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GCC Code Coverage Report

Directory:	.		Exec	Total	Coverage
File:	src/theory/quantifiers/skolemize.cpp	Lines:	182	204	89.2 %
Date:	2021-08-19	Branches:	410	980	41.8 %


/******************************************************************************
 * 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(QuantifiersState& qs,
                     TermRegistry& tr,
                     ProofNodeManager* pnm)
    : d_qstate(qs),
      d_treg(tr),
      d_skolemized(qs.getUserContext()),
      d_pnm(pnm),
      d_epg(pnm == nullptr ? nullptr
                           : new EagerProofGenerator(
                                 pnm, qs.getUserContext(), "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<TypeNode>& argTypes,
                                 std::vector<TNode>& fvs,
                                 std::vector<Node>& sk,
                                 Node& sub,
                                 std::vector<unsigned>& sub_vars)
{
  NodeManager* nm = NodeManager::currentNM();
  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<TypeNode> fvTypes;
    std::vector<TNode> fvs;
    Node sub;
    std::vector<unsigned> sub_vars;
    Node ret = mkSkolemizedBody(
        f, f[1], fvTypes, 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	9854	Skolemize::Skolemize(QuantifiersState& qs,
39		TermRegistry& tr,
40	9854	ProofNodeManager* pnm)
41		: d_qstate(qs),
42		d_treg(tr),
43	9854	d_skolemized(qs.getUserContext()),
44		d_pnm(pnm),
45		d_epg(pnm == nullptr ? nullptr
46		: new EagerProofGenerator(
47	19708	pnm, qs.getUserContext(), "Skolemize::epg"))
48		{
49	9854	}
50
51	10604	TrustNode Skolemize::process(Node q)
52		{
53	10604	Assert(q.getKind() == FORALL);
54		// do skolemization
55	10604	if (d_skolemized.find(q) != d_skolemized.end())
56		{
57	8211	return TrustNode::null();
58		}
59	4786	Node lem;
60	2393	ProofGenerator* pg = nullptr;
61	5121	if (isProofEnabled() && !options::dtStcInduction()
62	2714	&& !options::intWfInduction())
63		{
64		// if using proofs and not using induction, we use the justified
65		// skolemization
66	320	NodeManager* nm = NodeManager::currentNM();
67	320	SkolemManager* skm = nm->getSkolemManager();
68	640	std::vector<Node> echildren(q.begin(), q.end());
69	320	echildren[1] = echildren[1].notNode();
70	640	Node existsq = nm->mkNode(EXISTS, echildren);
71	640	Node res = skm->mkSkolemize(existsq, d_skolem_constants[q], "skv");
72	640	Node qnot = q.notNode();
73	640	CDProof cdp(d_pnm);
74	320	cdp.addStep(res, PfRule::SKOLEMIZE, {qnot}, {});
75	640	std::shared_ptr<ProofNode> pf = cdp.getProofFor(res);
76	640	std::vector<Node> assumps;
77	320	assumps.push_back(qnot);
78	640	std::shared_ptr<ProofNode> pfs = d_pnm->mkScope({pf}, assumps);
79	320	lem = nm->mkNode(IMPLIES, qnot, res);
80	320	d_epg->setProofFor(lem, pfs);
81	320	pg = d_epg.get();
82	640	Trace("quantifiers-sk")
83	320	<< "Skolemize (with proofs) : " << d_skolem_constants[q] << " for "
84	320	<< std::endl;
85	320	Trace("quantifiers-sk") << " " << q << std::endl;
86	320	Trace("quantifiers-sk") << " " << res << std::endl;
87		}
88		else
89		{
90		// otherwise, we use the more general skolemization with inductive
91		// strengthening, which does not support proofs
92	4146	Node body = getSkolemizedBody(q);
93	4146	NodeBuilder nb(kind::OR);
94	2073	nb << q << body.notNode();
95	2073	lem = nb;
96		}
97	2393	d_skolemized[q] = lem;
98		// triggered when skolemizing
99	2393	d_treg.processSkolemization(q, d_skolem_constants[q]);
100	2393	return TrustNode::mkTrustLemma(lem, pg);
101		}
102
103	33	bool Skolemize::getSkolemConstants(Node q, std::vector<Node>& skolems)
104		{
105		std::unordered_map<Node, std::vector<Node>>::iterator it =
106	33	d_skolem_constants.find(q);
107	33	if (it != d_skolem_constants.end())
108		{
109	33	skolems.insert(skolems.end(), it->second.begin(), it->second.end());
110	33	return true;
111		}
112		return false;
113		}
114
115		Node Skolemize::getSkolemConstant(Node q, unsigned i)
116		{
117		std::unordered_map<Node, std::vector<Node>>::iterator it =
118		d_skolem_constants.find(q);
119		if (it != d_skolem_constants.end())
120		{
121		if (i < it->second.size())
122		{
123		return it->second[i];
124		}
125		}
126		return Node::null();
127		}
128
129	114	void Skolemize::getSelfSel(const DType& dt,
130		const DTypeConstructor& dc,
131		Node n,
132		TypeNode ntn,
133		std::vector<Node>& selfSel)
134		{
135	228	TypeNode tspec;
136	114	if (dt.isParametric())
137		{
138		tspec = dc.getSpecializedConstructorType(n.getType());
139		Trace("sk-ind-debug") << "Specialized constructor type : " << tspec
140		<< std::endl;
141		Assert(tspec.getNumChildren() == dc.getNumArgs());
142		}
143	228	Trace("sk-ind-debug") << "Check self sel " << dc.getName() << " "
144	114	<< dt.getName() << std::endl;
145	114	NodeManager* nm = NodeManager::currentNM();
146	219	for (unsigned j = 0; j < dc.getNumArgs(); j++)
147		{
148	210	std::vector<Node> ssc;
149	105	if (dt.isParametric())
150		{
151		Trace("sk-ind-debug") << "Compare " << tspec[j] << " " << ntn
152		<< std::endl;
153		if (tspec[j] == ntn)
154		{
155		ssc.push_back(n);
156		}
157		}
158		else
159		{
160	210	TypeNode tn = dc[j].getRangeType();
161	105	Trace("sk-ind-debug") << "Compare " << tn << " " << ntn << std::endl;
162	105	if (tn == ntn)
163		{
164	57	ssc.push_back(n);
165		}
166		}
167	162	for (unsigned k = 0; k < ssc.size(); k++)
168		{
169		Node ss = nm->mkNode(
170	114	APPLY_SELECTOR_TOTAL, dc.getSelectorInternal(n.getType(), j), n);
171	57	if (std::find(selfSel.begin(), selfSel.end(), ss) == selfSel.end())
172		{
173	57	selfSel.push_back(ss);
174		}
175		}
176		}
177	114	}
178
179	2088	Node Skolemize::mkSkolemizedBody(Node f,
180		Node n,
181		std::vector<TypeNode>& argTypes,
182		std::vector<TNode>& fvs,
183		std::vector<Node>& sk,
184		Node& sub,
185		std::vector<unsigned>& sub_vars)
186		{
187	2088	NodeManager* nm = NodeManager::currentNM();
188	2088	SkolemManager* sm = nm->getSkolemManager();
189	2088	Assert(sk.empty() \|\| sk.size() == f[0].getNumChildren());
190		// calculate the variables and substitution
191	4176	std::vector<TNode> ind_vars;
192	4176	std::vector<unsigned> ind_var_indicies;
193	4176	std::vector<TNode> vars;
194	4176	std::vector<unsigned> var_indicies;
195	5369	for (unsigned i = 0; i < f[0].getNumChildren(); i++)
196		{
197	3281	if (isInductionTerm(f[0][i]))
198		{
199	86	ind_vars.push_back(f[0][i]);
200	86	ind_var_indicies.push_back(i);
201		}
202		else
203		{
204	3195	vars.push_back(f[0][i]);
205	3195	var_indicies.push_back(i);
206		}
207	6562	Node s;
208		// make the new function symbol or use existing
209	3281	if (i >= sk.size())
210		{
211	3258	if (argTypes.empty())
212		{
213	9726	s = sm->mkDummySkolem(
214	6484	"skv", f[0][i].getType(), "created during skolemization");
215		}
216		else
217		{
218	32	TypeNode typ = nm->mkFunctionType(argTypes, f[0][i].getType());
219		Node op = sm->mkDummySkolem(
220	32	"skop", typ, "op created during pre-skolemization");
221		// DOTHIS: set attribute on op, marking that it should not be selected
222		// as trigger
223	32	std::vector<Node> funcArgs;
224	16	funcArgs.push_back(op);
225	16	funcArgs.insert(funcArgs.end(), fvs.begin(), fvs.end());
226	16	s = nm->mkNode(kind::APPLY_UF, funcArgs);
227		}
228	3258	sk.push_back(s);
229		}
230		else
231		{
232	23	Assert(sk[i].getType() == f[0][i].getType());
233		}
234		}
235	2088	Node ret;
236	2088	if (vars.empty())
237		{
238	63	ret = n;
239		}
240		else
241		{
242	4050	std::vector<Node> var_sk;
243	5220	for (unsigned i = 0; i < var_indicies.size(); i++)
244		{
245	3195	var_sk.push_back(sk[var_indicies[i]]);
246		}
247	2025	Assert(vars.size() == var_sk.size());
248	2025	ret = n.substitute(vars.begin(), vars.end(), var_sk.begin(), var_sk.end());
249		}
250	2088	if (!ind_vars.empty())
251		{
252	63	Trace("sk-ind") << "Ind strengthen : (not " << f << ")" << std::endl;
253	63	Trace("sk-ind") << "Skolemized is : " << ret << std::endl;
254	126	Node n_str_ind;
255	126	TypeNode tn = ind_vars[0].getType();
256	126	Node k = sk[ind_var_indicies[0]];
257	126	Node nret = ret.substitute(ind_vars[0], k);
258		// note : everything is under a negation
259		// the following constructs ~( R( x, k ) => ~P( x ) )
260	63	if (options::dtStcInduction() && tn.isDatatype())
261		{
262	57	const DType& dt = tn.getDType();
263	114	std::vector<Node> disj;
264	171	for (unsigned i = 0; i < dt.getNumConstructors(); i++)
265		{
266	228	std::vector<Node> selfSel;
267	114	getSelfSel(dt, dt[i], k, tn, selfSel);
268	228	std::vector<Node> conj;
269	114	conj.push_back(nm->mkNode(APPLY_TESTER, dt[i].getTester(), k).negate());
270	171	for (unsigned j = 0; j < selfSel.size(); j++)
271		{
272	57	conj.push_back(ret.substitute(ind_vars[0], selfSel[j]).negate());
273		}
274	114	disj.push_back(conj.size() == 1 ? conj[0] : nm->mkNode(OR, conj));
275		}
276	57	Assert(!disj.empty());
277	57	n_str_ind = disj.size() == 1 ? disj[0] : nm->mkNode(AND, disj);
278		}
279	6	else if (options::intWfInduction() && tn.isInteger())
280		{
281	12	Node icond = nm->mkNode(GEQ, k, nm->mkConst(Rational(0)));
282	12	Node iret = ret.substitute(ind_vars[0],
283	12	nm->mkNode(MINUS, k, nm->mkConst(Rational(1))))
284	12	.negate();
285	6	n_str_ind = nm->mkNode(OR, icond.negate(), iret);
286	6	n_str_ind = nm->mkNode(AND, icond, n_str_ind);
287		}
288		else
289		{
290		Trace("sk-ind") << "Unknown induction for term : " << ind_vars[0]
291		<< ", type = " << tn << std::endl;
292		Assert(false);
293		}
294	63	Trace("sk-ind") << "Strengthening is : " << n_str_ind << std::endl;
295
296	126	std::vector<Node> rem_ind_vars;
297	63	rem_ind_vars.insert(
298	126	rem_ind_vars.end(), ind_vars.begin() + 1, ind_vars.end());
299	63	if (!rem_ind_vars.empty())
300		{
301	38	Node bvl = nm->mkNode(BOUND_VAR_LIST, rem_ind_vars);
302	19	nret = nm->mkNode(FORALL, bvl, nret);
303	19	nret = Rewriter::rewrite(nret);
304	19	sub = nret;
305	19	sub_vars.insert(
306	38	sub_vars.end(), ind_var_indicies.begin() + 1, ind_var_indicies.end());
307	19	n_str_ind = nm->mkNode(FORALL, bvl, n_str_ind.negate()).negate();
308		}
309	63	ret = nm->mkNode(OR, nret, n_str_ind);
310		}
311	4176	Trace("quantifiers-sk-debug") << "mkSkolem body for " << f
312	2088	<< " returns : " << ret << std::endl;
313		// if it has an instantiation level, set the skolemized body to that level
314	2088	if (f.hasAttribute(InstLevelAttribute()))
315		{
316		QuantAttributes::setInstantiationLevelAttr(
317		ret, f.getAttribute(InstLevelAttribute()));
318		}
319
320	2088	Trace("quantifiers-sk") << "Skolemize : " << sk << " for " << std::endl;
321	2088	Trace("quantifiers-sk") << " " << f << std::endl;
322
323	4176	return ret;
324		}
325
326	2073	Node Skolemize::getSkolemizedBody(Node f)
327		{
328	2073	Assert(f.getKind() == FORALL);
329	2073	std::unordered_map<Node, Node>::iterator it = d_skolem_body.find(f);
330	2073	if (it == d_skolem_body.end())
331		{
332	4128	std::vector<TypeNode> fvTypes;
333	4128	std::vector<TNode> fvs;
334	4128	Node sub;
335	4128	std::vector<unsigned> sub_vars;
336		Node ret = mkSkolemizedBody(
337	4128	f, f[1], fvTypes, fvs, d_skolem_constants[f], sub, sub_vars);
338	2064	d_skolem_body[f] = ret;
339		// store sub quantifier information
340	2064	if (!sub.isNull())
341		{
342		// if we are skolemizing one at a time, we already know the skolem
343		// constants of the sub-quantified formula, store them
344	19	Assert(d_skolem_constants[sub].empty());
345	42	for (unsigned i = 0; i < sub_vars.size(); i++)
346		{
347	23	d_skolem_constants[sub].push_back(d_skolem_constants[f][sub_vars[i]]);
348		}
349		}
350	2064	Assert(d_skolem_constants[f].size() == f[0].getNumChildren());
351	2064	SortInference* si = d_qstate.getSortInference();
352	2064	if (si != nullptr)
353		{
354		for (unsigned i = 0; i < d_skolem_constants[f].size(); i++)
355		{
356		// carry information for sort inference
357		si->setSkolemVar(f, f[0][i], d_skolem_constants[f][i]);
358		}
359		}
360	2064	return ret;
361		}
362	9	return it->second;
363		}
364
365	8969	bool Skolemize::isInductionTerm(Node n)
366		{
367	17938	TypeNode tn = n.getType();
368	8969	if (options::dtStcInduction() && tn.isDatatype())
369		{
370	3909	const DType& dt = tn.getDType();
371	3909	return !dt.isCodatatype();
372		}
373	5060	if (options::intWfInduction() && tn.isInteger())
374		{
375	1088	return true;
376		}
377	3972	return false;
378		}
379
380	12	void Skolemize::getSkolemTermVectors(
381		std::map<Node, std::vector<Node> >& sks) const
382		{
383	12	std::unordered_map<Node, std::vector<Node>>::const_iterator itk;
384	21	for (const auto& p : d_skolemized)
385		{
386	18	Node q = p.first;
387	9	itk = d_skolem_constants.find(q);
388	9	Assert(itk != d_skolem_constants.end());
389	9	sks[q].insert(sks[q].end(), itk->second.begin(), itk->second.end());
390		}
391	12	}
392
393	2393	bool Skolemize::isProofEnabled() const { return d_epg != nullptr; }
394
395		} // namespace quantifiers
396		} // namespace theory
397	29349	} // namespace cvc5