Solver Engine¶
angr’s solver engine is called Claripy. Claripy exposes the following design:
Claripy ASTs (the subclasses of claripy.ast.Base) provide a unified way to interact with concrete and symbolic expressions
Frontend
s provide different paradigms for evaluating these expressions. For example, theFullFrontend
solves expressions using something like an SMT solver backend, whileLightFrontend
handles them by using an abstract (and approximating) data domain backend.Each
Frontend
needs to, at some point, do actual operation and evaluations on an AST. ASTs don’t support this on their own. Instead,Backend
s translate ASTs into backend objects (i.e., Python primitives forBackendConcrete
, Z3 expressions forBackendZ3
, strided intervals forBackendVSA
, etc) and handle any appropriate statetracking objects (such as tracking the solver state in the case ofBackendZ3
). Roughly speaking, frontends take ASTs as inputs and use backends tobackend.convert()
those ASTs into backend objects that can be evaluated and otherwise reasoned about.FrontendMixin
s customize the operation ofFrontend
s. For example,ModelCacheMixin
caches solutions from an SMT solver.The combination of a Frontend, a number of FrontendMixins, and a number of Backends comprise a claripy
Solver
.
Internally, Claripy seamlessly mediates the cooperation of multiple disparate backends – concrete bitvectors, VSA constructs, and SAT solvers. It is pretty badass.
Most users of angr will not need to interact directly with Claripy (except for, maybe, claripy AST objects, which represent symbolic expressions) – angr handles most interactions with Claripy internally. However, for dealing with expressions, an understanding of Claripy might be useful.
Claripy ASTs¶
Claripy ASTs abstract away the differences between mathematical constructs that
Claripy supports. They define a tree of operations (i.e., (a + b) / c)
on
any type of underlying data. Claripy handles the application of these operations
on the underlying objects themselves by dispatching requests to the backends.
Currently, Claripy supports the following types of ASTs:
Name 
Description 
Supported By (Claripy Backends) 
Example Code 

BV 
This is a bitvector, whether symbolic (with a name) or concrete (with a value). It has a size (in bits). 
BackendConcrete, BackendVSA, BackendZ3 
Create a 32bit symbolic bitvector “x”: claripy.BVS(‘x’, 32) Create a 32bit bitvector with the value 0xc001b3475: claripy.BVV(0xc001b3a75, 32)`</li><li>Create a 32bit “strided interval” (see VSA documentation) that can be any divisibleby10 number between 1000 and 2000: `claripy.SI(name=’x’, bits=32, lower_bound=1000, upper_bound=2000, stride=10)`</li></ul> 
FP 
This is a floatingpoint number, whether symbolic (with a name) or concrete (with a value). 
BackendConcrete, BackendZ3 

Bool 
This is a boolean operation (True or False). 
BackendConcrete, BackendVSA, BackendZ3 

All of the above creation code returns claripy.AST objects, on which operations can then be carried out.
ASTs provide several useful operations.
>>> import claripy
>>> bv = claripy.BVV(0x41424344, 32)
# Size  you can get the size of an AST with .size()
>>> assert bv.size() == 32
# Reversing  .reversed is the reversed version of the BVV
>>> assert bv.reversed is claripy.BVV(0x44434241, 32)
>>> assert bv.reversed.reversed is bv
# Depth  you can get the depth of the AST
>>> print(bv.depth)
>>> assert bv.depth == 1
>>> x = claripy.BVS('x', 32)
>>> assert (x+bv).depth == 2
>>> assert ((x+bv)/10).depth == 3
Applying a condition (==, !=, etc) on ASTs will return an AST that represents the condition being carried out. For example:
>>> r = bv == x
>>> assert isinstance(r, claripy.ast.Bool)
>>> p = bv == bv
>>> assert isinstance(p, claripy.ast.Bool)
>>> assert p.is_true()
You can combine these conditions in different ways.
>>> q = claripy.And(claripy.Or(bv == x, bv * 2 == x, bv * 3 == x), x == 0)
>>> assert isinstance(p, claripy.ast.Bool)
The usefulness of this will become apparent when we discuss Claripy solvers.
In general, Claripy supports all of the normal Python operations (+, , , ==, etc), and provides additional ones via the Claripy instance object. Here’s a list of available operations from the latter.
Name 
Description 
Example 

LShR 
Logically shifts a bit expression (BVV, BV, SI) to the right. 

SignExt 
Signextends a bit expression. 

ZeroExt 
Zeroextends a bit expression. 

Extract 
Extracts the given bits (zeroindexed from the right, inclusive) from a bit expression. 
Extract the rightmost byte of x: 
Concat 
Concatenates several bit expressions together into a new bit expression. 

RotateLeft 
Rotates a bit expression left. 

RotateRight 
Rotates a bit expression right. 

Reverse 
Endianreverses a bit expression. 

And 
Logical And (on boolean expressions) 

Or 
Logical Or (on boolean expressions) 

Not 
Logical Not (on a boolean expression) 

If 
An Ifthenelse 
Choose the maximum of two expressions: 
ULE 
Unsigned less than or equal to. 
Check if x is less than or equal to y: 
ULT 
Unsigned less than. 
Check if x is less than y: 
UGE 
Unsigned greater than or equal to. 
Check if x is greater than or equal to y: 
UGT 
Unsigned greater than. 
Check if x is greater than y: 
SLE 
Signed less than or equal to. 
Check if x is less than or equal to y: 
SLT 
Signed less than. 
Check if x is less than y: 
SGE 
Signed greater than or equal to. 
Check if x is greater than or equal to y: 
SGT 
Signed greater than. 
Check if x is greater than y: 
Note
The default Python >
, <
, >=
, and <=
are unsigned in Claripy.
This is different than their behavior in Z3, because it seems more natural in
binary analysis.
Solvers¶
The main point of interaction with Claripy are the Claripy Solvers. Solvers expose an API to interpret ASTs in different ways and return usable values. There are several different solvers.
Name 
Description 

Solver 
This is analogous to a 
SolverVSA 
This solver uses VSA to reason about values. It is an approximating solver, but produces values without performing actual constraint solves. 
SolverReplacement 
This solver acts as a passthrough to a child solver, allowing the replacement of expressions onthefly. It is used as a helper by other solvers and can be used directly to implement exotic analyses. 
SolverHybrid 
This solver combines the SolverReplacement and the Solver (VSA and Z3) to allow for approximating values. You can specify whether or not you want an exact result from your evaluations, and this solver does the rest. 
SolverComposite 
This solver implements optimizations that solve smaller sets of constraints to speed up constraint solving. 
Some examples of solver usage:
# create the solver and an expression
>>> s = claripy.Solver()
>>> x = claripy.BVS('x', 8)
# now let's add a constraint on x
>>> s.add(claripy.ULT(x, 5))
>>> assert sorted(s.eval(x, 10)) == [0, 1, 2, 3, 4]
>>> assert s.max(x) == 4
>>> assert s.min(x) == 0
# we can also get the values of complex expressions
>>> y = claripy.BVV(65, 8)
>>> z = claripy.If(x == 1, x, y)
>>> assert sorted(s.eval(z, 10)) == [1, 65]
# and, of course, we can add constraints on complex expressions
>>> s.add(z % 5 != 0)
>>> assert s.eval(z, 10) == (1,)
>>> assert s.eval(x, 10) == (1,) # interestingly enough, since z can't be y, x can only be 1!
Custom solvers can be built by combining a Claripy Frontend (the class that handles the actual interaction with SMT solver or the underlying data domain) and some combination of frontend mixins (that handle things like caching, filtering out duplicate constraints, doing opportunistic simplification, and so on).
Claripy Backends¶
Backends are Claripy’s workhorses. Claripy exposes ASTs to the world, but when actual computation has to be done, it pushes those ASTs into objects that can be handled by the backends themselves. This provides a unified interface to the outside world while allowing Claripy to support different types of computation. For example, BackendConcrete provides computation support for concrete bitvectors and booleans, BackendVSA introduces VSA constructs such as StridedIntervals (and details what happens when operations are performed on them, and BackendZ3 provides support for symbolic variables and constraint solving.
There are a set of functions that a backend is expected to implement. For all of these functions, the “public” version is expected to be able to deal with claripy’s AST objects, while the “private” version should only deal with objects specific to the backend itself. This is distinguished with Python idioms: a public function will be named func() while a private function will be _func(). All functions should return objects that are usable by the backend in its private methods. If this can’t be done (i.e., some functionality is being attempted that the backend can’t handle), the backend should raise a BackendError. In this case, Claripy will move on to the next backend in its list.
All backends must implement a convert()
function. This function receives a
claripy AST and should return an object that the backend can handle in its
private methods. Backends should also implement a convert()
method, which
will receive anything that is not a claripy AST object (i.e., an integer or an
object from a different backend). If convert()
or convert()
receives
something that the backend can’t translate to a format that is usable
internally, the backend should raise BackendError, and thus won’t be used for
that object. All backends must also implement any functions of the base
Backend
abstract class that currently raise NotImplementedError()
.
Claripy’s contract with its backends is as follows: backends should be able to
handle, in their private functions, any object that they return from their
private or public functions. Claripy will never pass an object to any backend
private function that did not originate as a return value from a private or
public function of that backend. One exception to this is convert()
and
convert()
, as Claripy can try to stuff anything it feels like into
_convert() to see if the backend can handle that type of object.
Backend Objects¶
To perform actual, useful computation on ASTs, Claripy uses backend objects. A
BackendObject
is a result of the operation represented by the AST. Claripy
expects these objects to be returned from their respective backends, and will
pass such objects into that backend’s other functions.