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(* Title: HOL/HOLCF/IOA/ABP/Check.ML
Author: Olaf Müller
The Model Checker.
*)
structure Check =
struct
(* ----------------------------------------------------------------
P r o t o t y p e M o d e l C h e c k e r
----------------------------------------------------------------*)
fun check(extacts,intacts,string_of_a,startsI,string_of_s,
nexts,hom,transA,startsS) =
let fun check_s(s,unchecked,checked) =
let fun check_sa a unchecked =
let fun check_sas t unchecked =
(if member (op =) extacts a then
(if transA(hom s,a,hom t) then ( )
else (writeln("Error: Mapping of Externals!");
string_of_s s; writeln"";
string_of_a a; writeln"";
string_of_s t;writeln"";writeln"" ))
else (if hom(s)=hom(t) then ( )
else (writeln("Error: Mapping of Internals!");
string_of_s s; writeln"";
string_of_a a; writeln"";
string_of_s t;writeln"";writeln"" ));
if member (op =) checked t then unchecked else insert (op =) t unchecked)
in fold check_sas (nexts s a) unchecked end;
val unchecked' = fold check_sa (extacts @ intacts) unchecked
in (if member (op =) startsI s then
(if member (op =) startsS (hom s) then ()
else writeln("Error: At start states!"))
else ();
checks(unchecked',s::checked)) end
and checks([],_) = ()
| checks(s::unchecked,checked) = check_s(s,unchecked,checked)
in checks(startsI,[]) end;
(* ------------------------------------------------------
A B P E x a m p l e
-------------------------------------------------------*)
datatype msg = m | n | l;
datatype act = Next | S_msg of msg | R_msg of msg
| S_pkt of bool * msg | R_pkt of bool * msg
| S_ack of bool | R_ack of bool;
(* -------------------- Transition relation of Specification -----------*)
fun transA((u,s),a,(v,t)) =
(case a of
Next => v andalso t = s |
S_msg(q) => u andalso not(v) andalso t = s@[q] |
R_msg(q) => u = v andalso s = (q::t) |
S_pkt(b,q) => false |
R_pkt(b,q) => false |
S_ack(b) => false |
R_ack(b) => false);
(* ---------------------- Abstraction function --------------------------*)
fun hom((env,p,a,q,b,_,_)) = (env,q@(if (a=b) then tl(p) else p));
(* --------------------- Transition relation of Implementation ----------*)
fun nexts (s as (env,p,a,q,b,ch1,ch2)) action =
(case action of
Next => if p=[] then [(true,p,a,q,b,ch1,ch2)] else [] |
S_msg(mornorl) => if env then [(false,p@[mornorl],a,q,b,ch1,ch2)] else [] |
R_msg(mornorl) => if (q<>[] andalso mornorl=hd(q))
then [(env,p,a,tl(q),b,ch1,ch2)]
else [] |
S_pkt(h,mornorl) => if (p<>[] andalso mornorl=hd(p) andalso h=a)
then (if (ch1<>[] andalso hd(rev(ch1))=(h,mornorl))
then [s]
else [s,(env,p,a,q,b,ch1@[(h,mornorl)],ch2)])
else [] |
R_pkt(h,mornorl) => if (ch1<>[] andalso hd(ch1)=(h,mornorl))
then (if (h<>b andalso q=[])
then [(env,p,a,q@[mornorl],not(b),ch1,ch2),
(env,p,a,q@[mornorl],not(b),tl(ch1),ch2)]
else [s,(env,p,a,q,b,tl(ch1),ch2)])
else [] |
S_ack(h) => if (h=b)
then (if (ch2<>[] andalso h=hd(rev(ch2)))
then [s]
else [s,(env,p,a,q,b,ch1,ch2@[h])])
else [] |
R_ack(h) => if (ch2<>[] andalso hd(ch2)=h)
then (if h=a
then [(env,tl(p),not(a),q,b,ch1,ch2),
(env,tl(p),not(a),q,b,ch1,tl(ch2))]
else [s,(env,p,a,q,b,ch1,tl(ch2))])
else [])
val extactions = [Next,S_msg(m),R_msg(m),S_msg(n),R_msg(n),S_msg(l),R_msg(l)];
val intactions = [S_pkt(true,m),R_pkt(true,m),S_ack(true),R_ack(true),
S_pkt(false,m),R_pkt(false,m),S_ack(false),R_ack(false),
S_pkt(true,n),R_pkt(true,n),S_pkt(true,l),R_pkt(true,l),
S_pkt(false,n),R_pkt(false,n),S_pkt(false,l),R_pkt(false,l)];
(* ------------------------------------
Input / Output utilities
------------------------------------*)
fun print_list (lpar, rpar, pre: 'a -> unit) (lll : 'a list) =
let fun prec x = (Output.physical_stdout ","; pre x)
in
(case lll of
[] => (Output.physical_stdout lpar; Output.physical_stdout rpar)
| x::lll => (Output.physical_stdout lpar; pre x; List.app prec lll; Output.physical_stdout rpar))
end;
fun pr_bool true = Output.physical_stdout "true"
| pr_bool false = Output.physical_stdout "false";
fun pr_msg m = Output.physical_stdout "m"
| pr_msg n = Output.physical_stdout "n"
| pr_msg l = Output.physical_stdout "l";
fun pr_act a = Output.physical_stdout (case a of
Next => "Next"|
S_msg(ma) => "S_msg(ma)" |
R_msg(ma) => "R_msg(ma)" |
S_pkt(b,ma) => "S_pkt(b,ma)" |
R_pkt(b,ma) => "R_pkt(b,ma)" |
S_ack(b) => "S_ack(b)" |
R_ack(b) => "R_ack(b)");
fun pr_pkt (b,ma) = (Output.physical_stdout "<"; pr_bool b;Output.physical_stdout ", "; pr_msg ma; Output.physical_stdout ">");
val pr_bool_list = print_list("[","]",pr_bool);
val pr_msg_list = print_list("[","]",pr_msg);
val pr_pkt_list = print_list("[","]",pr_pkt);
fun pr_tuple (env,p,a,q,b,ch1,ch2) =
(Output.physical_stdout "{"; pr_bool env; Output.physical_stdout ", "; pr_msg_list p; Output.physical_stdout ", ";
pr_bool a; Output.physical_stdout ", "; pr_msg_list q; Output.physical_stdout ", ";
pr_bool b; Output.physical_stdout ", "; pr_pkt_list ch1; Output.physical_stdout ", ";
pr_bool_list ch2; Output.physical_stdout "}");
(* ---------------------------------
Main function call
---------------------------------*)
(*
check(extactions,intactions,pr_act, [(true,[],true,[],false,[],[])],
pr_tuple, nexts, hom, transA, [(true,[])]);
*)
(*
Little test example
datatype act = A;
fun transA(s,a,t) = (not(s)=t);
fun hom(i) = i mod 2 = 0;
fun nexts s A = [(s+1) mod 4];
check([A],[],K"A", [0], string_of_int, nexts, hom, transA, [true]);
fun nexts s A = [(s+1) mod 5];
*)
end;
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