module Conditions:sig
..end
val forall_intro : Wp.Lang.F.pred -> Wp.Lang.F.pred list * Wp.Lang.F.pred
Introduce universally quantified formulae: head forall quantifiers are instanciated to fresh variables in current pool and left-implies are extracted, recursively.
val exist_intro : Wp.Lang.F.pred -> Wp.Lang.F.pred
Introduce existential quantified formulae: head exist quantifiers are instanciated to fresh variables, recursively.
type
step = private {
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mutable id : |
(* | See | *) |
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size : |
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vars : |
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stmt : |
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descr : |
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deps : |
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warn : |
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condition : |
}
type
condition =
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Type of |
(* | Type section, not constraining for filtering | *) |
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Have of |
(* | Normal assumptions section | *) |
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When of |
(* | Assumptions introduced after simplifications | *) |
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Core of |
(* | Common hypotheses gather from parallel branches | *) |
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Init of |
(* | Initializers assumptions | *) |
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Branch of |
(* | If-Then-Else | *) |
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Either of |
(* | Disjunction | *) |
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State of |
(* | Memory Model snapshot | *) |
type
sequence
List of steps
typesequent =
sequence * Wp.Lang.F.pred
val pretty : (Stdlib.Format.formatter -> sequent -> unit) Stdlib.ref
val step : ?descr:string ->
?stmt:Cil_types.stmt ->
?deps:Property.t list ->
?warn:Wp.Warning.Set.t -> condition -> step
Creates a single step
val update_cond : ?descr:string ->
?deps:Property.t list ->
?warn:Wp.Warning.Set.t ->
step -> condition -> step
Updates the condition of a step and merges descr
, deps
and warn
val is_true : sequence -> bool
Contains only true or empty steps
val is_empty : sequence -> bool
No step at all
val vars_hyp : sequence -> Wp.Lang.F.Vars.t
Pre-computed and available in constant time.
val vars_seq : sequent -> Wp.Lang.F.Vars.t
At the cost of the union of hypotheses and goal.
val empty : sequence
empty sequence, equivalent to true assumption
val trivial : sequent
empty implies true
val sequence : step list -> sequence
val seq_branch : ?stmt:Cil_types.stmt ->
Wp.Lang.F.pred ->
sequence -> sequence -> sequence
Creates an If-Then-Else branch located at the provided stmt, if any.
val append : sequence -> sequence -> sequence
Conjunction
val concat : sequence list -> sequence
List conjunction
val iter : (step -> unit) -> sequence -> unit
Iterate only over the head steps of the sequence. Does not go deeper inside branches and disjunctions.
val list : sequence -> step list
Same domain than iter
.
val size : sequence -> int
Compute the total number of steps in the sequence, including nested sequences from branches and disjunctions. Pre-computed and available in constant time.
val steps : sequence -> int
Attributes unique indices to every step.id
in the sequence,
starting from zero. Recursively
Returns the number of steps in the sequence.
val index : sequent -> unit
Compute steps' id of sequent left hand-side.
Same as ignore (steps (fst s))
.
val step_at : sequence -> int -> step
Retrieve a step by id
in the sequence.
The index
function must have been called on the sequence before
retrieving the index properly.
Not_found
if the index is out of bounds.val is_trivial : sequent -> bool
Goal is true or hypotheses contains false.
val map_condition : (Wp.Lang.F.pred -> Wp.Lang.F.pred) ->
condition -> condition
Rewrite all root predicates in condition
val map_step : (Wp.Lang.F.pred -> Wp.Lang.F.pred) ->
step -> step
Rewrite all root predicates in step
val map_sequence : (Wp.Lang.F.pred -> Wp.Lang.F.pred) ->
sequence -> sequence
Rewrite all root predicates in sequence
val map_sequent : (Wp.Lang.F.pred -> Wp.Lang.F.pred) ->
sequent -> sequent
Rewrite all root predicates in hypotheses and goal
val insert : ?at:int ->
step -> sequent -> sequent
Insert a step in the sequent immediately at
the specified position.
Parameter at
can be size
to insert at the end of the sequent (default).
Invalid_argument
if the index is out of bounds.val replace : at:int ->
step -> sequent -> sequent
replace a step in the sequent, the one at
the specified position.
Invalid_argument
if the index is out of bounds.val replace_by_step_list : at:int ->
step list -> sequent -> sequent
replace a step in the sequent, the one at
the specified position.
Invalid_argument
if the index is out of bounds.val subst : (Wp.Lang.F.term -> Wp.Lang.F.term) ->
sequent -> sequent
Apply the atomic substitution recursively using Lang.F.p_subst f
.
Function f
should only transform the head of the predicate, and can assume
its sub-terms have been already substituted. The atomic substitution is also applied
to predicates.
f
should raise Not_found
on terms that must not be replaced
val introduction : sequent -> sequent option
Performs existential, universal and hypotheses introductions
val introduction_eq : sequent -> sequent
Same as introduction
but returns the same sequent is None
val lemma : Wp.Lang.F.pred -> sequent
Performs existential, universal and hypotheses introductions
val head : step -> Wp.Lang.F.pred
Predicate for Have and such, Condition for Branch, True for Either
val have : step -> Wp.Lang.F.pred
Predicate for Have and such, True for any other
val pred_cond : condition -> Wp.Lang.F.pred
val condition : sequence -> Wp.Lang.F.pred
With free variables kept.
val close : sequent -> Wp.Lang.F.pred
With free variables quantified.
val at_closure : (sequent -> sequent) -> unit
register a transformation applied just before close
Bundles are mergeable pre-sequences. This the key structure for merging hypotheses with linear complexity during backward weakest pre-condition calculus.
Bundle are constructed in backward order with respect to program control-flow, as driven by the wp calculus.
type
bundle
type'a
attributed =?descr:string ->
?stmt:Cil_types.stmt -> ?deps:Property.t list -> ?warn:Wp.Warning.Set.t -> 'a
val nil : bundle
Same as empty
val occurs : Wp.Lang.F.var -> bundle -> bool
val intersect : Wp.Lang.F.pred -> bundle -> bool
Variables of predicate and the bundle intersects
val merge : bundle list -> bundle
Performs a diff-based disjunction, introducing If-Then-Else or Either branches when possible. Linear complexity is achieved by assuming bundle ordering is consistent over the list.
val domain : Wp.Lang.F.pred list -> bundle -> bundle
Assumes a list of predicates in a Type
section on top of the bundle.
val intros : Wp.Lang.F.pred list -> bundle -> bundle
Assumes a list of predicates in a Have
section on top of the bundle.
val state : ?descr:string ->
?stmt:Cil_types.stmt ->
Wp.Mstate.state -> bundle -> bundle
Stack a memory model state on top of the bundle.
val assume : (?init:bool ->
?domain:bool ->
Wp.Lang.F.pred -> bundle -> bundle)
attributed
Assumes a predicate in the specified section,
with the specified decorations. On ~init:true
, the predicate is placed
in an Init
section. On ~domain:true
, the predicate is placed in a Type
section. Otherwized, it is placed in a standard Have
section.
val branch : (Wp.Lang.F.pred ->
bundle -> bundle -> bundle)
attributed
Construct a branch bundle, with merging of all common parts.
val either : (bundle list -> bundle) attributed
Construct a disjunction bundle, with merging of all common parts.
val extract : bundle -> Wp.Lang.F.pred list
Computes a formulae equivalent to the bundle. For debugging purpose only.
val bundle : bundle -> sequence
Closes the bundle and promote it into a well-formed sequence.
val clean : sequent -> sequent
val filter : sequent -> sequent
val parasite : sequent -> sequent
val init_filter : sequent -> sequent
val simplify : ?solvers:Wp.Lang.simplifier list ->
?intros:int -> sequent -> sequent
val pruning : ?solvers:Wp.Lang.simplifier list ->
sequent -> sequent