Summary:
Strengthen existential quantifier witnessing to enable witnessing an
existential with a term containing another existential if no universal
witness is available. Additionally, strengthen existential witnessing
to enable terms of interpreted theories to witness existential
variables.
Also strengthen and simplify the representation invariant checking for
existential witnessing code.
Reviewed By: jvillard
Differential Revision: D20120271
fbshipit-source-id: 4c44fe9ef
Summary:
Handle the case the universal context of a goal does not stay in sync
with that of the minuend.
The need for this indicates that there is some problematic redundancy
in the representation of solver goals.
Reviewed By: ngorogiannis
Differential Revision: D20120268
fbshipit-source-id: 44a4d6260
Summary:
It can happen that canonizing subterms can change the classification
of a term e.g. to the literal true. In such cases, it is not useful or
correct use `Equality.lookup` (which expects to only be used on
uninterpreted applications) to search for some other equation equal to
the literal and use its representative instead.
Reviewed By: ngorogiannis
Differential Revision: D20120279
fbshipit-source-id: 3e2160233
Summary: When equating Concat terms, drop any common prefix or suffix.
Reviewed By: ngorogiannis
Differential Revision: D20120264
fbshipit-source-id: afdeb990e
Summary: No code change, only reordering definitions in prep for later changes.
Reviewed By: ngorogiannis
Differential Revision: D20120263
fbshipit-source-id: b312dfc9a
Summary: Add `Equality.and_term` and replace most of `Sh.pure` with it.
Reviewed By: ngorogiannis
Differential Revision: D20029742
fbshipit-source-id: 07c2f1fe6
Summary:
Replace `Equality.Subst.trim` with `partition_valid` which has a
logical specification (and unsurprisingly fixes some corner case
bugs):
```
val partition_valid : Var.Set.t -> t -> t * Var.Set.t * t
(** Partition ∃xs. σ into equivalent ∃xs. τ ∧ ∃ks. ν where ks and ν
are maximal where ∃ks. ν is universally valid, xs ⊇ ks and ks ∩
fv(τ) = ∅. *)
```
Reviewed By: ngorogiannis
Differential Revision: D20004974
fbshipit-source-id: 5cb3b3835
Summary:
Sh.var_strength determines, in part, if an existential variable has
only a single occurrence. The objective of this is to determine that a
variable is merely a placeholder and not used to express additional
constraints. For this, it suffices to check the weaker condition that
there is a single occurrence in each branch of a DNF expansion.
Reviewed By: ngorogiannis
Differential Revision: D19973779
fbshipit-source-id: 2c90c61f4
Summary:
The result of promoting expect tests is not necessarily formatted, so
try to reduce iterations by formatting after testing.
Reviewed By: ngorogiannis
Differential Revision: D20004973
fbshipit-source-id: 53af4c034
Summary:
Changing `pps` to `staged_pps` was needed for `import_ppx`, but it has
since been removed.
Reviewed By: jvillard
Differential Revision: D19973778
fbshipit-source-id: 5e2d83157
Summary:
Currently the free variables of the equality relation of a formula are
contained in the free variables of the rest of the formula, so Sh.fv
ignores them. Propagating equality facts across the star-or structure
of a formula, as necessary for quantifier elimination, breaks this
invariant. Some use cases, such as detecting which variables survive
applying a witness substitution, need to ignore the variables that
appear in the equality relation. This diff adds an argument to
conditionally ignore the variables in the equality relations.
Reviewed By: ngorogiannis
Differential Revision: D19580430
fbshipit-source-id: 2d417d89b
Summary:
Add a field to LLAIR variables to indicate whether they are global or
local. Update the LLVM semantics for constant expression evaluation to
be relational, so that it doesn't have to have an answer for references
to undefined globals.
Reviewed By: jberdine
Differential Revision: D19446312
fbshipit-source-id: 9bbfd180e
Summary:
In an equation such as `x = ⟨n,a⟩`, `x` is implicitly an aggregate of
size `n` (or else the equation is ill-typed). Make this explicit by
normalizing such equations to e.g. `⟨|⟨n,a⟩|,x⟩ = ⟨n,a⟩`.
Reviewed By: ngorogiannis
Differential Revision: D19358546
fbshipit-source-id: 77f67a0da
Summary:
Strengthen Equality.solve_for_vars so that it will solve cases such as
```
∃ a. ⟨n,a⟩ = ⟨m,b⟩^⟨o,c⟩
```
Reviewed By: ngorogiannis
Differential Revision: D19356324
fbshipit-source-id: a57625ba6
Summary:
Due to paying closer attention to which terms are already normalized
by the accumulated solution substitution.
Reviewed By: ngorogiannis
Differential Revision: D19356323
fbshipit-source-id: e162414a0
Summary:
The function transforming terms passed to Sh.map might produce trivial
constraints, filter them out.
Reviewed By: ngorogiannis
Differential Revision: D19286628
fbshipit-source-id: e3d9926ce
Summary:
In order for Equality.solve to generate fresh variables, it needs to
be passed the universal context with respect to which variables must
be chosen fresh.
Reviewed By: ngorogiannis
Differential Revision: D19286630
fbshipit-source-id: ebbedd954
Summary:
Aggregate args of Extract and Concat must be aggregate terms, in
particular, not variables. This maintains the property that the size
of any aggregate can be computed.
Reviewed By: ngorogiannis
Differential Revision: D19286625
fbshipit-source-id: 1af1e4183
Summary:
The byte-array theory used for the contents of memory is strong
enough to express all the constraints arising during symbolic
execution without the ability to extract a slice out of a byte-array.
However, without Extract, it is not possible to solve some equations
for some variables, for example solving ⟨n,α⟩^⟨m,β⟩ = ⟨l,γ⟩ for α.
Solving such equations is needed for quantifier elimination and to
formulate the byte-array theory as a Shostak theory.
Reviewed By: ngorogiannis
Differential Revision: D19286632
fbshipit-source-id: 07dc112d0
Summary:
Revise the ad hoc treatment to drop tautologous constraints such as
∃x,y. x = y to only apply when x and y do not appear elsewhere.
Reviewed By: ngorogiannis
Differential Revision: D19282633
fbshipit-source-id: 7fb9951ec
Summary:
Equality.solve_for_var_contexts can produce solution substitutions
that witness existentials in more cases than the
single-existential-occurrence heuristic, and is more conservative in
cases where the latter is incomplete.
Reviewed By: ngorogiannis
Differential Revision: D19282634
fbshipit-source-id: f86f0a9cb
Summary:
```
val trim : bound:Var.Set.t -> Var.Set.t -> t -> t
(** [trim bound kills subst] is [subst] without mappings that mention
[kills] or [bound ∩ fv x] for removed entries [x ↦ u] *)
```
To be used for existential witnessing and quantifier elimination.
Reviewed By: ngorogiannis
Differential Revision: D19282644
fbshipit-source-id: d981a1cb4
Summary:
```
val solve_for_vars : Var.Set.t list -> t -> Subst.t
(** [solve_for_vars \[v₁;…\] r] is a solution substitution that is
entailed by [r] and consists of oriented equalities [x ↦ u] such that
[fv x ⊈ vᵢ ⊇ fv u] where [i] is minimal such that [vᵢ]
distinguishes [fv x] and [fv u], if one exists. *)
```
To be used for existential witnessing and quantifier elimination.
Reviewed By: ngorogiannis
Differential Revision: D19282636
fbshipit-source-id: c5b006cea
Summary:
It is necessary to normalize subterms of Memory and Concat terms or
else Equality.entails_eq is incomplete. They ought to be Interpreted,
but the solver for the byte-array theory is not yet ready for that.
Reviewed By: ngorogiannis
Differential Revision: D19282635
fbshipit-source-id: c06b6ca6d
Summary:
The equality relation is implied by the pure part, so cannot involve
more variables. Also, Sh.invariant checks that the equality relation
does not contain unbound variables.
Reviewed By: ngorogiannis
Differential Revision: D19282641
fbshipit-source-id: 21dd37a3b
Summary:
If `Term.solve_zero_eq` is passed `for_`, then that subterm is solved
for.
Reviewed By: ngorogiannis
Differential Revision: D19282647
fbshipit-source-id: 5d5b76af5
Summary:
Match the `x` suffix naming convention of Term pp functions that take
a classification function.
Reviewed By: ngorogiannis
Differential Revision: D19282639
fbshipit-source-id: fc340e4bc
Summary:
Equality relies on the result of solving an equation to be a "solution
substitution". In constrast to unconstrained Map's, solution
substitutions are idempotent and have constraints on the terms that
may appear in their domain (they must be "maximal solvables", that is,
variables or uninterpreted function applications, which would be
variables if explicit "variable abstraction" was done).
This diff factors out the manipulation of concrete Map's into a
Equality.Subst module, and uses these for the result of `solve`.
Reviewed By: ngorogiannis
Differential Revision: D19282637
fbshipit-source-id: 4fc825e59
Summary:
In preparation for constructing solution substitutions in solve, which
are closely tied to Equality.
Reviewed By: ngorogiannis
Differential Revision: D19282640
fbshipit-source-id: ca0f8ae29
Summary:
Identifying and separating one of the monomials in a polynomial, and
solving an equality for it, is much more dependent on the
representation of polynomial terms than the rest of solve.
Reviewed By: ngorogiannis
Differential Revision: D19282645
fbshipit-source-id: 645191ae0
Summary:
The exposed constructors for Memory and Concat Terms are only used in
a very special idiom: to construct an equality between a single Memory
chunk and the Concat of multiple Memory chunks. This diff specializes
and simplifies by exposing a Term.eq_concat constructor for this
idiom, and removes the underlying Term.memory and Term.concat
constructors.
Reviewed By: ngorogiannis
Differential Revision: D19221866
fbshipit-source-id: 4842737d2
Summary:
Trace.infok is like Trace.info but accepts a polymorphic printf
continuation instead of directly taking a format string and its
args. This is useful to write wrappers such as:
```
let trace k = [%Trace.infok k]
```
Reviewed By: ngorogiannis
Differential Revision: D19221883
fbshipit-source-id: 88e939b26
Summary:
The size of Splats is redundant, as they always appear as subterms of
a Memory chunk or a heap segment, both of which are sized.
Reviewed By: ngorogiannis
Differential Revision: D19221870
fbshipit-source-id: 74044d1ad
Summary:
Now that they are uncurried, congruence closure does not need the
order of subterms to be preserved. Sorting them reduces redundancy in
case the same equality in different orders is encountered, and
improved printing.
Reviewed By: ngorogiannis
Differential Revision: D19221875
fbshipit-source-id: c6bf4ccad
Summary:
Equality.classes was assuming a simpler representation, and was
incomplete as a result.
The 'representative' map is not kept in a normalized form, where
subterms are necessarily representatives. Therefore, applying the
representative map to subterms of terms in a class can reveal new
elements of the class. This mirrors how the `lookup` function in
`normalize` works.
Reviewed By: ngorogiannis
Differential Revision: D19221868
fbshipit-source-id: 4a2ed6d3f
Summary:
Reduce redundancy by printing adjacent segments as if they had been
concatenated together.
Reviewed By: ngorogiannis
Differential Revision: D19221881
fbshipit-source-id: 613105864
Summary:
Also, previous code was sometimes inconsistent regarding whether to
enumerate all subterms or only toplevel terms.
Reviewed By: ngorogiannis
Differential Revision: D19221873
fbshipit-source-id: e8644098b
Summary: It is easier to understand the order of args with diff_inter.
Reviewed By: ngorogiannis
Differential Revision: D19221869
fbshipit-source-id: b29ac83c8
Summary:
Add some test cases from Reuss and Shankar for equality that are
mishandled by Shostak's original algorithm.
Reviewed By: ngorogiannis
Differential Revision: D19221880
fbshipit-source-id: a6f9d51e3
Summary:
This diff enables parsing and auto-formatting documentation
comments (aka docstrings).
I have looked at this entire diff and manually made some changes to
improve the formatting. In some cases it looked like it would take too
much time, or benefit from someone more familiar with the code doing
it, and I instead disabled auto-formatting docstrings in those files.
Also, there are some source files where the docstrings are invalid,
and some where the structure detected by the parser appears not to
match what was intended. Auto-formatting has been disabled for these
files.
Reviewed By: ezgicicek
Differential Revision: D18755888
fbshipit-source-id: 68d72465d
Summary:
OCaml 4.08 supports a form of signature-local bindings, to that a type
can be defined in order to be used in other definitions, without
being part of the signature itself.
Reviewed By: ngorogiannis, jvillard
Differential Revision: D18736380
fbshipit-source-id: 0bb043de6
Summary:
Otherwise it is difficult to tell the difference between compilation
errors from previous versus current builds.
Reviewed By: ngorogiannis
Differential Revision: D18736376
fbshipit-source-id: 2e583f4ba
Summary:
OCaml 4.08 has a new warning (66) on unused `open!` statements. This
has a suboptimal interaction with `ppx_let`'s `let%map_open` which
leads to triggering the warning if any of a group of such let bindings
does not need the open.
In this case, the refactor is easy.
But, warning 66 is very dubious, so also just switch it off.
Reviewed By: jvillard
Differential Revision: D18708466
fbshipit-source-id: 77618ab6e
Summary:
It seems to be effectively unmaintained, as it still doesn't support
4.08.
Reviewed By: jvillard
Differential Revision: D18708467
fbshipit-source-id: dcb3361fc
Summary:
Term.solve makes the assumption that all distinct normalized constants
denote distinct values. This is fragile at best, and it is better to
enumerate the cases where solve discovers inconsistency.
Reviewed By: jvillard
Differential Revision: D18459619
fbshipit-source-id: 71f52557c
Summary:
Equality.or_ assumed a simpler representation of equality relations,
and was incomplete as a result.
Reviewed By: jvillard
Differential Revision: D18298138
fbshipit-source-id: cf91229f6
Summary:
The treatment of type conversions is too complicated, non-uniform,
etc. This diff attempts to simplify things by separating integer to
integer conversions, which are interpreted, from others, which are
essentially just uninterpreted functions. Integer conversions are now
handled using two expression and term forms: Signed and
Unsigned. These each interpret their argument as either a signed or
unsigned number of a given bitwidth:
```
| Signed of {bits: int}
(** [Ap1 (Signed {bits= n}, dst, arg)] is [arg] interpreted as an
[n]-bit signed integer and injected into the [dst] type. That is,
it two's-complement--decodes the low [n] bits of the infinite
two's-complement encoding of [arg]. The injection into [dst] is a
no-op, so [dst] must be an integer type with bitwidth at least
[n]. *)
| Unsigned of {bits: int}
(** [Ap1 (Unsigned {bits= n}, dst, arg)] is [arg] interpreted as an
[n]-bit unsigned integer and injected into the [dst] type. That
is, it unsigned-binary--decodes the low [n] bits of the infinite
two's-complement encoding of [arg]. The injection into [dst] is a
no-op, so [dst] must be an integer type with bitwidth greater than
[n]. *)
| Convert of {src: Typ.t}
(** [Ap1 (Convert {src}, dst, arg)] is [arg] converted from type [src]
to type [dst], possibly with loss of information. The [src] and
[dst] types must be [Typ.convertible] and must not both be
[Integer] types. *)
```
Reviewed By: ngorogiannis
Differential Revision: D18298140
fbshipit-source-id: 690f065b4
Summary:
LLAIR changed how it represents integer-to-integer conversions, and this
updates the semantics and proofs to show that the new way is correct.
Reviewed By: jberdine
Differential Revision: D18448616
fbshipit-source-id: b657fcd20
Summary:
The old version of simp_convert in LLAIR had a bug, but the sanity
theorem didn't catch it because it didn't enforce that the result fit
into the size it should have. This updates to newer version of
simp_convert and adds a theorem that the result fits.
Reviewed By: jberdine
Differential Revision: D18346833
fbshipit-source-id: 533c836bf
Summary:
Extend the APRON-backed interval analysis to handle a wider range
of LLAIR expressions.
Reviewed By: jvillard
Differential Revision: D17858072
fbshipit-source-id: c50f5bf20
Summary:
In some cases the result of an integer conversion needs to be
truncated by a bit.
Differential Revision: D18271179
fbshipit-source-id: e80740045
Summary:
Improve the invariants to show that phi instructions are correctly
translated. It remains to show that the invariants can be established
when jumping to the start of a block
Reviewed By: jberdine
Differential Revision: D18228272
fbshipit-source-id: 4330b4781
Summary:
Add a new interval abstract domain. This domain uses the APRON
numerical analysis library to keep track of the range of values held
by llair variables where possible. This works by translating LLAIR
expressions into APRON tree expressions, so only handles the
subset of the LLAIR expression language that can be embedded.
Note also that function summarization is not yet implemented.
Future commits will add summarization and improve coverage of
LLAIR's expression language.
Reviewed By: jberdine
Differential Revision: D17763517
fbshipit-source-id: 826ce4cc5
Summary:
Add some theorems establishing the correspondence between the
implementation of the Convert operation in OCaml and the definition of
Convert in the semantics. Essentially, the OCaml version is in terms of
extracting certain ranges of bits, whereas the semantics is in terms of
integer arithmetic (addition, modulus, and exponentiation)
Reviewed By: jberdine
Differential Revision: D18113878
fbshipit-source-id: c318596d0
Josh Berdine
Scott Owens
Benno Stein