mkSkolemize(existsq, d_skolem_constants[q], "skv");
    Node qnot = q.notNode();
    CDProof cdp(d_pnm);
    cdp.addStep(res, PfRule::SKOLEMIZE, {qnot}, {});
    std::shared_ptr<ProofNode> pf = cdp.getProofFor(res);
    std::vector<Node> assumps;
    assumps.push_back(qnot);
    std::shared_ptr<ProofNode> pfs = d_pnm->mkScope({pf}, assumps);
    lem = nm->mkNode(IMPLIES, qnot, res);
    d_epg->setProofFor(lem, pfs);
    pg = d_epg.get();
    Trace("quantifiers-sk")
        << "Skolemize (with proofs) : " << d_skolem_constants[q] << " for "
        << std::endl;
    Trace("quantifiers-sk") << "   " << q << std::endl;
    Trace("quantifiers-sk") << "   " << res << std::endl;
  }
  else
  {
    // otherwise, we use the more general skolemization with inductive
    // strengthening, which does not support proofs
    Node body = getSkolemizedBody(q);
    NodeBuilder nb(kind::OR);
    nb << q << body.notNode();
    lem = nb;
  }
  d_skolemized[q] = lem;
  // triggered when skolemizing
  d_treg.processSkolemization(q, d_skolem_constants[q]);
  return TrustNode::mkTrustLemma(lem, pg);
}

bool Skolemize::getSkolemConstants(Node q, std::vector<Node>& skolems)
{
  std::unordered_map<Node, std::vector<Node>>::iterator it =
      d_skolem_constants.find(q);
  if (it != d_skolem_constants.end())
  {
    skolems.insert(skolems.end(), it->second.begin(), it->second.end());
    return true;
  }
  return false;
}

Node Skolemize::getSkolemConstant(Node q, unsigned i)
{
  std::unordered_map<Node, std::vector<Node>>::iterator it =
      d_skolem_constants.find(q);
  if (it != d_skolem_constants.end())
  {
    if (i < it->second.size())
    {
      return it->second[i];
    }
  }
  return Node::null();
}

void Skolemize::getSelfSel(const DType& dt,
                           const DTypeConstructor& dc,
                           Node n,
                           TypeNode ntn,
                           std::vector<Node>& selfSel)
{
  TypeNode tspec;
  if (dt.isParametric())
  {
    tspec = dc.getSpecializedConstructorType(n.getType());
    Trace("sk-ind-debug") << "Specialized constructor type : " << tspec
                          << std::endl;
    Assert(tspec.getNumChildren() == dc.getNumArgs());
  }
  Trace("sk-ind-debug") << "Check self sel " << dc.getName() << " "
                        << dt.getName() << std::endl;
  NodeManager* nm = NodeManager::currentNM();
  for (unsigned j = 0; j < dc.getNumArgs(); j++)
  {
    std::vector<Node> ssc;
    if (dt.isParametric())
    {
      Trace("sk-ind-debug") << "Compare " << tspec[j] << " " << ntn
                            << std::endl;
      if (tspec[j] == ntn)
      {
        ssc.push_back(n);
      }
    }
    else
    {
      TypeNode tn = dc[j].getRangeType();
      Trace("sk-ind-debug") << "Compare " << tn << " " << ntn << std::endl;
      if (tn == ntn)
      {
        ssc.push_back(n);
      }
    }
    for (unsigned k = 0; k < ssc.size(); k++)
    {
      Node ss = nm->mkNode(
          APPLY_SELECTOR_TOTAL, dc.getSelectorInternal(n.getType(), j), n);
      if (std::find(selfSel.begin(), selfSel.end(), ss) == selfSel.end())
      {
        selfSel.push_back(ss);
      }
    }
  }
}

Node Skolemize::mkSkolemizedBody(Node f,
                                 Node n,
                                 std::vector<TNode>& fvs,
                                 std::vector<Node>& sk,
                                 Node& sub,
                                 std::vector<unsigned>& sub_vars)
{
  NodeManager* nm = NodeManager::currentNM();
  // compute the argument types from the free variables
  std::vector<TypeNode> argTypes;
  for (TNode v : fvs)
  {
    argTypes.push_back(v.getType());
  }
  SkolemManager* sm = nm->getSkolemManager();
  Assert(sk.empty() || sk.size() == f[0].getNumChildren());
  // calculate the variables and substitution
  std::vector<TNode> ind_vars;
  std::vector<unsigned> ind_var_indicies;
  std::vector<TNode> vars;
  std::vector<unsigned> var_indicies;
  for (unsigned i = 0; i < f[0].getNumChildren(); i++)
  {
    if (isInductionTerm(f[0][i]))
    {
      ind_vars.push_back(f[0][i]);
      ind_var_indicies.push_back(i);
    }
    else
    {
      vars.push_back(f[0][i]);
      var_indicies.push_back(i);
    }
    Node s;
    // make the new function symbol or use existing
    if (i >= sk.size())
    {
      if (argTypes.empty())
      {
        s = sm->mkDummySkolem(
            "skv", f[0][i].getType(), "created during skolemization");
      }
      else
      {
        TypeNode typ = nm->mkFunctionType(argTypes, f[0][i].getType());
        Node op = sm->mkDummySkolem(
            "skop", typ, "op created during pre-skolemization");
        // DOTHIS: set attribute on op, marking that it should not be selected
        // as trigger
        std::vector<Node> funcArgs;
        funcArgs.push_back(op);
        funcArgs.insert(funcArgs.end(), fvs.begin(), fvs.end());
        s = nm->mkNode(kind::APPLY_UF, funcArgs);
      }
      sk.push_back(s);
    }
    else
    {
      Assert(sk[i].getType() == f[0][i].getType());
    }
  }
  Node ret;
  if (vars.empty())
  {
    ret = n;
  }
  else
  {
    std::vector<Node> var_sk;
    for (unsigned i = 0; i < var_indicies.size(); i++)
    {
      var_sk.push_back(sk[var_indicies[i]]);
    }
    Assert(vars.size() == var_sk.size());
    ret = n.substitute(vars.begin(), vars.end(), var_sk.begin(), var_sk.end());
  }
  if (!ind_vars.empty())
  {
    Trace("sk-ind") << "Ind strengthen : (not " << f << ")" << std::endl;
    Trace("sk-ind") << "Skolemized is : " << ret << std::endl;
    Node n_str_ind;
    TypeNode tn = ind_vars[0].getType();
    Node k = sk[ind_var_indicies[0]];
    Node nret = ret.substitute(ind_vars[0], k);
    // note : everything is under a negation
    // the following constructs ~( R( x, k ) => ~P( x ) )
    if (options::dtStcInduction() && tn.isDatatype())
    {
      const DType& dt = tn.getDType();
      std::vector<Node> disj;
      for (unsigned i = 0; i < dt.getNumConstructors(); i++)
      {
        std::vector<Node> selfSel;
        getSelfSel(dt, dt[i], k, tn, selfSel);
        std::vector<Node> conj;
        conj.push_back(nm->mkNode(APPLY_TESTER, dt[i].getTester(), k).negate());
        for (unsigned j = 0; j < selfSel.size(); j++)
        {
          conj.push_back(ret.substitute(ind_vars[0], selfSel[j]).negate());
        }
        disj.push_back(conj.size() == 1 ? conj[0] : nm->mkNode(OR, conj));
      }
      Assert(!disj.empty());
      n_str_ind = disj.size() == 1 ? disj[0] : nm->mkNode(AND, disj);
    }
    else if (options::intWfInduction() && tn.isInteger())
    {
      Node icond = nm->mkNode(GEQ, k, nm->mkConst(Rational(0)));
      Node iret = ret.substitute(ind_vars[0],
                                 nm->mkNode(MINUS, k, nm->mkConst(Rational(1))))
                      .negate();
      n_str_ind = nm->mkNode(OR, icond.negate(), iret);
      n_str_ind = nm->mkNode(AND, icond, n_str_ind);
    }
    else
    {
      Trace("sk-ind") << "Unknown induction for term : " << ind_vars[0]
                      << ", type = " << tn << std::endl;
      Assert(false);
    }
    Trace("sk-ind") << "Strengthening is : " << n_str_ind << std::endl;

    std::vector<Node> rem_ind_vars;
    rem_ind_vars.insert(
        rem_ind_vars.end(), ind_vars.begin() + 1, ind_vars.end());
    if (!rem_ind_vars.empty())
    {
      Node bvl = nm->mkNode(BOUND_VAR_LIST, rem_ind_vars);
      nret = nm->mkNode(FORALL, bvl, nret);
      nret = Rewriter::rewrite(nret);
      sub = nret;
      sub_vars.insert(
          sub_vars.end(), ind_var_indicies.begin() + 1, ind_var_indicies.end());
      n_str_ind = nm->mkNode(FORALL, bvl, n_str_ind.negate()).negate();
    }
    ret = nm->mkNode(OR, nret, n_str_ind);
  }
  Trace("quantifiers-sk-debug") << "mkSkolem body for " << f
                                << " returns : " << ret << std::endl;
  // if it has an instantiation level, set the skolemized body to that level
  if (f.hasAttribute(InstLevelAttribute()))
  {
    QuantAttributes::setInstantiationLevelAttr(
        ret, f.getAttribute(InstLevelAttribute()));
  }

  Trace("quantifiers-sk") << "Skolemize : " << sk << " for " << std::endl;
  Trace("quantifiers-sk") << "   " << f << std::endl;

  return ret;
}

Node Skolemize::getSkolemizedBody(Node f)
{
  Assert(f.getKind() == FORALL);
  std::unordered_map<Node, Node>::iterator it = d_skolem_body.find(f);
  if (it == d_skolem_body.end())
  {
    std::vector<TNode> fvs;
    Node sub;
    std::vector<unsigned> sub_vars;
    Node ret =
        mkSkolemizedBody(f, f[1], fvs, d_skolem_constants[f], sub, sub_vars);
    d_skolem_body[f] = ret;
    // store sub quantifier information
    if (!sub.isNull())
    {
      // if we are skolemizing one at a time, we already know the skolem
      // constants of the sub-quantified formula, store them
      Assert(d_skolem_constants[sub].empty());
      for (unsigned i = 0; i < sub_vars.size(); i++)
      {
        d_skolem_constants[sub].push_back(d_skolem_constants[f][sub_vars[i]]);
      }
    }
    Assert(d_skolem_constants[f].size() == f[0].getNumChildren());
    SortInference* si = d_qstate.getSortInference();
    if (si != nullptr)
    {
      for (unsigned i = 0; i < d_skolem_constants[f].size(); i++)
      {
        // carry information for sort inference
        si->setSkolemVar(f, f[0][i], d_skolem_constants[f][i]);
      }
    }
    return ret;
  }
  return it->second;
}

bool Skolemize::isInductionTerm(Node n)
{
  TypeNode tn = n.getType();
  if (options::dtStcInduction() && tn.isDatatype())
  {
    const DType& dt = tn.getDType();
    return !dt.isCodatatype();
  }
  if (options::intWfInduction() && tn.isInteger())
  {
    return true;
  }
  return false;
}

void Skolemize::getSkolemTermVectors(
    std::map<Node, std::vector<Node> >& sks) const
{
  std::unordered_map<Node, std::vector<Node>>::const_iterator itk;
  for (const auto& p : d_skolemized)
  {
    Node q = p.first;
    itk = d_skolem_constants.find(q);
    Assert(itk != d_skolem_constants.end());
    sks[q].insert(sks[q].end(), itk->second.begin(), itk->second.end());
  }
}

bool Skolemize::isProofEnabled() const { return d_epg != nullptr; }

}  // namespace quantifiers
}  // namespace theory
}  // namespace cvc5


Generated by: GCOVR (Version 3.2)

Line	Exec	Source
1		/******************************************************************************
2		* Top contributors (to current version):
3		* Andrew Reynolds, Mathias Preiner, Andres Noetzli
4		*
5		* This file is part of the cvc5 project.
6		*
7		* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS
8		* in the top-level source directory and their institutional affiliations.
9		* All rights reserved. See the file COPYING in the top-level source
10		* directory for licensing information.
11		* ****************************************************************************
12		*
13		* Implementation of skolemization utility.
14		*/
15
16		#include "theory/quantifiers/skolemize.h"
17
18		#include "expr/dtype.h"
19		#include "expr/dtype_cons.h"
20		#include "expr/skolem_manager.h"
21		#include "options/quantifiers_options.h"
22		#include "options/smt_options.h"
23		#include "proof/proof.h"
24		#include "proof/proof_node_manager.h"
25		#include "theory/quantifiers/quantifiers_attributes.h"
26		#include "theory/quantifiers/quantifiers_state.h"
27		#include "theory/quantifiers/term_registry.h"
28		#include "theory/quantifiers/term_util.h"
29		#include "theory/rewriter.h"
30		#include "theory/sort_inference.h"
31
32		using namespace cvc5::kind;
33
34		namespace cvc5 {
35		namespace theory {
36		namespace quantifiers {
37
38	9942	Skolemize::Skolemize(Env& env,
39		QuantifiersState& qs,
40		TermRegistry& tr,
41	9942	ProofNodeManager* pnm)
42		: EnvObj(env),
43		d_qstate(qs),
44		d_treg(tr),
45	9942	d_skolemized(userContext()),
46		d_pnm(pnm),
47		d_epg(pnm == nullptr
48		? nullptr
49	19884	: new EagerProofGenerator(pnm, userContext(), "Skolemize::epg"))
50		{
51	9942	}
52
53	10686	TrustNode Skolemize::process(Node q)
54		{
55	10686	Assert(q.getKind() == FORALL);
56		// do skolemization
57	10686	if (d_skolemized.find(q) != d_skolemized.end())
58		{
59	8288	return TrustNode::null();
60		}
61	4796	Node lem;
62	2398	ProofGenerator* pg = nullptr;
63	5134	if (isProofEnabled() && !options::dtStcInduction()
64	2722	&& !options::intWfInduction())
65		{
66		// if using proofs and not using induction, we use the justified
67		// skolemization
68	323	NodeManager* nm = NodeManager::currentNM();
69	323	SkolemManager* skm = nm->getSkolemManager();
70	646	std::vector<Node> echildren(q.begin(), q.end());
71	323	echildren[1] = echildren[1].notNode();
72	646	Node existsq = nm->mkNode(EXISTS, echildren);
73	646	Node res = skm->mkSkolemize(existsq, d_skolem_constants[q], "skv");
74	646	Node qnot = q.notNode();
75	646	CDProof cdp(d_pnm);
76	323	cdp.addStep(res, PfRule::SKOLEMIZE, {qnot}, {});
77	646	std::shared_ptr<ProofNode> pf = cdp.getProofFor(res);
78	646	std::vector<Node> assumps;
79	323	assumps.push_back(qnot);
80	646	std::shared_ptr<ProofNode> pfs = d_pnm->mkScope({pf}, assumps);
81	323	lem = nm->mkNode(IMPLIES, qnot, res);
82	323	d_epg->setProofFor(lem, pfs);
83	323	pg = d_epg.get();
84	646	Trace("quantifiers-sk")
85	323	<< "Skolemize (with proofs) : " << d_skolem_constants[q] << " for "
86	323	<< std::endl;
87	323	Trace("quantifiers-sk") << " " << q << std::endl;
88	323	Trace("quantifiers-sk") << " " << res << std::endl;
89		}
90		else
91		{
92		// otherwise, we use the more general skolemization with inductive
93		// strengthening, which does not support proofs
94	4150	Node body = getSkolemizedBody(q);
95	4150	NodeBuilder nb(kind::OR);
96	2075	nb << q << body.notNode();
97	2075	lem = nb;
98		}
99	2398	d_skolemized[q] = lem;
100		// triggered when skolemizing
101	2398	d_treg.processSkolemization(q, d_skolem_constants[q]);
102	2398	return TrustNode::mkTrustLemma(lem, pg);
103		}
104
105	33	bool Skolemize::getSkolemConstants(Node q, std::vector<Node>& skolems)
106		{
107		std::unordered_map<Node, std::vector<Node>>::iterator it =
108	33	d_skolem_constants.find(q);
109	33	if (it != d_skolem_constants.end())
110		{
111	33	skolems.insert(skolems.end(), it->second.begin(), it->second.end());
112	33	return true;
113		}
114		return false;
115		}
116
117		Node Skolemize::getSkolemConstant(Node q, unsigned i)
118		{
119		std::unordered_map<Node, std::vector<Node>>::iterator it =
120		d_skolem_constants.find(q);
121		if (it != d_skolem_constants.end())
122		{
123		if (i < it->second.size())
124		{
125		return it->second[i];
126		}
127		}
128		return Node::null();
129		}
130
131	114	void Skolemize::getSelfSel(const DType& dt,
132		const DTypeConstructor& dc,
133		Node n,
134		TypeNode ntn,
135		std::vector<Node>& selfSel)
136		{
137	228	TypeNode tspec;
138	114	if (dt.isParametric())
139		{
140		tspec = dc.getSpecializedConstructorType(n.getType());
141		Trace("sk-ind-debug") << "Specialized constructor type : " << tspec
142		<< std::endl;
143		Assert(tspec.getNumChildren() == dc.getNumArgs());
144		}
145	228	Trace("sk-ind-debug") << "Check self sel " << dc.getName() << " "
146	114	<< dt.getName() << std::endl;
147	114	NodeManager* nm = NodeManager::currentNM();
148	219	for (unsigned j = 0; j < dc.getNumArgs(); j++)
149		{
150	210	std::vector<Node> ssc;
151	105	if (dt.isParametric())
152		{
153		Trace("sk-ind-debug") << "Compare " << tspec[j] << " " << ntn
154		<< std::endl;
155		if (tspec[j] == ntn)
156		{
157		ssc.push_back(n);
158		}
159		}
160		else
161		{
162	210	TypeNode tn = dc[j].getRangeType();
163	105	Trace("sk-ind-debug") << "Compare " << tn << " " << ntn << std::endl;
164	105	if (tn == ntn)
165		{
166	57	ssc.push_back(n);
167		}
168		}
169	162	for (unsigned k = 0; k < ssc.size(); k++)
170		{
171		Node ss = nm->mkNode(
172	114	APPLY_SELECTOR_TOTAL, dc.getSelectorInternal(n.getType(), j), n);
173	57	if (std::find(selfSel.begin(), selfSel.end(), ss) == selfSel.end())
174		{
175	57	selfSel.push_back(ss);
176		}
177		}
178		}
179	114	}
180
181	2084	Node Skolemize::mkSkolemizedBody(Node f,
182		Node n,
183		std::vector<TNode>& fvs,
184		std::vector<Node>& sk,
185		Node& sub,
186		std::vector<unsigned>& sub_vars)
187		{
188	2084	NodeManager* nm = NodeManager::currentNM();
189		// compute the argument types from the free variables
190	4168	std::vector<TypeNode> argTypes;
191	2096	for (TNode v : fvs)
192		{
193	12	argTypes.push_back(v.getType());
194		}
195	2084	SkolemManager* sm = nm->getSkolemManager();
196	2084	Assert(sk.empty() \|\| sk.size() == f[0].getNumChildren());
197		// calculate the variables and substitution
198	4168	std::vector<TNode> ind_vars;
199	4168	std::vector<unsigned> ind_var_indicies;
200	4168	std::vector<TNode> vars;
201	4168	std::vector<unsigned> var_indicies;
202	5356	for (unsigned i = 0; i < f[0].getNumChildren(); i++)
203		{
204	3272	if (isInductionTerm(f[0][i]))
205		{
206	86	ind_vars.push_back(f[0][i]);
207	86	ind_var_indicies.push_back(i);
208		}
209		else
210		{
211	3186	vars.push_back(f[0][i]);
212	3186	var_indicies.push_back(i);
213		}
214	6544	Node s;
215		// make the new function symbol or use existing
216	3272	if (i >= sk.size())
217		{
218	3249	if (argTypes.empty())
219		{
220	9723	s = sm->mkDummySkolem(
221	6482	"skv", f[0][i].getType(), "created during skolemization");
222		}
223		else
224		{
225	16	TypeNode typ = nm->mkFunctionType(argTypes, f[0][i].getType());
226		Node op = sm->mkDummySkolem(
227	16	"skop", typ, "op created during pre-skolemization");
228		// DOTHIS: set attribute on op, marking that it should not be selected
229		// as trigger
230	16	std::vector<Node> funcArgs;
231	8	funcArgs.push_back(op);
232	8	funcArgs.insert(funcArgs.end(), fvs.begin(), fvs.end());
233	8	s = nm->mkNode(kind::APPLY_UF, funcArgs);
234		}
235	3249	sk.push_back(s);
236		}
237		else
238		{
239	23	Assert(sk[i].getType() == f[0][i].getType());
240		}
241		}
242	2084	Node ret;
243	2084	if (vars.empty())
244		{
245	63	ret = n;
246		}
247		else
248		{
249	4042	std::vector<Node> var_sk;
250	5207	for (unsigned i = 0; i < var_indicies.size(); i++)
251		{
252	3186	var_sk.push_back(sk[var_indicies[i]]);
253		}
254	2021	Assert(vars.size() == var_sk.size());
255	2021	ret = n.substitute(vars.begin(), vars.end(), var_sk.begin(), var_sk.end());
256		}
257	2084	if (!ind_vars.empty())
258		{
259	63	Trace("sk-ind") << "Ind strengthen : (not " << f << ")" << std::endl;
260	63	Trace("sk-ind") << "Skolemized is : " << ret << std::endl;
261	126	Node n_str_ind;
262	126	TypeNode tn = ind_vars[0].getType();
263	126	Node k = sk[ind_var_indicies[0]];
264	126	Node nret = ret.substitute(ind_vars[0], k);
265		// note : everything is under a negation
266		// the following constructs ~( R( x, k ) => ~P( x ) )
267	63	if (options::dtStcInduction() && tn.isDatatype())
268		{
269	57	const DType& dt = tn.getDType();
270	114	std::vector<Node> disj;
271	171	for (unsigned i = 0; i < dt.getNumConstructors(); i++)
272		{
273	228	std::vector<Node> selfSel;
274	114	getSelfSel(dt, dt[i], k, tn, selfSel);
275	228	std::vector<Node> conj;
276	114	conj.push_back(nm->mkNode(APPLY_TESTER, dt[i].getTester(), k).negate());
277	171	for (unsigned j = 0; j < selfSel.size(); j++)
278		{
279	57	conj.push_back(ret.substitute(ind_vars[0], selfSel[j]).negate());
280		}
281	114	disj.push_back(conj.size() == 1 ? conj[0] : nm->mkNode(OR, conj));
282		}
283	57	Assert(!disj.empty());
284	57	n_str_ind = disj.size() == 1 ? disj[0] : nm->mkNode(AND, disj);
285		}
286	6	else if (options::intWfInduction() && tn.isInteger())
287		{
288	12	Node icond = nm->mkNode(GEQ, k, nm->mkConst(Rational(0)));
289	12	Node iret = ret.substitute(ind_vars[0],
290	12	nm->mkNode(MINUS, k, nm->mkConst(Rational(1))))
291	12	.negate();
292	6	n_str_ind = nm->mkNode(OR, icond.negate(), iret);
293	6	n_str_ind = nm->mkNode(AND, icond, n_str_ind);
294		}
295		else
296		{
297		Trace("sk-ind") << "Unknown induction for term : " << ind_vars[0]
298		<< ", type = " << tn << std::endl;
299		Assert(false);
300		}
301	63	Trace("sk-ind") << "Strengthening is : " << n_str_ind << std::endl;
302
303	126	std::vector<Node> rem_ind_vars;
304	63	rem_ind_vars.insert(
305	126	rem_ind_vars.end(), ind_vars.begin() + 1, ind_vars.end());
306	63	if (!rem_ind_vars.empty())
307		{
308	38	Node bvl = nm->mkNode(BOUND_VAR_LIST, rem_ind_vars);
309	19	nret = nm->mkNode(FORALL, bvl, nret);
310	19	nret = Rewriter::rewrite(nret);
311	19	sub = nret;
312	19	sub_vars.insert(
313	38	sub_vars.end(), ind_var_indicies.begin() + 1, ind_var_indicies.end());
314	19	n_str_ind = nm->mkNode(FORALL, bvl, n_str_ind.negate()).negate();
315		}
316	63	ret = nm->mkNode(OR, nret, n_str_ind);
317		}
318	4168	Trace("quantifiers-sk-debug") << "mkSkolem body for " << f
319	2084	<< " returns : " << ret << std::endl;
320		// if it has an instantiation level, set the skolemized body to that level
321	2084	if (f.hasAttribute(InstLevelAttribute()))
322		{
323		QuantAttributes::setInstantiationLevelAttr(
324		ret, f.getAttribute(InstLevelAttribute()));
325		}
326
327	2084	Trace("quantifiers-sk") << "Skolemize : " << sk << " for " << std::endl;
328	2084	Trace("quantifiers-sk") << " " << f << std::endl;
329
330	4168	return ret;
331		}
332
333	2075	Node Skolemize::getSkolemizedBody(Node f)
334		{
335	2075	Assert(f.getKind() == FORALL);
336	2075	std::unordered_map<Node, Node>::iterator it = d_skolem_body.find(f);
337	2075	if (it == d_skolem_body.end())
338		{
339	4132	std::vector<TNode> fvs;
340	4132	Node sub;
341	4132	std::vector<unsigned> sub_vars;
342		Node ret =
343	4132	mkSkolemizedBody(f, f[1], fvs, d_skolem_constants[f], sub, sub_vars);
344	2066	d_skolem_body[f] = ret;
345		// store sub quantifier information
346	2066	if (!sub.isNull())
347		{
348		// if we are skolemizing one at a time, we already know the skolem
349		// constants of the sub-quantified formula, store them
350	19	Assert(d_skolem_constants[sub].empty());
351	42	for (unsigned i = 0; i < sub_vars.size(); i++)
352		{
353	23	d_skolem_constants[sub].push_back(d_skolem_constants[f][sub_vars[i]]);
354		}
355		}
356	2066	Assert(d_skolem_constants[f].size() == f[0].getNumChildren());
357	2066	SortInference* si = d_qstate.getSortInference();
358	2066	if (si != nullptr)
359		{
360		for (unsigned i = 0; i < d_skolem_constants[f].size(); i++)
361		{
362		// carry information for sort inference
363		si->setSkolemVar(f, f[0][i], d_skolem_constants[f][i]);
364		}
365		}
366	2066	return ret;
367		}
368	9	return it->second;
369		}
370
371	9188	bool Skolemize::isInductionTerm(Node n)
372		{
373	18376	TypeNode tn = n.getType();
374	9188	if (options::dtStcInduction() && tn.isDatatype())
375		{
376	3909	const DType& dt = tn.getDType();
377	3909	return !dt.isCodatatype();
378		}
379	5279	if (options::intWfInduction() && tn.isInteger())
380		{
381	1324	return true;
382		}
383	3955	return false;
384		}
385
386	12	void Skolemize::getSkolemTermVectors(
387		std::map<Node, std::vector<Node> >& sks) const
388		{
389	12	std::unordered_map<Node, std::vector<Node>>::const_iterator itk;
390	21	for (const auto& p : d_skolemized)
391		{
392	18	Node q = p.first;
393	9	itk = d_skolem_constants.find(q);
394	9	Assert(itk != d_skolem_constants.end());
395	9	sks[q].insert(sks[q].end(), itk->second.begin(), itk->second.end());
396		}
397	12	}
398
399	2398	bool Skolemize::isProofEnabled() const { return d_epg != nullptr; }
400
401		} // namespace quantifiers
402		} // namespace theory
403	29577	} // namespace cvc5