Class: Udb::Z3FiniteArray

Inherits:
Object
  • Object
show all
Extended by:
T::Sig
Defined in:
lib/udb/z3.rb

Overview

Models a finite-sized array in Z3 using explicit scalar variables

Z3 arrays are normally unbounded, but we need finite arrays with explicit size for parameter validation. This class models an array as:

  • A size variable (Z3::IntExpr)
  • Individual scalar variables for each potential element

Limitations:

  • Cannot truly represent unbounded arrays (would require ForAll/Exists quantifiers not available in the Z3 Ruby bindings)
  • Maximum practical size is 64 elements (hardcoded limit)
  • Arrays larger than 64 are capped at 64 with an error if more are needed

Instance Method Summary collapse

Constructor Details

#initialize(solver, name, sort, constraints, bitvec_width: nil)

Parameters:

  • solver (Z3Solver)
  • name (String)
  • sort (T.class_of(Z3::IntSort), T.class_of(Z3::BoolSort), T.class_of(Z3::BitvecSort))
  • constraints (ArrayConstraints)
  • bitvec_width (Integer, nil) (defaults to: nil) 


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# File 'lib/udb/z3.rb', line 138

def initialize(solver, name, sort, constraints, bitvec_width: nil)
  @name = name
  @solver = solver
  @subtype_sort =
    T.let(
      if sort == Z3::BitvecSort
        sort.new(T.must(bitvec_width))
      else
        sort.new
      end,
      Z3::Sort
    )
  @constraints = constraints
  # Determine array size: use max_size if specified, otherwise cap at 64
  # The 64-element limit is a practical constraint to keep the solver tractable
  @num_items =
    T.let(
      if @constraints.max_size.nil?
        64
      else
        if T.must(@constraints.max_size) > 64
          64
        else
          T.must(@constraints.max_size)
        end
      end,
      Integer
    )
  # Create Z3 variables for each array element and apply constraints
  @items = T.let(
    Array.new(@num_items) { |index|
      v = @subtype_sort.var("#{@name}_idx#{index}")
      constrain_element(index, v)
    },
    T::Array[T.any(Z3::BitvecExpr, Z3::IntExpr, Z3::BoolExpr)]
  )
  # Create a size variable to track the logical array length
  @size = T.let(Z3.Int("#{@name}_size"), Z3::IntExpr)
  unless @constraints.min_size.nil?
    solver.assert_as @size >= @constraints.min_size, "#{@name}_size_lower_bound"
  end
  unless @constraints.max_size.nil?
    solver.assert_as @size <= @constraints.max_size, "#{@name}_size_upper_bound"
  end
  # Handle "contains" constraint: at least one element must match the schema
  unless @constraints.contains.nil?
    target_value = @subtype_sort.var("#{@name}_contain_value")
    T.must(@constraints.contains).mthd.call(@solver, target_value, T.must(@constraints.contains).schema, assert: true)
    exprs = @items.map do |item|
      item == target_value
    end
    solver.assert T.unsafe(Z3).Or(*exprs)
  end
  # Handle uniqueness constraint: all elements must be distinct
  if @constraints.unique
    solver.assert T.unsafe(Z3).Distinct(*@items)
  end
end

Instance Method Details

#!=(ary) ⇒ Z3::BoolExpr

Parameters:

  • ary (Array<Integer, String, Boolean>)

Returns:

  • (Z3::BoolExpr) 


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# File 'lib/udb/z3.rb', line 297

def !=(ary)
  ~(self == ary)
end

#==(ary) ⇒ Z3::BoolExpr

Check array equality (same elements in same positions)

Equality is defined as:

  • Same logical size
  • Same values at each position up to the size

Special cases:

  • Empty arrays: size == 0
  • Arrays larger than our model: raise error or return false
  • Arrays smaller than min_size: return false

Parameters:

  • ary (Array<Integer, String, Boolean>) —

    The Ruby array to compare against

Returns:

  • (Z3::BoolExpr) —

    Expression that is true if arrays are equal



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# File 'lib/udb/z3.rb', line 269

def ==(ary)
  if ary.empty?
    @size == 0
  elsif ary.size > @num_items
    # Check if this is a real constraint violation or just our 64-element limit
    if @constraints.max_size.nil?
      # This is an artificial limit from our 64-element cap
      raise "Comparison of array larger than proof model can handle. May need to increase the 64-entry limit"
    elsif T.must(@constraints.max_size) > @num_items
      raise "Comparison of array larger than proof model can handle. May need to increase the 64-entry limit"
    else
      # Array can't be equal because it exceeds the schema's max_size
      return Z3.False
    end
  elsif !@constraints.min_size.nil? && (ary.size < T.must(@constraints.min_size))
    # Array is too small to satisfy min_size constraint
    return Z3.False
  else
    # Build equality expression: size matches and all elements match
    exprs = ary.each_index.map do |i|
      # Use hash for strings since Z3 doesn't have native string support
      @items.fetch(i) == (ary[i].is_a?(String) ? ary[i].hash : ary[i])
    end
    T.unsafe(Z3).And(@size == ary.size, *exprs)
  end
end

#[](idx) ⇒ Z3::BitvecExpr, ...

Parameters:

  • idx (Integer)

Returns:

  • (Z3::BitvecExpr, Z3::IntExpr, Z3::BoolExpr) 


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# File 'lib/udb/z3.rb', line 198

def [](idx)
  if idx >= @num_items
    raise "array index (#{idx}) is out of bounds (#{@num_items}). May need to increase the upper limit of Z3FiniteArray from 64"
  end
  @items.fetch(idx)
end

#constrain_element(i, v) ⇒ Z3::Expr

Apply type constraints to array element at a specific index

This method applies JSON schema constraints to an array element based on:

  1. Position-specific schemas (item_by_idx) - for tuple-style arrays
  2. General schema (item_rest) - for remaining positions

Parameters:

  • i (Integer) —

    The array index

  • v (Z3::Expr) —

    The Z3 variable representing the element

Returns:

  • (Z3::Expr) —

    The same variable (for chaining)



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# File 'lib/udb/z3.rb', line 215

def constrain_element(i, v)
  if !@constraints.item_by_idx.empty?
    already_constrained = T.let(false, T::Boolean)
    @constraints.item_by_idx.each do |idx, typ_constr|
      if idx == i
        already_constrained = true
        assertions =
          typ_constr.mthd.call(@solver, v, typ_constr.schema, assert: false)
        assertions.each { |a| @solver.assert a }
      end
    end
    # Apply general schema if no position-specific schema was found
    if !already_constrained && !@constraints.item_rest.nil?
      assertions =
        T.must(@constraints.item_rest).mthd.call(@solver, v, T.must(@constraints.item_rest).schema, assert: false)
      assertions.each { |a| @solver.assert a }
    end
  elsif !@constraints.item_rest.nil?
    T.must(@constraints.item_rest).mthd.call(@solver, v, T.must(@constraints.item_rest).schema)
  end
  v
end

#has_value?(val) ⇒ Z3::BoolExpr

Check if the array contains a specific value

Returns a Z3 expression that is true if at least one element within the logical array size equals the given value. For strings, we use hash values since Z3 doesn't natively support string types.

Parameters:

  • val (Integer, Boolean, String, Z3::Expr) —

    The value to search for

Returns:

  • (Z3::BoolExpr) —

    Expression that is true if value is present



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# File 'lib/udb/z3.rb', line 247

def has_value?(val)
  exprs = @items.each_with_index.map do |i, idx|
    # Use hash for strings since Z3 doesn't have native string support
    (i == (val.is_a?(String) ? val.hash : val)) & (@size > idx)
  end
  T.unsafe(Z3).Or(*exprs)
end

#max_size ⇒ Integer?

Returns:

  • (Integer, nil) 


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# File 'lib/udb/z3.rb', line 305

def max_size = @constraints.max_size

#size_term ⇒ Z3::IntExpr

Returns:

  • (Z3::IntExpr) 


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# File 'lib/udb/z3.rb', line 302

def size_term = @size