index a5d9495..b0b5d0e 100644 (file)
@@ -56,14 +56,23 @@ class Polyhedron(Domain):

@property
def equalities(self):
+        """
+        Return a list of the equalities in a set.
+        """
return self._equalities

@property
def inequalities(self):
+        """
+        Return a list of the inequalities in a set.
+        """
return self._inequalities

@property
def constraints(self):
+        """
+        Return ta list of the constraints of a set.
+        """
return self._constraints

@property
@@ -72,13 +81,13 @@ class Polyhedron(Domain):

def disjoint(self):
"""
-        Return this set as disjoint.
+        Return a set as disjoint.
"""
return self

def isuniverse(self):
"""
-        Return true if this set is the Universe set.
+        Return true if a set is the Universe set.
"""
islbset = self._toislbasicset(self.equalities, self.inequalities,
self.symbols)
@@ -88,7 +97,7 @@ class Polyhedron(Domain):

def aspolyhedron(self):
"""
-        Return polyhedral hull of this set.
+        Return polyhedral hull of a set.
"""
return self

@@ -106,12 +115,41 @@ class Polyhedron(Domain):
return True

def subs(self, symbol, expression=None):
+        """
+        Subsitute the given value into an expression and return the resulting
+        expression.
+        """
equalities = [equality.subs(symbol, expression)
for equality in self.equalities]
inequalities = [inequality.subs(symbol, expression)
for inequality in self.inequalities]
return Polyhedron(equalities, inequalities)

+    def _asinequalities(self):
+        inequalities = list(self.equalities)
+        inequalities.extend([-expression for expression in self.equalities])
+        inequalities.extend(self.inequalities)
+        return inequalities
+
+    def widen(self, other):
+        if not isinstance(other, Polyhedron):
+            raise ValueError('argument must be a Polyhedron instance')
+        inequalities1 = self._asinequalities()
+        inequalities2 = other._asinequalities()
+        inequalities = []
+        for inequality1 in inequalities1:
+            if other <= Polyhedron(inequalities=[inequality1]):
+                inequalities.append(inequality1)
+        for inequality2 in inequalities2:
+            for i in range(len(inequalities1)):
+                inequalities3 = inequalities1[:i] + inequalities[i + 1:]
+                inequalities3.append(inequality2)
+                polyhedron3 = Polyhedron(inequalities=inequalities3)
+                if self == polyhedron3:
+                    inequalities.append(inequality2)
+                    break
+        return Polyhedron(inequalities=inequalities)
+
@classmethod
def _fromislbasicset(cls, islbset, symbols):
islconstraints = islhelper.isl_basic_set_constraints(islbset)
@@ -184,42 +222,39 @@ class Polyhedron(Domain):
return domain

def __repr__(self):
-        if self.isempty():
-            return 'Empty'
-        elif self.isuniverse():
-            return 'Universe'
+        strings = []
+        for equality in self.equalities:
+            strings.append('Eq({}, 0)'.format(equality))
+        for inequality in self.inequalities:
+            strings.append('Ge({}, 0)'.format(inequality))
+        if len(strings) == 1:
+            return strings[0]
else:
-            strings = []
-            for equality in self.equalities:
-                strings.append('Eq({}, 0)'.format(equality))
-            for inequality in self.inequalities:
-                strings.append('Ge({}, 0)'.format(inequality))
-            if len(strings) == 1:
-                return strings[0]
-            else:
-                return 'And({})'.format(', '.join(strings))
+            return 'And({})'.format(', '.join(strings))
+

def _repr_latex_(self):
-        if self.isempty():
-            return '\$\\emptyset\$'
-        elif self.isuniverse():
-            return '\$\\Omega\$'
-        else:
-            strings = []
-            for equality in self.equalities:
-                strings.append('{} = 0'.format(equality._repr_latex_().strip('\$')))
-            for inequality in self.inequalities:
-                strings.append('{} \\ge 0'.format(inequality._repr_latex_().strip('\$')))
-            return '\${}\$'.format(' \\wedge '.join(strings))
+        strings = []
+        for equality in self.equalities:
+            strings.append('{} = 0'.format(equality._repr_latex_().strip('\$')))
+        for inequality in self.inequalities:
+            strings.append('{} \\ge 0'.format(inequality._repr_latex_().strip('\$')))
+        return '\$\${}\$\$'.format(' \\wedge '.join(strings))

@classmethod
def fromsympy(cls, expr):
+        """
+        Convert a sympy object to an expression.
+        """
domain = Domain.fromsympy(expr)
if not isinstance(domain, Polyhedron):
raise ValueError('non-polyhedral expression: {!r}'.format(expr))
return domain

def tosympy(self):
+        """
+        Return an expression as a sympy object.
+        """
import sympy
constraints = []
for equality in self.equalities:
@@ -228,6 +263,55 @@ class Polyhedron(Domain):
constraints.append(sympy.Ge(inequality.tosympy(), 0))
return sympy.And(*constraints)

+class EmptyType(Polyhedron):
+
+    __slots__ = Polyhedron.__slots__
+
+    def __new__(cls):
+        self = object().__new__(cls)
+        self._equalities = (Rational(1),)
+        self._inequalities = ()
+        self._constraints = self._equalities
+        self._symbols = ()
+        self._dimension = 0
+        return self
+
+    def widen(self, other):
+        if not isinstance(other, Polyhedron):
+            raise ValueError('argument must be a Polyhedron instance')
+        return other
+
+    def __repr__(self):
+        return 'Empty'
+
+    def _repr_latex_(self):
+        return '\$\$\\emptyset\$\$'
+
+Empty = EmptyType()
+
+
+class UniverseType(Polyhedron):
+
+    __slots__ = Polyhedron.__slots__
+
+    def __new__(cls):
+        self = object().__new__(cls)
+        self._equalities = ()
+        self._inequalities = ()
+        self._constraints = ()
+        self._symbols = ()
+        self._dimension = ()
+        return self
+
+    def __repr__(self):
+        return 'Universe'
+
+    def _repr_latex_(self):
+        return '\$\$\\Omega\$\$'
+
+Universe = UniverseType()
+
+
def _polymorphic(func):
@functools.wraps(func)
def wrapper(left, right):
@@ -249,46 +333,42 @@ def _polymorphic(func):
@_polymorphic
def Lt(left, right):
"""
-    Return true if the first set is less than the second.
+    Assert first set is less than the second set.
"""
return Polyhedron([], [right - left - 1])

@_polymorphic
def Le(left, right):
"""
-    Return true the first set is less than or equal to the second.
+    Assert first set is less than or equal to the second set.
"""
return Polyhedron([], [right - left])

@_polymorphic
def Eq(left, right):
"""
-    Return true if the sets are equal.
+    Assert first set is equal to the second set.
"""
return Polyhedron([left - right], [])

@_polymorphic
def Ne(left, right):
"""
-    Return true if the sets are NOT equal.
+    Assert first set is not equal to the second set.
"""
return ~Eq(left, right)

@_polymorphic
def Gt(left, right):
"""
-    Return true if the first set is greater than the second set.
+    Assert first set is greater than the second set.
"""
return Polyhedron([], [left - right - 1])

@_polymorphic
def Ge(left, right):
"""
-    Return true if the first set is greater than or equal the second set.
+    Assert first set is greater than or equal to the second set.
"""
return Polyhedron([], [left - right])

-
-Empty = Eq(1, 0)
-
-Universe = Polyhedron([])