1.4 PyASN1 subtype constraints
Most ASN.1 types can correspond to an infinite set of values. To adapt to
particular application's data model and needs, ASN.1 provides a mechanism
for limiting the infinite set to values, that make sense in particular case.
Imposing value constraints on an ASN.1 type can also be seen as creating
a subtype from its base type.
In pyasn1, constraints take shape of immutable objects capable
of evaluating given value against constraintspecific requirements.
Constraint object is a property of pyasn1 type. Like TagSet property,
associated with every pyasn1 type, constraints can never be modified
in place. The only way to modify pyasn1 type constraint is to associate
new constraint object to a new pyasn1 type object.
A handful of different flavors of constraints are defined in ASN.1.
We will discuss them one by one in the following chapters and also explain
how to combine and apply them to types.
1.4.1 Single value constraint
This kind of constraint allows for limiting type to a finite, specified set
of values.
DialButton ::= OCTET STRING (
"0"  "1"  "2"  "3"  "4"  "5"  "6"  "7"  "8"  "9"
)

Its pyasn1 implementation would look like:
>>> from pyasn1.type import constraint
>>> c = constraint.SingleValueConstraint(
'0','1','2','3','4','5','6','7','8','9'
)
>>> c
SingleValueConstraint(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
>>> c('0')
>>> c('A')
Traceback (most recent call last):
...
pyasn1.type.error.ValueConstraintError:
SingleValueConstraint(0, 1, 2, 3, 4, 5, 6, 7, 8, 9) failed at: A
>>>

As can be seen in the snippet above, if a value violates the constraint, an
exception will be thrown. A constrainted pyasn1 type object holds a
reference to a constraint object (or their combination, as will be explained
later) and calls it for value verification.
>>> from pyasn1.type import univ, constraint
>>> class DialButton(univ.OctetString):
... subtypeSpec = constraint.SingleValueConstraint(
... '0','1','2','3','4','5','6','7','8','9'
... )
>>> DialButton('0')
DialButton(b'0')
>>> DialButton('A')
Traceback (most recent call last):
...
pyasn1.type.error.ValueConstraintError:
SingleValueConstraint(0, 1, 2, 3, 4, 5, 6, 7, 8, 9) failed at: A
>>>

Constrained pyasn1 value object can never hold a violating value.
1.4.2 Value range constraint
A pair of values, compliant to a type to be constrained, denote low and upper
bounds of allowed range of values of a type.
Teenagers ::= INTEGER (13..19)

And in pyasn1 terms:
>>> from pyasn1.type import univ, constraint
>>> class Teenagers(univ.Integer):
... subtypeSpec = constraint.ValueRangeConstraint(13, 19)
>>> Teenagers(14)
Teenagers(14)
>>> Teenagers(20)
Traceback (most recent call last):
...
pyasn1.type.error.ValueConstraintError:
ValueRangeConstraint(13, 19) failed at: 20
>>>

Value range constraint usually applies to numeric types.
ASN.1 MIN and MAX operands can be substituted with floating
point infinity values.
NegativeInt ::= INTEGER (MIN..1)
PositiveInt ::= INTEGER (1..MAX)

And in pyasn1 terms:
>>> from pyasn1.type import univ, constraint
>>> class NegativeInt(univ.Integer):
... subtypeSpec = constraint.ValueRangeConstraint(float('inf'), 1)
>>> NegativeInt(1)
NegativeInt(1)
>>> NegativeInt(0)
Traceback (most recent call last):
...
pyasn1.type.error.ValueConstraintError:
ValueConstraintError: ValueRangeConstraint() failed at: "0" at NegativeInt
>>> class PositiveInt(univ.Integer):
... subtypeSpec = constraint.ValueRangeConstraint(1, float('inf'))
>> PositiveInt(1)
PositiveInt(1)
>> PositiveInt(4)
PositiveInt(4)
>> PositiveInt(1)
Traceback (most recent call last):
...
pyasn1.type.error.ValueConstraintError:
ValueConstraintError: ValueRangeConstraint() failed at: "1" at PositiveInt

1.4.3 Size constraint
It is sometimes convenient to set or limit the allowed size of a data item
to be sent from one application to another to manage bandwidth and memory
consumption issues. Size constraint specifies the lower and upper bounds
of the size of a valid value.
TwoBits ::= BIT STRING (SIZE (2))

Express the same grammar in pyasn1:
>>> from pyasn1.type import univ, constraint
>>> class TwoBits(univ.BitString):
... subtypeSpec = constraint.ValueSizeConstraint(2, 2)
>>> TwoBits((1,1))
TwoBits("'11'B")
>>> TwoBits((1,1,0))
Traceback (most recent call last):
...
pyasn1.type.error.ValueConstraintError:
ValueSizeConstraint(2, 2) failed at: (1, 1, 0)
>>>

Size constraint can be applied to potentially massive values  bit or octet
strings, SEQUENCE OF/SET OF values.
1.4.4 Alphabet constraint
The permitted alphabet constraint is similar to Single value constraint
but constraint applies to individual characters of a value.
MorseCode ::= PrintableString (FROM ("."""" "))

And in pyasn1:
>>> from pyasn1.type import char, constraint
>>> class MorseCode(char.PrintableString):
... subtypeSpec = constraint.PermittedAlphabetConstraint(".", "", " ")
>>> MorseCode("......")
MorseCode('......')
>>> MorseCode("?")
Traceback (most recent call last):
...
pyasn1.type.error.ValueConstraintError:
PermittedAlphabetConstraint(".", "", " ") failed at: "?"
>>>

Current implementation does not handle ranges of characters in constraint
(FROM "A".."Z" syntax), one has to list the whole set in a range.
1.4.5 Constraint combinations
Up to this moment, we used a single constraint per ASN.1 type. The standard,
however, allows for combining multiple individual constraints into
intersections, unions and exclusions.
In pyasn1 data model, all of these methods of constraint combinations are
implemented as constraintlike objects holding individual constraint (or
combination) objects. Like terminal constraint objects, combination objects
are capable to perform value verification at its set of enclosed constraints
according to the logic of particular combination.
Constraints intersection verification succeeds only if a value is
compliant to each constraint in a set. To begin with, the following
specification will constitute a valid telephone number:
PhoneNumber ::= NumericString (FROM ("0".."9")) (SIZE 11)

Constraint intersection object serves the logic above:
>>> from pyasn1.type import char, constraint
>>> class PhoneNumber(char.NumericString):
... subtypeSpec = constraint.ConstraintsIntersection(
... constraint.PermittedAlphabetConstraint('0','1','2','3','4','5','6','7','8','9'),
... constraint.ValueSizeConstraint(11, 11)
... )
>>> PhoneNumber('79039343212')
PhoneNumber('79039343212')
>>> PhoneNumber('?9039343212')
Traceback (most recent call last):
...
pyasn1.type.error.ValueConstraintError:
ConstraintsIntersection(
PermittedAlphabetConstraint('0','1','2','3','4','5','6','7','8','9'),
ValueSizeConstraint(11, 11)) failed at:
PermittedAlphabetConstraint('0','1','2','3','4','5','6','7','8','9') failed at: "?039343212"
>>> PhoneNumber('9343212')
Traceback (most recent call last):
...
pyasn1.type.error.ValueConstraintError:
ConstraintsIntersection(
PermittedAlphabetConstraint('0','1','2','3','4','5','6','7','8','9'),
ValueSizeConstraint(11, 11)) failed at:
ValueSizeConstraint(10, 10) failed at: "9343212"
>>>

Union of constraints works by making sure that a value is compliant
to any of the constraint in a set. For instance:
CapitalOrSmall ::= IA5String (FROM ('A','B','C')  FROM ('a','b','c'))

It's important to note, that a value must fully comply to any single
constraint in a set. In the specification above, a value of all small or
all capital letters is compliant, but a mix of small&capitals is not.
Here's its pyasn1 analogue:
>>> from pyasn1.type import char, constraint
>>> class CapitalOrSmall(char.IA5String):
... subtypeSpec = constraint.ConstraintsUnion(
... constraint.PermittedAlphabetConstraint('A','B','C'),
... constraint.PermittedAlphabetConstraint('a','b','c')
... )
>>> CapitalOrSmall('ABBA')
CapitalOrSmall('ABBA')
>>> CapitalOrSmall('abba')
CapitalOrSmall('abba')
>>> CapitalOrSmall('Abba')
Traceback (most recent call last):
...
pyasn1.type.error.ValueConstraintError:
ConstraintsUnion(PermittedAlphabetConstraint('A', 'B', 'C'),
PermittedAlphabetConstraint('a', 'b', 'c')) failed at: failed for "Abba"
>>>

Finally, the exclusion constraint simply negates the logic of value
verification at a constraint. In the following example, any integer value
is allowed in a type but not zero.
NoZero ::= INTEGER (ALL EXCEPT 0)

In pyasn1 the above definition would read:
>>> from pyasn1.type import univ, constraint
>>> class NoZero(univ.Integer):
... subtypeSpec = constraint.ConstraintsExclusion(
... constraint.SingleValueConstraint(0)
... )
>>> NoZero(1)
NoZero(1)
>>> NoZero(0)
Traceback (most recent call last):
...
pyasn1.type.error.ValueConstraintError:
ConstraintsExclusion(SingleValueConstraint(0)) failed at: 0
>>>

The depth of such a constraints tree, built with constraint combination objects
at its nodes, has not explicit limit. Value verification is performed in a
recursive manner till a definite solution is found.
1.5 Types relationships
In the course of data processing in an application, it is sometimes
convenient to figure out the type relationships between pyasn1 type or
value objects. Formally, two things influence pyasn1 types relationship:
tag set and subtype constraints. One pyasn1 type is considered
to be a derivative of another if their TagSet and Constraint objects are
a derivation of one another.
The following example illustrates the concept (we use the same tagset but
different constraints for simplicity):
>>> from pyasn1.type import univ, constraint
>>> i1 = univ.Integer(subtypeSpec=constraint.ValueRangeConstraint(3,8))
>>> i2 = univ.Integer(subtypeSpec=constraint.ConstraintsIntersection(
... constraint.ValueRangeConstraint(3,8),
... constraint.ValueRangeConstraint(4,7)
... ) )
>>> i1.isSameTypeWith(i2)
False
>>> i1.isSuperTypeOf(i2)
True
>>> i1.isSuperTypeOf(i1)
True
>>> i2.isSuperTypeOf(i1)
False
>>>

As can be seen in the above code snippet, there are two methods of any pyasn1
type/value object that test types for their relationship:
isSameTypeWith() and isSuperTypeOf(). The former is
selfdescriptive while the latter yields true if the argument appears
to be a pyasn1 object which has tagset and constraints derived from those
of the object being called.
