Class: Udb::LogicNode

Inherits:
Object
  • Object
show all
Extended by:
T::Sig
Defined in:
lib/udb/logic.rb,
lib/udb/eqn.rb

Overview

Abstract syntax tree of the condition logic

Defined Under Namespace

Classes: CanonicalizationType, ConditionalEndterm, EqntottResult, LogicSymbolFormat, MemoizedState, PairMintermsResult, PrimeImplicantsResult, SizeExplosion

Constant Summary collapse

ChildType = 
T.type_alias { T.any(LogicNode, TermType) }
True = 
LogicNode.new(LogicNodeType::True, [])
False = 
LogicNode.new(LogicNodeType::False, [])
Xlen32 = 
LogicNode.new(LogicNodeType::Term, [XlenTerm.new(32).freeze]).freeze
Xlen64 = 
LogicNode.new(LogicNodeType::Term, [XlenTerm.new(64).freeze]).freeze
EvalCallbackType = 
T.type_alias { T.proc.params(arg0: TermType).returns(SatisfiedResult) }
ReplaceCallbackType = 
T.type_alias { T.proc.params(arg0: LogicNode).returns(LogicNode) }
LOGIC_SYMBOLS = 
{
  LogicSymbolFormat::C => {
    TRUE: "1",
    FALSE: "0",
    NOT: "!",
    AND: "&&",
    OR: "||",
    XOR: "^",
    IMPLIES: "->" # making this up; there is no implication operator in C
  },
  LogicSymbolFormat::Eqn => {
    TRUE: "ONE",
    FALSE: "ZERO",
    NOT: "!",
    AND: "&",
    OR: "|",
    XOR: "DOES NOT EXIST",
    IMPLIES: "DOES NOT EXIST"
  },
  LogicSymbolFormat::English => {
    TRUE: "true",
    FALSE: "false",
    NOT: "NOT ",
    AND: "AND",
    OR: "OR",
    XOR: "XOR",
    IMPLIES: "IMPLIES"
  },
  LogicSymbolFormat::Predicate => {
    TRUE: "true",
    FALSE: "false",
    NOT: "\u00ac",
    AND: "\u2227",
    OR: "\u2228",
    XOR: "\u2295",
    IMPLIES: "\u2192"
  }
}

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(type, children)

Parameters:



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# File 'lib/udb/logic.rb', line 1258

def initialize(type, children)
  if [LogicNodeType::Term, LogicNodeType::Not].include?(type) && children.size != 1
    raise ArgumentError, "Children must be singular"
  end
  if [LogicNodeType::And, LogicNodeType::Or, LogicNodeType::Xor, LogicNodeType::None, LogicNodeType::If].include?(type) && children.size < 2
    raise ArgumentError, "Children must have at least two elements"
  end

  @children = children
  @children.freeze
  @node_children = (@type == LogicNodeType::Term) ? nil : T.cast(@children, T::Array[LogicNode])


  if [LogicNodeType::True, LogicNodeType::False].include?(type) && !children.empty?
    raise ArgumentError, "Children must be empty"
  elsif type == LogicNodeType::Term
    # ensure the children are TermType
    children.each { |child| T.assert_type!(T.cast(child, TermType), TermType) }
  else
    # raise ArgumentError, "All Children must be LogicNodes" unless children.all? { |child| child.is_a?(LogicNode) }
  end

  @type = type
  @type.freeze

  # used for memoization in transformation routines
  @memo = MemoizedState.new(
    is_cnf: nil,
    is_nested_cnf: nil,
    is_reduced: nil,
    terms: nil,
    literals: nil,
    is_satisfiable: nil,
    equisat_cnf: nil,
    equiv_cnf: nil
  )
end

Instance Attribute Details

#children ⇒ Array<ChildType> (readonly)

Returns:



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# File 'lib/udb/logic.rb', line 1217

def children
  @children
end

#memo ⇒ Object

Returns the value of attribute memo.



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# File 'lib/udb/logic.rb', line 1255

def memo
  @memo
end

#type ⇒ LogicNodeType (readonly)

Returns:



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# File 'lib/udb/logic.rb', line 1214

def type
  @type
end

Class Method Details

.find_prime_implicants(mterms, group_by) ⇒ PrimeImplicantsResult

given a list of minterms/maxterms, each represented by a string of “0” and “1”, return the prime implicants, represented by a string of “0”, “1”, and “-”

Parameters:

  • mterms (Array<String>)
  • group_by (String)

Returns:



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# File 'lib/udb/logic.rb', line 1442

def self.find_prime_implicants(mterms, group_by)
  groups = group_mterms(mterms, group_by)

  # Pair mterms until no further simplification is possible
  prime_implicants = T.let([], T::Array[String])
  matched = T.let(Set.new, T::Set[String])
  while groups.size > 1
    new_groups = Hash.new { |h, k| h[k] = [] }
    matched.clear
    groups.keys.sort.each_cons(2) do |k1, k2|
      res = pair_mterms(T.must(groups[T.must(k1)]), T.must(groups[T.must(k2)]))
      matched.merge(res.matched_mterms)
      new_group = res.new_group
      new_groups[k1] += new_group unless new_group.empty?
    end
    prime_implicants += groups.values.flatten.reject { |mterm| matched.include?(mterm) }
    groups = new_groups
  end
  prime_implicants += groups.values.flatten.reject { |mterm| matched.include?(mterm) }
  prime_implicants.uniq!

  coverage = Hash.new { |h, k| h[k] = [] }

  mterms.each do |minterm|
    prime_implicants.each_with_index do |implicant, idx|
      if prime_implicant_covers_mterm?(implicant, minterm)
        coverage[minterm] << idx
      end
    end
  end

  essential_indices = []
  uncovered = mterms.dup

  # Find essential prime implicants
  coverage.each do |mterm, implicant_indices|
    if implicant_indices.size == 1
      idx = implicant_indices.first
      unless essential_indices.include?(idx)
        essential_indices << idx
        # Remove all minterms covered by this implicant
        uncovered.reject! { |m| prime_implicant_covers_mterm?(prime_implicants.fetch(idx), m) }
      end
    end
  end

  minimal_indices = essential_indices.dup
  # Greedy selection for remaining minterms
  while uncovered.any?
    best_idx = T.cast(prime_implicants.each_with_index.max_by do |implicant, idx|
      uncovered.count { |m| prime_implicant_covers_mterm?(implicant, m) }
    end, T::Array[Integer]).last

    minimal_indices << best_idx
    uncovered.reject! { |m| prime_implicant_covers_mterm?(prime_implicants.fetch(T.must(best_idx)), m) }
  end

  PrimeImplicantsResult.new(
    essential: essential_indices.map { |i| prime_implicants.fetch(i) },
    minimal:  minimal_indices.map { |i| prime_implicants.fetch(i) }
  )
end

.group_mterms(mterms, group_by) ⇒ Hash{Integer => Array<String>}

Parameters:

  • mterms (Array<String>)
  • group_by (String)

Returns:

  • (Hash{Integer => Array<String>}) 


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# File 'lib/udb/logic.rb', line 1384

def self.group_mterms(mterms, group_by)
  groups = T.let({}, T::Hash[Integer, T::Array[String]])
  mterms.each do |mterm|
    n = mterm.count(group_by)
    groups[n] ||= []
    groups.fetch(n) << mterm
  end
  groups
end

.inc_brute_force_sat_solves ⇒ Object 



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# File 'lib/udb/logic.rb', line 1190

def self.inc_brute_force_sat_solves
  @num_brute_force_sat_solves += 1
end

.inc_minisat_cache_hits ⇒ Object 



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# File 'lib/udb/logic.rb', line 1206

def self.inc_minisat_cache_hits
  @num_minisat_cache_hits += 1
end

.inc_minisat_sat_solves ⇒ Object 



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# File 'lib/udb/logic.rb', line 1198

def self.inc_minisat_sat_solves
  @num_minisat_sat_solves += 1
end

.make_eval_cb(&blk) ⇒ EvalCallbackType

Parameters:

Returns:



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# File 'lib/udb/logic.rb', line 1657

def self.make_eval_cb(&blk)
  blk
end

.make_replace_cb(&blk) ⇒ ReplaceCallbackType

Parameters:

Returns:



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# File 'lib/udb/logic.rb', line 1663

def self.make_replace_cb(&blk)
  blk
end

.num_brute_force_sat_solves ⇒ Object 



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# File 'lib/udb/logic.rb', line 1186

def self.num_brute_force_sat_solves
  @num_brute_force_sat_solves
end

.num_minisat_cache_hits ⇒ Object 



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# File 'lib/udb/logic.rb', line 1202

def self.num_minisat_cache_hits
  @num_minisat_cache_hits
end

.num_minisat_sat_solves ⇒ Object 



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# File 'lib/udb/logic.rb', line 1194

def self.num_minisat_sat_solves
  @num_minisat_sat_solves
end

.pair_mterms(group1, group2) ⇒ PairMintermsResult

Parameters:

  • group1 (Array<String>)
  • group2 (Array<String>)

Returns:



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# File 'lib/udb/logic.rb', line 1400

def self.pair_mterms(group1, group2)
  new_group = []
  matched = Set.new
  group1.each do |m1|
    group2.each do |m2|
      diff_count = 0
      diff_index = -1
      loop_index = 0
      m1.each_char do |bit|
        if bit != m2[loop_index]
          diff_count += 1
          diff_index = loop_index
        end
        loop_index += 1
      end
      if diff_count == 1
        new_mterm = m1.dup
        new_mterm[diff_index] = "-"
        new_group << new_mterm
        matched.add(m1)
        matched.add(m2)
      end
    end
  end
  PairMintermsResult.new(new_group: new_group.uniq, matched_mterms: matched)
end

.prime_implicant_covers_mterm?(implicant, minterm) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/udb/logic.rb', line 1428

def self.prime_implicant_covers_mterm?(implicant, minterm)
  implicant.chars.zip(minterm.chars).all? do |i_bit, m_bit|
    i_bit == "-" || i_bit == m_bit
  end
end

.reset_stats ⇒ Object

statistics counters



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# File 'lib/udb/logic.rb', line 1176

def self.reset_stats
  @num_brute_force_sat_solves = 0
  @time_brute_force_sat_solves = 0
  @num_minisat_sat_solves = 0
  @time_minisat_sat_solves = 0
  @num_minisat_cache_hits = 0
end

Instance Method Details

#always_implies?(other) ⇒ Boolean

Parameters:

Returns:

  • (Boolean) 


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# File 'lib/udb/logic.rb', line 3031

def always_implies?(other)
  # can test that by seeing if the contradiction is satisfiable, i.e.:
  # if self -> other , contradition would be self & not other
  contradiction = LogicNode.new(
    LogicNodeType::And,
    [
      self,
      LogicNode.new(LogicNodeType::Not, [other])
    ]
  )
  !contradiction.satisfiable?
end

#cnf? ⇒ Boolean

returns true iff tree is in Conjunctive Normal Form

Returns:

  • (Boolean) 


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# File 'lib/udb/logic.rb', line 2800

def cnf?
  unless @memo.is_cnf.nil?
    return @memo.is_cnf
  end

  ret =
    case @type
    when LogicNodeType::Term, LogicNodeType::True, LogicNodeType::False
      true
    when LogicNodeType::Not
      node_children.fetch(0).type == LogicNodeType::Term
    when LogicNodeType::Or
      node_children.all? do |child|
        [
          child.type == LogicNodeType::True,
          child.type == LogicNodeType::False,
          child.type == LogicNodeType::Term,
          child.type == LogicNodeType::Not && \
            child.node_children.fetch(0).type == LogicNodeType::Term
        ].any?
      end
    when LogicNodeType::Xor, LogicNodeType::If, LogicNodeType::None
      false
    when LogicNodeType::And
      node_children.all? { |child| child.cnf_conjunction_term? }
    else
      T.absurd(@type)
    end

  @memo.is_cnf = ret
end

#cnf_conjunction_term? ⇒ Boolean

This method is part of a private API. You should avoid using this method if possible, as it may be removed or be changed in the future.

returns true iff tree is a valid term in a cnf conjunction

Returns:

  • (Boolean) 


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# File 'lib/udb/logic.rb', line 2862

def cnf_conjunction_term?
  case @type
  when LogicNodeType::Term, LogicNodeType::True, LogicNodeType::False
    true
  when LogicNodeType::Not
    node_children.fetch(0).type == LogicNodeType::Term
  when LogicNodeType::Or
    # or is only valid if only contains literals
    node_children.all? do |child|
      [
        child.type == LogicNodeType::True,
        child.type == LogicNodeType::False,
        child.type == LogicNodeType::Term,
        ((child.type == LogicNodeType::Not) && \
          child.node_children.fetch(0).type == LogicNodeType::Term)
      ].any?
    end
  when LogicNodeType::And, LogicNodeType::Xor, LogicNodeType::If, LogicNodeType::None
    false
  else
    T.absurd(@type)
  end
end

#collect_tseytin(subformulae)

This method is part of a private API. You should avoid using this method if possible, as it may be removed or be changed in the future.

This method returns an undefined value.

Parameters:



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# File 'lib/udb/logic.rb', line 3315

def collect_tseytin(subformulae)
  case @type
  when LogicNodeType::And
    # (¬A ∨ ¬B ∨ p) ∧ (A ∨ ¬p) ∧ (B ∨ ¬p)
    a = node_children.fetch(0).tseytin_prop
    b = node_children.fetch(1).tseytin_prop
    subformulae <<
      LogicNode.new(
        LogicNodeType::And,
        [
          LogicNode.new(LogicNodeType::Or,
            [
              LogicNode.new(LogicNodeType::Not, [a]),
              LogicNode.new(LogicNodeType::Not, [b]),
              tseytin_prop
            ]
          ),
          LogicNode.new(LogicNodeType::Or,
            [
              a,
              LogicNode.new(LogicNodeType::Not, [tseytin_prop])
            ]
          ),
          LogicNode.new(LogicNodeType::Or,
            [
              b,
              LogicNode.new(LogicNodeType::Not, [tseytin_prop])
            ]
          )
        ]
      )
    node_children.fetch(0).collect_tseytin(subformulae)
    node_children.fetch(1).collect_tseytin(subformulae)
  when LogicNodeType::Or
    # (A ∨ B ∨ ¬p) ∧ (¬A ∨ p) ∧ (¬B ∨ p)
    a = node_children.fetch(0).tseytin_prop
    b = node_children.fetch(1).tseytin_prop
    subformulae <<
      LogicNode.new(
        LogicNodeType::And,
        [
          LogicNode.new(LogicNodeType::Or, [a, b, LogicNode.new(LogicNodeType::Not, [tseytin_prop])]),
          LogicNode.new(LogicNodeType::Or, [LogicNode.new(LogicNodeType::Not, [a]), tseytin_prop]),
          LogicNode.new(LogicNodeType::Or, [LogicNode.new(LogicNodeType::Not, [b]), tseytin_prop])
        ]
      )
    node_children.fetch(0).collect_tseytin(subformulae)
    node_children.fetch(1).collect_tseytin(subformulae)
  when LogicNodeType::Not
    # (A ∨ p) ∧ (¬A ∨ ¬p)
    a = node_children.fetch(0).tseytin_prop
    subformulae <<
      LogicNode.new(
        LogicNodeType::And,
        [
          LogicNode.new(LogicNodeType::Or, [a, tseytin_prop]),
          LogicNode.new(LogicNodeType::Or, [
            LogicNode.new(LogicNodeType::Not, [a]),
            LogicNode.new(LogicNodeType::Not, [tseytin_prop]),
          ])
        ]
      )
    node_children.fetch(0).collect_tseytin(subformulae)
  when LogicNodeType::True, LogicNodeType::False
    # pass
  when LogicNodeType::Term
    # pass
  else
    raise "? #{@type}"
  end
end

#distribute_not ⇒ LogicNode

This method is part of a private API. You should avoid using this method if possible, as it may be removed or be changed in the future.

Returns:



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# File 'lib/udb/logic.rb', line 3302

def distribute_not
  # recursively apply demorgan until we get to terms
  raise "Not a negation" unless @type == LogicNodeType::Not

  distribute_not_helper(self)
end

#dnf? ⇒ Boolean

returns true iff tree is in Disjunctive Normal Form

Returns:

  • (Boolean) 


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# File 'lib/udb/logic.rb', line 2834

def dnf?
  case @type
  when LogicNodeType::Term, LogicNodeType::True, LogicNodeType::False
    true
  when LogicNodeType::Not
    node_children.fetch(0).type == LogicNodeType::Term
  when LogicNodeType::Or
    node_children.all? { |child| child.dnf_disjunctive_term? }
  when LogicNodeType::And
    node_children.all? do |child|
      [
        child.type == LogicNodeType::True,
        child.type == LogicNodeType::False,
        child.type == LogicNodeType::Term,
        child.type == LogicNodeType::Not && \
          child.node_children.fetch(0).type == LogicNodeType::Term
      ].any?
    end
  when LogicNodeType::Xor, LogicNodeType::If, LogicNodeType::None
    false
  else
    T.absurd(@type)
  end
end

#dnf_disjunctive_term? ⇒ Boolean

This method is part of a private API. You should avoid using this method if possible, as it may be removed or be changed in the future.

returns true iff tree is a valid term in a dnf disjunction

Returns:

  • (Boolean) 


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# File 'lib/udb/logic.rb', line 2889

def dnf_disjunctive_term?
  case @type
  when LogicNodeType::Term, LogicNodeType::True, LogicNodeType::False
    true
  when LogicNodeType::Not
    node_children.fetch(0).type == LogicNodeType::Term
  when LogicNodeType::And
    # and is only valid if only contains literals
    node_children.all? do |child|
      [
        child.type == LogicNodeType::True,
        child.type == LogicNodeType::False,
        child.type == LogicNodeType::Term,
        ((child.type == LogicNodeType::Not) && \
          child.node_children.fetch(0).type == LogicNodeType::Term)
      ]
    end
  when LogicNodeType::Or, LogicNodeType::Xor, LogicNodeType::If, LogicNodeType::None
    false
  else
    T.absurd(@type)
  end
end

#do_to_eqntott(tree, term_map) ⇒ String

Parameters:

Returns:

  • (String) 


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# File 'lib/udb/logic.rb', line 3223

def do_to_eqntott(tree, term_map)
  t = tree.type
  case t
  when LogicNodeType::True
    "1"
  when LogicNodeType::False
    "0"
  when LogicNodeType::And
    "(#{tree.node_children.map { |child| do_to_eqntott(child, term_map) }.join(" & ")})"
  when LogicNodeType::Or
    "(#{tree.node_children.map { |child| do_to_eqntott(child, term_map) }.join(" | ")})"
  when LogicNodeType::Xor
    do_to_eqntott(tree.nnf, term_map)
  when LogicNodeType::None
    do_to_eqntott(LogicNode.new(LogicNodeType::Not, [LogicNode.new(LogicNodeType::Or, tree.children)]), term_map)
  when LogicNodeType::Term
    term_map.fetch(T.cast(tree.children.fetch(0), TermType))
  when LogicNodeType::Not
    "!(#{do_to_eqntott(tree.node_children.fetch(0), term_map)})"
  when LogicNodeType::If
    do_to_eqntott(tree.nnf, term_map)
  else
    T.absurd(t)
  end
end

#eql?(other) ⇒ Boolean

Parameters:

  • other (T.untyped)

Returns:

  • (Boolean) 


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# File 'lib/udb/logic.rb', line 3697

def eql?(other)
  return false unless other.is_a?(LogicNode)

  to_h.eql?(other.to_h)
end

#equisat_cnf ⇒ LogicNode

coverts self to an equisatisfiable formula in Conjunctive Normal Form and returns it as a new formula (self is unmodified)

Returns:



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# File 'lib/udb/logic.rb', line 2773

def equisat_cnf
  return @memo.equisat_cnf unless @memo.equisat_cnf.nil?
  return self if @type == LogicNodeType::True
  return self if @type == LogicNodeType::False

  # strategy: try conversion using Demorgan's laws first. If that appears to be getting too
  # large (exponential in the worst case), fall back on the tseytin transformation
  @memo.equisat_cnf =
    if @memo.equiv_cnf.nil?
      if terms.count > 4 || literals.count > 10
        tseytin
      else
        # try demorgan first, then fall back if it gets too big
        begin
          equiv_cnf
        rescue SizeExplosion
          tseytin
        end
      end
    else
      # we already calculated an equivalent cnf, which is also equisatisfiable
      @mem.equiv_cnf
    end
end

#equisatisfiable?(other) ⇒ Boolean

Parameters:

Returns:

  • (Boolean) 


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# File 'lib/udb/logic.rb', line 3166

def equisatisfiable?(other)
  if satisfiable?
    other.satisfiable?
  else
    !other.satisfiable?
  end
end

#equiv_cnf(raise_on_explosion: true) ⇒ LogicNode

coverts self to an equivalent formula in Conjunctive Normal Form and returns it as a new formula (self is unmodified)

iteratively uses Demorgan’s Laws. May explode since the worst case is exponential in the number of clauses

Parameters:

  • raise_on_explosion (Boolean) (defaults to: true)

Returns:



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# File 'lib/udb/logic.rb', line 2749

def equiv_cnf(raise_on_explosion: true)
  @memo.equiv_cnf ||=
    begin
      r = reduce
      return r if r.type == LogicNodeType::True || r.type == LogicNodeType::False

      n = r.nnf

      candidate = n.reduce
      candidate = n.group_by_2
      unflattened = do_equiv_cnf(candidate, raise_on_explosion:)
      result = flatten_cnf(unflattened).reduce
      if result.frozen?
        raise "?" unless result.memo.is_cnf == true
      else
        result.memo.is_cnf = true
      end
      result
    end
end

#equivalent?(other) ⇒ Boolean

Returns true iff self and other are logically equivalent (identical truth tables).

Parameters:

Returns:

  • (Boolean) —

    true iff self and other are logically equivalent (identical truth tables)



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# File 'lib/udb/logic.rb', line 3176

def equivalent?(other)
  # equivalent (A <=> B) if the biconditional is true:
  #   (A -> B) && (B -> A)
  # or, expressed without implication:
  #   (!A || B) && (!B || A)

  # equivalence is a tautology iff ~(A <=> B) is a contradiction,
  # i.e., !(A <=> B) is UNSATISFIABLE
  #       !((!A || B) && (!B || A)) is UNSATISFIABLE

  r = self
  other = other
  contradiction = LogicNode.new(
    LogicNodeType::Not,
    [
      LogicNode.new(
        LogicNodeType::And,
        [
          LogicNode.new(
            LogicNodeType::Or,
            [
              LogicNode.new(LogicNodeType::Not, [r]),
              other
            ]
          ),
          LogicNode.new(
            LogicNodeType::Or,
            [
              LogicNode.new(LogicNodeType::Not, [r]),
              self
            ]
          )
        ]
      )
    ]
  )
  contradiction.unsatisfiable?
end

#espresso(result_type, exact) ⇒ LogicNode

minimize the function using espresso

Parameters:

Returns:



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# File 'lib/udb/logic.rb', line 3550

def espresso(result_type, exact)
  nterms = terms.size

  pla =
    if nterms > 4 || literals.size >= 32

      eqn_result =
        if result_type == CanonicalizationType::SumOfProducts
          to_eqntott
        elsif result_type == CanonicalizationType::ProductOfSums
          LogicNode.new(LogicNodeType::Not, [self]).to_eqntott
        else
          T.absurd(result_type)
        end
      tt = T.let(nil, T.nilable(String))
      Tempfile.open do |f|
        f.write <<~FILE
          NAME=f;
          #{eqn_result.eqn};
        FILE
        f.flush

        tt = `eqntott -l #{f.path}`
        unless $?.success?
          raise "eqntott failure"
        end
      end

      if T.must(tt).lines.any? { |l| l =~ /^\.p 0/ }
        if result_type == CanonicalizationType::SumOfProducts
          # short circuit here, it's trivially false
          return LogicNode.new(LogicNodeType::False, [])
        else
          # short circuit here, it's trivially true
          return LogicNode.new(LogicNodeType::True, [])
        end
      end
      tt
    else

      term_idx = T.let({}, T::Hash[TermType, Integer])
      terms.each_with_index do |term, idx|
        term_idx[term] = idx
      end

      # define the callback outside the loop to avoid allocating a new block on every iteration
      val_out_of_loop = 0
      cb = LogicNode.make_eval_cb do |term|
        ((val_out_of_loop >> term_idx.fetch(term)) & 1).zero? ? SatisfiedResult::No : SatisfiedResult::Yes
      end

      tt = T.let([], T::Array[T::Array[String]])
      (1 << nterms).times do |val|
        val_out_of_loop = val
        if result_type == CanonicalizationType::SumOfProducts
          if eval_cb(cb) == SatisfiedResult::Yes
            tt << [val.to_s(2).rjust(nterms, "0").reverse, "1"]
          else
            tt << [val.to_s(2).rjust(nterms, "0").reverse, "0"]
          end
        elsif result_type == CanonicalizationType::ProductOfSums
          if eval_cb(cb) == SatisfiedResult::Yes
            tt << [val.to_s(2).rjust(nterms, "0").reverse, "0"]
          else
            tt << [val.to_s(2).rjust(nterms, "0").reverse, "1"]
          end
        end
      end

      <<~INFILE
        .i #{nterms}
        .o 1
        .na f
        .ob out
        .p #{tt.size}
        #{tt.map { |t| t.join(" ") }.join("\n")}
      INFILE
    end

  Tempfile.open do |f|
    f.write pla
    f.flush

    cmd =
      if exact
        "espresso -Dsignature #{f.path}"
      else
        "espresso -efast #{f.path}"
      end
    result = `#{cmd} 2>&1`
    unless $?.success?
      raise "espresso failure\n#{result}"
    end

    sop_terms = []
    always_true = T.let(false, T::Boolean)
    result.lines.each_with_index do |line, idx|
      next if line[0] == "."
      next if line[0] == "#"

      if line =~ /^([01\-]{#{terms.size}}) 1/
        term = $1
        conjunction_kids = []
        terms.size.times do |i|
          if term[i] == "1"
            conjunction_kids << LogicNode.new(LogicNodeType::Term, [terms.fetch(i)])
          elsif term[i] == "0"
            conjunction_kids << LogicNode.new(LogicNodeType::Not, [LogicNode.new(LogicNodeType::Term, [terms.fetch(i)])])
          else
            raise "unexpected" unless term[i] == "-"
          end
        end
        if conjunction_kids.size == 1
          sop_terms << conjunction_kids.fetch(0)
        elsif conjunction_kids.size > 0
          sop_terms << LogicNode.new(LogicNodeType::And, conjunction_kids)
        else
          # always true
          always_true = true
        end
      end
    end

    sop =
      if sop_terms.size == 1
        sop_terms.fetch(0)
      elsif sop_terms.size > 0
        LogicNode.new(LogicNodeType::Or, sop_terms)
      else
        always_true ? LogicNode.new(LogicNodeType::True, []) : LogicNode.new(LogicNodeType::False, [])
      end

    if result_type == CanonicalizationType::SumOfProducts
      sop
    else
      # result is actually !result, so negate it and then distribute
      LogicNode.new(LogicNodeType::Not, [sop]).distribute_not
    end
  end

end

#eval_cb(callback) ⇒ SatisfiedResult

Parameters:

Returns:

  • (SatisfiedResult) 


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# File 'lib/udb/logic.rb', line 1686

def eval_cb(callback)
  case @type
  when LogicNodeType::True
    SatisfiedResult::Yes
  when LogicNodeType::False
    SatisfiedResult::No
  when LogicNodeType::Term
    child = T.cast(@children.fetch(0), TermType)
    callback.call(child)
  when LogicNodeType::If
    cond_ext_ret = node_children.fetch(0)
    res = cond_ext_ret.eval_cb(callback)
    if res == SatisfiedResult::Yes
      node_children.fetch(1).eval_cb(callback)
    elsif res == SatisfiedResult::Maybe
      ## if "then" is true, then res doesn't matter....
      node_children.fetch(1).eval_cb(callback) == SatisfiedResult::Yes \
        ? SatisfiedResult::Yes
        : SatisfiedResult::Maybe
    else
      # if antecedent is false, implication is true
      SatisfiedResult::Yes
    end
  when LogicNodeType::Not
    res = node_children.fetch(0).eval_cb(callback)
    case res
    when SatisfiedResult::Yes
      SatisfiedResult::No
    when SatisfiedResult::No
      SatisfiedResult::Yes
    when SatisfiedResult::Maybe
      SatisfiedResult::Maybe
    else
      T.absurd(res)
    end
  when LogicNodeType::And
    yes_cnt = T.let(0, Integer)
    node_children.each do |child|
      res1 = child.eval_cb(callback)
      if res1 == SatisfiedResult::No
        return SatisfiedResult::No
      end

      if res1 == SatisfiedResult::Yes
        yes_cnt += 1
      end
    end
    if yes_cnt == node_children.size
      SatisfiedResult::Yes
    else
      SatisfiedResult::Maybe
    end
  when LogicNodeType::Or
    no_cnt = 0
    node_children.each do |child|
      res1 = child.eval_cb(callback)
      return SatisfiedResult::Yes if res1 == SatisfiedResult::Yes

      no_cnt += 1 if res1 == SatisfiedResult::No
    end
    if no_cnt == node_children.size
      SatisfiedResult::No
    else
      SatisfiedResult::Maybe
    end
  when LogicNodeType::None
    no_cnt = 0
    node_children.each do |child|
      res1 = child.eval_cb(callback)
      return SatisfiedResult::No if res1 == SatisfiedResult::Yes

      no_cnt += 1 if res1 == SatisfiedResult::No
    end
    if no_cnt == node_children.size
      SatisfiedResult::Yes
    else
      SatisfiedResult::Maybe
    end
  when LogicNodeType::Xor
    yes_cnt = T.let(0, Integer)
    has_maybe = T.let(false, T::Boolean)
    node_children.each do |child|
      res1 = child.eval_cb(callback)

      has_maybe ||= (res1 == SatisfiedResult::Maybe)
      yes_cnt += 1 if res1 == SatisfiedResult::Yes
      if yes_cnt > 1
        return SatisfiedResult::No
      end
    end
    if yes_cnt == 1 && !has_maybe
      SatisfiedResult::Yes
    elsif has_maybe
      SatisfiedResult::Maybe
    else
      SatisfiedResult::No
    end
  else
    T.absurd(@type)
  end
end

#from_dimacs(dimacs) ⇒ LogicNode

Parameters:

  • dimacs (String)

Returns:



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# File 'lib/udb/logic.rb', line 3461

def from_dimacs(dimacs)
  nodes = dimacs.each_line.map do |line|
    if line =~ /^(((-?\d+) )+)0/
      ts = T.let($1.strip.split(" "), T::Array[String])
      if ts.size == 1
        t = ts.fetch(0)
        if t[0] == "-"
          index = t[1..].to_i - 1
          LogicNode.new(
            LogicNodeType::Not,
            [LogicNode.new(LogicNodeType::Term, [terms.fetch(index)])]
          )
        else
          index = t.to_i - 1
          LogicNode.new(LogicNodeType::Term, [terms.fetch(index)])
        end
      else
        LogicNode.new(LogicNodeType::Or,
          ts.map do |t|
            if t[0] == "-"
              i = t[1..].to_i - 1
              LogicNode.new(
                LogicNodeType::Not,
                [LogicNode.new(LogicNodeType::Term, [terms.fetch(i)])]
              )
            else
              i = t.to_i - 1
              LogicNode.new(LogicNodeType::Term, [terms.fetch(i)])
            end
          end
        )
      end
    else
      nil
    end
  end.compact

  if nodes.size == 1
    nodes.fetch(0)
  else
    LogicNode.new(LogicNodeType::And, nodes)
  end
end

#group_by_2 ⇒ LogicNode

Returns rewrites the tree so that no node has more than 2 children.

Examples:

(A || B || C) => ((A || B) || C)

Returns:

  • (LogicNode) —

    rewrites the tree so that no node has more than 2 children



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# File 'lib/udb/logic.rb', line 2370

def group_by_2
  do_group_by_2(self)
end

#grouped_by_2?(node) ⇒ Boolean

does each node have at most two children?

Parameters:

Returns:

  • (Boolean) 


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# File 'lib/udb/logic.rb', line 2345

def grouped_by_2?(node)
  t = node.type
  case t
  when LogicNodeType::And, LogicNodeType::Or
    node.children.size == 2 && \
      grouped_by_2?(node.node_children.fetch(0)) && \
      grouped_by_2?(node.node_children.fetch(1))
  when LogicNodeType::Not
    grouped_by_2?(node.node_children.fetch(0))
  when LogicNodeType::Term
    true
  when LogicNodeType::None, LogicNodeType::If, LogicNodeType::Xor
    raise "?"
  when LogicNodeType::True, LogicNodeType::False
    true
  else
    T.absurd(t)
  end
end

#hash ⇒ Integer

This method is part of a private API. You should avoid using this method if possible, as it may be removed or be changed in the future.

Returns:

  • (Integer) 


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# File 'lib/udb/logic.rb', line 1881

def hash
  if @type == LogicNodeType::True
    true.hash
  elsif @type == LogicNodeType::False
    false.hash
  elsif @type == LogicNodeType::Term
    @children[0].to_s.hash
  elsif @type == LogicNodeType::Not
    [:not, node_children.fetch(0).hash].hash
  elsif @type == LogicNodeType::And
    [:and, node_children.map(&:hash)].hash
  elsif @type == LogicNodeType::Or
    [:or, node_children.map(&:hash)].hash
  elsif @type == LogicNodeType::Xor
    [:xor, node_children.map(&:hash)].hash
  elsif @type == LogicNodeType::None
    [:none, node_children.map(&:hash)].hash
  elsif @type == LogicNodeType::If
    [:if, node_children.map(&:hash)].hash
  else
    T.absurd(@type)
  end
end

#literals ⇒ Array<TermType>

unlike #terms, this list will include leaves that are equivalent

Returns:

  • (Array<TermType>) —

    all literals in the tree



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# File 'lib/udb/logic.rb', line 1373

def literals
  @memo.literals ||=
  if @type == LogicNodeType::Term
    [@children.fetch(0)]
  else
    node_children.map { |child| child.literals }.flatten
  end
end

#minimal_unsat_subsets ⇒ Array<LogicNode>

return minimally unsatisfiable subsets of the unstatisfiable formula

Returns:



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# File 'lib/udb/logic.rb', line 3507

def minimal_unsat_subsets
  r = reduce
  c = r.equiv_cnf(raise_on_explosion: false)
  Tempfile.create(%w/formula .cnf/) do |f|
    f.write c.to_dimacs
    f.flush

    Tempfile.create do |rf|
      # run must, re-use the tempfile for the result
      `must -o #{rf.path} #{f.path}`
      unless $?.success?
        raise "could not find minimal subsets"
      end

      rf.rewind
      result = rf.read

      mus_dimacs = T.let([], T::Array[String])
      cur_dimacs = T.let(nil, T.nilable(String))
      result.each_line do |line|
        if line =~ /MUS #\d+/
          mus_dimacs << cur_dimacs unless cur_dimacs.nil?
          cur_dimacs = ""
        else
          cur_dimacs = T.must(cur_dimacs) + line
        end
      end
      mus_dimacs << T.must(cur_dimacs)

      return mus_dimacs.map { |d| c.from_dimacs(d) }
    end
  end
end

#minimize(result_type) ⇒ LogicNode

convert to either sum-of-products form or product-of-sums form and minimize the result

Parameters:

Returns:



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# File 'lib/udb/logic.rb', line 1636

def minimize(result_type)
  if terms.size <= 4
    quine_mccluskey(result_type)
  else
    # special-case check for when the formula is large but obviously already minimized
    # added this because espresso runtime for Shcounterenw requirements was painfully long
    if result_type == CanonicalizationType::ProductOfSums && terms.size > 32 && nnf.nested_cnf? && terms.size == literals.size
      equiv_cnf
    else
      espresso(result_type, true)
    end
  end
end

#nested_cnf? ⇒ Boolean

returns true iff tree, if flattened, would be cnf allows nested ANDs as long as there is no ancestor OR allows nested ORs as long as there is no decendent AND

Returns:

  • (Boolean) 


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# File 'lib/udb/logic.rb', line 2960

def nested_cnf?
  unless @memo.is_nested_cnf.nil?
    return @memo.is_nested_cnf
  end

  ret =
    case @type
    when LogicNodeType::Term, LogicNodeType::True, LogicNodeType::False
      true
    when LogicNodeType::Not
      node_children.fetch(0).type == LogicNodeType::Term
    when LogicNodeType::And
      node_children.all? do |child|
        child.nested_cnf_conjunction_term?(false)
      end
    when LogicNodeType::Or
      # or is only valid if only it recursively contains only literals or disjunctions
      node_children.all? do |child|
        [
          child.type == LogicNodeType::True,
          child.type == LogicNodeType::False,
          child.type == LogicNodeType::Term,
          ((child.type == LogicNodeType::Not) && \
            child.node_children.fetch(0).type == LogicNodeType::Term),
          child.type == LogicNodeType::Or && \
            child.node_children.all? { |grandchild| grandchild.nested_cnf_conjunction_term?(true) }
        ].any?
      end
    when LogicNodeType::Xor, LogicNodeType::If, LogicNodeType::None
      false
    else
      T.absurd(@type)
    end
  @memo.is_nested_cnf = ret
end

#nested_cnf_conjunction_term?(ancestor_or) ⇒ Boolean

This method is part of a private API. You should avoid using this method if possible, as it may be removed or be changed in the future.

returns true iff tree is a valid term in a nested cnf conjunction

Parameters:

  • ancestor_or (Boolean)

Returns:

  • (Boolean) 


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# File 'lib/udb/logic.rb', line 2916

def nested_cnf_conjunction_term?(ancestor_or)
  case @type
  when LogicNodeType::Term, LogicNodeType::True, LogicNodeType::False
    true
  when LogicNodeType::Not
    node_children.fetch(0).type == LogicNodeType::Term
  when LogicNodeType::Or
    node_children.all? do |child|
      [
        child.type == LogicNodeType::True,
        child.type == LogicNodeType::False,
        child.type == LogicNodeType::Term,
        ((child.type == LogicNodeType::Not) && \
          child.node_children.fetch(0).type == LogicNodeType::Term),
        child.type == LogicNodeType::Or && child.nested_cnf_conjunction_term?(true)
      ].any?
    end
  when LogicNodeType::And
    return false if ancestor_or

    node_children.all? do |child|
      [
        child.type == LogicNodeType::True,
        child.type == LogicNodeType::False,
        child.type == LogicNodeType::Term,
        ((child.type == LogicNodeType::Not) && \
          child.node_children.fetch(0).type == LogicNodeType::Term),
        (child.type == LogicNodeType::Or && \
          child.nested_cnf_conjunction_term?(true)),
        (child.type == LogicNodeType::And && \
          child.nested_cnf_conjunction_term?(ancestor_or))
      ].any?
    end
  when LogicNodeType::Xor, LogicNodeType::If, LogicNodeType::None
    false
  else
    T.absurd(@type)
  end
end

#nnf ⇒ LogicNode

Returns self, converted to Negation Normal Form.

Returns:

  • (LogicNode) —

    self, converted to Negation Normal Form



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# File 'lib/udb/logic.rb', line 2216

def nnf
  do_nnf(self)
end

#nnf? ⇒ Boolean

Returns true iff self is in Negation Normal Form.

Returns:

  • (Boolean) —

    true iff self is in Negation Normal Form



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# File 'lib/udb/logic.rb', line 2221

def nnf?
  if @type == LogicNodeType::Not
    node_children.fetch(0).type == LogicNodeType::Term
  elsif @type == LogicNodeType::Term
    true
  else
    node_children.all? { |child| child.nnf? }
  end
end

#node_children ⇒ Array<LogicNode>

This method is part of a private API. You should avoid using this method if possible, as it may be removed or be changed in the future.

Returns:



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# File 'lib/udb/logic.rb', line 1298

def node_children
  @node_children
end

#partial_evaluate(cb) ⇒ LogicNode

partially evalute – replace anything known with true/false, and otherwise leave it alone

Parameters:

Returns:



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# File 'lib/udb/logic.rb', line 1790

def partial_evaluate(cb)
  case @type
  when LogicNodeType::Term
    res = cb.call(T.cast(@children.fetch(0), TermType))
    if res == SatisfiedResult::Yes
      True
    elsif res == SatisfiedResult::No
      False
    else
      self
    end
  else
    LogicNode.new(@type, node_children.map { |child| child.partial_evaluate(cb) })
  end
end

#reduce ⇒ LogicNode

reduce the equation by removing easy identities:

(A || B || .. || true) => true (A || B || .. || Z || !Z) => true (A && B && .. && false) => false (A && B && .. && Z && !Z) => false NONE(A, B, …, true) => false false -> A => true true -> A => A

Returns:



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# File 'lib/udb/logic.rb', line 2601

def reduce
  unless @memo.is_reduced.nil?
    raise "?" unless @memo.is_reduced == true
    return self
  end

  reduced =
    case @type
    when LogicNodeType::And
      reduced = LogicNode.new(LogicNodeType::And, node_children.map { |child| child.reduce })
      # see if there is a false term or a contradiction (a && !a)
      # if so, reduce to false
      must_be_false = reduced.node_children.any? do |child|

        # a false anywhere will make the conjunction false
        child.type == LogicNodeType::False ||

          # a contradiction (a && !a) will make the conjunction false
          (child.type == LogicNodeType::Term &&
            reduced.node_children.any? do |other_child|

              other_child.type == LogicNodeType::Not && \
              other_child.node_children.fetch(0).type == LogicNodeType::Term && \
              child.children.fetch(0) == other_child.node_children.fetch(0).children.fetch(0)
            end)
      end
      if must_be_false
        False
      else

        # eliminate True
        true_reduced_children = reduced.node_children.reject { |c| c.type == LogicNodeType::True }
        if true_reduced_children.size != reduced.children.size
          reduced =
            if true_reduced_children.size == 0
              True
            elsif true_reduced_children.size == 1
              true_reduced_children.fetch(0)
            else
              LogicNode.new(LogicNodeType::And, true_reduced_children)
            end
        end

        reduced
      end
    when LogicNodeType::Or
      reduced = LogicNode.new(LogicNodeType::Or, node_children.map { |child| child.reduce })
      # see if there is a true term or a tautology (a || !a)
      # if so, reduce to true
      must_be_true = reduced.node_children.any? do |child|

        # a true anywhere will make the disjunction true
        child.type == LogicNodeType::True ||

          # a tautology (a || !a) will make the disjunction true
          (child.type == LogicNodeType::Term &&
            reduced.node_children.any? do |other_child|

              other_child.type == LogicNodeType::Not && \
              other_child.node_children.fetch(0).type == LogicNodeType::Term && \
              child.children.fetch(0) == other_child.node_children.fetch(0).children.fetch(0)
            end)
      end
      if must_be_true
        True
      else

        # eliminate False
        false_reduced_children = reduced.node_children.reject { |c| c.type == LogicNodeType::False }
        if false_reduced_children.size != reduced.children.size
          reduced =
            if false_reduced_children.size == 0
              False
            elsif false_reduced_children.size == 1
              false_reduced_children.fetch(0)
            else
              LogicNode.new(LogicNodeType::Or, false_reduced_children)
            end
        end

        reduced
      end
    when LogicNodeType::Xor
      reduced = LogicNode.new(LogicNodeType::Xor, node_children.map { |child| child.reduce })
      xor_with_self = reduced.children.size == 2 &&
        reduced.node_children.fetch(0).type == LogicNodeType::Term &&
        reduced.node_children.fetch(1).type == LogicNodeType::Term &&
        reduced.node_children.fetch(0).children.fetch(0) == reduced.node_children.fetch(1).children.fetch(0)
      if xor_with_self
        # xor with self if always false
        False
      else
        reduced
      end
    when LogicNodeType::If
      reduced = LogicNode.new(LogicNodeType::If, node_children.map { |child| child.reduce })
      antecedent = reduced.node_children.fetch(0)
      consequent = reduced.node_children.fetch(1)
      if antecedent.type == LogicNodeType::True
        consequent
      elsif antecedent.type == LogicNodeType::False
        return True
      elsif consequent.type == LogicNodeType::True
        return True
      elsif consequent.type == LogicNodeType::False
        return LogicNode.new(LogicNodeType::Not, [antecedent])
      else
        reduced
      end
    when LogicNodeType::Not
      reduced = LogicNode.new(LogicNodeType::Not, node_children.map { |child| child.reduce })
      child = reduced.node_children.fetch(0)
      if child.type == LogicNodeType::Not
        # !!a = a
        reduced.node_children.fetch(0).node_children.fetch(0)
      elsif child.type == LogicNodeType::False
        # !false = true
        return True
      elsif child.type == LogicNodeType::True
        # !true = false
        return False
      else
        reduced
      end
    when LogicNodeType::None
      if node_children.any? { |c| c.type == LogicNodeType::True }
        True
      else
        self.dup
      end
    when LogicNodeType::True, LogicNodeType::False, LogicNodeType::Term
      self
    else
      T.absurd(@type)
    end

  if reduced.memo.is_reduced.nil?
    reduced.memo.is_reduced = true
  end
  reduced
end

#replace_terms(callback) ⇒ LogicNode

Parameters:

Returns:



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# File 'lib/udb/logic.rb', line 1668

def replace_terms(callback)
  case @type
  when LogicNodeType::True, LogicNodeType::False
    self
  when LogicNodeType::Term
    callback.call(self)
  when LogicNodeType::If, LogicNodeType::Not, LogicNodeType::And,
       LogicNodeType::Or, LogicNodeType::None, LogicNodeType::Xor
    LogicNode.new(
      @type,
      node_children.map { |c| c.replace_terms(callback) }
    )
  else
    T.absurd(@type)
  end
end

#satisfiability_depends_on_ext_req?(ext_req) ⇒ Boolean

If ext_req is false, can this logic tree be satisfied?

Parameters:

Returns:

  • (Boolean) 


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# File 'lib/udb/logic.rb', line 1325

def satisfiability_depends_on_ext_req?(ext_req)
  # the tree needs something in ext_vers if it is always
  # unsatisfiable when the corresponding ExtensionTerms are false
  cb = LogicNode.make_eval_cb do |term|
    case term
    when ExtensionTerm
      ext_req.satisfied_by?(term.to_ext_req(ext_req.cfg_arch)) \
        ? SatisfiedResult::No
        : SatisfiedResult::Maybe
    when ParameterTerm
      SatisfiedResult::Maybe
    when FreeTerm
      SatisfiedResult::No
    when XlenTerm
      SatisfiedResult::Maybe
    else
      T.absurd(term)
    end
  end
  eval_cb(cb) == SatisfiedResult::No
end

#satisfiable? ⇒ Boolean

Returns true iff self is satisfiable (possible to be true for some combination of term values).

Returns:

  • (Boolean) —

    true iff self is satisfiable (possible to be true for some combination of term values)



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# File 'lib/udb/logic.rb', line 3091

def satisfiable?
  @memo.is_satisfiable ||=
    begin
      nterms = terms.size

      if nterms < 8 && literals.size <= 128
        # just brute force it
        LogicNode.inc_brute_force_sat_solves
        term_idx = T.let({}, T::Hash[TermType, Integer])
        terms.each_with_index do |term, idx|
          term_idx[term] = idx
        end
        # define the callback outside the loop to avoid allocating a new block on every iteration
        val_out_of_loop = 0
        cb = LogicNode.make_eval_cb do |term|
          ((val_out_of_loop >> term_idx.fetch(term)) & 1).zero? ? SatisfiedResult::No : SatisfiedResult::Yes
        end

        if nterms.zero?
          return eval_cb(cb) == SatisfiedResult::Yes
        else
          (2**nterms).to_i.times do |i|
            val_out_of_loop = i
            if eval_cb(cb) == SatisfiedResult::Yes
              return true
            end
          end
        end
        return false

      else
        # use SAT solver
        LogicNode.inc_minisat_sat_solves

        @@cache ||= {}
        cache_key = hash
        if @@cache.key?(cache_key)
          LogicNode.inc_minisat_cache_hits
          return @@cache[cache_key]
        end

        c = self.cnf? ? self : equisat_cnf
        # raise "cnf error" unless c.cnf?

        if c.type == LogicNodeType::True
          return true
        elsif c.type == LogicNodeType::False
          return false
        end

        t = c.terms

        solver = MiniSat::Solver.new

        term_map = T.let({}, T::Hash[TermType, MiniSat::Variable])
        t.each do |term|
          unless term_map.key?(term)
            term_map[term] = solver.new_var
          end
        end
        raise "term mapping failed" unless t.uniq == term_map.keys

        build_solver(solver, flatten_cnf(c), term_map, nil)

        solver.solve
        @@cache[cache_key] = solver.satisfied?
      end
    end
end

#terms ⇒ Array<TermType>

Returns The unique terms (leafs) of this tree.

Returns:

  • (Array<TermType>) —

    The unique terms (leafs) of this tree



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# File 'lib/udb/logic.rb', line 1349

def terms
  @memo.terms ||=
    begin
      t = literals.uniq
      raise "Problem with parameter hashing\n#{t.map(&:to_s).uniq}\n#{t.map(&:to_s)}" unless t.map(&:to_s).uniq == t.map(&:to_s)
      t
    end
end

#terms_no_antecendents ⇒ Array<TermType>

Returns The unique terms (leafs) of this tree, exculding antecendents of an IF.

Returns:

  • (Array<TermType>) —

    The unique terms (leafs) of this tree, exculding antecendents of an IF



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# File 'lib/udb/logic.rb', line 1360

def terms_no_antecendents
  if @type == LogicNodeType::If
    node_children.fetch(1).terms_no_antecendents
  elsif @type == LogicNodeType::Term
    [T.cast(@children.fetch(0), TermType)]
  else
    node_children.map { |child| child.terms_no_antecendents }.flatten.uniq
  end
end

#to_asciidoc(include_versions:) ⇒ String

Parameters:

  • include_versions (Boolean)

Returns:

  • (String) 


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# File 'lib/udb/logic.rb', line 1968

def to_asciidoc(include_versions:)
  case @type
  when LogicNodeType::Term
    term = T.cast(children.fetch(0), TermType)
    if term.is_a?(ExtensionTerm)
      if include_versions
        "`#{term.name}`#{term.comparison}#{term.version.canonical}"
      else
        "`#{term.name}`"
      end
    elsif term.is_a?(ParameterTerm)
      term.to_asciidoc
    elsif term.is_a?(FreeTerm)
      raise "Should not occur"
    elsif term.is_a?(XlenTerm)
      term.to_asciidoc
    else
      T.absurd(term)
    end
  when LogicNodeType::False
    "false"
  when LogicNodeType::True
    "true"
  when LogicNodeType::Not
    if node_children.fetch(0).type == LogicNodeType::Term
      term = node_children.fetch(0).children.fetch(0)
      if term.is_a?(ParameterTerm)
        negation = term.negate
        unless negation.nil?
          return negation.to_asciidoc
        end
      end
    end
    "!#{node_children.fetch(0).to_asciidoc(include_versions:)}"
  when LogicNodeType::And
    "++(++#{node_children.map { |c| c.to_asciidoc(include_versions:) }.join(" && ")})"
  when LogicNodeType::Or
    "++(++#{node_children.map { |c| c.to_asciidoc(include_versions:) }.join(" pass:[||] ")})"
  when LogicNodeType::If
    "++(++#{node_children.fetch(0).to_asciidoc(include_versions:)} -> #{node_children.fetch(1).to_asciidoc(include_versions:)})"
  when LogicNodeType::Xor
    "++(++#{node_children.map { |c| c.to_asciidoc(include_versions:) }.join(" &#2295; ")})"
  when LogicNodeType::None
    "!++(++#{node_children.map { |c| c.to_asciidoc(include_versions:) }.join(" pass:[||] ")})"
  else
    T.absurd(@type)
  end
end

#to_dimacs ⇒ String

Returns:

  • (String) 


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# File 'lib/udb/logic.rb', line 3420

def to_dimacs
  if @type == LogicNodeType::Term
    <<~DIMACS
      p cnf 1 1
      1 0
    DIMACS
  elsif @type == LogicNodeType::Not && node_children.fetch(0).type == LogicNodeType::Term
    <<~DIMACS
      p cnf 1 1
      -1 0
    DIMACS
  elsif @type == LogicNodeType::True || @type == LogicNodeType::False
    raise "Cannot represent true/false in DIMACS"
  elsif @type == LogicNodeType::And
    lines = ["p cnf #{terms.size} #{@children.size}"]
    lines += node_children.map do |child|
      if child.type == LogicNodeType::Or
        term_line = child.node_children.map do |grandchild|
          if grandchild.type == LogicNodeType::Not
            (-(T.must(terms.index(grandchild.node_children.fetch(0).node_children.fetch(0))) + 1)).to_s
          elsif grandchild.type == LogicNodeType::Term
            (T.must(terms.index(grandchild.node_children.fetch(0))) + 1).to_s
          end
        end.join(" ")
        "#{term_line} 0"
      elsif child.type == LogicNodeType::Term
        "#{T.must(terms.index(child.children.fetch(0))) + 1} 0"
      elsif child.type == LogicNodeType::Not
        "-#{T.must(terms.index(child.node_children.fetch(0).children.fetch(0))) + 1} 0"
      else
        raise "Not CNF"
      end
    end

    lines.join("\n")
  else
    raise "Not CNF"
  end
end

#to_eqntott ⇒ EqntottResult

return equation suitable for ‘eqntott` input

Returns:



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# File 'lib/udb/logic.rb', line 3256

def to_eqntott
  next_term_name = "a"
  term_map = T.let({}, T::Hash[TermType, String])
  t = terms
  t.each do |term|
    unless term_map.key?(term)
      term_map[term] = next_term_name
      next_term_name = next_term_name.next
    end
  end

  EqntottResult.new(eqn: "out = #{do_to_eqntott(self, term_map)}", term_map: term_map.invert)
end

#to_h(term_determined = false) ⇒ Boolean, Hash{String => T.untyped}

convert to a UDB schema

Parameters:

  • term_determined (Boolean) (defaults to: false)

Returns:

  • (Boolean, Hash{String => T.untyped}) 


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# File 'lib/udb/logic.rb', line 2043

def to_h(term_determined = false)
  if @type == LogicNodeType::True
    true
  elsif @type == LogicNodeType::False
    false
  elsif @type == LogicNodeType::Term
    if term_determined
      @children.fetch(0).to_h
    else
      child = T.cast(@children.fetch(0), TermType)
      case child
      when ExtensionTerm
        { "extension" => @children.fetch(0).to_h }
      when ParameterTerm
        { "param" => @children.fetch(0).to_h }
      when FreeTerm
        { "free" => child.id } # only needed for #hash
      when XlenTerm
        @children.fetch(0).to_h
      else
        T.absurd(child)
      end
    end
  elsif @type == LogicNodeType::Not
    child = node_children.fetch(0)
    if !term_determined && terms_no_antecendents.all? { |term| term.is_a?(ExtensionTerm) }
      { "extension" => { "not" => child.to_h(true) } }
    elsif !term_determined && terms_no_antecendents.all? { |term| term.is_a?(ParameterTerm) }
      { "param" => { "not" => child.to_h(true) } }
    else
      { "not" => child.to_h(term_determined) }
    end
  elsif @type == LogicNodeType::And
    if !term_determined && terms_no_antecendents.all? { |term| term.is_a?(ExtensionTerm) }
      { "extension" => { "allOf" => node_children.map { |child| child.to_h(true) } } }
    elsif !term_determined && terms_no_antecendents.all? { |term| term.is_a?(ParameterTerm) }
      { "param" => { "allOf" => node_children.map { |child| child.to_h(true) } } }
    else
      { "allOf" => node_children.map { |child| child.to_h(term_determined) } }
    end
  elsif @type == LogicNodeType::Or
    if !term_determined && terms_no_antecendents.all? { |term| term.is_a?(ExtensionTerm) }
      { "extension" => { "anyOf" => node_children.map { |child| child.to_h(true) } } }
    elsif !term_determined && terms_no_antecendents.all? { |term| term.is_a?(ParameterTerm) }
      { "param" => { "anyOf" => node_children.map { |child| child.to_h(true) } } }
    else
      { "anyOf" => node_children.map { |child| child.to_h(term_determined) } }
    end
  elsif @type == LogicNodeType::Xor
    if !term_determined && terms_no_antecendents.all? { |term| term.is_a?(ExtensionTerm) }
      { "extension" => { "oneOf" => node_children.map { |child| child.to_h(true) } } }
    elsif !term_determined && terms_no_antecendents.all? { |term| term.is_a?(ParameterTerm) }
      { "param" => { "oneOf" => node_children.map { |child| child.to_h(true) } } }
    else
      { "oneOf" => node_children.map { |child| child.to_h(term_determined) } }
    end
  elsif @type == LogicNodeType::None
    if !term_determined && terms_no_antecendents.all? { |term| term.is_a?(ExtensionTerm) }
      { "extension" => { "noneOf" => node_children.map { |child| child.to_h(true) } } }
    elsif !term_determined && terms_no_antecendents.all? { |term| term.is_a?(ParameterTerm) }
      { "param" => { "noneOf" => node_children.map { |child| child.to_h(true) } } }
    else
      { "noneOf" => node_children.map { |child| child.to_h(term_determined) } }
    end
  elsif @type == LogicNodeType::If
    {
      "if" => node_children.fetch(0).to_h(false),
      "then" => node_children.fetch(1).to_h(term_determined)
    }
  else
    T.absurd(@type)
  end
end

#to_idl(cfg_arch) ⇒ String

Parameters:

Returns:

  • (String) 


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# File 'lib/udb/logic.rb', line 2018

def to_idl(cfg_arch)
  case @type
  when LogicNodeType::True
    "true"
  when LogicNodeType::False
    "false"
  when LogicNodeType::Term
    T.cast(@children.fetch(0), TermType).to_idl(cfg_arch)
  when LogicNodeType::Not
    "!#{node_children.fetch(0).to_idl(cfg_arch)}"
  when LogicNodeType::And
    "(#{node_children.map { |c| c.to_idl(cfg_arch) }.join(" && ") })"
  when LogicNodeType::Or
    "(#{node_children.map { |c| c.to_idl(cfg_arch) }.join(" || ")})"
  when LogicNodeType::Xor, LogicNodeType::None
    nnf.to_idl(cfg_arch)
  when LogicNodeType::If
    "(!(#{node_children.fetch(0).to_idl(cfg_arch)}) || (#{node_children.fetch(1).to_idl(cfg_arch)}))"
  else
    T.absurd(@type)
  end
end

#to_s(format: LogicSymbolFormat::Predicate) ⇒ String

Parameters:

Returns:

  • (String) 


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# File 'lib/udb/logic.rb', line 1906

def to_s(format: LogicSymbolFormat::Predicate)
  if @type == LogicNodeType::True
    LOGIC_SYMBOLS[format][:TRUE]
  elsif @type == LogicNodeType::False
    LOGIC_SYMBOLS[format][:FALSE]
  elsif @type == LogicNodeType::Term
    @children[0].to_s
  elsif @type == LogicNodeType::Not
    "#{LOGIC_SYMBOLS[format][:NOT]}#{node_children.fetch(0).to_s(format:)}"
  elsif @type == LogicNodeType::And
    "(#{node_children.map { |c| c.to_s(format:) }.join(" #{LOGIC_SYMBOLS[format][:AND]} ")})"
  elsif @type == LogicNodeType::Or
    "(#{node_children.map { |c| c.to_s(format:) }.join(" #{LOGIC_SYMBOLS[format][:OR]} ")})"
  elsif @type == LogicNodeType::Xor
    "(#{node_children.map { |c| c.to_s(format:) }.join(" #{LOGIC_SYMBOLS[format][:XOR]} ")})"
  elsif @type == LogicNodeType::None
    "#{LOGIC_SYMBOLS[format][:NOT]}(#{node_children.map { |c| c.to_s(format:) }.join(" #{LOGIC_SYMBOLS[format][:OR]} ")})"
  elsif @type == LogicNodeType::If
    "(#{node_children.fetch(0).to_s(format:)} #{LOGIC_SYMBOLS[format][:IMPLIES]} #{node_children.fetch(1).to_s(format:)})"
  else
    T.absurd(@type)
  end
end

#to_s_pretty ⇒ String

return a nice, human-readable form that may gloss over details

Returns:

  • (String) 


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# File 'lib/udb/logic.rb', line 1856

def to_s_pretty
  if @type == LogicNodeType::True
    "true"
  elsif @type == LogicNodeType::False
    "false"
  elsif @type == LogicNodeType::Term
    @children.fetch(0).to_s_pretty
  elsif @type == LogicNodeType::Not
    "not #{@children.fetch(0).to_s_pretty}"
  elsif @type == LogicNodeType::And
    "(#{node_children.map { |c| c.to_s_pretty }.join(" and ")})"
  elsif @type == LogicNodeType::Or
    "(#{node_children.map { |c| c.to_s_pretty }.join(" or ")})"
  elsif @type == LogicNodeType::Xor
    "(#{node_children.map { |c| c.to_s_pretty }.join(" xor ")})"
  elsif @type == LogicNodeType::None
    "none of (#{node_children.map { |c| c.to_s_pretty }.join(", ")})"
  elsif @type == LogicNodeType::If
    "if #{node_children.fetch(0).to_s_pretty} then #{node_children.fetch(1).to_s_pretty})"
  else
    T.absurd(@type)
  end
end

#to_s_with_value(callback, format: LogicSymbolFormat::Predicate) ⇒ String

Parameters:

Returns:

  • (String) 


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# File 'lib/udb/logic.rb', line 1931

def to_s_with_value(callback, format: LogicSymbolFormat::Predicate)
  if @type == LogicNodeType::True
    LOGIC_SYMBOLS[format][:TRUE]
  elsif @type == LogicNodeType::False
    LOGIC_SYMBOLS[format][:FALSE]
  elsif @type == LogicNodeType::Term
    v = callback.call(T.cast(@children.fetch(0), TermType))
    str =
      case v
      when SatisfiedResult::Yes
        "{true}"
      when SatisfiedResult::No
        "{false}"
      when SatisfiedResult::Maybe
        "{unknown}"
      else
        T.absurd(v)
      end
    "`#{@children.fetch(0)}`#{str}"
  elsif @type == LogicNodeType::Not
    "#{LOGIC_SYMBOLS[format][:NOT]}#{node_children.fetch(0).to_s_with_value(callback, format:)}"
  elsif @type == LogicNodeType::And
    "(#{node_children.map { |c| c.to_s_with_value(callback, format:) }.join(" #{LOGIC_SYMBOLS[format][:AND]} ")})"
  elsif @type == LogicNodeType::Or
    "(#{node_children.map { |c| c.to_s_with_value(callback, format:) }.join(" #{LOGIC_SYMBOLS[format][:OR]} ")})"
  elsif @type == LogicNodeType::Xor
    "(#{node_children.map { |c| c.to_s_with_value(callback, format:) }.join(" #{LOGIC_SYMBOLS[format][:XOR]} ")})"
  elsif @type == LogicNodeType::None
    "#{LOGIC_SYMBOLS[format][:NOT]}(#{node_children.map { |c| c.to_s_with_value(callback, format:) }.join(" #{LOGIC_SYMBOLS[format][:OR]} ")})"
  elsif @type == LogicNodeType::If
    "(#{node_children.fetch(0).to_s_with_value(callback, format:)} #{LOGIC_SYMBOLS[format][:IMPLIES]} #{node_children.fetch(1).to_s_with_value(callback, format:)})"
  else
    T.absurd(@type)
  end
end

#to_z3(cfg_arch, solver = Z3Solver.new) ⇒ Z3::BoolExpr

Parameters:

Returns:

  • (Z3::BoolExpr) 


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# File 'lib/udb/logic.rb', line 3045

def to_z3(cfg_arch, solver = Z3Solver.new)
  case @type
  when LogicNodeType::Term
    t = @children.fetch(0)
    if t.is_a?(ParameterTerm) || t.is_a?(ExtensionTerm)
      t.to_z3(solver, cfg_arch)
    else
      raise "unexpected" if t.is_a?(FreeTerm) || t.is_a?(LogicNode)

      t.to_z3(solver)
    end
  when LogicNodeType::Or
    T.unsafe(Z3).Or(*node_children.map { |c| c.to_z3(cfg_arch, solver) })
  when LogicNodeType::And
    T.unsafe(Z3).And(*node_children.map { |c| c.to_z3(cfg_arch, solver) })
  when LogicNodeType::Xor
    if node_children.size == 2
      T.unsafe(Z3).Xor(*node_children.map { |c| c.to_z3(cfg_arch, solver) })
    else
      # see https://stackoverflow.com/questions/14888174/how-do-i-determine-if-exactly-one-boolean-is-true-without-type-conversion#33268481
      uneven_number_is_true = T.unsafe(Z3).Xor(*node_children.map { |c| c.to_z3(cfg_arch, solver) })
      max_one_is_true =
        T.unsafe(Z3).And(
          *node_children.combination(2).map do |pair|
            !(pair.fetch(0).to_z3(cfg_arch, solver) & pair.fetch(1).to_z3(cfg_arch, solver))
          end
        )
      uneven_number_is_true & max_one_is_true
    end
  when LogicNodeType::True
    Z3.True
  when LogicNodeType::False
    Z3.False
  when LogicNodeType::Not
    !node_children.fetch(0).to_z3(cfg_arch, solver)
  when LogicNodeType::None
    !node_children.map { |c| c.to_z3(cfg_arch, solver) }.reduce(:|)
  when LogicNodeType::If
    node_children.fetch(0).to_z3(cfg_arch, solver).implies(node_children.fetch(1).to_z3(cfg_arch, solver))
  else
    T.absurd(@type)
  end
end

#tseytin ⇒ LogicNode

This method is part of a private API. You should avoid using this method if possible, as it may be removed or be changed in the future.

Returns:



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# File 'lib/udb/logic.rb', line 3401

def tseytin
  subformulae = []
  r = reduce
  return r if [LogicNodeType::Term, LogicNodeType::True, LogicNodeType::False].any?(r.type)

  grouped = r.group_by_2
  grouped.collect_tseytin(subformulae)

  if subformulae.size == 0
    raise "? #{r}"
  elsif subformulae.size == 1
    subformulae.fetch(0)
  else
    equisatisfiable_formula = LogicNode.new(LogicNodeType::And, subformulae + [grouped.tseytin_prop])
    flatten_cnf(equisatisfiable_formula).reduce
  end
end

#tseytin_prop ⇒ LogicNode

a free variable representing this formula

Returns:



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# File 'lib/udb/logic.rb', line 3389

def tseytin_prop
  case @type
  when LogicNodeType::Term, LogicNodeType::True, LogicNodeType::False
    self
  else
    @tseytin_prop ||=
      LogicNode.new(LogicNodeType::Term, [FreeTerm.new])
  end
end

#unsatisfiable? ⇒ Boolean

Returns true iff self is unsatisfiable (not possible to be true for any combination of term values).

Returns:

  • (Boolean) —

    true iff self is unsatisfiable (not possible to be true for any combination of term values)



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# File 'lib/udb/logic.rb', line 3163

def unsatisfiable? = !satisfiable?