Summary:
The SLEdge internal first-order theory solver targets the "word
problem", where a query has the form `C ⊢ L` where `C` is a
conjunction of literals and `L` is a single literal. This can be
abused to implement a naive SMT solver using an expansion to
disjunctive-normal form and checking `C ⊢ false` for each branch `C`
of the DNF. This is not useful as an SMT solver, but can be used for
testing.
Reviewed By: ngorogiannis
Differential Revision: D23459524
fbshipit-source-id: 5483e5a84
Summary: Formula.disjuncts was a quickly written approximation of DNF.
Reviewed By: ngorogiannis
Differential Revision: D23459513
fbshipit-source-id: 79fd60a7b
Summary:
It was incorrect in case any but the first of of the Formula.disjuncts
was inconsistent.
Reviewed By: ngorogiannis
Differential Revision: D23459519
fbshipit-source-id: 394677e38
Summary:
The only use of the ill-specified Sh.with_pure function is to ignore
the pure part when computing free variables. So add an argument to
Sh.fv to achieve that explicitly and remove Sh.with_pure.
Reviewed By: ngorogiannis
Differential Revision: D23459517
fbshipit-source-id: 8767799ca
Summary:
Strengthen normalization performed by Term and Formula constructors to
eliminate literal 0 subterms and true or false subformulas, as well as
cases where subterms or subformulas are either equal or opposite.
This strengthens the ability of Context.implies to prove formulas that
involve embedding or projecting between terms and formulas, as the
added normalization sometimes reduces if-then-else formulas to
literals that are then directly provable.
Reviewed By: ngorogiannis
Differential Revision: D23459512
fbshipit-source-id: 6d4d90399
Summary:
The dune build info embedded into executables is broken with dune <
2.7 and an flambda compiler.
Reviewed By: ngorogiannis
Differential Revision: D23459510
fbshipit-source-id: 18b3e3e15
Summary:
`Sh.norm` relies on `Eq (v, v)` formulas for `v` a variable to be
normalized to `Tt`, which is how eliminated variables are actually
removed from the representation.
Reviewed By: jvillard
Differential Revision: D22571132
fbshipit-source-id: 6d5f3efd7
Summary:
Move normalization that is necessary for `embed_into_fml` to be left
inverse to `embed_into_cnd` into the general `Fml` constructors.
Reviewed By: jvillard
Differential Revision: D22571137
fbshipit-source-id: 575c6bc45
Summary:
In order to ensure that the normalizing constructors are not
circumvented.
Reviewed By: jvillard
Differential Revision: D22571139
fbshipit-source-id: 32032c6fa
Summary:
The default printer is `pp_classes`, while `pp` is for debugging the
internal representation manipulation, so it is renamed to `pp_raw`.
Reviewed By: jvillard
Differential Revision: D22571135
fbshipit-source-id: 2d624e279
Summary:
`Formula.is_true` and `is_false` are now trivial one-line wrappers,
remove them for clarity.
Reviewed By: jvillard
Differential Revision: D22571143
fbshipit-source-id: 3f058eab4
Summary:
It is more confusing than necessary to use logical formula terminology
for the Context interface, considering that Formula represents
formulas and Context represents a (solver state resulting from a) set
of assumptions.
Reviewed By: jvillard
Differential Revision: D22571136
fbshipit-source-id: 087c97a02
Summary:
The unary forms are primitive in ICS, and in uncoming changes which
involve considering the product of a term and an equality relation, it
is more efficient to have unary constructors since the product is then
linear instead of quadratic in the size of the equality relation.
Reviewed By: jvillard
Differential Revision: D22571138
fbshipit-source-id: e0b745cc8
Summary:
Add a Predsym module for uninterpreted (unary) predicate symbols, and
positive and negative literals applying them to a term. As with
uninterpreted functions, tuple terms are used to represent predicates
of other arities.
Using this support, change the Ord and Uno formulas to uninterpreted
literals.
Reviewed By: jvillard
Differential Revision: D22571140
fbshipit-source-id: 5022a91e2
Summary:
`Context.difference` is now just a convenience function that does not
need to be defined internally.
Reviewed By: jvillard
Differential Revision: D22571141
fbshipit-source-id: 58aea9488
Summary: Also, when printing in raw mode, do not print the context.
Reviewed By: jvillard
Differential Revision: D22571145
fbshipit-source-id: b3596d9cc
Summary:
Make the relationship between Sh.is_empty and Sh.pure_approx stronger
and more precise. In particular:
> If [is_empty q], then [pure_approx q] is equivalent to
> [pure (pure_approx q)].
This enables replacing Solver.excise_pure with a simpler pure_entails
function. In particular, the heavy reliance on normalization of pure
formulas to true or false literals is eliminated, and only pure
entailment is needed.
Reviewed By: jvillard
Differential Revision: D22571146
fbshipit-source-id: 2fca64a61
Summary:
Generalize Fol interface to allow checking if a context implies any
formula, rather than restricting to only equalities.
Reviewed By: jvillard
Differential Revision: D22571144
fbshipit-source-id: 726bd87fd
Summary:
There is nothing specific to the Ses representation in the
implementation, and no uses within Ses.
Reviewed By: jvillard
Differential Revision: D22571150
fbshipit-source-id: 8952f0301
Summary:
In Ses, the constant term of a polynomial is represented as a
redundant multiplication by 1. Fix Fol.of_ses to recognize and
normalize this.
Reviewed By: jvillard
Differential Revision: D22571131
fbshipit-source-id: 3e1a12e5f
Summary:
The Ses constructors might simplify terms when called from
Fol.to_ses. Fix Fol.ses_map to account for this.
Reviewed By: jvillard
Differential Revision: D22571151
fbshipit-source-id: 1d573ac5f
Summary:
There is nothing specific to the Ses representation in the
implementation, and no uses within Ses.
Reviewed By: jvillard
Differential Revision: D22455725
fbshipit-source-id: 6f0059873
Summary:
In preparation for more smoothly interoperating with ICS's functional
array theory.
Reviewed By: jvillard
Differential Revision: D22401039
fbshipit-source-id: 4de39c38a
Summary:
It is not needed or very meaningful since the addition of type-based
disambiguation.
Reviewed By: jvillard
Differential Revision: D22401035
fbshipit-source-id: 31996f946
Summary:
The first-order context is induced by the pure part, so no need to
compare it.
Reviewed By: jvillard
Differential Revision: D22381645
fbshipit-source-id: 29fff13a3
Summary:
In order to allow implementations of the single Fol interface using
multiple backend first-order logic solvers, add explicit definitions
of terms and formulas in the Fol module, and implement Context in
terms of them.
The Fol interface supports freely mixing Terms and Formulas, in
particular there is `Term.ite : cnd:Formula.t -> thn:Term.t ->
els:Term.t -> Term.t` which allows Formulas to appear in Terms. The
Fol implementation performs enough normalization to enable using an
internal representation of terms that is strictly partitioned into
"theory terms" and "formulas", which are stratified below "conditional
terms" and then below "general terms". This partitioning and
stratification enables using backend solvers that do not support
mixing formulas in terms.
Reviewed By: jvillard
Differential Revision: D22170506
fbshipit-source-id: a014ee7d7
Summary:
The eventual aim is for the conversion of Llair to Fol to be external
to Fol. Fol should not need to depend on Llair, nor vice versa. This
is not yet possible, but a step forward is to move the conversion
functions into separate modules outside the core Fol modules.
Reviewed By: ngorogiannis
Differential Revision: D22170522
fbshipit-source-id: 4860b4c07
Summary:
The `Subst` module is not used by `Ses`, so move it out of the
Ses-internal APIs.
Reviewed By: ngorogiannis
Differential Revision: D22170513
fbshipit-source-id: a189a1440
Summary:
Change Term and Equality rename functions to accept a partial
application of Var.Subst.apply to the renaming substitution.
Reviewed By: ngorogiannis
Differential Revision: D22170520
fbshipit-source-id: 003d8b27e
Summary:
The convention is for modules that are intended to be `open`ed, that
define syntax and infix operations, are named `Import`. This diff
combines the `Option.Monad_infix` and `Option.Monad_syntax` modules
into `Option.Import` to follow this convention.
Reviewed By: ngorogiannis
Differential Revision: D22170507
fbshipit-source-id: 44378fd56
Summary:
Exponents in polynomials are represented by rationals for code reuse
purposes, but only integral exponents are supported. Strengthen the
invariant check to clarify this.
Reviewed By: ngorogiannis
Differential Revision: D22170517
fbshipit-source-id: 81ae38f4e
Summary:
Refactor `Equality.ppx_classes_diff` into `diff_classes` to construct
the difference between classes maps explicitly, and change
`ppx_classes` to accept such a difference instead of computing it
internally.
This more flexibly composable interface allows elimination of extra
calls to `Equality.entails` to check if the difference is empty.
Reviewed By: jvillard
Differential Revision: D22038488
fbshipit-source-id: c19c18fc8
Summary:
The list interpreted as a conjunction of individual terms in `Sh.pure`
is now redundant with `Term.And`. This patch removes the redundant
list.
Reviewed By: jvillard
Differential Revision: D22035852
fbshipit-source-id: 49c01a078
Summary:
With the current handling of fresh variable generation during symbolic
execution, it is now possible to delay generating fresh variables in
individual small axioms until the precondition is known. In
particular, the existential variables of the precondition formula can
be bound, and then the small axiom can be generated with variables
fresh with respect to them. Previously, the small axioms were
generated with fresh variables that could later clash with the
precondition's existentials, necessitating renaming. This
double-freshening is now eliminated.
Reviewed By: jvillard
Differential Revision: D21974022
fbshipit-source-id: f217bfb9f
Summary:
When fresh variables are generated to name the overwritten value in an
assignment, they should be included in the ghost variables of the
resulting small axiom. This change should have been included in the
elimination of SSA.
Also strengthen assertion checking of small specs during symbolic
execution.
Reviewed By: jvillard
Differential Revision: D21974019
fbshipit-source-id: a66d8dac6
Summary:
Currently the symbolic execution code in `Exec` manually threads
universal and existential variable contexts through virtually every
function. It is easy to mistakenly pass on a context that is not the
latest-extended one, or to forget to add generated variables to the
contexts.
This patch adds a state monad, `Fresh`, to manage the generation of
fresh variables in `Exec`. This is a standard state monad where the
state is two sets of variables: those to which fresh variables must be
chosen fresh, and those which have been generated. This yields an
abstraction where an `'a Fresh.t` value represents a value of type
`'a` which may contain as-yet-unnamed variables, and `Fresh.gen ~wrt
a` generates names that are fresh with respect to `wrt` for all
unnamed variables in `a`, and yields the set of generated variables
together with `a` expressed in terms of those variables.
Reviewed By: jvillard
Differential Revision: D21974018
fbshipit-source-id: 1917e82c0
Summary: Minor code simplification and optimization of `extend_us` in no-op case.
Reviewed By: jvillard
Differential Revision: D21974021
fbshipit-source-id: a8b12b564
Summary:
Change the `Var.Subst` `freshen` and `restrict` constructors to return
the domain and range of the substitution explicitly. Clients generally
need to compute them immediately, and they are at least partially
constructed during the initial substitution construction anyhow. This
may be an incidental minor optimization.
This allows removing the `apply_set` operation, as it's use can be
handled directly from the domain and range sets.
This also allows `Sh.rename` to be split into a function that assumes
that the substitution is restricted to the vocabulary of the formula,
and a wrapper that does this restriction and calls through. This
allows `Sh.freshen_xs` to be simplified slightly, and avoids some
redundant restriction, domain, and range computations.
Reviewed By: jvillard
Differential Revision: D21974017
fbshipit-source-id: aa8b3db24
Summary:
`Domain_sh.from_call.subst` is a substitution that replaces shadowed
variables with fresh ones, which is constructed by `Domain_sh.call`
and used by `Domain_sh.retn`, after inverting it. This patch changes
the stored substitution to the inverted one, and renames it to
`unshadow` for clarity.
After this change, the stored substitutions have the property that
they map variables to program variables. This is desirable since it
avoids the question about the uninverted substitution of whether the
variables in the range of the uninverted substitution are "fresh".
Reviewed By: jvillard
Differential Revision: D21974020
fbshipit-source-id: d469c89f9
Summary:
Logically there is nothing specific to memory contents (as
byte-arrays) or aggregate (struct/array) values, the theory is for
sequences of non-fixed sized elements.
Reviewed By: jvillard
Differential Revision: D21721019
fbshipit-source-id: b2b730a50
Summary:
`Term.eq_concat` is not primitive and complicates the `Term`
interface. Move it to a couple clients as a convenience wrapper.
Reviewed By: jvillard
Differential Revision: D21721026
fbshipit-source-id: 0d74aa251
Summary:
Previously `null` and `zero` had different sorts/types, but now they
are equivalent.
Reviewed By: jvillard
Differential Revision: D21721023
fbshipit-source-id: 485219f6a
Summary:
Multiplication by a constant is primitive in the linear arithmetic
solver, while general multiplication is not, so for clarity and
predictability, use constants where possible.
Reviewed By: jvillard
Differential Revision: D21721020
fbshipit-source-id: 3497d06c9
Summary:
It is suboptimal for `Sh` to destruct terms with detailed knowledge of
their representation. So add `Term.const_of` to obtain the constant
summand of a polynomial term.
Reviewed By: jvillard
Differential Revision: D21721022
fbshipit-source-id: 4af858896
Summary:
It is suboptimal for `Sh` to destruct terms with detailed knowledge of
their representation. So add `Term.d_int` to destruct an integer term.
Reviewed By: jvillard
Differential Revision: D21721024
fbshipit-source-id: 5f13794b6
Summary:
It is suboptimal for `Sh` to destruct terms with detailed knowledge of
their representation. So add `Term.disjuncts` to obtain the toplevel
disjuncts of a term.
Reviewed By: jvillard
Differential Revision: D21721016
fbshipit-source-id: 809da9b1b
Summary:
It has no dependencies on the rest of the sledge codebase and might be
more generally useful.
Reviewed By: jvillard
Differential Revision: D21720980
fbshipit-source-id: b4f061e73
Summary:
Now that the frontend translates LLVM's undef to nondet instructions,
not expressions, Nondet in Exp and Term are not needed.
Reviewed By: jvillard
Differential Revision: D21720969
fbshipit-source-id: e8acaf432
Summary:
Instead of relying on Exp.nondet to encode the semantics of LLVM's
undef, translate each to a per-function unique register, with a nondet
assignment to it prior to each use. This avoids the need for
Exp.nondet, which is ill-formed in the sense that expressions denote
values, not sets of values (with particular constraints on what ways
in which the choice must be angelic vs demonic). This change
essentially allows the backend to be sane, and makes it the frontend's
problem to deal with LLVM's undef.
This treatment, like the treatment based on Exp.nondet, is expected to
result in LLAIR code with different semantics of undef compared to the
semantics of LLVM described in the
[LangRef](https://llvm.org/docs/LangRef.html#undefined-values). In
particular, the LLVM LangRef states
> An ‘undef’ “variable” can arbitrarily change its value over its
> “live range”. This is true because the variable doesn’t actually
> have a live range. Instead, the value is logically read from
> arbitrary registers that happen to be around when needed, so the
> value is not necessarily consistent over time.
To model this ability of undef to arbitrarily change its value over
its live range, it is likely that additional nondet assignments would
need to be added. Exactly where it not currently known.
Reviewed By: jvillard
Differential Revision: D21720976
fbshipit-source-id: 90c2a0d26
Summary:
Refactor frontend translation of LLVM values, opcodes, etc. to support
emitting not only a LLAIR expression, but also a sequence of
instructions to be prefixed onto the uses of the resulting expression.
This is currently unused, as all prefixes are empty. Later, it will be
used to translate e.g. `undef` to `r := nondet(); r`.
Reviewed By: jvillard
Differential Revision: D21720972
fbshipit-source-id: b89bb57de
Summary:
Refer to Llair modules using `Llair.` qualifier, except for in
`Frontend`, which makes so much use of `Llair` that it is now opened
(`Llair` only contains types and modules, so `open` is safe).
Reviewed By: jvillard
Differential Revision: D21720979
fbshipit-source-id: dd42075d9
Summary:
The term representing an exp should not rely on more info than is
carried by the exp.
Reviewed By: jvillard
Differential Revision: D21720989
fbshipit-source-id: b65bf3678
Summary:
It is now possible to not spew dune files all over the repo, and opam
files aren't needed either.
Reviewed By: jvillard
Differential Revision: D21720978
fbshipit-source-id: 553e1d154
Summary:
```
val ( let@ ) : ('a -> 'b) -> 'a -> 'b
(** [let@ x = e in b] is equivalent to [e @@ fun x -> b], that is,
[e (fun x -> b)] *)
```
Reviewed By: jvillard
Differential Revision: D21721025
fbshipit-source-id: d8efdebbe
Josh Berdine