(* Title: Pure/Syntax/earley0A
ID: $Id$
Author: Tobias Nipkow
Changes:
PARSER: renamed Prod to prod
renamed mk_early_gram to mk_earley_gram
*)
signature PARSER =
sig
structure XGram: XGRAM
structure ParseTree: PARSE_TREE
local open XGram ParseTree ParseTree.Lexicon in
type Gram
val compile_xgram: string list * Token prod list -> Gram
val parse: Gram * string * Token list -> ParseTree
val parsable: Gram * string -> bool
exception SYNTAX_ERR of Token list
val print_gram: Gram * Lexicon -> unit
end
end;
functor EarleyFun(structure XGram:XGRAM and ParseTree:PARSE_TREE): PARSER =
struct
structure XGram = XGram;
structure ParseTree = ParseTree;
(* Linked lists: *)
infix 5 &;
datatype 'a LList = nilL | op & of 'a * ('a LListR)
withtype 'a LListR = 'a LList ref;
(* Apply proc to all elements in a linked list *)
fun seqll (proc: '_a -> unit) : ('_a LListR -> unit) =
let fun seq (ref nilL) = () |
seq (ref((a:'_a)&l)) = (proc a; seq l)
in seq end;
fun llist_to_list (ref nilL) = [] |
llist_to_list (ref(a&ll)) = a::(llist_to_list ll);
val len = length;
local open Array XGram ParseTree ParseTree.Lexicon in
nonfix sub;
fun forA(p: int -> unit, a: 'a array) : unit =
let val ub = length a
fun step(i) = if i=ub then () else (p(i); step(i+1));
in step 0 end;
fun itA(a0:'a, b: 'b array)(f:'a * 'b -> 'a) : 'a =
let val ub = length b
fun acc(a,i) = if i=ub then a else acc(f(a,sub(b,i)),i+1)
in acc(a0,0) end;
(*
Gram: name of nt -> number, nt number -> productions array,
nt number -> list of nt's reachable via copy ops
*)
datatype Symbol = T of Token | NT of int * int
and Op = Op of OpSyn * string * int
withtype OpSyn = Symbol array
and OpListA = Op array * int TokenMap
and FastAcc = int TokenMap;
type Gram = int Symtab.table * OpListA array * int list array;
fun non_term(Nonterminal(s,_)) = if predef_term(s)=end_token then [s] else []
| non_term(_) = [];
fun non_terms(Prod(_,symbs,_,_)) = flat(map non_term symbs);
(* mk_pre_grammar converts a list of productions in external format into an
internal Gram object. *)
val dummyTM:FastAcc = mkTokenMap[];
fun mk_pre_grammar(prods): Gram =
let fun same_res(Prod(t1,_,_,_), Prod(t2,_,_,_)) = t1=t2;
val partitioned0 = partition_eq same_res prods;
val nts0 = map (fn Prod(ty,_,_,_)::_ => ty) partitioned0;
val nts' = distinct(flat(map non_terms prods)) \\ nts0;
val nts = nts' @ nts0;
val partitioned = (replicate (len nts') []) @ partitioned0;
val ntis = nts ~~ (0 upto (len(nts)-1));
val tab = foldr Symtab.update (ntis,Symtab.null);
fun nt_or_vt(s,p) =
(case predef_term(s) of
end_token => let val Some(i) = Symtab.lookup(tab,s) in NT(i,p) end
| tk => T(tk));
fun mksyn(Terminal(t)) = [T(t)]
| mksyn(Nonterminal(t)) = [nt_or_vt t]
| mksyn(_) = [];
fun prod2op(Prod(nt,sy,opn,p)) =
let val syA = arrayoflist(flat(map mksyn sy)) in Op(syA,opn,p) end;
fun mkops prods = (arrayoflist(map prod2op prods),dummyTM);
val opLA = arrayoflist(map mkops partitioned);
val subs = array(length opLA,[]) : int list array;
fun newcp v (a,Op(syA,_,p)) =
if p=copy_pri
then let val NT(k,_) = sub(syA,0)
in if k mem v then a else k ins a end
else a;
fun reach v i =
let val new = itA ([],#1(sub(opLA,i))) (newcp v)
val v' = new union v
in flat(map (reach v') new) union v' end;
fun rch(i) = update(subs,i,reach[i]i);
in forA(rch,subs); (tab,opLA,subs) end;
val RootPref = "__";
(* Lookahead tables for speeding up parsing. Lkhd is a mapping from
nonterminals (in the form of OpList) to sets (lists) of token strings *)
type Lkhd = Token list list list;
(* subst_syn(s,k) syn = [ pref k ts | ts is a token string derivable from sy
under substitution s ] *)
(* This is the general version.
fun cross l1 l2 = flat(map (fn e2 => (map (fn e1 => e1@e2) l1)) l2);
(* pref k [x1,...,xn] is [x1,...,xk] if 0<=k<=n and [x1,...,xn] otherwise *)
fun pref 0 l = []
| pref _ [] = []
| pref k (e::l) = e::(pref (k-1) l);
fun subst_syn(s:Lkhd,k) =
let fun subst(ref(symb & syn)):Token list list =
let val l1 = case symb of T t => [[t]] |
NT(oplr,_) => let val Some l = assoc(s,!oplr) in l end
in distinct(map (pref k) (cross l1 (subst syn))) end |
subst _ = [[]]
in subst end;
*)
(* This one is specialized to lookahead 1 and a bit too generous *)
fun subst_syn(s:Lkhd,1) syA =
let fun subst i = if i = length(syA) then [[]] else
case sub(syA,i) of
NT(j,_) => let val pre = nth_elem(j,s)
in if [] mem pre then (pre \ []) union subst(i+1)
else pre end |
T(tk) => [[tk]];
in subst 0 end;
(* mk_lkhd(G,k) returns a table which associates with every nonterminal N in
G the list of pref k s for all token strings s with N -G->* s *)
fun mk_lkhd(opLA:OpListA array,k:int):Lkhd =
let fun step(s:Lkhd):Lkhd =
let fun subst_op(l,Op(sy,_,_)) = subst_syn(s,k)sy union l;
fun step2(l,(opA,_)) = l@[itA([],opA)subst_op];
in writeln"."; itA([],opLA)step2 end;
fun iterate(s:Lkhd):Lkhd = let val s' = step s
in if map len s = map len s' then s
else iterate s' end
in writeln"Computing lookahead tables ...";
iterate (replicate (length opLA) []) end;
(* create look ahead tables *)
fun mk_earley_gram(g as (tab,opLA,_):Gram):Gram =
let val lkhd = mk_lkhd(opLA,1);
fun mk_fa(i):FastAcc =
let val opA = #1(sub(opLA,i));
fun start(j) = let val Op(sy,_,_) = sub(opA,j);
val pre = subst_syn(lkhd,1) sy
in (j,if [] mem pre then [] else map hd pre) end;
in mkTokenMap(map start (0 upto(length(opA)-1))) end;
fun updt(i) = update(opLA,i,(#1(sub(opLA,i)),mk_fa(i)));
in forA(updt,opLA); g end;
fun compile_xgram(roots,prods) =
let fun mk_root nt = Prod(RootPref^nt,
[Nonterminal(nt,0),Terminal(end_token)],"",0);
val prods' = (map mk_root roots) @ prods
in mk_earley_gram(mk_pre_grammar(prods')) end;
(* State: nonterminal#, production#, index in production,
index of originating state set,
parse trees generated so far,
*)
datatype State = St of int * int * int * int * ParseTree list
withtype StateSet = State LListR * (State -> unit) LListR;
type Compl = State -> unit;
type StateSetList = StateSet array;
(* Debugging:
val print_SL = seqll(fn St(nti,pi,ip,fs,ptl)=>
(print_int nti; prs" "; print_int pi; prs" "; print_int ip; prs" ";
print_int fs; prs" "; print_int(len ptl); prs"\n"));
fun print_SS(s1,delr) = (writeln"================="; print_SL s1);
fun count_ss(ref nilL) = 0
| count_ss(ref(_ & ss)) = count_ss(ss)+1;
fun print_stat(state_sets) =
let fun pr i = let val(s1,_)=sub(state_sets,i)
in prs" "; print_int(count_ss s1) end;
in prs"["; forA(pr,state_sets); prs"]\n" end;
*)
fun mt_stateS():StateSet = (ref nilL, ref nilL);
fun mt_states(n):StateSetList = array(n,mt_stateS());
fun ismt_stateS((ref nilL,_):StateSet) = true | ismt_stateS _ = false;
fun fst_state((ref(st & _),_): StateSet) = st;
fun apply_all_states(f,(slr,_):StateSet) = seqll f slr;
fun add_state(nti,pi,ip,from,ptl,(sllr,delr):StateSet) =
let fun add(ref(St(nti',pi',ip',from',_) & rest)) =
if nti=nti' andalso pi=pi' andalso ip=ip' andalso from=from'
then ()
else add rest |
add(last as ref nilL) =
let val newst = St(nti,pi,ip,from,ptl)
in last := newst & ref nilL;
seqll (fn compl => compl newst) delr
end;
in add sllr end;
fun complete(nti,syA,opn,p,ptl,ss,si as (_,delr):StateSet,opLA,rchA) =
let val pt = mk_pt(opn,ptl)
fun compl(St(ntj,pj,jp,from,ptl)) =
let val Op(syj,_,_) = sub(fst(sub(opLA,ntj)),pj) in
if jp=length(syj) then () else
case sub(syj,jp) of
NT(nt,p') => if p >= p' andalso nti mem sub(rchA,nt)
then add_state(ntj,pj,jp+1,from,ptl@[pt], si)
else ()
| _ => ()
end
in apply_all_states(compl,ss);
if length(syA)=0 (* delayed completion in case of empty production: *)
then delr := compl & ref(!delr) else ()
end;
fun predict(tk,isi,si,p',opLA) = fn nti =>
let val (opA,tm) = sub(opLA,nti);
fun add(pi) = let val opr as Op(syA,_,p) = sub(opA,pi)
in if p < p' then () else add_state(nti,pi,0,isi,[],si) end
in seq add (applyTokenMap(tm,tk)) end;
fun parsable((tab,_,_):Gram, root:string) =
not(Symtab.lookup(tab,RootPref^root) = None);
exception SYNTAX_ERR of Token list;
fun unknown c = error("System Error - Trying to parse unknown category "^c);
fun parse((tab,opLA,rchA):Gram, root:string, tl: Token list): ParseTree =
let val tl' = tl@[end_token];
val state_sets = mt_states(len tl' +1);
val s0 = mt_stateS();
val rooti = case Symtab.lookup(tab,RootPref^root) of
Some(ri) => ri | None => unknown root;
fun lr (tl,isi,si,t) =
if ismt_stateS(si) then raise SYNTAX_ERR(t::tl) else
case tl of
[] => () |
t::tl =>
let val si1 = mt_stateS();
fun process(St(nti,pi,ip,from,ptl)) =
let val opA = #1(sub(opLA,nti))
val Op(syA,opn,p) = sub(opA,pi) in
if ip = length(syA)
then complete(nti,syA,opn,p,ptl,
sub(state_sets,from),si,opLA,rchA)
else case sub(syA,ip) of
NT(ntj,p) =>
seq (predict(t,isi,si,p,opLA)) (sub(rchA,ntj))
| T(t') =>
if matching_tokens(t,t')
then add_state(nti,pi,ip+1,from,
if valued_token(t)
then ptl@[Tip(t)] else ptl,
si1)
else () end;
in apply_all_states(process,si);
update(state_sets,isi+1,si1);
lr(tl,isi+1,si1,t) end
in update(state_sets,0,s0);
add_state(rooti,0,0,0,[],s0);
lr(tl',0,s0,end_token(*dummy*));
(*print_stat state_sets;*)
let val St(_,_,_,_,[pt]) = fst_state(sub(state_sets,len tl'))
in pt end
end;
fun print_gram ((st,opAA,rchA):Gram,lex) =
let val tts = Lexicon.name_of_token;
val al = map (fn (x,y)=>(y,x)) (Symtab.alist_of st);
fun nt i = let val Some(s) = assoc(al,i) in s end;
fun print_sy(T(end_token)) = prs". " |
print_sy(T(tk)) = (prs(tts tk); prs" ") |
print_sy(NT(i,p)) = (prs((nt i)^"[");print_int p;prs"] ");
fun print_opA(i) =
let val lhs = nt i;
val (opA,_)=sub(opAA,i);
fun print_op(j) =
let val Op(sy,n,p) = sub(opA,j)
in prs(lhs^" = "); forA(fn i=>print_sy(sub(sy,i)),sy);
if n="" then () else prs(" => \""^n^"\"");
prs" (";print_int p;prs")\n"
end;
in forA(print_op,opA) end;
fun print_rch(i) = (print_int i; prs" -> ";
print_list("[","]\n",print_int) (sub(rchA,i)))
in forA(print_opA,opAA) (*; forA(print_rch,rchA) *) end;
end;
end;