Source file Conditions.ml
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open Qed.Logic
open Cil_types
open Lang
open Lang.F
let dkey_pruning = Wp_parameters.register_category "pruning"
type category =
| KEEP (** Has probes, but equivalent to True *)
| TRUE (** Logically equivalent to True *)
| FALSE (** Logically equivalent to False *)
| MAYBE (** Any Hypothesis *)
let c_and c1 c2 =
match c1 , c2 with
| FALSE , _ | _ , FALSE -> FALSE
| MAYBE , _ | _ , MAYBE -> MAYBE
| TRUE , TRUE -> TRUE
| (KEEP | TRUE) , (KEEP | TRUE) -> KEEP
let c_or c1 c2 =
match c1 , c2 with
| FALSE , FALSE -> FALSE
| TRUE , TRUE -> TRUE
| _ -> MAYBE
let rec cfold_and a f = function
| [] -> a | e::es -> cfold_and (c_and a (f e)) f es
let rec cfold_or a f = function
| [] -> a | e::es -> cfold_or (c_or a (f e)) f es
let c_conj f es = cfold_and TRUE f es
let c_disj f = function [] -> FALSE | e::es -> cfold_or (f e) f es
type step = {
mutable id : int ;
size : int ;
vars : Vars.t ;
stmt : stmt option ;
descr : string option ;
deps : Property.t list ;
warn : Warning.Set.t ;
condition : condition ;
}
and sequence = {
seq_size : int ;
seq_vars : Vars.t ;
seq_core : Pset.t ;
seq_catg : category ;
seq_list : step list ;
}
and condition =
| Type of pred
| Have of pred
| When of pred
| Core of pred
| Init of pred
| Branch of pred * sequence * sequence
| Either of sequence list
| State of Mstate.state
| Probe of Probe.t * term
let vars_seqs w = List.fold_left (fun xs s -> Vars.union xs s.seq_vars) Vars.empty w
let vars_list s = List.fold_left (fun xs s -> Vars.union xs s.vars) Vars.empty s
let size_list s = List.fold_left (fun n s -> n + s.size) 0 s
let vars_cond = function
| Type q | When q | Have q | Core q | Init q -> F.varsp q
| Branch(p,sa,sb) -> Vars.union (F.varsp p) (Vars.union sa.seq_vars sb.seq_vars)
| Either cases -> vars_seqs cases
| State _ -> Vars.empty
| Probe(_,t) -> F.vars t
let size_cond = function
| Type _ | When _ | Have _ | Core _ | Init _ | State _ | Probe _ -> 1
| Branch(_,sa,sb) -> 1 + sa.seq_size + sb.seq_size
| Either cases -> List.fold_left (fun n s -> n + s.seq_size) 1 cases
let vars_hyp hs = hs.seq_vars
let vars_seq (hs,g) = Vars.union (F.varsp g) hs.seq_vars
let is_core p = match F.e_expr p with
| Qed.Logic.Eq _ -> true
| _ -> false
let rec add_core s p = match F.p_expr p with
| Qed.Logic.And ps -> List.fold_left add_core Pset.empty ps
| _ -> if is_core p then Pset.add p s else s
let core_cond = function
| Type _ | State _ | Probe _ -> Pset.empty
| Have p | When p | Core p | Init p -> add_core Pset.empty p
| Branch(_,sa,sb) -> Pset.inter sa.seq_core sb.seq_core
| Either [] -> Pset.empty
| Either (c::cs) ->
List.fold_left (fun w s -> Pset.inter w s.seq_core) c.seq_core cs
let add_core_step ps s = Pset.union ps (core_cond s.condition)
let core_list s = List.fold_left add_core_step Pset.empty s
let catg_seq s = s.seq_catg
let catg_cond = function
| State _ -> TRUE
| Probe _ -> KEEP
| Have p | Type p | When p | Core p | Init p ->
begin
match F.is_ptrue p with
| No -> FALSE
| Maybe -> MAYBE
| Yes -> TRUE
end
| Either cs -> c_disj catg_seq cs
| Branch(_,a,b) -> c_or a.seq_catg b.seq_catg
let catg_step s = catg_cond s.condition
let catg_list l = c_conj catg_step l
let sequence l = {
seq_size = size_list l ;
seq_vars = vars_list l ;
seq_core = core_list l ;
seq_catg = catg_list l ;
seq_list = l ;
}
let rec equal_cond ca cb =
match ca,cb with
| Probe(p,a) , Probe(q,b) -> Probe.equal p q && a == b
| State _ , State _ -> true
| Type p , Type q
| Have p , Have q
| When p , When q
| Core p , Core q
| Init p , Init q
-> p == q
| Branch(p,a,b) , Branch(q,a',b') ->
p == q && equal_seq a a' && equal_seq b b'
| Either u, Either v ->
Qed.Hcons.equal_list equal_seq u v
| Probe _ , _ | _ , Probe _
| State _ , _ | _ , State _
| Type _ , _ | _ , Type _
| Have _ , _ | _ , Have _
| When _ , _ | _ , When _
| Core _ , _ | _ , Core _
| Init _ , _ | _ , Init _
| Branch _ , _ | _ , Branch _
-> false
and equal_step a b =
equal_cond a.condition b.condition
and equal_list sa sb =
Qed.Hcons.equal_list equal_step sa sb
and equal_seq sa sb =
equal_list sa.seq_list sb.seq_list
module Core =
struct
let rec fpred core p = match F.p_expr p with
| Qed.Logic.And ps -> F.p_conj (List.map (fpred core) ps)
| _ -> if Pset.mem p core then p_true else p
let fcond core = function
| Core p -> Core (fpred core p)
| Have p -> Have (fpred core p)
| When p -> When (fpred core p)
| Init p -> Init (fpred core p)
| (Type _ | Branch _ | Either _ | State _ | Probe _) as cond -> cond
let fstep core step =
let condition = fcond core step.condition in
let vars = vars_cond condition in
{ step with condition ; vars }
let factorize a b =
if Wp_parameters.Core.get () then
let core = Pset.inter a.seq_core b.seq_core in
if Pset.is_empty core then None else
let ca = List.map (fstep core) a.seq_list in
let cb = List.map (fstep core) b.seq_list in
Some (F.p_conj (Pset.elements core) , sequence ca , sequence cb)
else None
end
module Bundle :
sig
type t
val empty : t
val vars : t -> Vars.t
val is_empty : t -> bool
val category : t -> category
val add : step -> t -> t
val factorize : t -> t -> t * t * t
val big_inter : t list -> t
val diff : t -> t -> t
val head : t -> Mstate.state option
val freeze: ?join:step -> t -> sequence
val map : (condition -> 'a) -> t -> 'a list
end =
struct
module SEQ = Qed.Listset.Make
(struct
type t = int * step
let equal (k1,_) (k2,_) = k1 = k2
let compare (k1,s1) (k2,s2) =
let rank = function
| Type _ -> 0
| When _ -> 1
| _ -> 2
in
let r = rank s1.condition - rank s2.condition in
if r = 0 then Stdlib.compare k2 k1 else r
end)
type t = Vars.t * SEQ.t
let vars = fst
let cid = ref 0
let fresh () = incr cid ; assert (!cid > 0) ; !cid
let add s (xs,t) = Vars.union xs s.vars , SEQ.add (fresh (),s) t
let empty = Vars.empty , []
let is_empty = function (_,[]) -> true | _ -> false
let head = function _,(_,{ condition = State s }) :: _ -> Some s | _ -> None
let build seq =
let xs = List.fold_left
(fun xs (_,s) -> Vars.union xs s.vars) Vars.empty seq in
xs , seq
let factorize (_,a) (_,b) =
let l,m,r = SEQ.factorize a b in
build l , build m , build r
let big_inter cs = build (SEQ.big_inter (List.map snd cs))
let diff (_,a) (_,b) = build (SEQ.diff a b)
let freeze ?join (seq_vars,bundle) =
let seq = List.map snd bundle in
let seq_list = match join with None -> seq | Some s -> seq @ [s] in
let seq_size = size_list seq in
let seq_catg = catg_list seq in
{ seq_size ; seq_vars ; seq_core = Pset.empty ; seq_catg ; seq_list }
let map f b = List.map (fun (_,s) -> f s.condition) (snd b)
let category (_,bundle) = c_conj (fun (_,s) -> catg_step s) bundle
end
type bundle = Bundle.t
type sequent = sequence * F.pred
let pretty = ref (fun _fmt _seq -> ())
let equal (a : sequent) (b : sequent) : bool =
F.eqp (snd a) (snd b) && equal_seq (fst a) (fst b)
let is_true = function { seq_catg = TRUE | KEEP } -> true | _ -> false
let is_empty = function { seq_catg = TRUE } -> true | _ -> false
let is_false = function { seq_catg = FALSE } -> true | _ -> false
let is_absurd_h h = match h.condition with
| State _ | Probe _ -> false
| (Type p | Core p | When p | Have p | Init p) -> p == F.p_false
| Branch(_,p,q) -> is_false p && is_false q
| Either w -> List.for_all is_false w
let is_trivial_h h = match h.condition with
| State _ | Probe _ -> false
| (Type p | Core p | When p | Have p | Init p) -> p == F.p_true
| Branch(_,a,b) -> is_true a && is_true b
| Either [] -> false
| Either w -> List.for_all is_true w
let is_trivial_hs_p hs p = p == F.p_true || List.exists is_absurd_h hs
let is_trivial_hsp (hs,p) = is_trivial_hs_p hs p
let is_trivial (s:sequent) = is_trivial_hs_p (fst s).seq_list (snd s)
let rec pred_cond = function
| State _ | Probe _ -> F.p_true
| When p | Type p | Have p | Core p | Init p -> p
| Branch(p,a,b) -> F.p_if p (pred_seq a) (pred_seq b)
| Either cases -> F.p_any pred_seq cases
and pred_seq seq = F.p_all (fun s -> pred_cond s.condition) seq.seq_list
let bundle = Bundle.map pred_cond bundle
let bundle = Bundle.freeze ?join:None
let intersect p bundle = Vars.intersect (F.varsp p) (Bundle.vars bundle)
let occurs x bundle = Vars.mem x (Bundle.vars bundle)
let nil = Bundle.empty
let noid = (-1)
let step ?descr ?stmt ?(deps=[]) ?(warn=Warning.Set.empty) cond =
{
id = noid ;
size = size_cond cond ;
vars = vars_cond cond ;
stmt = stmt ;
descr = descr ;
warn = warn ;
deps = deps ;
condition = cond ;
}
let update_cond ?descr ?(deps=[]) ?(warn=Warning.Set.empty) h c =
let descr = match h.descr, descr with
| None, _ -> descr ;
| Some _, None -> h.descr ;
| Some decr1, Some descr2 -> Some (decr1 ^ "-" ^ descr2)
in {
id = noid ;
condition = c ;
stmt = h.stmt ;
size = size_cond c ;
vars = vars_cond c ;
descr = descr ;
deps = deps@h.deps ;
warn = Warning.Set.union h.warn warn ;
}
type 'a disjunction = D_TRUE | D_FALSE | D_EITHER of 'a list
let disjunction phi es =
let positives = ref false in
let remains = List.filter
(fun e ->
match phi e with
| TRUE | KEEP -> positives := true ; false
| MAYBE -> true
| FALSE -> false
) es in
match remains with
| [] -> if !positives then D_TRUE else D_FALSE
| cs -> D_EITHER cs
let prenex_intro p =
try
let open Qed.Logic in
let rec walk hs xs p =
match F.p_expr p with
| Imply(h,p) -> walk (h::hs) xs p
| Bind(Forall,_,_) -> bind hs xs p
| _ ->
if hs = [] then raise Exit ;
F.p_forall (List.rev xs) (F.p_hyps (List.concat hs) p)
and bind hs xs p =
let pool = Lang.get_pool () in
let ctx,t = e_open ~pool ~forall:true
~exists:false ~lambda:false (e_prop p) in
let xs = List.fold_left (fun xs (_,x) -> x::xs) xs (List.rev ctx) in
walk hs xs (F.p_bool t)
and crawl p =
match F.p_expr p with
| Imply(h,p) -> F.p_hyps h (crawl p)
| Bind(Forall,_,_) -> bind [] [] p
| _ -> raise Exit
in crawl p
with Exit -> p
let rec exist_intro p =
let open Qed.Logic in
match F.p_expr p with
| And ps -> F.p_all exist_intro ps
| Bind(Exists,_,_) ->
let pool = Lang.get_pool () in
let _,t = e_open ~pool ~exists:true
~forall:false ~lambda:false (e_prop p) in
exist_intro (F.p_bool t)
| _ ->
if Wp_parameters.Prenex.get ()
then prenex_intro p
else p
let rec exist_intros = function
| [] -> []
| p::hs -> begin
let open Qed.Logic in
match F.p_expr p with
| And ps -> exist_intros (ps@hs)
| Bind(Exists,_,_) ->
let pool = Lang.get_pool () in
let _,t = F.QED.e_open ~pool ~exists:true
~forall:false ~lambda:false (e_prop p) in
exist_intros ((F.p_bool t)::hs)
| _ ->
p::(exist_intros hs)
end
let rec forall_intro p =
let open Qed.Logic in
match F.p_expr p with
| Bind(Forall,_,_) ->
let pool = Lang.get_pool () in
let _,t = F.QED.e_open ~pool ~forall:true
~exists:false ~lambda:false (e_prop p) in
forall_intro (F.p_bool t)
| Imply(hs,p) ->
let hs = exist_intros hs in
let hp,p = forall_intro p in
hs @ hp , p
| Or qs ->
let hps,ps = List.fold_left (fun (hs,ps) q ->
let hp,p = forall_intro q in
(hp @ hs), (p::ps)) ([],[]) qs
in
let hps,ps = List.fold_left (fun (hs,ps) q ->
match F.repr (F.e_prop q) with
| Neq _ -> ((F.p_not q)::hs), ps
| _ -> hs, (q::ps)) (hps,[]) ps
in
hps, (F.p_disj ps)
| _ ->
[] , p
type 'a attributed =
( ?descr:string ->
?stmt:stmt ->
?deps:Property.t list ->
?warn:Warning.Set.t ->
'a )
let domain ps hs =
if ps = [] then hs else
Bundle.add (step (Type (p_conj ps))) hs
let intros ps hs =
if ps = [] then hs else
let p = F.p_all exist_intro ps in
Bundle.add (step ~descr:"Goal" (When p)) hs
let state ?descr ?stmt state hs =
Bundle.add (step ?descr ?stmt (State state)) hs
let probe ~loc ?descr ?stmt ~name term hs =
let p = Probe.create ~loc ?stmt ~name () in
Bundle.add (step ?descr ?stmt (Probe(p,term))) hs
let assume ?descr ?stmt ?deps ?warn ?(init=false) ?(domain=false) p hs =
match F.is_ptrue p with
| Yes -> hs
| No ->
let cond = if init then Init p else if domain then Type p else Have p in
let s = step ?descr ?stmt ?deps ?warn cond in
Bundle.add s Bundle.empty
| Maybe ->
begin
match Bundle.category hs with
| MAYBE | TRUE | KEEP ->
let p = exist_intro p in
let cond =
if init then Init p else if domain then Type p else Have p in
let s = step ?descr ?stmt ?deps ?warn cond in
Bundle.add s hs
| FALSE -> hs
end
let join = function None -> None | Some s -> Some (step (State s))
let branch ?descr ?stmt ?deps ?warn p ha hb =
match F.is_ptrue p with
| Yes -> ha
| No -> hb
| Maybe ->
match Bundle.category ha , Bundle.category hb with
| TRUE , TRUE -> Bundle.empty
| _ , FALSE -> assume ?descr ?stmt ?deps ?warn p ha
| FALSE , _ -> assume ?descr ?stmt ?deps ?warn (p_not p) hb
| _ ->
let ha,hs,hb = Bundle.factorize ha hb in
if Bundle.is_empty ha && Bundle.is_empty hb then hs else
let join = join (Bundle.head hs) in
let a = Bundle.freeze ?join ha in
let b = Bundle.freeze ?join hb in
let s = step ?descr ?stmt ?deps ?warn (Branch(p,a,b)) in
Bundle.add s hs
let either ?descr ?stmt ?deps ?warn cases =
match disjunction Bundle.category cases with
| D_TRUE -> Bundle.empty
| D_FALSE ->
let s = step ?descr ?stmt ?deps ?warn (Have p_false) in
Bundle.add s Bundle.empty
| D_EITHER cases ->
let trunk = Bundle.big_inter cases in
let cases = List.map (fun case -> Bundle.diff case trunk) cases in
match disjunction Bundle.category cases with
| D_TRUE -> trunk
| D_FALSE ->
let s = step ?descr ?stmt ?deps ?warn (Have p_false) in
Bundle.add s Bundle.empty
| D_EITHER cases ->
let cases = List.map Bundle.freeze cases in
let s = step ?descr ?stmt ?deps ?warn (Either cases) in
Bundle.add s trunk
let merge cases = either ~descr:"Merge" cases
let rec flat_catg = function
| [] -> TRUE
| s::cs ->
match catg_step s with
| TRUE -> flat_catg cs
| r -> r
let flat_cons step tail =
match flat_catg tail with
| FALSE -> tail
| _ -> step :: tail
let flat_concat head tail =
match flat_catg head with
| TRUE -> tail
| FALSE -> head
| MAYBE|KEEP ->
match flat_catg tail with
| TRUE -> head
| FALSE -> tail
| MAYBE|KEEP -> head @ tail
let core_residual step core = {
id = noid ;
size = 1 ;
vars = F.varsp core ;
condition = Core core ;
descr = None ;
warn = Warning.Set.empty ;
deps = [] ;
stmt = step.stmt ;
}
let core_branch step p a b =
let condition =
match a.seq_catg , b.seq_catg with
| (TRUE | KEEP) , (TRUE|KEEP) -> Have p_true
| FALSE , FALSE -> Have p_false
| _ -> Branch(p,a,b)
in update_cond step condition
let rec flatten_sequence m = function
| [] -> []
| step :: seq ->
match step.condition with
| State _ | Probe _ -> flat_cons step (flatten_sequence m seq)
| Have p | Type p | When p | Core p | Init p ->
begin
match F.is_ptrue p with
| Yes -> m := true ; flatten_sequence m seq
| No -> if seq <> [] then m := true ; [step]
| Maybe -> flat_cons step (flatten_sequence m seq)
end
| Branch(p,a,b) ->
begin
match F.is_ptrue p with
| Yes -> m := true ; flat_concat a.seq_list (flatten_sequence m seq)
| No -> m := true ; flat_concat b.seq_list (flatten_sequence m seq)
| Maybe ->
let sa = a.seq_list in
let sb = b.seq_list in
match a.seq_catg , b.seq_catg with
| (TRUE|KEEP) , (TRUE|KEEP) ->
m := true ; flatten_sequence m seq
| _ , FALSE ->
m := true ;
let step = update_cond step (Have p) in
step :: sa @ flatten_sequence m seq
| FALSE , _ ->
m := true ;
let step = update_cond step (Have (p_not p)) in
step :: sb @ flatten_sequence m seq
| _ ->
begin
match Core.factorize a b with
| None -> step :: flatten_sequence m seq
| Some( core , a , b ) ->
m := true ;
let score = core_residual step core in
let scond = core_branch step p a b in
score :: scond :: flatten_sequence m seq
end
end
| Either [] -> if seq <> [] then m := true ; [step]
| Either cases ->
match disjunction catg_seq cases with
| D_TRUE -> m := true ; flatten_sequence m seq
| D_FALSE -> m := true ; [ update_cond step (Have p_false) ]
| D_EITHER [hc] ->
m := true ; flat_concat hc.seq_list (flatten_sequence m seq)
| D_EITHER cs ->
let step = update_cond step (Either cs) in
flat_cons step (flatten_sequence m seq)
let rec map_condition f = function
| Probe(p,t) -> Probe(p,F.p_lift f t)
| State s -> State (Mstate.apply (F.p_lift f) s)
| Have p -> Have (f p)
| Type p -> Type (f p)
| When p -> When (f p)
| Core p -> Core (f p)
| Init p -> Init (f p)
| Branch(p,a,b) -> Branch(f p,map_sequence f a,map_sequence f b)
| Either cs -> Either (List.map (map_sequence f) cs)
and map_step f h = update_cond h (map_condition f h.condition)
and map_steplist f = function
| [] -> []
| h::hs ->
let h = map_step f h in
if is_absurd_h h then [h] else
let hs = map_steplist f hs in
if is_trivial_h h then hs else h :: hs
and map_sequence f s =
sequence (map_steplist f s.seq_list)
and map_sequent f (hs,g) = map_sequence f hs , f g
module Ground = Letify.Ground
let rec ground_flow ~fwd env h =
match h.condition with
| Probe(p,t) -> update_cond h (Probe (p,Ground.e_apply env t))
| State s ->
let s = Mstate.apply (Ground.e_apply env) s in
update_cond h (State s)
| Type _ | Have _ | When _ | Core _ | Init _ ->
let phi = if fwd then Ground.forward else Ground.backward in
let cond = map_condition (phi env) h.condition in
update_cond h cond
| Branch(p,a,b) ->
let p,wa,wb = Ground.branch env p in
let a = ground_flowseq ~fwd wa a in
let b = ground_flowseq ~fwd wb b in
update_cond h (Branch(p,a,b))
| Either ws ->
let ws = List.map (fun w -> ground_flowseq ~fwd (Ground.copy env) w) ws in
update_cond h (Either ws)
and ground_flowseq ~fwd env hs =
sequence (ground_flowlist ~fwd env hs.seq_list)
and ground_flowlist ~fwd env hs =
if fwd
then ground_flowdir ~fwd env hs
else List.rev (ground_flowdir ~fwd env (List.rev hs))
and ground_flowdir ~fwd env = function
| [] -> []
| h::hs ->
let h = ground_flow ~fwd env h in
if is_absurd_h h then [h] else
let hs = ground_flowdir ~fwd env hs in
if is_trivial_h h then hs else h :: hs
let ground (hs,g) =
let hs = ground_flowlist ~fwd:true (Ground.top ()) hs in
let hs = ground_flowlist ~fwd:false (Ground.top ()) hs in
let env = Ground.top () in
let hs = ground_flowlist ~fwd:true env hs in
hs , Ground.p_apply env g
module Sigma = Letify.Sigma
module Defs = Letify.Defs
let used_of_dseq ds =
Array.fold_left (fun ys (_,step) -> Vars.union ys step.vars) Vars.empty ds
let bind_dseq target (di,_) sigma =
Letify.bind (Letify.bind sigma di target) di (Defs.domain di)
let locals sigma ~target ~required ?(step=Vars.empty) k dseq =
let t = ref target in
let e = ref (Vars.union required step) in
Array.iteri
(fun i (_,step) ->
if i > k then t := Vars.union !t step.vars ;
if i <> k then e := Vars.union !e step.vars ;
) dseq ;
Vars.diff !t (Sigma.domain sigma) , !e
let dseq_of_step sigma step =
let defs =
match step.condition with
| Init p | Have p | When p | Core p -> Defs.extract (Sigma.p_apply sigma p)
| Type _ | Branch _ | Either _ | State _ | Probe _ -> Defs.empty
in defs , step
let letify_assume sref (_,step) =
let current = !sref in
begin
match step.condition with
| Type _ | Branch _ | Either _ | State _ | Probe _ -> ()
| Init p | Have p | When p | Core p ->
if Wp_parameters.Simpl.get () then
sref := Sigma.assume current p
end ; current
let rec letify_type sigma used p = match F.p_expr p with
| And ps -> p_all (letify_type sigma used) ps
| _ ->
let p = Sigma.p_apply sigma p in
let vs = F.varsp p in
if Vars.intersect used vs || Vars.is_empty vs then p else F.p_true
let rec letify_seq sigma0 ~target ~export (seq : step list) =
let dseq = Array.map (dseq_of_step sigma0) (Array.of_list seq) in
let sigma1 = Array.fold_right (bind_dseq target) dseq sigma0 in
let sref = ref sigma1 in
let dsigma = Array.map (letify_assume sref) dseq in
let sigma2 = !sref in
let outside = Vars.union export target in
let inside = used_of_dseq dseq in
let used = Vars.diff (Vars.union outside inside) (Sigma.domain sigma2) in
let required = Vars.union outside (Sigma.codomain sigma2) in
let sequence =
Array.mapi (letify_step dseq dsigma ~used ~required ~target) dseq in
let modified = ref (not (Sigma.equal sigma0 sigma1)) in
let sequence = flatten_sequence modified (Array.to_list sequence) in
!modified , sigma1 , sigma2 , sequence
and letify_step dseq dsigma ~required ~target ~used i (d,s) =
let sigma = dsigma.(i) in
let cond = match s.condition with
| Probe(p,t) -> Probe (p,Sigma.e_apply sigma t)
| State s -> State (Mstate.apply (Sigma.e_apply sigma) s)
| Init p ->
let p = Sigma.p_apply sigma p in
let ps = Letify.add_definitions sigma d required [p] in
Init (p_conj ps)
| Have p ->
let p = Sigma.p_apply sigma p in
let ps = Letify.add_definitions sigma d required [p] in
Have (p_conj ps)
| Core p ->
let p = Sigma.p_apply sigma p in
let ps = Letify.add_definitions sigma d required [p] in
Core (p_conj ps)
| When p ->
let p = Sigma.p_apply sigma p in
let ps = Letify.add_definitions sigma d required [p] in
When (p_conj ps)
| Type p ->
Type (letify_type sigma used p)
| Branch(p,a,b) ->
let p = Sigma.p_apply sigma p in
let step = F.varsp p in
let (target,export) = locals sigma ~target ~required ~step i dseq in
let sa = Sigma.assume sigma p in
let sb = Sigma.assume sigma (p_not p) in
let a = letify_case sa ~target ~export a in
let b = letify_case sb ~target ~export b in
Branch(p,a,b)
| Either cases ->
let (target,export) = locals sigma ~target ~required i dseq in
Either (List.map (letify_case sigma ~target ~export) cases)
in update_cond s cond
and letify_case sigma ~target ~export seq =
let (_,_,_,s) = letify_seq sigma ~target ~export seq.seq_list
in sequence s
let equivalent_exp solvers e =
List.fold_left (fun e s -> s#equivalent_exp e) e solvers
let stronger_goal solvers p =
List.fold_left (fun p s -> s#stronger_goal p) p solvers
let weaker_hyp solvers p =
List.fold_left (fun p s -> s#weaker_hyp p) p solvers
let equivalent_branch solvers p =
List.fold_left (fun p s -> s#equivalent_branch p) p solvers
let apply_goal solvers p =
let stronger_and_then_assume p =
let p' = stronger_goal solvers p in
List.iter (fun s -> s#assume (p_not p')) solvers;
p'
in
match F.p_expr p with
| Or ps ->
let unmodified,qs = List.fold_left (fun (unmodified,qs) p ->
let p' = stronger_and_then_assume p in
(unmodified && (Lang.F.eqp p p')), (p'::qs))
(true,[]) ps
in if unmodified then p else p_disj qs
| _ -> stronger_and_then_assume p
let apply_hyp modified solvers h =
let weaken_and_then_assume p =
let p' = weaker_hyp solvers p in
if not (Lang.F.eqp p p') then modified := true;
List.iter (fun s -> s#assume p') solvers; p'
in
let weaken p = match F.p_expr p with
| And ps ->
let unmodified,qs = List.fold_left (fun (unmodified,qs) p ->
let p' = weaken_and_then_assume p in
(unmodified && (Lang.F.eqp p p')), (p'::qs))
(true,[]) ps
in if unmodified then p else p_conj qs
| _ -> weaken_and_then_assume p
in
match h.condition with
| Probe(p,t) -> update_cond h (Probe (p,equivalent_exp solvers t))
| State s -> update_cond h (State (Mstate.apply (equivalent_exp solvers) s))
| Init p -> update_cond h (Init (weaken p))
| Type p -> update_cond h (Type (weaken p))
| Have p -> update_cond h (Have (weaken p))
| When p -> update_cond h (When (weaken p))
| Core p -> update_cond h (Core (weaken p))
| Branch(p,_,_) -> List.iter (fun s -> s#target p) solvers; h
| Either _ -> h
let decide_branch modified solvers h =
match h.condition with
| Branch(p,a,b) ->
let q = equivalent_branch solvers p in
if q != p then
( modified := true ; update_cond h (Branch(q,a,b)) )
else h
| _ -> h
let add_infer modified s hs =
let p = p_conj s#infer in
if p != p_true then
( modified := true ; step ~descr:s#name (Have p) :: hs )
else
hs
type outcome =
| NoSimplification
| Simplified of hsp
| Trivial
and hsp = step list * pred
let apply_simplifiers (solvers : simplifier list) (hs,g) =
if solvers = [] then NoSimplification
else
try
let modified = ref false in
let solvers = List.map (fun s -> s#copy) solvers in
let hs = List.map (apply_hyp modified solvers) hs in
List.iter (fun s -> s#target g) solvers ;
List.iter (fun s -> s#fixpoint) solvers ;
let hs = List.map (decide_branch modified solvers) hs in
let hs = List.fold_right (add_infer modified) solvers hs in
let p = apply_goal solvers g in
if p != g || !modified then
Simplified (hs,p)
else
NoSimplification
with Contradiction ->
Trivial
let empty = {
seq_size = 0 ;
seq_vars = Vars.empty ;
seq_core = Pset.empty ;
seq_catg = TRUE ;
seq_list = [] ;
}
let trivial = empty , F.p_true
let append sa sb =
if sa.seq_size = 0 then sb else
if sb.seq_size = 0 then sa else
let seq_size = sa.seq_size + sb.seq_size in
let seq_vars = Vars.union sa.seq_vars sb.seq_vars in
let seq_core = Pset.union sa.seq_core sb.seq_core in
let seq_list = sa.seq_list @ sb.seq_list in
let seq_catg = c_and sa.seq_catg sb.seq_catg in
{ seq_size ; seq_vars ; seq_core ; seq_catg ; seq_list }
let concat slist =
if slist = [] then empty else
let seq_size = List.fold_left (fun n s -> n + s.seq_size) 0 slist in
let seq_list = List.concat (List.map (fun s -> s.seq_list) slist) in
let seq_vars = List.fold_left (fun w s -> Vars.union w s.seq_vars)
Vars.empty slist in
let seq_core = List.fold_left (fun w s -> Pset.union w s.seq_core)
Pset.empty slist in
let seq_catg = c_conj catg_seq slist in
{ seq_size ; seq_vars ; seq_core ; seq_catg ; seq_list }
let seq_branch ?stmt p sa sb =
sequence [step ?stmt (Branch(p,sa,sb))]
let lemma ~loc g =
let cc g =
let hs,p = forall_intro g in
let hs = List.map (fun p -> step (Have p)) hs in
let hs =
if Wp_parameters.CounterExamples.get () then
let freevars = Vars.union (vars_list hs) (F.varsp p) in
List.fold_right
(fun x hs ->
let p = Probe.create ~loc ~name:(Var.basename x) () in
step (Probe(p,e_var x)) :: hs
) (Vars.elements freevars) hs
else hs in
sequence hs , p
in Lang.local ~vars:(F.varsp g) cc g
let introduction (hs,g) =
let flag = ref false in
let intro p = let q = exist_intro p in if q != p then flag := true ; q in
let hj = List.map (map_step intro) hs.seq_list in
let hi,p = forall_intro g in
let hi = List.map (fun p -> step (Have p)) hi in
if not !flag && hi == [] then
if p == g then None else Some (hs , p)
else
Some (sequence (hi @ hj) , p)
let introduction_eq s = match introduction s with
| Some s' -> s'
| None -> s
module ConstantFolder =
struct
open Qed
type sigma = {
mutable cst : bool Tmap.t ;
mutable dom : Vars.t ;
mutable def : term Tmap.t ;
mutable cache : F.sigma option ;
}
let rec is_cst s e = match F.repr e with
| True | False | Kint _ | Kreal _ -> true
| Fun(_,es) ->
begin
try Tmap.find e s.cst
with Not_found ->
let cst = List.for_all (is_cst s) es in
s.cst <- Tmap.add e cst s.cst ; cst
end
| _ -> false
let set_def s p a e =
try
let e0 = Tmap.find a s.def in
match F.is_true (F.e_eq e e0) with
| Logic.Yes -> ()
| Logic.No -> raise Contradiction
| Logic.Maybe ->
if F.compare e e0 < 0 then s.def <- Tmap.add a e s.def
with Not_found ->
begin
s.dom <- Vars.union (F.vars a) s.dom ;
s.def <- Tmap.add a e s.def ;
s.def <- Tmap.add p p s.def ;
s.cache <- None ;
end
let collect_set_def s p = Lang.iter_consequence_literals
(fun literal -> match Lang.F.repr literal with
| Logic.Eq(a,b) ->
if is_cst s a then set_def s literal b a ;
if is_cst s b then set_def s literal a b ;
| _ -> ()) p
let collect s = function
| Have p | When p | Core p | Init p -> collect_set_def s (F.e_prop p)
| Type _ | Branch _ | Either _ | State _ | Probe _ -> ()
let subst s =
match s.cache with
| Some m -> m
| None ->
let m = Lang.sigma () in
F.Subst.add_fun m (fun e -> Tmap.find e s.def) ;
s.cache <- Some m ; m
let e_apply s e = F.e_subst (subst s) e
let p_apply s p = F.p_subst (subst s) p
let rec c_apply s = function
| Probe(p,t) -> Probe (p,e_apply s t)
| State m -> State (Mstate.apply (e_apply s) m)
| Type p -> Type (p_apply s p)
| Init p -> Init (p_apply s p)
| Have p -> Have (p_apply s p)
| When p -> When (p_apply s p)
| Core p -> Core (p_apply s p)
| Branch(p,sa,sb) -> Branch( p_apply s p , seq_apply s sa , seq_apply s sb )
| Either cs -> Either (List.map (seq_apply s) cs)
and s_apply s (step : step) : step =
update_cond step (c_apply s step.condition)
and seq_apply s seq =
sequence (List.map (s_apply s) seq.seq_list)
let simplify (hs,p) =
let s = {
cst = Tmap.empty ;
def = Tmap.empty ;
dom = Vars.empty ;
cache = None ;
} in
try
List.iter (fun h -> collect s h.condition) hs ;
let hs = List.map (s_apply s) hs in
let p = p_apply s p in
hs , p
with Contradiction ->
[] , F.p_true
end
let rec fixpoint limit solvers sigma s0 =
if limit > 0 then compute limit solvers sigma s0 else s0
and compute limit solvers sigma s0 =
Async.yield ();
let s1 =
if Wp_parameters.Ground.get () then ground s0
else s0 in
let hs,p = ConstantFolder.simplify s1 in
let target = F.varsp p in
let export = Vars.empty in
let modified , sigma1 , sigma2 , hs =
letify_seq sigma ~target ~export hs in
let p = Sigma.p_apply sigma2 p in
let s2 = ground (hs , p) in
if is_trivial_hsp s2 then [],p_true
else
if modified || (limit > 0 && not (equal_list (fst s0) (fst s2)))
then fixpoint (pred limit) solvers sigma1 s2
else
match apply_simplifiers solvers s2 with
| Simplified s3 -> fixpoint (pred limit) solvers sigma1 s3
| Trivial -> [],p_true
| NoSimplification -> s2
let letify_hsp ?(solvers=[]) hsp = fixpoint 10 solvers Sigma.empty hsp
let rec simplify ?(solvers=[]) ?(intros=10) (seq,p0) =
let hs,p = fixpoint 10 solvers Sigma.empty (seq.seq_list,p0) in
let sequent = sequence hs , p in
match introduction sequent with
| Some introduced ->
if intros > 0 then
simplify ~solvers ~intros:(pred intros) introduced
else introduced
| None ->
sequent
let residual p = {
id = noid ;
size = 1 ;
vars = F.varsp p ;
stmt = None ;
descr = Some "Residual" ;
deps = [] ;
warn = Warning.Set.empty ;
condition = When p ;
}
let rec add_case p = function
| ( { condition = (Type _) } as step ):: tail ->
step :: add_case p tail
| hs -> residual p :: hs
let test_case p (s:hsp) =
let w = letify_hsp (add_case p (fst s) , snd s) in
if is_trivial_hsp w then None else Some w
let tc = ref 0
let rec test_cases (s : hsp) = function
| [] -> s
| (p,_) :: tail ->
Async.yield () ;
match test_case p s , test_case (p_not p) s with
| None , None -> incr tc ; [],F.p_true
| Some w , None -> incr tc ; test_cases w tail
| None , Some w -> incr tc ; test_cases w tail
| Some _ , Some _ -> test_cases s tail
let rec collect_cond m = function
| When _ | Have _ | Type _ | Init _ | Core _ | State _ | Probe _ -> ()
| Branch(p,a,b) -> Letify.Split.add m p ; collect_seq m a ; collect_seq m b
| Either cs -> List.iter (collect_seq m) cs
and collect_seq m seq = collect_steps m seq.seq_list
and collect_steps m steps = List.iter (fun s -> collect_cond m s.condition) steps
let pruning ?(solvers=[]) seq =
if is_trivial seq then seq
else
begin
let hs = (fst seq).seq_list in
let p = snd seq in
ignore solvers ;
let m = Letify.Split.create () in
collect_steps m hs ;
tc := 0 ;
let hsp = test_cases (hs,p) (Letify.Split.select m) in
if !tc > 0 && Wp_parameters.has_dkey dkey_pruning then
if is_trivial_hsp hsp then
Wp_parameters.feedback "[Pruning] Trivial"
else
Wp_parameters.feedback "[Pruning] %d branche(s) removed" !tc ;
let hs,p = hsp in
sequence hs , p
end
let rec collect_cond u = function
| State _ -> ()
| Probe(_,t) -> Cleaning.as_term u t
| When p -> Cleaning.as_have u p
| Have p -> Cleaning.as_have u p
| Core p -> Cleaning.as_have u p
| Type p -> Cleaning.as_type u p
| Init p -> Cleaning.as_init u p
| Branch(p,a,b) -> Cleaning.as_atom u p ; collect_seq u a ; collect_seq u b
| Either cs -> List.iter (collect_seq u) cs
and collect_seq u seq = collect_steps u seq.seq_list
and collect_steps u steps =
List.iter (fun s -> collect_cond u s.condition) steps
let rec clean_cond u = function
| State _ | Probe _ as cond -> cond
| When p -> When (Cleaning.filter_pred u p)
| Have p -> Have (Cleaning.filter_pred u p)
| Core p -> Core (Cleaning.filter_pred u p)
| Type p -> Type (Cleaning.filter_pred u p)
| Init p -> Init (Cleaning.filter_pred u p)
| Branch(p,a,b) -> Branch(p,clean_seq u a,clean_seq u b)
| Either cases -> Either(List.map (clean_seq u) cases)
and clean_seq u s =
let s = clean_steps u s.seq_list in
{ seq_size = size_list s ;
seq_vars = vars_list s ;
seq_core = Pset.empty ;
seq_catg = catg_list s ;
seq_list = s }
and clean_steps u = function
| [] -> []
| s :: seq ->
let c = clean_cond u s.condition in
let seq = clean_steps u seq in
match catg_cond c with
| TRUE -> seq
| FALSE -> [update_cond s c]
| KEEP | MAYBE -> update_cond s c :: seq
let clean (s,p) =
let u = Cleaning.create () in
Cleaning.as_atom u p ; collect_steps u s.seq_list ;
sequence (clean_steps u s.seq_list) , p
module Filter =
struct
module Gmap = Qed.Mergemap.Make(Fun)
module Gset = Qed.Mergeset.Make(Fun)
module Fset = Qed.Mergeset.Make(Field)
module FP =
struct
type t = Gset.t * Fset.t
let empty = Gset.empty , Fset.empty
let union (a,u) (b,v) = Gset.union a b , Fset.union u v
let subset (a,u) (b,v) = Gset.subset a b && Fset.subset u v
let intersect (a,u) (b,v) = Gset.intersect a b || Fset.intersect u v
end
type used = {
mutable fixpoint : bool ;
mutable footprint : FP.t Tmap.t ;
mutable footcalls : Fset.t Gmap.t ;
mutable gs : FP.t ;
mutable xs : Vars.t ;
}
[@@@ warning "-32"]
let pp_gset fmt (u,v) =
begin
Format.fprintf fmt "@[<hov 2>{" ;
Gset.iter (fun f -> Format.fprintf fmt "@ %a" Lang.Fun.pretty f) u ;
Format.fprintf fmt "," ;
Fset.iter (fun f -> Format.fprintf fmt "@ %a" Lang.Field.pretty f) v ;
Format.fprintf fmt " }@]" ;
end
let pp_used fmt used =
begin
Format.fprintf fmt "@[<hov 2>{" ;
Vars.iter (fun x -> Format.fprintf fmt "@ %a" Lang.F.Var.pretty x) used.xs ;
Format.fprintf fmt "," ;
Gset.iter (fun f -> Format.fprintf fmt "@ %a" Lang.Fun.pretty f) (fst used.gs) ;
Format.fprintf fmt "," ;
Fset.iter (fun f -> Format.fprintf fmt "@ %a" Lang.Field.pretty f) (snd used.gs) ;
Format.fprintf fmt " }@]" ;
end
[@@@ warning "+32"]
let fsetmap phi es =
List.fold_left
(fun fs e -> Fset.union fs (phi e))
Fset.empty es
let rec gvars_of_term ~deep m t =
try Tmap.find t m.footprint
with Not_found ->
let collect_subterms acc =
let gs = ref acc in
let collect m gs e = gs := FP.union !gs (gvars_of_term ~deep m e) in
F.lc_iter (collect m gs) t ;
let s = !gs in
m.footprint <- Tmap.add t s m.footprint ; s
in
match F.repr t with
| Fun(f,[]) ->
Gset.singleton f , Fset.empty
| Fun(f,_) when not deep || is_coloring_lfun f ->
Gset.empty , fset_of_lfun ~deep m f
| Fun(f,_) ->
collect_subterms (Gset.empty , fset_of_lfun ~deep m f)
| Rget(_,fd) ->
Gset.empty , Fset.singleton fd
| Rdef fts ->
Gset.empty ,
List.fold_left (fun fs (f,_) -> Fset.add f fs)
Fset.empty fts
| _ ->
collect_subterms FP.empty
and gvars_of_pred m p = gvars_of_term m (F.e_prop p)
and fset_of_tau (t : Lang.tau) =
match t with
| Qed.Logic.Array(ta,tb) ->
Fset.union (fset_of_tau ta) (fset_of_tau tb)
| Qed.Logic.Record fts ->
fsetmap (fun (f,t) -> Fset.add f (fset_of_tau t)) fts
| Qed.Logic.Data(adt,ts) ->
Fset.union (fsetmap fset_of_tau ts) (fset_of_adt adt)
| _ -> Fset.empty
and fset_of_adt adt =
fsetmap fset_of_field (Lang.fields_of_adt adt)
and fset_of_field fd =
let tf = Lang.tau_of_field fd in
Fset.add fd (fset_of_tau tf)
and fset_of_lemma ~deep m d =
snd (gvars_of_pred ~deep m d.Definitions.l_lemma)
and fset_of_var x = fset_of_tau (F.tau_of_var x)
and fset_of_lfun ~deep m f =
try Gmap.find f m.footcalls
with Not_found ->
m.footcalls <- Gmap.add f Fset.empty m.footcalls ;
let fs =
try
let open Definitions in
let d = Definitions.find_symbol f in
let ds = fsetmap fset_of_var d.d_params in
let df =
match d.d_definition with
| Logic _ -> Fset.empty
| Function(_,_,t) -> snd (gvars_of_term ~deep m t)
| Predicate(_,p) -> snd (gvars_of_pred ~deep m p)
| Inductive ds -> fsetmap (fset_of_lemma ~deep m) ds
in Fset.union ds df
with Not_found ->
Fset.empty
in m.footcalls <- Gmap.add f fs m.footcalls ; fs
let collect_term m t =
begin
m.gs <- FP.union m.gs (gvars_of_term ~deep:true m t) ;
m.xs <- Vars.union m.xs (F.vars t) ;
end
let collect_have m p =
begin
m.gs <- FP.union m.gs (gvars_of_pred ~deep:true m p) ;
m.xs <- Vars.union m.xs (F.varsp p) ;
end
let rec collect_condition m = function
| Probe(_,t) -> collect_term m t
| Have p | When p | Core p -> collect_have m p
| Type _ | Init _ | State _ -> ()
| Branch(p,sa,sb) -> collect_have m p ; collect_seq m sa ; collect_seq m sb
| Either cs -> List.iter (collect_seq m) cs
and collect_step m s = collect_condition m s.condition
and collect_seq m s = List.iter (collect_step m) s.seq_list
let rec filter_pred m p =
match F.p_expr p with
| And ps -> F.p_all (filter_pred m) ps
| _ ->
if Vars.subset (F.varsp p) m.xs then
begin
let gs = gvars_of_pred ~deep:false m p in
if FP.subset gs m.gs then p else
if FP.intersect gs m.gs then
(m.fixpoint <- false ; m.gs <- FP.union gs m.gs ; p)
else p_true
end
else p_true
let rec filter_steplist m = function
| [] -> []
| s :: w ->
match s.condition with
| State _ | Probe _ | Have _ | When _ | Core _ | Branch _ | Either _ ->
s :: filter_steplist m w
| Type p ->
let p = filter_pred m p in
let w = filter_steplist m w in
if p != F.p_true then
let s = update_cond s (Type p) in
s :: w
else w
| Init p ->
let p = filter_pred m p in
let w = filter_steplist m w in
if p != F.p_true then
let s = update_cond s (Init p) in
s :: w
else w
let make (seq,g) =
let m = {
gs = FP.empty ;
xs = Vars.empty ;
fixpoint = false ;
footprint = Tmap.empty ;
footcalls = Gmap.empty ;
} in
List.iter (collect_step m) seq.seq_list ; collect_have m g ;
Kernel.debug ~level:3 "Collected %a" pp_used m ;
let rec loop () =
m.fixpoint <- true ;
let hs' = filter_steplist m seq.seq_list in
if m.fixpoint then ( sequence hs' , g ) else loop ()
in loop ()
end
let filter = Filter.make
module Parasite =
struct
open Qed.Logic
type usage = Used | Def of F.term
type domain = usage Vmap.t
[@@@ warning "-32"]
let pretty fmt w =
Format.fprintf fmt "@[<hov 2>{" ;
Vmap.iter
(fun x u -> match u with
| Used -> Format.fprintf fmt "@ %a" F.pp_var x
| Def e -> Format.fprintf fmt "@ @[<hov 2>%a:=%a;@]" F.pp_var x F.pp_term e
) w ;
Format.fprintf fmt " }@]"
[@@@ warning "+32"]
let cyclic w x e =
let m = ref Vars.empty in
let once x = if Vars.mem x !m then false else (m := Vars.add x !m ; true) in
let rec walk_y w x y =
if F.Var.equal x y then raise Exit ;
if once x then
let r = try Vmap.find x w with Not_found -> Used in
match r with Used -> () | Def e -> walk_e w x e
and walk_e w x e = Vars.iter (walk_y w x) (F.vars e) in
try walk_e w x e ; false with Exit -> true
let rec add_used (w : domain) xs = Vars.fold add_usedvar xs w
and add_usedvar x w =
try match Vmap.find x w with
| Used -> w
| Def e -> add_used (Vmap.add x Used w) (F.vars e)
with Not_found -> Vmap.add x Used w
let add_def (w : domain) x e =
try
let xs = F.vars e in
if cyclic w x e then add_used (add_usedvar x w) xs
else
match Vmap.find x w with
| Used -> add_used w xs
| Def e0 -> if F.equal e0 e then w else add_used (Vmap.add x Used w) xs
with Not_found -> Vmap.add x (Def e) w
let kind x w =
try Some (Vmap.find x w)
with Not_found -> None
let add_eq (w : domain) x y =
match kind x w , kind y w with
| None , None ->
let cmp = F.Var.compare x y in
if cmp > 0 then add_def w x (F.e_var y) else
if cmp < 0 then add_def w y (F.e_var x) else
w
| None , Some Used -> add_def w x (F.e_var y)
| Some Used , None -> add_def w y (F.e_var x)
| Some(Def e),(None | Some Used)
| (None|Some Used),Some (Def e)
-> add_usedvar x (add_usedvar y (add_used w (F.vars e)))
| Some Used,Some Used -> w
| Some(Def a),Some(Def b) ->
let xs = Vars.union (F.vars a) (F.vars b) in
add_usedvar x (add_usedvar y (add_used w xs))
let branch p wa wb =
let pool = ref (F.varsp p) in
let w0 = Vmap.union
(fun _x u v ->
match u,v with
| Used,Used -> Used
| Def a,Def b -> Def( F.e_if (F.e_prop p) a b )
| Def e,Used | Used,Def e ->
pool := Vars.union !pool (F.vars e) ; Used
) wa wb in
add_used w0 !pool
let rec usage w p =
match F.repr p with
| And ps -> List.fold_left usage w ps
| Eq(a,b) ->
begin match F.repr a , F.repr b with
| Fvar x , Fvar y -> add_eq w x y
| Fvar x , _ -> add_def w x b
| _ , Fvar y -> add_def w y a
| _ -> add_used w (F.vars p)
end
| _ -> add_used w (F.vars p)
let rec collect_step w s =
match s.condition with
| Type _ | State _ -> w
| Probe(_,t) -> usage w t
| Have p | Core p | Init p | When p -> usage w (F.e_prop p)
| Branch(p,a,b) ->
let wa = collect_seq w a in
let wb = collect_seq w b in
branch p wa wb
| Either ws ->
List.fold_left collect_seq w ws
and collect_seq w s = List.fold_left collect_step w s.seq_list
let parasites w =
Vmap.fold
(fun x u xs -> match u with Used -> xs | Def _ -> Vars.add x xs)
w Vars.empty
let rec filter xs p =
match F.p_expr p with
| And ps -> p_all (filter xs) ps
| _ -> if Vars.intersect (F.varsp p) xs then F.p_true else p
let filter (hs,g) =
let w = collect_seq (add_used Vmap.empty (F.varsp g)) hs in
let xs = parasites w in
if Vars.is_empty xs then (hs,g)
else map_sequence (filter xs) hs , g
end
let parasite = Parasite.filter
module InitFilter =
struct
let add_state filter s = s :: filter
let rec collect_step filter s =
match s.condition with
| State s -> add_state filter s
| Have _ | Core _ | Init _ | When _ | Type _ | Probe _ -> filter
| Branch(_p,a,b) -> collect_seq (collect_seq filter a) b
| Either ws -> List.fold_left collect_seq filter ws
and collect_seq filter s =
List.fold_left collect_step filter s.seq_list
exception Found
let has_init filter pred =
let visited = ref Tset.empty in
let rec term_is_init_in_states states t =
let raise_if_is_init t s =
if Lang.F.is_primitive t then ()
else
match Mstate.lookup s t with
| Mlval(_, KInit) | Mchunk(_, KInit) -> raise Found
| _ -> ()
in
if Tset.mem t !visited then ()
else begin
visited := Tset.add t !visited ;
List.iter (raise_if_is_init t) states ;
Lang.F.lc_iter (term_is_init_in_states states) t
end
in
try term_is_init_in_states filter (F.e_prop pred) ; false
with Found -> true
let rec do_filter filter p =
let on_sub_nodes = do_filter filter in
match F.p_expr p with
| And ps -> p_all on_sub_nodes ps
| If(e,a,b) -> F.p_if e (on_sub_nodes a) (on_sub_nodes b)
| _ when has_init filter p -> p_true
| _ -> p
let filter (hs, g) =
let filter = collect_seq [] hs in
if has_init filter g then (hs, g)
else map_sequence (do_filter filter) hs, g
end
let init_filter = InitFilter.filter
let close_cond = function
| Type _ when Wp_parameters.SimplifyType.get () -> p_true
| c -> pred_cond c
let closure = ref []
let at_closure f = closure := f::!closure
let alter_closure sequent = List.fold_left (fun seq f -> f seq) sequent !closure
let hyps s = List.map (fun s -> close_cond s.condition) s.seq_list
let head s =
match s.condition with
| Have p | When p | Core p | Init p | Type p | Branch(p,_,_) -> p
| Either _ | State _ | Probe _ -> p_true
let have s =
match s.condition with
| Have p | When p | Core p | Init p | Type p -> p
| Branch _ | Either _ | State _ | Probe _ -> p_true
let condition s = F.p_conj (hyps s)
let property sequent =
let s,goal = alter_closure sequent in
(F.p_hyps (hyps s) goal)
let list seq = seq.seq_list
let iter f seq = List.iter f seq.seq_list
let probes seq =
let pool = ref Probe.Map.empty in
let rec collect_step s =
match s.condition with
| Probe(p,t) -> pool := Probe.Map.add p t !pool
| Branch(_,a,b) -> collect_seq a ; collect_seq b
| Either cs -> List.iter collect_seq cs
| _ -> ()
and collect_seq s = List.iter collect_step s.seq_list
in collect_seq seq ; !pool
let rec index_list k = function
| [] -> k
| s::w -> index_list (index_step k s) w
and index_step k s =
s.id <- k ; let k = succ k in
match s.condition with
| Have _ | When _ | Type _ | Core _ | Init _ | State _ | Probe _ -> k
| Branch(_,a,b) -> index_list (index_list k a.seq_list) b.seq_list
| Either cs -> index_case k cs
and index_case k = function
| [] -> k
| c::cs -> index_case (index_list k c.seq_list) cs
let steps seq = index_list 0 seq.seq_list
let index (seq,_) = ignore (steps seq)
let rec at_list k = function
| [] -> assert false
| s::w ->
if k = 0 then s else
let n = s.size in
if k < n then at_step (k-1) s.condition else at_list (k - n) w
and at_step k = function
| Have _ | When _ | Type _ | Core _ | Init _ | State _ | Probe _ ->
assert false
| Branch(_,a,b) ->
let n = a.seq_size in
if k < n then
at_list k a.seq_list
else
at_list (k-n) b.seq_list
| Either cs -> at_case k cs
and at_case k = function
| [] -> assert false
| c::cs ->
let n = c.seq_size in
if k < n then at_list k c.seq_list else at_case (k - n) cs
let step_at seq k =
if 0 <= k && k < seq.seq_size
then at_list k seq.seq_list
else raise Not_found
let in_sequence_add_list ~replace =
let rec in_list k h w =
if k = 0 then
List.rev_append (List.rev h)
(if replace
then match w with
| [] -> assert false
| _::w -> w
else w)
else
match w with
| [] -> assert false
| s::w ->
let n = s.size in
if k < n then
let cond = in_step (k-1) h s.condition in
update_cond s cond :: w
else s :: in_list (k-n) h w
and in_step k h = function
| Have _ | When _ | Type _ | Core _ | Init _ | State _ | Probe _ ->
assert false
| Branch(p,a,b) ->
let n = a.seq_size in
if k < n then
Branch(p,in_sequence_add_list k h a,b)
else
Branch(p,a,in_sequence_add_list (k-n) h b)
| Either cs -> Either (in_case k h cs)
and in_case k h = function
| [] -> assert false
| c::cs ->
let n = c.seq_size in
if k < n
then in_sequence_add_list k h c :: cs
else c :: in_case (k-n) h cs
and in_sequence_add_list k h s = sequence (in_list k h s.seq_list)
in in_sequence_add_list
let in_sequence ~replace id h = in_sequence_add_list ~replace id [h]
let size seq = seq.seq_size
let insert ?at step sequent =
let seq,goal = sequent in
let at = match at with None -> seq.seq_size | Some k -> k in
if 0 <= at && at <= seq.seq_size
then in_sequence ~replace:false at step seq , goal
else raise Not_found
let replace ~at step sequent =
let seq,goal = sequent in
if 0 <= at && at <= seq.seq_size
then in_sequence ~replace:true at step seq , goal
else raise Not_found
let replace_by_step_list ~at step_list sequent =
let seq,goal = sequent in
if 0 <= at && at <= seq.seq_size
then in_sequence_add_list ~replace:true at step_list seq , goal
else raise Not_found
let subst f s = map_sequent (Lang.p_subst f) s