package lascar

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package lascar
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Functor for computing the external product, in different flavors, of two LTS

Parameters

module S1 : T
module S2 : T

Signature

include T with type state = S1.state * S2.state and type label = S1.label option * S2.label option
type state = S1.state * S2.state

The type of state identifiers

type label = S1.label option * S2.label option

The type of transition labels

module Repr : Ltsa.T with type state = state and type label = label and type attr = unit

The underlying representation : a LTS(A) for which state attributes have type unit.

type t = Repr.t
val repr_of : t -> Repr.t
val of_repr : Repr.t -> t
type transition = state * label * state

The type for transitions. A transition is a triplet (s1,l,s2), where s1 is the source state, s2 the destination state and l the transition label

type itransition = label * state

The type for initial transitions. An initial transition is a pair (l,s), where s is the destination state and l the transition label

module State : STATE with type t = state
module Label : LABEL with type t = label
module States : Set.S with type elt = state
val states : t -> States.t

Returns the set of states

val states' : t -> state list

Returns the list of states

val istates : t -> States.t

Returns the set of initial states

val istates' : t -> state list

Returns the list of initial states

val transitions : t -> transition list

Returns the list of transitions

val itransitions : t -> itransition list

Returns the list of initial transitions

val string_of_state : state -> string

A synonym of State.to_string

val string_of_label : label -> string

A synonym of Label.to_string

val string_of_transition : transition -> string

Inspectors

val is_state : t -> state -> bool

is_state s q returns true iff q is a state in s

val is_init_state : t -> state -> bool

is_init s q returns true iff q is an initial state in s

val is_reachable : t -> state -> bool

is_reachable s q returns true iff q is a reachable state in s, i.e. if it can be reached from an initial state using the transitio relation.

val is_transition : t -> transition -> bool

is_transition t q returns true iff t is a transition in s

val succs : t -> state -> States.t

succs s q returns the set of immediate successors in s, i.e. the set of state q' such that there exists a transition (q,l,q') in R. Raise Invalid_argument if q is not in s.

val succs' : t -> state -> (state * label) list

succs' s q returns the list of immediate successors, with the associated transition label, of state q in s. Raise Invalid_argument if q is not in s.

val preds : t -> state -> States.t

preds s q returns the set of immediate predecessors of state q in s, i.e. the set of state q' such that there exists a transition (q',l,q) in R. Raise Invalid_argument if q is not in s.

val preds' : t -> state -> (state * label) list

preds' s q returns the list of immediate predecessors, with the associated transition label, of state q in s. Raise Invalid_argument if q is not in s.

val succs_hat : t -> state -> States.t

Transitive closure of succs. succs_hat s q returns all the successors (immediate or not) of q in s

val preds_hat : t -> state -> States.t

Transitive closure of preds. preds_hat s q returns all the predecessors (immediate or not) of q in s

Building functions

val empty : t

The empty LTS (no state, no transition)

val create : states:state list -> itrans:(label * state) list -> trans:(state * label * state) list -> t

create qs q0s ts builds a LTS from

  • a list of states identifiers
  • a list of initial transitions, where each transition is given as (label,dst_state)
  • a list of transitions ts, where each transition is given as (src_state,label,dst_state)
val add_state : state -> t -> t

add_state q s returns the LTS obtained by adding state q to s. Returns s is q is already a state in s

exception Invalid_state of state
val add_transition : (state * label * state) -> t -> t

add_transition (q1,l,q2) s returns the LTS obtained by adding transition from state q1 to state q2, with label l to LTS s. Raises Invalid_state if q1 or q2 are not states of s

val add_itransition : (label * state) -> t -> t

add_itransition (l,q) s returns the LTS obtained by adding initial transition to state q, with label l to LTS s. Raises Invalid_state if q are is not a state of s

val remove_state : state -> t -> t

remove_state q s returns the LTS obtained by removing state q, and all attached transitions, from s. Raises Invalid_state is q is not a state in s

Global iterators

val iter_states : (state -> unit) -> t -> unit

iter_states f s applies function f to all states of s

val fold_states : (state -> 'a -> 'a) -> t -> 'a -> 'a

fold_states f s z computes f xN ... (f x2 (f x1 z))..., where x1, ..., xN are all the states of s

val iter_transitions : (transition -> unit) -> t -> unit

iter_transitions f s applies function f to all transitions of s

val fold_transitions : (transition -> 'a -> 'a) -> t -> 'a -> 'a

fold_transitions f s z computes f xN ... (f x2 (f x1 z))..., where x1, ..., xN are all the transitions of s

val iter_itransitions : (itransition -> unit) -> t -> unit

fold_transitions f s z computes f xN ... (f x2 (f x1 z))..., where x1, ..., xN are all the transitions of s

iter_itransitions f s applies function f to all initial transitions of s

val fold_itransitions : (itransition -> 'a -> 'a) -> t -> 'a -> 'a

fold_itransitions f s z computes f xN ... (f x2 (f x1 z))..., where x1, ..., xN are all the initial transitions of s

State iterators

val fold_succs : t -> state -> (state -> label -> 'a -> 'a) -> 'a -> 'a

fold_succs s x f z computes f xN lN ... (f x2 (f x1 l1 z) l2)..., where x1, ..., xN are all the successors of state x in LTS s, and l1, ..., lN the associated transitions labels

val iter_succs : t -> state -> (state -> label -> unit) -> unit

iter_succs s x f z computes f x1 l1; ... ;f xN lN, where x1, ..., xN are all the successors of state x in LTS s, and l1, ..., lN the associated transitions labels

val fold_preds : t -> state -> (state -> label -> 'a -> 'a) -> 'a -> 'a

fold_preds s x f z computes f xN lN ... (f x2 (f x1 l1 z) l2)..., where x1, ..., xN are all the predecessors of state x in LTS s, and l1, ..., lN the associated transitions labels

val iter_preds : t -> state -> (state -> label -> unit) -> unit

iter_preds s x f z computes f x1 l1; ... ;f xN lN, where x1, ..., xN are all the predecessors of state x in LTS s, and l1, ..., lN the associated transitions labels

Global transformations

val map_state : (state -> state) -> t -> t

map_state f s returns the LTS obtained by replacing each state q by f q in s. Result is undefined if f is not injective.

val map_label : (label -> label) -> t -> t

map_states f s returns the LTS obtained by replacing each transition label l by f l in s.

val map_transition : ((state option * label * state) -> state option * label * state) -> t -> t

map_transition f s returns the LTS obtained by replacing each transition t by f t in s. Each non-initial transition qs,l,qd is replaced by qs',l',qd', where (Some qs',l',qd') = f (Some qs,l,qd). If present, the initial transition l,qi is replaced by l',qi' where (None,l',qi') = f (None, l, qi). Warning: updating the source and/or destination state in a transition may result in a incoherent LTS description. This function should essentially be viewed as a variant of map_label in which the transformation function f can take the source and destination state into account.

val clean : t -> t

Removes unreachable nodes and associated transitions

Output functions

val dot_output : string -> ?fname:string -> ?options:Utils.Dot.graph_style list -> ?marked_states:(state * Utils.Dot.node_style) list -> ?extra_nodes:(string * Utils.Dot.node_style) list -> ?implicit_transitions:transition list -> t -> unit

dot_output name s writes a .dot representation of s with name name in file. The name of the file is name.dot or specified with the fname optional argument. With the optional argument append, the description is appended to the specified file. Global graph drawing options can be specified with the options optional argument. States listed with the optional argument marked_states will be drawn with the specified style. Extra nodes, to be added to the generated graph, can be specified with the extra_nodes optional argument. Transitions listed in the implicit_transitions optional argument will not be drawn.

val dot_output_oc : string -> out_channel -> ?options:Utils.Dot.graph_style list -> ?marked_states:(state * Utils.Dot.node_style) list -> ?extra_nodes:(string * Utils.Dot.node_style) list -> ?implicit_transitions:transition list -> t -> unit

dot_output_coc name oc s is a variant of dot_output in which the description of s is written to the (previously opened) output channel oc.

val dot_output_execs : string -> ?fname:string -> ?options:Utils.Dot.graph_style list -> int -> t -> unit

dot_output_execs name depth s writes a .dot representation, with name name of the execution trees obtained by calling unwind depth s. The name of the file is name.dot or specified with the fname optional argument. Drawing options can be specified with the options optional argument.

val tex_output : string -> ?fname:string -> ?listed_transitions:label list option -> t -> unit

tex_output name fname s writes a .tex representation of s with name name. The name of the output file is name.dot or specified with the fname optional argument. When the optional argument listed_transitions is Some l, only transitions listed in l are written, otherwise all transitions of s are written.

val free_product : S1.t -> S2.t -> t

free_product s1 s2 computes the free product of the two LTS s1 and s2.

If s1=<Q1,L1,I1,R1> and s2=<Q2,L2,I2,R2>, then the free_product s1 s2 is <Q,L,I,R> where

  • Q = Q1xQ2
  • L = L1 U L2 U L1xL2
  • I = I1xI2
  • R, subset of QxLxQ, is {((q1,q2),l1,(q1',q2)) | (q1,l1,q1') in R1, q2 in Q2} U {((q1,q2),l2,(q1,q2')) | q1 in Q1, (q2,l2,q2') in R2} U {((q1,q2),(l2,l2),(q1',q2')) | (q1,l1,q1') in R1, (q2,l2,q2') in R2}

. In the result, transition labels

  • l1 are encoded as (Some l1, None)
  • l2 as (None, Some l2)
  • (l1,l2) as (Some l1, Some l2)

.

val synch_product : ((S1.label option * S2.label option) -> bool) -> S1.t -> S2.t -> t

synch_product p s1 s2 computes the synchronized product of the two LTS s1 and s2. The restricted product is the obtained by first computing the free product of s1 and s2 and then keeping only transitions (q,l,q') for which the transition label l satisfies the predicate p.

val synchronized_product : (S1.label option * S2.label option) list -> S1.t -> S2.t -> t

synchronized_product sync s1 s2 is a variant of synch_product in which the synchronisation function is given in extension as a list of allowed transitions.

val asynchronous_product : S1.t -> S2.t -> t

asynchronous_product s1 s2 computes the asynchronous product of the two LTS s1 and s2. This is a synchronized_product in which the synchronisation list contains only labels (Some l1,None) or (None,Some l2)).

val synchronous_product : S1.t -> S2.t -> t

synchronous_product p s1 s2 computes the synchronous product of the two LTS s1 and s2. This is a synchronized_product in which the synchronisation list contains only labels (Some l1,Some l2).

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