Summary:
Add shortcut code paths to return early in some cases guaranteed to be
the identity function.
Reviewed By: ngorogiannis
Differential Revision: D15468704
fbshipit-source-id: f137049c6
Summary:
It is pointless to track membership of atomic exps in the congruence
relation, as they cannot have any subexps which might later become
equal to something else.
Reviewed By: jvillard
Differential Revision: D15424820
fbshipit-source-id: 048dbc9e1
Summary:
For some Exp forms, Exp.solve is not complete, and this is necessary
since the result of solve is a substitution that needs to encode the
input equation as a conjunction of equations each between a variable
and an exp. This is tantamount to, stronger even than, the theory
being convex. So Exp.solve is not complete for some exps, and some of
those have constructors that perform some simplification. For example,
`(1 ≠ 0)` simplifies to `-1` (i.e. true). To enable deductions such as
`((x ≠ 0) = b) && x = 1 |- b = -1` needs the equality solver to
substitute through subexps of simplifiable exps like = and ≠, as it
does for interpreted exps like + and ×. At the same time, since
Exp.solve for non-interpreted exps cannot be complete, to enable
deductions such as `((x ≠ 0) = (y ≠ 0)) && x = 1 |- y ≠ 0` needs the
equality solver to congruence-close over subexps of simplifiable exps
such as = and ≠, as it does for uninterpreted exps.
To strengthen the equality solver in these sorts of cases, this diff
adds a new class of exps for = and ≠, and revises the equality solver
to handle them in a hybrid fashion between interpreted and
uninterpreted.
I am not currently sure whether or not this breaks the termination
proof, but I have also not managed to adapt usual divergent cases to
break this. One notable point is that simplifying = and ≠ exps always
produces genuinely simpler and smaller exps, in contrast to
e.g. polynomial simplification and gaussian elimination.
Note that the real solution to this problem is likely to be to
eliminate the i1 type in favor or a genuine boolean type, and
translate all integer operations on i1 to boolean/logical ones. Then
the disjunction implicit in e.g. equations between disequations would
appear as actual disjunction, and could be dealt with as such.
Reviewed By: jvillard
Differential Revision: D15424823
fbshipit-source-id: 67d62df1f
Summary:
There are two motivations for this:
1. Distinguish between `Unreachable`, which silently terminates
execution a la `assume false`; and `Abort`, which vocally
terminates execution a la `assert false`.
2. Distinguish between undefined functions, which have `Unreachable`
bodies, and bomb functions such as:
```
define void bomb() {
tail call void llvm.trap()
unreachable
}
```
Reviewed By: ngorogiannis
Differential Revision: D15408246
fbshipit-source-id: b64354cdb
Summary: Also fix the spec for posix_memalign, and minor cleanup.
Reviewed By: ngorogiannis
Differential Revision: D14403648
fbshipit-source-id: 6b1cb3e3a
Summary:
The SL solver is currently not always able to append segments which
have been split symbolically, that is, at an internal point expressed
using a variable, rather than merely a constant.
Also, existential instantiation, that is, the choice of witnesses
during proof search, is currently sensitive to the order of
subformulas. This can lead to fragile incompleteness.
Reviewed By: mbouaziz
Differential Revision: D14481991
fbshipit-source-id: 80fe2f0a8
Summary:
Strengthen the Sh.seg constructor and Sh.is_false test to account for
the axiom that `null -[_;_)-> ⟨_,_⟩` is inconsistent.
Reviewed By: ngorogiannis
Differential Revision: D14481986
fbshipit-source-id: 7016e7451
Summary:
The dnf implementation dates to before nested existentials were
added. Updating it was overlooked, and it is just wrong.
Reviewed By: ngorogiannis
Differential Revision: D14481988
fbshipit-source-id: 9bba570f0
Summary:
P ∨ (∃x. Q ∨ R) could be simplified to (∃x. P ∨ Q ∨ R) and capture
occurrences of x in P.
Reviewed By: ngorogiannis
Differential Revision: D14481990
fbshipit-source-id: 92b474d59
Summary:
Also minor change to make strlen implementation syntactically closer
to spec.
Reviewed By: ngorogiannis
Differential Revision: D14403647
fbshipit-source-id: 48c771329
Summary:
This diff adds support in symbolic execution for calls to intrinsic
functions, to be used in lieu of adding a separate Llair instruction
for each intrinsic. This involves:
- adding skeleton support in Exec for symbolically execution an
intrinsic function call;
- exposing this in Domain;
- allowing symbolic execution of block terminators (e.g. function
call) to possibly fail; and
- generalizing Report for failing terminators.
Reviewed By: ngorogiannis
Differential Revision: D14403652
fbshipit-source-id: d86d9d1b8
Summary:
Interpreted subexps were not handled correctly: they must not be in
the carrier, but their non-interpreted subexps should.
Reviewed By: jvillard
Differential Revision: D14344291
fbshipit-source-id: 995896640
Summary:
In case the starting locations of two heap segments are
related (provably equal up to some offset), add equations between
their enclosing block to the goal. In these cases, the enclosing
blocks must be the same, so no completeness is lost. This has the
effect of instantiating existentials in the enclosing block prior to
others, which can avoid incomplete instantiation guesses.
Reviewed By: mbouaziz
Differential Revision: D14323550
fbshipit-source-id: 89a34a2c8
Summary: An initial set of basic sanity checks for frame inference.
Reviewed By: mbouaziz
Differential Revision: D14323549
fbshipit-source-id: d7cd4235f
Summary:
- Change representation of Concat expressions from curried binary
operator to an nary one. This enables normalizing Concat expressions
with respect to associativity.
- Generalize Exp.solve to return a map rather than a pair of exps, to
enable expressing cases where solving an equation yields multiple
equations.
- Strengthen solver with implied equalities between sums of sizes of
concatenations of byte arrays.
Reviewed By: ngorogiannis
Differential Revision: D14297865
fbshipit-source-id: b40871559
Summary:
This patch adds an embarrassingly inefficient implementation of a
decision procedure for equality in the theories of uninterpreted
functions and linear arithmetic. A Shostak-style approach, where a
single congruence closure structure is shared by all theories, is
used. This is mostly based on the corrected variant of Shostak's
algorithm from:
Harald Rueβ and Natarajan Shankar. 2001. Deconstructing Shostak. In
Proceedings of the 16th Annual IEEE Symposium on Logic in Computer
Science (LICS '01).
Reviewed By: jvillard
Differential Revision: D14251655
fbshipit-source-id: 8a080145f
Summary:
Trace.report is essentially redundant with Trace.fail, and does not
behave as well wrt flushing when raising exceptions.
Reviewed By: ngorogiannis
Differential Revision: D14251657
fbshipit-source-id: 69a61c915
Summary:
Represent Add and Mul directly as associative and commutative nary
operations, rather than have Add and Mul operators and a separate AppN
nary application.
Reviewed By: ngorogiannis
Differential Revision: D14231544
fbshipit-source-id: 4fb7a06cf
Summary:
- Add nary expressions implemented using a form of multisets which
support any integer multiplicity
- Reimplement polynomials using new nary expressions
- Move the decomposition of exps into "base plus offset" form into
Exp, to enforce simplification invariants
- Revise expression simplification to cooperate with congruence
closure (mainly: simplification should not invent new
subexpressions)
- Reimplement congruence closure plus integer offsets to
+ cope with new representation of polynomials using nary expression forms
+ be diligent about maintaining which expressions are in the relation
+ add lots of invariant checking for the correlations between the
componnents of the congruence closure data structures
Reviewed By: jvillard
Differential Revision: D14075512
fbshipit-source-id: 2dbaf3d11
Summary:
Even pretty-printed congruence relations are verbose, and most
operations do not change much of the relation. So on return, print
only the symmetric difference between input and output relations.
Reviewed By: mbouaziz
Differential Revision: D14075513
fbshipit-source-id: b1f0ae6d0
Summary:
Require Exp clients to provide the type of the result of arithmetic
operations.
Reviewed By: mbouaziz
Differential Revision: D12854511
fbshipit-source-id: cc91a39ca
Summary:
Types of integer constants, in particular their bit-width, are
necessary for:
- correctly interpreting bitwise operations (e.g. `-1 xor 1` at type
`i1` is `0` while without the type the result is `-2`), and;
- distinguishing between integers and booleans, which are one-bit
integers, since booleans admit stronger algebraic simplification.
Note that code does genuinely treat 1-bit integers interchangeably as
booleans and integers, e.g. with expressions such as `e + (b != 42)`.
Therefore a lighter-weight early syntactic distinction between boolean
and bitwise operations is nontrivial/impossible to make robust.
This patch:
- adds the type to the representation of Exp.Integer;
- adds checks that Integer values fit within their specified bit-width
- factors out code handling 1-bit integers as booleans into `Z`, as it
is easy to make mistakes when forgetting that `-1`, not `1`, is the
representation of `true`;
- corrects the treatment of Exp.Convert in some cases involving
treating negative integers as unsigned;
- corrects and strengthens Exp simplification based on the bit-width
information;
- removes the `e - e ==> 0` simplification, due to not having the type
for `0`.
Reviewed By: mbouaziz
Differential Revision: D10488407
fbshipit-source-id: ff4320a29
Josh Berdine
Mehdi Bouaziz