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+/* Derivation and subsumption rules for constraints.
+ Copyright (C) 2013-2015 Free Software Foundation, Inc.
+ Contributed by Andrew Sutton (andrew.n.sutton@gmail.com)
+
+This file is part of GCC.
+
+GCC is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3, or (at your option)
+any later version.
+
+GCC is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with GCC; see the file COPYING3. If not see
+<http://www.gnu.org/licenses/>. */
+
+#include "config.h"
+#include "system.h"
+#include "coretypes.h"
+#include "tm.h"
+#include "hash-set.h"
+#include "machmode.h"
+#include "vec.h"
+#include "double-int.h"
+#include "input.h"
+#include "alias.h"
+#include "symtab.h"
+#include "wide-int.h"
+#include "inchash.h"
+#include "tree.h"
+#include "stringpool.h"
+#include "attribs.h"
+#include "intl.h"
+#include "flags.h"
+#include "cp-tree.h"
+#include "c-family/c-common.h"
+#include "c-family/c-objc.h"
+#include "cp-objcp-common.h"
+#include "tree-inline.h"
+#include "decl.h"
+#include "toplev.h"
+#include "type-utils.h"
+
+#include <list>
+
+namespace {
+
+// Helper algorithms
+
+// Increment iter distance(first, last) times.
+template<typename I1, typename I2, typename I3>
+ I1 next_by_distance (I1 iter, I2 first, I3 last)
+ {
+ for ( ; first != last; ++first, ++iter)
+ ;
+ return iter;
+ }
+
+/*---------------------------------------------------------------------------
+ Proof state
+---------------------------------------------------------------------------*/
+
+/* A term list is a list of atomic constraints. It is used
+ to maintain the lists of assumptions and conclusions in a
+ proof goal.
+
+ Each term list maintains an iterator that refers to the current
+ term. This can be used by various tactics to support iteration
+ and stateful manipulation of the list. */
+struct term_list : std::list<tree>
+{
+ term_list ();
+ term_list (const term_list &x);
+ term_list& operator= (const term_list &x);
+
+ tree current_term () { return *current; }
+ const_tree current_term () const { return *current; }
+
+
+ void insert (tree t);
+ tree erase ();
+
+ void start ();
+ void next ();
+ bool done() const;
+
+ iterator current;
+};
+
+inline
+term_list::term_list ()
+ : std::list<tree> (), current (end ())
+{ }
+
+inline
+term_list::term_list (const term_list &x)
+ : std::list<tree> (x)
+ , current (next_by_distance (begin (), x.begin (), x.current))
+{ }
+
+inline term_list&
+term_list::operator= (const term_list &x)
+{
+ std::list<tree>::operator=(x);
+ current = next_by_distance (begin (), x.begin (), x.current);
+ return *this;
+}
+
+/* Try saving the term T into the list of terms. If
+ T is already in the list of terms, then no action is
+ performed. Otherwise, insert T before the current
+ position, making this term current.
+
+ Note that not inserting terms is an optimization
+ that corresponds to the structural rule of
+ contraction.
+
+ NOTE: With the contraction rule, this data structure
+ would be more efficiently represented as an ordered set
+ or hash set. */
+void
+term_list::insert (tree t)
+{
+ /* Search the current term list. If there is already
+ a matching term, do not add the new one. */
+ for (iterator i = begin(); i != end(); ++i)
+ if (cp_tree_equal (*i, t))
+ return;
+
+ current = std::list<tree>::insert (current, t);
+}
+
+/* Remove the current term from the list, repositioning to
+ the term following the removed term. Note that the new
+ position could be past the end of the list.
+
+ The removed term is returned. */
+inline tree
+term_list::erase ()
+{
+ tree t = *current;
+ current = std::list<tree>::erase (current);
+ return t;
+}
+
+/* Initialize the current term to the first in the list. */
+inline void
+term_list::start ()
+{
+ current = begin ();
+}
+
+/* Advance to the next term in the list. */
+inline void
+term_list::next ()
+{
+ ++current;
+}
+
+/* Returns true when the current position is past the end. */
+inline bool
+term_list::done () const
+{
+ return current == end ();
+}
+
+
+/* A goal (or subgoal) models a sequent of the form
+ 'A |- C' where A and C are lists of assumptions and
+ conclusions written as propositions in the constraint
+ language (i.e., lists of trees).
+*/
+struct proof_goal
+{
+ term_list assumptions;
+ term_list conclusions;
+};
+
+/* A proof state owns a list of goals and tracks the
+ current sub-goal. The class also provides facilities
+ for managing subgoals and constructing term lists. */
+struct proof_state : std::list<proof_goal>
+{
+ proof_state ();
+
+ iterator branch (iterator i);
+};
+
+/* An alias for proof state iterators. */
+typedef proof_state::iterator goal_iterator;
+
+/* Initialize the state with a single empty goal,
+ and set that goal as the current subgoal. */
+inline
+proof_state::proof_state ()
+ : std::list<proof_goal> (1)
+{ }
+
+
+/* Branch the current goal by creating a new subgoal,
+ returning a reference to // the new object. This does
+ not update the current goal. */
+inline proof_state::iterator
+proof_state::branch (iterator i)
+{
+ gcc_assert (i != end());
+ proof_goal& g = *i;
+ return insert (++i, g);
+}
+
+/*---------------------------------------------------------------------------
+ Logical rules
+---------------------------------------------------------------------------*/
+
+/*These functions modify the current state and goal by decomposing
+ logical expressions using the logical rules of sequent calculus for
+ first order logic.
+
+ Note that in each decomposition rule, the term T has been erased
+ from term list before the specific rule is applied. */
+
+/* The left logical rule for conjunction adds both operands
+ to the current set of constraints. */
+void
+left_conjunction (proof_state &, goal_iterator i, tree t)
+{
+ gcc_assert (TREE_CODE (t) == CONJ_CONSTR);
+
+ /* Insert the operands into the current branch. Note that the
+ final order of insertion is left-to-right. */
+ term_list &l = i->assumptions;
+ l.insert (TREE_OPERAND (t, 1));
+ l.insert (TREE_OPERAND (t, 0));
+}
+
+/* The left logical rule for disjunction creates a new goal,
+ adding the first operand to the original set of
+ constraints and the second operand to the new set
+ of constraints. */
+void
+left_disjunction (proof_state &s, goal_iterator i, tree t)
+{
+ gcc_assert (TREE_CODE (t) == DISJ_CONSTR);
+
+ /* Branch the current subgoal. */
+ goal_iterator j = s.branch (i);
+ term_list &l1 = i->assumptions;
+ term_list &l2 = j->assumptions;
+
+ /* Insert operands into the different branches. */
+ l1.insert (TREE_OPERAND (t, 0));
+ l2.insert (TREE_OPERAND (t, 1));
+}
+
+/* The left logical rules for parameterized constraints
+ adds its operand to the current goal. The list of
+ parameters are effectively discarded. */
+void
+left_parameterized_constraint (proof_state &, goal_iterator i, tree t)
+{
+ gcc_assert (TREE_CODE (t) == PARM_CONSTR);
+ term_list &l = i->assumptions;
+ l.insert (PARM_CONSTR_OPERAND (t));
+}
+
+/*---------------------------------------------------------------------------
+ Decomposition
+---------------------------------------------------------------------------*/
+
+/* The following algorithms decompose expressions into sets of
+ atomic propositions. In terms of the sequent calculus, these
+ functions exercise the logical rules only.
+
+ This is equivalent, for the purpose of determining subsumption,
+ to rewriting a constraint in disjunctive normal form. It also
+ allows the resulting assumptions to be used as declarations
+ for the purpose of separate checking. */
+
+/* Apply the left logical rules to the proof state. */
+void
+decompose_left_term (proof_state &s, goal_iterator i)
+{
+ term_list &l = i->assumptions;
+ tree t = l.current_term ();
+ switch (TREE_CODE (t))
+ {
+ case CONJ_CONSTR:
+ left_conjunction (s, i, l.erase ());
+ break;
+ case DISJ_CONSTR:
+ left_disjunction (s, i, l.erase ());
+ break;
+ case PARM_CONSTR:
+ left_parameterized_constraint (s, i, l.erase ());
+ break;
+ default:
+ l.next ();
+ break;
+ }
+}
+
+/* Apply the left logical rules of the sequent calculus
+ until the current goal is fully decomposed into atomic
+ constraints. */
+void
+decompose_left_goal (proof_state &s, goal_iterator i)
+{
+ term_list& l = i->assumptions;
+ l.start ();
+ while (!l.done ())
+ decompose_left_term (s, i);
+}
+
+/* Apply the left logical rules of the sequent calculus
+ until the antecedents are fully decomposed into atomic
+ constraints. */
+void
+decompose_left (proof_state& s)
+{
+ goal_iterator iter = s.begin ();
+ goal_iterator end = s.end ();
+ for ( ; iter != end; ++iter)
+ decompose_left_goal (s, iter);
+}
+
+/* Returns a vector of terms from the term list L. */
+tree
+extract_terms (term_list& l)
+{
+ tree result = make_tree_vec (l.size());
+ term_list::iterator iter = l.begin();
+ term_list::iterator end = l.end();
+ for (int n = 0; iter != end; ++iter, ++n)
+ TREE_VEC_ELT (result, n) = *iter;
+ return result;
+}
+
+/* Extract the assumptions from the proof state S
+ as a vector of vectors of atomic constraints. */
+inline tree
+extract_assumptions (proof_state& s)
+{
+ tree result = make_tree_vec (s.size ());
+ goal_iterator iter = s.begin ();
+ goal_iterator end = s.end ();
+ for (int n = 0; iter != end; ++iter, ++n)
+ TREE_VEC_ELT (result, n) = extract_terms (iter->assumptions);
+ return result;
+}
+
+} // namespace
+
+/* Decompose the required expression T into a constraint set: a
+ vector of vectors containing only atomic propositions. If T is
+ invalid, return an error. */
+tree
+decompose_assumptions (tree t)
+{
+ if (!t || t == error_mark_node)
+ return t;
+
+ /* Create a proof state, and insert T as the sole assumption. */
+ proof_state s;
+ term_list &l = s.begin ()->assumptions;
+ l.insert (t);
+
+ /* Decompose the expression into a constraint set, and then
+ extract the terms for the AST. */
+ decompose_left (s);
+ return extract_assumptions (s);
+}
+
+
+/*---------------------------------------------------------------------------
+ Subsumption Rules
+---------------------------------------------------------------------------*/
+
+namespace {
+
+bool subsumes_constraint (tree, tree);
+bool subsumes_conjunction (tree, tree);
+bool subsumes_disjunction (tree, tree);
+bool subsumes_parameterized_constraint (tree, tree);
+bool subsumes_atomic_constraint (tree, tree);
+
+/* Returns true if the assumption A matches the conclusion C. This
+ is generally the case when A and C have the same syntax.
+
+ NOTE: There will be specialized matching rules to accommodate
+ type equivalence, conversion, inheritance, etc. But this is not
+ in the current concepts draft. */
+inline bool
+match_terms (tree a, tree c)
+{
+ return cp_tree_equal (a, c);
+}
+
+/* Returns true if the list of assumptions AS subsumes the atomic
+ proposition C. This is the case when we can find a proposition
+ in AS that entails the conclusion C. */
+bool
+subsumes_atomic_constraint (tree as, tree c)
+{
+ for (int i = 0; i < TREE_VEC_LENGTH (as); ++i)
+ if (match_terms (TREE_VEC_ELT (as, i), c))
+ return true;
+ return false;
+}
+
+/* Returns true when both operands of C are subsumed by the
+ assumptions AS. */
+inline bool
+subsumes_conjunction (tree as, tree c)
+{
+ tree l = TREE_OPERAND (c, 0);
+ tree r = TREE_OPERAND (c, 1);
+ return subsumes_constraint (as, l) && subsumes_constraint (as, r);
+}
+
+/* Returns true when either operand of C is subsumed by the
+ assumptions AS. */
+inline bool
+subsumes_disjunction (tree as, tree c)
+{
+ tree l = TREE_OPERAND (c, 0);
+ tree r = TREE_OPERAND (c, 1);
+ return subsumes_constraint (as, l) || subsumes_constraint (as, r);
+}
+
+/* Returns true when the operand of C is subsumed by the
+ assumptions in AS. The parameters are not considered in
+ the subsumption rules. */
+bool
+subsumes_parameterized_constraint (tree as, tree c)
+{
+ tree t = PARM_CONSTR_OPERAND (c);
+ return subsumes_constraint (as, t);
+}
+
+
+/* Returns true when the list of assumptions AS subsumes the
+ concluded proposition C. This is a simple recursive descent
+ on C, matching against propositions in the assumption list AS. */
+bool
+subsumes_constraint (tree as, tree c)
+{
+ switch (TREE_CODE (c))
+ {
+ case CONJ_CONSTR:
+ return subsumes_conjunction (as, c);
+ case DISJ_CONSTR:
+ return subsumes_disjunction (as, c);
+ case PARM_CONSTR:
+ return subsumes_parameterized_constraint (as, c);
+ default:
+ return subsumes_atomic_constraint (as, c);
+ }
+}
+
+/* Returns true if the LEFT constraints subsume the RIGHT constraints.
+ This is done by checking that the RIGHT requirements follow from
+ each of the LEFT subgoals. */
+bool
+subsumes_constraints_nonnull (tree left, tree right)
+{
+ gcc_assert (check_constraint_info (left));
+ gcc_assert (check_constraint_info (right));
+
+ /* Check that the required expression in RIGHT is subsumed by each
+ subgoal in the assumptions of LEFT. */
+ tree as = CI_ASSUMPTIONS (left);
+ tree c = CI_NORMALIZED_CONSTRAINTS (right);
+ for (int i = 0; i < TREE_VEC_LENGTH (as); ++i)
+ if (!subsumes_constraint (TREE_VEC_ELT (as, i), c))
+ return false;
+ return true;
+}
+
+} /* namespace */
+
+/* Returns true if the LEFT constraints subsume the RIGHT
+ constraints. */
+bool
+subsumes (tree left, tree right)
+{
+ if (left == right)
+ return true;
+ if (!left)
+ return false;
+ if (!right)
+ return true;
+ return subsumes_constraints_nonnull (left, right);
+}