(***********************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) (* 0 & s.[0]='$' let dummy_loc = (0,0) let loc = function | Node (loc,_,_) -> loc | Nvar (loc,_) -> loc | Nmeta (loc,_) -> loc | Slam (loc,_,_) -> loc | Smetalam (loc,_,_) -> loc | Num (loc,_) -> loc | Id (loc,_) -> loc | Str (loc,_) -> loc | Path (loc,_) -> loc | Dynamic (loc,_) -> loc (* building a node with dummy location *) let ope(op,l) = Node(dummy_loc,op,l) let slam(idl,b) = Slam(dummy_loc,idl,b) let ide s = Id(dummy_loc,s) let nvar s = Nvar(dummy_loc,s) let num n = Num(dummy_loc,n) let string s = Str(dummy_loc,s) let path sl = Path(dummy_loc,sl) let dynamic d = Dynamic(dummy_loc,d) let rec set_loc loc = function | Node(_,op,al) -> Node(loc, op, List.map (set_loc loc) al) | Slam(_,idl,b) -> Slam(loc,idl, set_loc loc b) | Smetalam(_,idl,b) -> Smetalam(loc,idl, set_loc loc b) | Nvar(_,s) -> Nvar(loc,s) | Nmeta(_,s) -> Nmeta(loc,s) | Id(_,s) -> Id(loc,s) | Str(_,s) -> Str(loc,s) | Num(_,s) -> Num(loc,s) | Path(_,sl) -> Path(loc,sl) | Dynamic(_,d) -> Dynamic(loc,d) let path_section loc sp = Coqast.Path(loc, sp) let section_path sp = sp (* ast destructors *) let num_of_ast = function | Num(_,n) -> n | ast -> invalid_arg_loc (loc ast, "Ast.num_of_ast") let nvar_of_ast = function | Nvar(_,s) -> s | ast -> invalid_arg_loc (loc ast, "Ast.nvar_of_ast") let id_of_ast = function | Id(_,s) -> s | ast -> invalid_arg_loc (loc ast, "Ast.nvar_of_ast") (* patterns of ast *) type pat = | Pquote of t | Pmeta of string * tok_kind | Pnode of string * patlist | Pslam of identifier option * pat | Pmeta_slam of string * pat and patlist = | Pcons of pat * patlist | Plmeta of string | Pnil and tok_kind = Tnum | Tid | Tstr | Tpath | Tvar | Tany | Tlist (* semantic actions of grammar rules *) type act = | Aast of pat | Aastlist of patlist | Acase of act * (pat * act) list | Acaselist of act * (patlist * act) list (* values associated to variables *) type v = | Vast of t | Vastlist of t list type env = (string * v) list (* Pretty-printing *) let rec print_ast ast = match ast with | Num(_,n) -> int n | Str(_,s) -> qs s | Path(_,sl) -> str (string_of_path sl) | Id (_,s) -> str "{" ++ str s ++ str "}" | Nvar(_,s) -> str (string_of_id s) | Nmeta(_,s) -> str s | Node(_,op,l) -> hov 3 (str "(" ++ str op ++ spc () ++ print_astl l ++ str ")") | Slam(_,None,ast) -> hov 1 (str "[<>]" ++ print_ast ast) | Slam(_,Some x,ast) -> hov 1 (str "[" ++ str (string_of_id x) ++ str "]" ++ cut () ++ print_ast ast) | Smetalam(_,id,ast) -> hov 1 (str id ++ print_ast ast) | Dynamic(_,d) -> hov 0 (str "") and print_astl astl = prlist_with_sep pr_spc print_ast astl let print_ast_cast = function | Tany -> (mt ()) | Tvar -> (str":var") | Tid -> (str":id") | Tstr -> (str":str") | Tpath -> (str":path") | Tnum -> (str":num") | Tlist -> (str":list") let rec print_astpat = function | Pquote ast -> str"'" ++ print_ast ast | Pmeta(s,tk) -> str s ++ print_ast_cast tk | Pmeta_slam(s,b) -> hov 1 (str "[" ++ str s ++ str"]" ++ cut () ++ print_astpat b) | Pnode(op,al) -> hov 2 (str"(" ++ str op ++ spc () ++ print_astlpat al ++ str")" ) | Pslam(None,b) -> hov 1 (str"[<" ++ cut () ++ print_astpat b) | Pslam(Some id,b) -> hov 1 (str"[" ++ str(string_of_id id) ++ str"]" ++ cut () ++ print_astpat b) and print_astlpat = function | Pnil -> (mt ()) | Pcons(h,Pnil) -> hov 1 (print_astpat h) | Pcons(h,t) -> hov 1 (print_astpat h ++ spc () ++ print_astlpat t) | Plmeta(s) -> (str"| " ++ str s) let print_val = function | Vast a -> print_ast a | Vastlist al -> hov 1 (str"[" ++ prlist_with_sep pr_spc print_ast al ++ str"]") (* Ast values environments *) let grammar_type_error (loc,s) = anomaly_loc (loc,s,(str"grammar type error: " ++ str s)) (* Coercions enforced by the user *) let check_cast loc a k = match (k,a) with | (Tany, _) -> () | (Tid, Id _) -> () | (Tvar, Nvar _) -> () | (Tpath, Path _) -> () | (Tstr, Str _) -> () | (Tnum, Num _) -> () | (Tlist, _) -> grammar_type_error (loc,"Ast.cast_val") | _ -> user_err_loc (loc,"Ast.cast_val", (str"cast _" ++ print_ast_cast k ++ str"failed")) let rec coerce_to_var = function | Nvar(_,id) as var -> var | Nmeta(_,id) as var -> var | Node(_,"QUALID",[Nvar(_,id) as var]) -> var | Node(_,"QUALIDARG",[Nvar(_,id) as var]) -> var | ast -> user_err_loc (loc ast,"Ast.coerce_to_var", (str"This expression should be a simple identifier")) let coerce_to_id a = match coerce_to_var a with | Nvar (_,id) -> id (* | Nmeta(_,id) -> id_of_string id*) | ast -> invalid_arg "coerce_to_id" let env_assoc_value loc v env = try List.assoc v env with Not_found -> anomaly_loc (loc,"Ast.env_assoc_value", (str"metavariable " ++ str v ++ str" is unbound.")) let env_assoc_list sigma (loc,v) = match env_assoc_value loc v sigma with | Vastlist al -> al | Vast a -> [a] let env_assoc sigma k (loc,v) = match env_assoc_value loc v sigma with | Vast a -> check_cast loc a k; a | _ -> grammar_type_error (loc,"Ast.env_assoc: "^v^" is an ast list") let env_assoc_nvars sigma (dloc,v) = match env_assoc_value dloc v sigma with | Vastlist al -> List.map coerce_to_id al | Vast ast -> [coerce_to_id ast] let build_lams dloc idl ast = List.fold_right (fun id lam -> Slam(dloc,Some id,lam)) idl ast (* Substitution *) (* Locations in quoted ast are wrong (they refer to the right hand side of a grammar rule). A default location dloc is used whenever we create an ast constructor. Locations in the binding list are trusted. *) let rec pat_sub dloc sigma pat = match pat with | Pmeta(pv,c) -> env_assoc sigma c (dloc,pv) | Pmeta_slam(pv,p) -> let idl = env_assoc_nvars sigma (dloc,pv) in build_lams dloc idl (pat_sub dloc sigma p) | Pquote a -> set_loc dloc a | Pnode(op,pl) -> Node(dloc, op, patl_sub dloc sigma pl) | Pslam(os,p) -> Slam(dloc, os, pat_sub dloc sigma p) and patl_sub dloc sigma pl = match pl with | Pnil -> [] | Plmeta pv -> env_assoc_list sigma (dloc,pv) | Pcons(Pmeta(pv,Tlist), ptl) -> (env_assoc_list sigma (dloc,pv))@(patl_sub dloc sigma ptl) | Pcons(p1,ptl) -> (pat_sub dloc sigma p1)::(patl_sub dloc sigma ptl) (* Converting and checking free meta-variables *) type entry_env = (string * entry_type) list let type_of_meta env loc pv = try List.assoc pv env with Not_found -> user_err_loc (loc,"Ast.type_of_meta", (str"variable " ++ str pv ++ str" is unbound")) let check_ast_meta env loc pv = if (type_of_meta env loc pv) <> ETast then user_err_loc (loc,"Ast.check_ast_meta", (str"variable " ++ str pv ++ str" is a List")) let rec val_of_ast env ast = match ast with | Nmeta(loc,pv) -> check_ast_meta env loc pv; Pmeta(pv,Tany) (* | Id(loc,pv) when isMeta pv -> check_ast_meta env loc pv; Pmeta(pv,Tid) *) | Node(_,"$QUOTE",[qast]) -> Pquote (set_loc dummy_loc qast) | Smetalam(loc,s,a) -> let _ = type_of_meta env loc s in (* ids are coerced to id lists *) Pmeta_slam(s, val_of_ast env a) | (Path _|Num _|Id _|Str _|Nvar _) -> Pquote (set_loc dummy_loc ast) | Slam(_,os,b) -> Pslam(os, val_of_ast env b) | Node(loc,op,_) when isMeta op -> user_err_loc(loc,"Ast.val_of_ast", (str"no metavariable in operator position.")) | Node(_,op,args) -> Pnode(op, vall_of_astl env args) | Dynamic(loc,_) -> invalid_arg_loc(loc,"val_of_ast: dynamic") and vall_of_astl env astl = match astl with | (Node(loc,"$LIST",[Nmeta(locv,pv)]))::asttl -> if type_of_meta env locv pv = ETastl then if asttl = [] then Plmeta pv else Pcons(Pmeta(pv,Tlist), vall_of_astl env asttl) else user_err_loc (loc,"Ast.vall_of_astl", (str"variable " ++ str pv ++ str" is not a List")) | ast::asttl -> Pcons (val_of_ast env ast, vall_of_astl env asttl) | [] -> Pnil (* Alpha-conversion *) let rec alpha_var id1 id2 = function | (i1,i2)::_ when i1=id1 -> i2 = id2 | (i1,i2)::_ when i2=id2 -> i1 = id1 | _::idl -> alpha_var id1 id2 idl | [] -> id1 = id2 let rec alpha alp a1 a2 = match (a1,a2) with | (Node(_,op1,tl1),Node(_,op2,tl2)) -> (op1 = op2) & (List.length tl1 = List.length tl2) & (List.for_all2 (alpha alp) tl1 tl2) | (Nvar(_,id1),Nvar(_,id2)) -> alpha_var id1 id2 alp | (Slam(_,None,body1),Slam(_,None,body2)) -> alpha alp body1 body2 | (Slam(_,Some s1,body1),Slam(_,Some s2,body2)) -> alpha ((s1,s2)::alp) body1 body2 | (Id(_,s1),Id(_,s2)) -> s1=s2 | (Str(_,s1),Str(_,s2)) -> s1=s2 | (Num(_,n1),Num(_,n2)) -> n1=n2 | (Path(_,sl1),Path(_,sl2)) -> sl1=sl2 | ((Smetalam _ | Nmeta _ | Dynamic _), _) -> false | (_, (Smetalam _ | Nmeta _ | Dynamic _)) -> false | _ -> false let alpha_eq (a1,a2)= alpha [] a1 a2 let alpha_eq_val = function | (Vast a1, Vast a2) -> alpha_eq (a1,a2) | (Vastlist al1, Vastlist al2) -> (List.length al1 = List.length al2) & List.for_all2 (fun x y -> alpha_eq (x,y)) al1 al2 | _ -> false let rec occur_var_ast s = function | Node(loc,op,args) -> List.exists (occur_var_ast s) args | Nvar(_,s2) -> s = s2 | Smetalam _ | Nmeta _ -> anomaly "occur_var: metas should not occur here" | Slam(_,sopt,body) -> (Some s <> sopt) & occur_var_ast s body | Id _ | Str _ | Num _ | Path _ -> false | Dynamic _ -> (* Hum... what to do here *) false let rec replace_vars_ast l = function | Node(loc,op,args) -> Node (loc,op, List.map (replace_vars_ast l) args) | Nvar(loc,s) as a -> (try Nvar (loc, List.assoc s l) with Not_found -> a) | Smetalam _ | Nmeta _ -> anomaly "replace_var: metas should not occur here" | Slam(loc,None,body) -> Slam(loc,None,replace_vars_ast l body) | Slam(loc,Some s,body) as a -> if List.mem_assoc s l then a else Slam(loc,Some s,replace_vars_ast l body) | Id _ | Str _ | Num _ | Path _ as a -> a | Dynamic _ as a -> (* Hum... what to do here *) a exception No_match of string let no_match_loc (loc,s) = Stdpp.raise_with_loc loc (No_match s) (* Binds value v to variable var. If var is already bound, checks if its value is alpha convertible with v. This allows non-linear patterns. Important note: The Metavariable $_ is a special case; it cannot be bound, which is like _ in the ML matching. *) let bind_env sigma var v = if var = "$_" then sigma else try let vvar = List.assoc var sigma in if alpha_eq_val (v,vvar) then sigma else raise (No_match "Ast.bind_env: values do not match") with Not_found -> (var,v)::sigma let bind_env_ast sigma var ast = try bind_env sigma var (Vast ast) with e -> Stdpp.raise_with_loc (loc ast) e let alpha_define sigma loc ps s = try let _ = List.assoc ps sigma in sigma with Not_found -> if ps = "$_" then sigma else (ps, Vast(Nvar(loc,s)))::sigma (* Match an ast with an ast pattern. Returns the new environnement. *) let rec amatch alp sigma spat ast = match (spat,ast) with | (Pquote a, _) -> if alpha alp a ast then sigma else no_match_loc (loc ast,"quote does not match") | (Pmeta(pv,Tany), _) -> bind_env_ast sigma pv ast | (Pmeta(pv,Tvar), Nvar _) -> bind_env_ast sigma pv ast | (Pmeta(pv,Tid), Id _) -> bind_env_ast sigma pv ast | (Pmeta(pv,Tnum), Num _) -> bind_env_ast sigma pv ast | (Pmeta(pv,Tstr), Str _) -> bind_env_ast sigma pv ast | (Pmeta(pv,Tpath), Path _) -> bind_env_ast sigma pv ast | (Pmeta(pv,Tlist),_) -> grammar_type_error (loc ast,"Ast.amatch") | (Pmeta_slam(pv,pb), Slam(loc, Some s, b)) -> amatch alp (bind_env_ast sigma pv (Nvar(loc,s))) pb b | (Pmeta_slam(pv,pb), Smetalam(loc, s, b)) -> anomaly "amatch: match a pattern with an open ast" | (Pnode(nodp,argp), Node(loc,op,args)) when nodp = op -> (try amatchl alp sigma argp args with e -> Stdpp.raise_with_loc loc e) | (Pslam(None,bp), Slam(_,None,b)) -> amatch alp sigma bp b | (Pslam(Some ps,bp), Slam(_,Some s,b)) -> amatch ((ps,s)::alp) sigma bp b | _ -> no_match_loc (loc ast, "Ast.amatch") and amatchl alp sigma spatl astl = match (spatl,astl) with | (Pnil, []) -> sigma | (Pcons(pat,patl), ast::asttl) -> amatchl alp (amatch alp sigma pat ast) patl asttl | (Plmeta pv, _) -> bind_env sigma pv (Vastlist astl) | _ -> raise (No_match "Ast.amatchl") let ast_match = amatch [] let astl_match = amatchl [] let first_match pat_of_fun env ast sl = let rec aux = function | [] -> None | (h::t) -> (try Some (h, ast_match env (pat_of_fun h) ast) with (No_match _| Stdpp.Exc_located (_,No_match _)) -> aux t) in aux sl let first_matchl patl_of_fun env astl sl = let rec aux = function | [] -> None | (h::t) -> (try Some (h, astl_match env (patl_of_fun h) astl) with (No_match _| Stdpp.Exc_located (_,No_match _)) -> aux t) in aux sl let bind_patvar env loc v etyp = try if List.assoc v env = etyp then env else user_err_loc (loc,"Ast.bind_patvar", (str"variable " ++ str v ++ str" is bound several times with different types")) with Not_found -> if v="$_" then env else (v,etyp)::env let make_astvar env loc v cast = let env' = bind_patvar env loc v ETast in (Pmeta(v,cast), env') (* Note: no metavar in operator position. necessary ? *) let rec pat_of_ast env ast = match ast with | Nmeta(loc,pv) -> make_astvar env loc pv Tany (* Obsolète | Id(loc,pv) when isMeta pv -> make_astvar env loc pv Tid *) | Smetalam(loc,s,a) -> let senv = bind_patvar env loc s ETast in let (pa,env') = pat_of_ast senv a in (Pmeta_slam(s, pa), env') | Node(_,"$VAR",[Nmeta(loc,pv)]) -> make_astvar env loc pv Tvar | Node(_,"$ID",[Nmeta(loc,pv)]) -> make_astvar env loc pv Tid | Node(_,"$NUM",[Nmeta(loc,pv)]) -> make_astvar env loc pv Tnum | Node(_,"$STR",[Nmeta(loc,pv)]) -> make_astvar env loc pv Tstr | Node(_,"$PATH",[Nmeta(loc,pv)]) -> make_astvar env loc pv Tpath | Node(_,"$QUOTE",[qast]) -> (Pquote (set_loc dummy_loc qast), env) (* This may occur when the meta is not textual but bound by coerce_to_id*) | Slam(loc,Some id,b) when isMeta (string_of_id id) -> let s = string_of_id id in let senv = bind_patvar env loc s ETast in let (pb,env') = pat_of_ast senv b in (Pmeta_slam(s, pb), env') | Slam(_,os,b) -> let (pb,env') = pat_of_ast env b in (Pslam(os,pb), env') | Node(loc,op,_) when isMeta op -> user_err_loc(loc,"Ast.pat_of_ast", (str"no metavariable in operator position.")) | Node(_,op,args) -> let (pargs, env') = patl_of_astl env args in (Pnode(op,pargs), env') | (Path _|Num _|Id _|Str _|Nvar _) -> (Pquote (set_loc dummy_loc ast), env) | Dynamic(loc,_) -> invalid_arg_loc(loc,"pat_of_ast: dynamic") and patl_of_astl env astl = match astl with | [Node(_,"$LIST",[Nmeta(loc,pv)])] -> let penv = bind_patvar env loc pv ETastl in (Plmeta pv, penv) | [] -> (Pnil,env) | ast::asttl -> let (p1,env1) = pat_of_ast env ast in let (ptl,env2) = patl_of_astl env1 asttl in (Pcons (p1,ptl), env2) let to_pat env ast = match ast with | Node(_,"ASTPAT",[p]) -> pat_of_ast env p | _ -> invalid_arg_loc (loc ast,"Ast.to_pat") (* Ast with cases and metavariables *) let print_sig = function | [] -> mt () | sigma -> str"with constraints :" ++ brk(1,1) ++ v 0 (prlist_with_sep pr_spc (fun (x,v) -> str x ++ str" = " ++ hov 0 (print_val v)) sigma) let case_failed loc sigma e pats = user_err_loc (loc,"Ast.eval_act", str"Grammar case failure. The ast" ++ spc () ++ print_ast e ++ spc () ++ str"does not match any of the patterns :" ++ brk(1,1) ++ v 0 (prlist_with_sep pr_spc print_astpat pats) ++ fnl () ++ print_sig sigma) let caselist_failed loc sigma el pats = user_err_loc (loc,"Ast.eval_act", str"Grammar case failure. The ast list" ++ brk(1,1) ++ print_astl el ++ spc () ++ str"does not match any of the patterns :" ++ brk(1,1) ++ v 0 (prlist_with_sep pr_spc print_astlpat pats) ++ fnl () ++ print_sig sigma) let rec eval_act dloc sigma act = match act with | Aast pat -> Vast (pat_sub dloc sigma pat) | Aastlist patl -> Vastlist (patl_sub dloc sigma patl) | Acase(e,ml) -> (match eval_act dloc sigma e with | Vast esub -> (match first_match fst sigma esub ml with | Some((_,a),sigma_pat) -> eval_act dloc sigma_pat a | _ -> case_failed dloc sigma esub (List.map fst ml)) | _ -> grammar_type_error (dloc,"Ast.eval_act")) | Acaselist(e,ml) -> (match eval_act dloc sigma e with | Vastlist elsub -> (match first_matchl fst sigma elsub ml with | Some((_,a),sigma_pat) -> eval_act dloc sigma_pat a | _ -> caselist_failed dloc sigma elsub (List.map fst ml)) | _ -> grammar_type_error (dloc,"Ast.eval_act")) (* TODO: case sur des variables uniquement -> pas de pb de conflit Ast/List *) let rec act_of_ast vars etyp ast = match ast with | Node(_,"$CASE",(a::et::cl)) -> let atyp = entry_type et in let pa = act_of_ast vars atyp a in (match atyp with | ETast -> let acl = List.map (case vars etyp) cl in Acase (pa,acl) | ETastl -> let acl = List.map (caselist vars etyp) cl in Acaselist (pa,acl)) | Node(_,"ASTLIST",al) when etyp = ETastl -> Aastlist (vall_of_astl vars al) | a when etyp = ETast -> Aast (val_of_ast vars a) | _ -> invalid_arg_loc (loc ast,"Ast.act_of_ast: ill-typed") and case vars etyp ast = match ast with | Node(_,"CASE",[Node(loca,"ASTLIST",pl);a]) -> (match pl with | [p] -> let (apl,penv) = pat_of_ast vars p in let aa = act_of_ast penv etyp a in (apl,aa) | _ -> user_err_loc (loca,"Ast.case", (str"case pattern for an ast should be a single ast"))) | _ -> invalid_arg_loc (loc ast,"Ast.case") and caselist vars etyp ast = match ast with | Node(_,"CASE",[Node(_,"ASTLIST",pl);a]) -> let (apl,penv) = patl_of_astl vars pl in let aa = act_of_ast penv etyp a in (apl,aa) | _ -> invalid_arg_loc (loc ast,"Ast.caselist") let to_act_check_vars env etyp ast = match ast with | Node(_,"ASTACT",[a]) -> act_of_ast env etyp a | _ -> invalid_arg_loc (loc ast,"Ast.to_act_env")