package lascar

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package lascar
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type symbol
type state
include Ltsa.T with type label := symbol and type state := state and type attr := bool
type transition = state * symbol * 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 = symbol * 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

type t

The type of Labeled Transition Systems with state attributes

module State : Ltsa.STATE with type t = state
module Label : Ltsa.LABEL with type t = symbol
module Attr : Ltsa.ATTR with type t = bool
module States : Utils.SetExt.S with type elt = state
module Attrs : Map.S with type key = state
module Tree : Utils.Tree.S with type node = state and type edge = symbol
val states : t -> States.t

Returns the set of states

val states' : t -> (state * bool) list

Returns the set of states, with attached attribute as a assocation list

val istates : t -> States.t

Returns the set of initial states

val istates' : t -> state list

Returns the set of initial states as a list

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 : symbol -> string

A synonym of Label.to_string

val string_of_attr : bool -> string

A synonym of Attr.to_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 * symbol) 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 * symbol) 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

val attr_of : t -> state -> bool

attr_of s q returns the attribute of state q in s. Raise Not_found if there is no state q in s

Building functions

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

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

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

add_itransition (l,q) s returns the LTSA obtained by adding initial transition to state q, with label l to LTSA 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 LTSA 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 -> bool -> unit) -> t -> unit

iter_states f s applies function f to all states (with associated attribute) of s

val fold_states : (state -> bool -> '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

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 -> symbol -> '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 LTSA s, and l1, ..., lN the associated transitions labels

val iter_succs : t -> state -> (state -> symbol -> 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 LTSA s, and l1, ..., lN the associated transitions labels

val fold_preds : t -> state -> (state -> symbol -> '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 LTSA s, and l1, ..., lN the associated transitions labels

val iter_preds : t -> state -> (state -> symbol -> 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 LTSA s, and l1, ..., lN the associated transitions labels

Global transformations

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

map_state f s returns the LTSA obtained by replacing each state q by f q in s. State attributes are left unchanged. Result is undefined if f is not injective.

val map_attr : (bool -> bool) -> t -> t

map_attr f s returns the LTSA obtained by replacing each state attribute a by f a in s.

val map_state_attr : ((state * bool) -> state * bool) -> t -> t

map_state_attr f s returns the LTSA obtained by replacing each pair of state and associated attributes (q,a) by f (q,a) in s. As for map_state, the result is undefined if f is not injective its first argument.

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

map_label f s returns the LTSA obtained by replacing each transition label l by f l in s.

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

map_transition f s returns the LTSA 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_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:symbol 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.

module LTSA : Ltsa.T with type state = state and type label = symbol and type attr = bool
module Symbol : Nfa.SYMBOL with type t = symbol
module Symbols : Set.S with type elt = symbol
val lts_of : t -> LTSA.t

Return the underlying representation of the NFA as a LTS

val empty : symbol list -> t

Creates an empty NFA (no states, no transitions) with a given symbol set.

val add_state : (state * bool * bool) -> t -> t

add_state (q,i,f) a returns the NFA obtained by adding state q to s. i and f resp. indicates whether q is an initial and/or an accepting state. Raises !Ltsa.Invalid_state if i is true and there's already an accepting state in a. Returns a is q is already a state in a

val create : states:state list -> symbols:symbol list -> istate:state -> trans:(state * symbol * state list) list -> astates:state list -> t

create qs ss q0 rel aqs builds a NFA from

  • a list of states qs
  • a list of symbols (alphabet) ss
  • an initial state q0
  • a transition relation rel given as a list of triplets (src_state,symbol,dst_states)
  • a list of accepting states aqs

Raises Failure if q0 does not appear in qs.

val symbols : t -> Symbols.t

Returns the set of symbols

val symbols' : t -> symbol list

Returns the set of symbols as a list

val acc_states : t -> States.t

Returns the set of accepting states

val acc_states' : t -> state list

Returns the set of accepting states as a list

val istate : t -> state option

Returns the initial state, when specified

val string_of_symbol : symbol -> string
val is_acc_state : t -> state -> bool

TODO : union and star operations

val trans : t -> state -> symbol -> States.t

trans a q s returns the set of states q' such that (q,s,q') belongs to the transition relation of a

val trans' : t -> state -> symbol -> state list

trans' is like trans but returns a list

val trans_hat : t -> state -> symbol list -> States.t

trans_hat a q ss is the transitive generalisation of trans. It returns the set of states which can reached when a sequence of symbols ss is given to a, starting at state q

val trans_hat' : t -> state -> symbol list -> state list

trans_hat' is like trans_hat but returns a list

val accept : t -> symbol list -> bool

accept a ss returns true iff ss is accepted by a. I.e., if trans_hat a q ss contains at least one accepting state. Raises Failure is no initial state has been specified in a.

val is_in_cycle : t -> state -> bool

cycles a q tests whether state q in automata a belongs to a cycle

val totalize : t -> state -> t

totalize a q returns a "totalized" version of automaton a by adding an extra "sink" state q. Raises Invalid_arg if q is already a state of a.

val unwind : int -> t -> LTSA.Tree.t

unwind depth s unwinds LTS system s to produce an execution tree (rooted at initial state) up to the specified depth.

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

dot_output name fname s writes a .dot representation of s with name name in file fname. Global graph drawing options can be specified with the options optional argument.

val dot_output_oc : string -> out_channel -> ?options:Utils.Dot.graph_style list -> t -> unit

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

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