claripy.md

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
• Frontends provide different paradigms for evaluating these expressions. For example, the FullFrontend solves expressions using something like an SMT solver backend, while LightFrontend 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, Backends translate ASTs into backend objects (i.e., Python primitives for BackendConcrete, Z3 expressions for BackendZ3, strided intervals for BackendVSA, etc) and handle any appropriate state-tracking objects (such as tracking the solver state in the case of BackendZ3). Roughly speaking, frontends take ASTs as inputs and use backends to backend.convert() those ASTs into backend objects that can be evaluated and otherwise reasoned about.
• FrontendMixins customize the operation of Frontends. 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 co-operation 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 32-bit symbolic bitvector "x": claripy.BVS('x', 32) Create a 32-bit bitvector with the value 0xc001b3475: claripy.BVV(0xc001b3a75, 32) Create a 32-bit "strided interval" (see VSA documentation) that can be any divisible-by-10 number between 1000 and 2000: claripy.SI(name='x', bits=32, lower_bound=1000, upper_bound=2000, stride=10)
FP	This is a floating-point number, whether symbolic (with a name) or concrete (with a value).	BackendConcrete, BackendZ3	Create a claripy.fp.FSORT_DOUBLE symbolic floating point "b": claripy.FPS('b', claripy.fp.FSORT_DOUBLE) Create a claripy.fp.FSORT_FLOAT floating point with value 3.2: claripy.FPV(3.2, claripy.fp.FSORT_FLOAT)
Bool	This is a boolean operation (True or False).	BackendConcrete, BackendVSA, BackendZ3	claripy.BoolV(True), or claripy.true or claripy.false, or by comparing two ASTs (i.e., claripy.BVS('x', 32) < claripy.BVS('y', 32)

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.	claripy.LShR(x, 10)
SignExt	Sign-extends a bit expression.	claripy.SignExt(32, x) or x.sign_extend(32)
ZeroExt	Zero-extends a bit expression.	claripy.ZeroExt(32, x) or x.zero_extend(32)
Extract	Extracts the given bits (zero-indexed from the right, inclusive) from a bit expression.	Extract the rightmost byte of x: claripy.Extract(7, 0, x) or x[7:0]
Concat	Concatenates several bit expressions together into a new bit expression.	claripy.Concat(x, y, z)
RotateLeft	Rotates a bit expression left.	claripy.RotateLeft(x, 8)
RotateRight	Rotates a bit expression right.	claripy.RotateRight(x, 8)
Reverse	Endian-reverses a bit expression.	claripy.Reverse(x) or x.reversed
And	Logical And (on boolean expressions)	claripy.And(x == y, x > 0)
Or	Logical Or (on boolean expressions)	claripy.Or(x == y, y < 10)
Not	Logical Not (on a boolean expression)	claripy.Not(x == y) is the same as x != y
If	An If-then-else	Choose the maximum of two expressions: claripy.If(x > y, x, y)
ULE	Unsigned less than or equal to.	Check if x is less than or equal to y: claripy.ULE(x, y)
ULT	Unsigned less than.	Check if x is less than y: claripy.ULT(x, y)
UGE	Unsigned greater than or equal to.	Check if x is greater than or equal to y: claripy.UGE(x, y)
UGT	Unsigned greater than.	Check if x is greater than y: claripy.UGT(x, y)
SLE	Signed less than or equal to.	Check if x is less than or equal to y: claripy.SLE(x, y)
SLT	Signed less than.	Check if x is less than y: claripy.SLT(x, y)
SGE	Signed greater than or equal to.	Check if x is greater than or equal to y: claripy.SGE(x, y)
SGT	Signed greater than.	Check if x is greater than y: claripy.SGT(x, 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 z3.Solver(). It is a solver that tracks constraints on symbolic variables and uses a constraint solver (currently, Z3) to evaluate symbolic expressions.
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 pass-through to a child solver, allowing the replacement of expressions on-the-fly. 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.