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
Josh Berdine
Scott Owens