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Platform dedicated to the analysis of source code written in C

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doc/frama-c.kernel/Frama_c_kernel/Interpreted_automata/index.html

Module `Frama_c_kernel.Interpreted_automata`

An interpreted automaton is a convenient formalization of programs for abstract interpretation. It is a control flow graph where states are control point and edges are transitions. It keeps track of conditions on which a transition can be taken (guards) as well as actions which are computed when a transition is taken. It can then be interpreted w.r.t. the operational semantics to reproduce the behavior of the program or w.r.t. to the collection semantics to compute a set of reachable states.

This intermediate representation abstracts almost completely the notion of statement in CIL. Edges are either CIL expressions for guards, CIL instructions for actions or a return Edge. Thus, it saves the higher abstraction layers from interpreting CIL statements and from attaching guards to statement successors.

type info =

| NoneInfo
| LoopHead of int

type 'a control =

| Edges
(*
control flow is only given by vertex edges.
*)
| Loop of 'a
(*
start of a Loop stmt, with breaking vertex.
*)
| If of {
1. cond : Cil_types.exp;
2. vthen : 'a;
3. velse : 'a;
}
(*
edges are guaranteed to be two guards `Then` else `Else` with the given condition and successor vertices.
*)
| Switch of {
1. value : Cil_types.exp;
2. cases : (Cil_types.exp * 'a) list;
3. default : 'a;
}
(*
edges are guaranteed to be issued from a `switch()` statement with the given cases and default vertices.
*)

Control flow informations for outgoing edges, if any.

Vertices are control points. When a vertice is the *start* of a statement, this statement is kept in vertex_stmt. Currently, this statement is kept for two reasons: to know when callbacks should be called and when annotations should be read.

type vertex = private {

vertex_kf : Cil_types.kernel_function;
vertex_key : int;
mutable vertex_start_of : Cil_types.stmt option;
mutable vertex_info : info;
mutable vertex_control : vertex control;

}

type assert_kind =

| Invariant
| Assert
| Check
| Assume

type 'vertex labels = 'vertex Cil_datatype.Logic_label.Map.t

Maps binding the labels from an annotation to the vertices they refer to in the graph.

type 'vertex annotation = {

kind : assert_kind;
predicate : Cil_types.identified_predicate;
labels : 'vertex labels;
property : Property.t;

}

type 'vertex transition =

| Skip
| Return of Cil_types.exp option * Cil_types.stmt
| Guard of Cil_types.exp * guard_kind * Cil_types.stmt
| Prop of 'vertex annotation * Cil_types.stmt
| Instr of Cil_types.instr * Cil_types.stmt
| Enter of Cil_types.block
| Leave of Cil_types.block

Each transition can either be a skip (do nothing), a return, a guard represented by a Cil expression, a Cil instruction, an ACSL annotation or entering/leaving a block. The edge is annotated with the statement from which the transition has been generated. This is currently used to choose alarms locations.

and guard_kind =

| Then
| Else

val pretty_transition : vertex transition Pretty_utils.formatter

type 'vertex edge = private {

edge_kf : Cil_types.kernel_function;
edge_key : int;
edge_kinstr : Cil_types.kinstr;
edge_transition : 'vertex transition;
edge_loc : Cil_types.location;

}

val pretty_edge : vertex edge Pretty_utils.formatter

module G : 
  Graph.Sig.I
    with type V.t = vertex
     and type E.t = vertex * vertex edge * vertex
     and type V.label = vertex
     and type E.label = vertex edge

type graph = G.t

type wto = vertex Wto.partition

Weak Topological Order is given by a list (in topological order) of components of the graph, which are themselves WTOs

module Vertex : Datatype.S_with_collections with type t = vertex

Datatype for vertices

module Edge : Datatype.S_with_collections with type t = vertex edge

Datatype for edges

An interpreted automaton for a given function is a graph whose edges are guards and commands and always containing two special nodes which are the entry point and the return point of the function. It also comes with a table linking Cil statements to their starting and ending vertex

type automaton = {

graph : graph;
entry_point : vertex;
return_point : vertex;
stmt_table : (vertex * vertex) Cil_datatype.Stmt.Hashtbl.t;

}

module Automaton : Datatype.S with type t = automaton

Datatype for automata

module WTO : sig ... end

Datatype for WTOs

val get_automaton : Cil_types.kernel_function -> automaton

Get the automaton for the given kernel_function without annotations

val get_wto : Cil_types.kernel_function -> wto

Get the wto for the automaton of the given kernel_function

val exit_strategy : graph -> vertex Wto.component -> wto

Extract an exit strategy from a component, i.e. a sub-wto where all vertices lead outside the wto without passing through the head.

type 'a labeling = [

| `Stmt
| `Vertex
| `Both
| `Custom of Format.formatter -> 'a -> unit

]

val output_to_dot : 
  out_channel ->
  ?labeling:vertex labeling ->
  ?wto:wto ->
  automaton ->
  unit

Output the automaton in dot format

type wto_index = vertex list

the position of a statement in a wto given as the list of component heads

module WTOIndex : Datatype.S with type t = wto_index

Datatype for wto_index

val get_wto_index : Cil_types.kernel_function -> vertex -> wto_index

returns
the wto_index for a statement

val wto_index_diff : wto_index -> wto_index -> vertex list * vertex list

returns
the components left and the components entered when going from one index to another

val get_wto_index_diff : 
  Cil_types.kernel_function ->
  vertex ->
  vertex ->
  vertex list * vertex list

returns
the components left and the components entered when going from one vertex to another

val is_wto_head : Cil_types.kernel_function -> vertex -> bool

returns
wether v is a component head or not

val is_back_edge : Cil_types.kernel_function -> (vertex * vertex) -> bool

returns
wether v1,v2 is a back edge of a loop, i.e. if the vertex v1 is a wto head of any component where v2 is included. This assumes that (v1,v2) is actually an edge present in the control flow graph.

module Compute : sig ... end

This module defines the previous functions without memoization

module UnrollUnnatural : sig ... end

Could enter a loop only by head nodes

Dataflow computation: simple data-flow analysis using interpreted automata. See tests/misc/interpreted_automata_dataflow.ml for a complete example using this dataflow computation.

module type Domain = sig ... end

Input domain for a simple dataflow analysis.

module type DataflowAnalysis = sig ... end

Simple dataflow analysis

module ForwardAnalysis (D : Domain) : DataflowAnalysis with type state = D.t

Forward dataflow analysis. The domain must provide a forward transfer function that computes the state after a transition from the state before.

module BackwardAnalysis (D : Domain) : DataflowAnalysis with type state = D.t

Backward dataflow analysis. The domain must provide a backward transfer function that computes the state before a transition from the state after.