open Pure
open Num
-(*
- The number of arguments which can applied to numbers
- safely, depending on the encoding of numbers.
- For Scott's encoding, two.
-*)
-let num_more_args = 2;;
+(* exceptions *)
+exception Pacman
+exception Bottom
+exception Lambda
+exception Backtrack of string
+
+(* verbosity *)
+let _very_verbose = false;;
+(** Display measure of every term when printing problem *)
+let _measure_of_terms = false;;
+
+let verbose s =
+ if _very_verbose then prerr_endline s
+;;
+
+let convergent_dummy = `N(-1);;
type discriminating_set = (int * nf) list;;
; sigma: (int * nf) list (* the computed substitution *)
; deltas: discriminating_set ref list (* collection of all branches *)
; initialSpecialK: int
+ ; label : string
+ ; var_names : string list (* names of the original free variables *)
; trail: discriminating_set list list
};;
-(* exceptions *)
-exception Pacman
-exception Bottom
-exception Backtrack of string
+let label_of_problem {label} = label;;
+
+let string_of_var l x =
+ try
+ List.nth l x
+ with Failure "nth" -> "`" ^ string_of_int x
+;;
+let string_of_term p t = print ~l:p.var_names (t :> nf);;
let first bound p var f =
let p = {p with trail = (List.map (!) p.deltas)::p.trail} in
let rec aux i =
if i > bound then
- raise (Backtrack ("no more alternatives for " ^ string_of_var var))
+ raise (Backtrack ("no more alternatives for " ^ string_of_var p.var_names var))
else
- try(try
+ try
f p i
- with Pacman | Bottom -> raise (Backtrack "Pacman/Bottom"))
with Backtrack s ->
-prerr_endline ("!!BACKTRACK!! " ^ s);
+prerr_endline (">>>>>> BACKTRACK (reason: " ^ s ^") measure=$ ");
List.iter (fun (r,l) -> r := l) (List.combine p.deltas (List.hd p.trail)) ;
-prerr_endline("Now trying var="^string_of_var var^" i="^string_of_int i);
+prerr_endline("Now trying var="^string_of_var p.var_names var^" i="^string_of_int (i+1));
aux (i+1)
in
aux 1
@ p.ps
;;
-let sum_arities p =
+let measure_of_term, measure_of_terms =
let rec aux = function
| `N _ | `Bottom | `Pacman -> 0
| `Var(_,ar) -> if ar = min_int then 0 else max 0 ar (*assert (ar >= 0); ar*)
| `Lam(_,t) -> aux t
| `I(v,args) -> aux (`Var v) + aux_many (Listx.to_list args :> nf list)
- | `Match(u,(_,ar),_,_,args) -> aux (u :> nf) + (if ar = min_int then 0 else ar - 1) + aux_many (args :> nf list)
+ | `Match(u,(_,ar),_,_,args) -> aux (u :> nf) + (if ar <= 0 then 0 else ar - 1) + aux_many (args :> nf list)
and aux_many tms = List.fold_right ((+) ++ aux) tms 0 in
- aux_many (all_terms p :> nf list)
- ;;
+ (fun t -> aux (t :> nf)), (fun l -> aux_many (l :> nf list))
+;;
+
+let sum_arities p = measure_of_terms (all_terms p)
let problem_measure p = sum_arities p;;
let string_of_measure = string_of_int;;
let string_of_problem label ({freshno; div; conv; ps; deltas} as p) =
- Console.print_hline ();
- prerr_string ("\n(* DISPLAY PROBLEM (" ^ label ^ ") - ");
- let nl = "\n" in
- let deltas = String.concat (nl^" ") (List.map (fun r -> String.concat " <> " (List.map (fun (i,_) -> string_of_int i) !r)) deltas) in
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- "measure="^string_of_measure(problem_measure p) (* ^ " freshno = " ^ string_of_int freshno*)
- ^ nl ^ " Discriminating sets (deltas):"
- ^ nl ^ " " ^ deltas ^ (if deltas = " " then "" else nl) ^ "*)" ^ nl
- ^" (* DIVERGENT *)" ^ nl
- ^" "^ (match div with None -> "None" | Some div -> "(Some\""^ print ~l (div :> nf) ^"\" ") ^ nl
- ^" (* CONVERGENT *) [" ^ nl
- ^ String.concat "\n " (List.map (fun t -> "(* _: *) " ^ (if t = `N (-1) then "" else "\""^ print ~l (t :> nf) ^"\";")) conv) ^
- (if conv = [] then "" else nl)
- ^ "] (* NUMERIC *) [" ^ nl ^ " "
- ^ String.concat "\n " (List.mapi (fun i t -> " (* "^ string_of_int i ^" *) \"" ^ print ~l (t :> nf) ^ "\";") ps)
- ^ nl ^ "] [\"*\"];;" ^ nl
+ let aux_measure_terms t = if _measure_of_terms then "(" ^ string_of_int (measure_of_term t) ^ ") " else "" in
+ let deltas = String.concat ("\n# ") (List.map (fun r -> String.concat " <> " (List.map (fun (i,_) -> string_of_int i) !r)) deltas) in
+ let l = p.var_names in
+ String.concat "\n" ([
+ "";
+ "# DISPLAY PROBLEM (" ^ label ^ ") " ^ "measure=" ^ string_of_measure (problem_measure p);
+ if List.length p.deltas > 1 then (
+ "# Discriminating sets (deltas):\n" ^
+ "# " ^ deltas
+ ) else "# ";
+ "#";
+ "$" ^ p.label;
+ (match div with None -> "# D" | Some div -> "D " ^ aux_measure_terms div ^ print ~l (div :> nf));
+ ]
+ @ List.map (fun t -> if t = convergent_dummy then "# C" else "C " ^ aux_measure_terms t ^ print ~l (t :> nf)) conv
+ @ List.mapi (fun i t -> string_of_int i ^ " " ^ aux_measure_terms t ^ print ~l (t :> nf)) ps
+ @ [""])
;;
let simple_expand_match ps =
let rec aux_nob level = function
- | #i_num_var as t -> aux_i_num_var level t
+ | #i_num_var as t -> (aux_i_num_var level t :> nf)
| `Lam(b,t) -> `Lam(b,aux (level+1) t)
| `Pacman as t -> t
and aux level = function
| #nf_nob as t -> aux_nob level t
and aux_i_num_var level = function
| `Match(u,v,bs_lift,bs,args) as torig ->
- let u = aux_i_num_var level u in
+ let (u : i_num_var) = aux_i_num_var level u in
bs := List.map (fun (n, x) -> n, aux 0 x) !bs;
(try
(match u with
| #i_n_var as u ->
- let i = index_of (lift (-level) u) (ps :> nf list) (* can raise Not_found *)
- in let t = mk_match (`N i) v bs_lift bs (args :> nf list) in
+ let i = index_of ~eq:eta_eq (lift (-level) u) (ps :> nf list) in (* can raise Not_found *)
+ let t = cast_to_i_num_var (mk_match (`N i) v bs_lift bs (args :> nf list)) in
if t <> torig then
- aux level (t :> nf)
- else raise Not_found
+ aux_i_num_var level t
+ else raise Not_found
| _ -> raise Not_found)
with Not_found ->
- mk_appl (`Match(cast_to_i_num_var u,v,bs_lift,bs,[])) (List.map (aux_nob level) args))
- | `I(v,args) -> mk_appl (`Var v) (List.map (aux_nob level) (Listx.to_list args))
+ cast_to_i_num_var (mk_appl (`Match(u,v,bs_lift,bs,[])) (List.map (aux_nob level) args)))
+ | `I(v,args) -> cast_to_i_num_var (mk_appl (`Var v) (List.map (aux_nob level) (Listx.to_list args)))
| `N _ | `Var _ as t -> t
in aux_i_num_var 0
;;
;;
let rec super_simplify_ps ps =
+ fixpoint (List.map (fun x -> cast_to_i_n_var (simple_expand_match ps (x :> i_num_var))))
+;;
+
+let rec super_simplify_ps_with_match ps =
fixpoint (List.map (cast_to_i_num_var ++ (simple_expand_match ps)))
;;
let super_simplify ({div; ps; conv} as p) =
- let ps = super_simplify_ps p.ps (p.ps :> i_num_var list) in
- let conv = super_simplify_ps ps (p.conv :> i_num_var list) in
+ let ps = super_simplify_ps p.ps p.ps in
+ let conv = super_simplify_ps ps p.conv in
let div = option_map (fun div ->
- let divs = super_simplify_ps p.ps ([div] :> i_num_var list) in
+ let divs = super_simplify_ps p.ps ([div] :> i_n_var list) in
List.hd divs) div in
- {p with div=option_map cast_to_i_var div; ps=List.map cast_to_i_n_var ps; conv=List.map cast_to_i_n_var conv}
+ {p with div=option_map cast_to_i_var div; ps; conv}
-let cast_to_ps =
+let cast_to_ps_with_match =
function
#i_num_var as y -> (y : i_num_var)
- | `Bottom | `Pacman -> raise (Backtrack "foo")
+ | `Bottom | `Pacman -> raise (Backtrack "BOT/PAC in ps")
| t ->
prerr_endline (print (t :> nf));
assert false (* algorithm failed *)
let t = subst false false x inst (t :> nf) in
(*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
let freshno,new_t,acc_new_ps =
- expand_match (freshno,acc_ps@`Var(max_int/3,-666)::todo_ps,acc_new_ps) t
+ try
+ expand_match (freshno,acc_ps@`Var(max_int/3,-666)::todo_ps,acc_new_ps) t
+ with Pacman | Bottom -> raise (Backtrack "Pacman/Bottom in ps")
in
aux_ps (freshno,acc_ps@[new_t],acc_new_ps) todo_ps
| [] -> acc
| t::todo_conv ->
(*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
- let t = try
- subst false false x inst (t :> nf)
- with Pacman -> `N(-1) in (* DUMMY CONVERGENT *)
+ let t = subst false false x inst (t :> nf) in
(*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
- let freshno,new_t,acc_new_ps = expand_match (freshno,ps,acc_new_ps) t in
+ let freshno,new_t,acc_new_ps =
+ try
+ expand_match (freshno,ps,acc_new_ps) t
+ with Pacman | Lambda -> freshno,convergent_dummy,acc_new_ps
+ | Bottom -> raise (Backtrack "Bottom in conv") in
aux_conv ps (freshno,acc_conv@[new_t],acc_new_ps) todo_conv
(* cut&paste from aux' above *)
function
| None -> freshno, None, acc_new_ps
| Some t ->
+ let t = subst false false x inst (t :> nf) in
try
- let t = subst false false x inst (t :> nf) in
let freshno,new_t,acc_new_ps = expand_match (freshno,ps,acc_new_ps) t in
- freshno,Some(cast_to_i_var new_t),acc_new_ps
- with Bottom -> freshno, None, acc_new_ps
+ (* backtrack if it is a number or a variable *)
+ match new_t with
+ | `N _ -> raise (Backtrack "div=`N")
+ | `Var _
+ | `I _ as new_t -> freshno, Some(new_t), acc_new_ps
+ with
+ | Bottom -> freshno, None, acc_new_ps
+ | Pacman -> raise (Backtrack "div=PAC")
and expand_match ((freshno,acc_ps,acc_new_ps) as acc) t =
match t with
match u with
| `N i -> acc_new_ps,i
| _ ->
- let ps = List.map (fun t -> cast_to_ps (subst false false x inst (t:> nf))) (acc_ps@acc_new_ps) in
- let super_simplified_ps = super_simplify_ps ps ps in
+ let ps = List.map (fun t -> cast_to_ps_with_match (subst false false x inst (t:> nf))) (acc_ps@acc_new_ps) in
+ let super_simplified_ps = super_simplify_ps_with_match ps ps in
(*prerr_endline ("CERCO u:" ^ print (fst u :> nf));
List.iter (fun x -> prerr_endline ("IN: " ^ print (fst x :> nf))) ps;
List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplified_ps;*)
- match index_of_opt ~eq:eta_eq super_simplified_ps u with
+ match index_of_opt ~eq:eta_eq super_simplified_ps (u :> i_num_var) with
Some i -> acc_new_ps, i
| None -> acc_new_ps@[u], len_ps + List.length acc_new_ps
in
let t = mk_match (`N i) orig bs_lift bs (args :> nf list) in
(*prerr_endline ("NUOVO t:" ^ print (fst t :> nf) ^ " more_args=" ^ string_of_int (snd t));*)
expand_match (freshno,acc_ps,acc_new_ps) t
- | `Lam _ -> assert false (* algorithm invariant/loose typing *)
+ | `Lam _ -> raise Lambda (* assert false (* algorithm invariant/loose typing *) *)
| `Bottom -> raise Bottom
| `Pacman -> raise Pacman
| #i_n_var as x ->
let x = simple_expand_match (acc_ps@acc_new_ps) x in
- freshno,cast_to_i_num_var x,acc_new_ps in
+ freshno,cast_to_i_n_var x,acc_new_ps in
- let freshno,old_ps,new_ps = aux_ps (freshno,[],[]) (ps :> i_num_var list) in
- let freshno,conv,new_ps = aux_conv old_ps (freshno,[],new_ps) (conv :> i_num_var list) in
+ let freshno,old_ps,new_ps = aux_ps (freshno,[],[]) ps in
+ let freshno,conv,new_ps = aux_conv old_ps (freshno,[],new_ps) conv in
let freshno,div,new_ps = aux_div old_ps (freshno,new_ps) (div :> i_num_var option) in
let ps = List.map cast_to_i_n_var (old_ps @ new_ps) in
let conv = List.map cast_to_i_n_var conv in
-(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
-prerr_endline ("# INST: " ^ string_of_var x ^ " := " ^ print ~l inst));
let p = {p with freshno; div; conv; ps} in
+ prerr_endline ("# INST: " ^ string_of_var p.var_names x ^ " := " ^ string_of_term p inst);
( (* check if double substituting a variable *)
if List.exists (fun (x',_) -> x = x') sigma
- then failwithProblem p ("Variable "^ string_of_var x ^"replaced twice")
+ then failwithProblem p ("Variable "^ string_of_var p.var_names x ^"replaced twice")
);
let p = {p with sigma = sigma@[x,inst]} in
let p = super_simplify p in
- prerr_endline (string_of_problem "instantiate" p);
p
;;
-exception Dangerous
+exception TriggerMatchReduction of int;;
+exception Dangerous;;
-let arity_of arities k =
- let _,pos,y = List.find (fun (v,_,_) -> v=k) arities in
- let arity = match y with `Var _ -> 0 | `I(_,args) -> Listx.length args | _ -> assert false in
- arity + if pos = -1 then - 1 else 0
+let arity_of arities hd =
+ let pos,_,nargs = List.find (fun (_,hd',_) -> hd=hd') arities in
+ nargs + if pos = -1 then - 1 else 0
;;
let rec dangerous arities showstoppers =
(match t with
`N _ -> List.iter (dangerous arities showstoppers) args
| `Match _ as t -> dangerous arities showstoppers t ; List.iter (dangerous arities showstoppers) args
- | `Var(x,_) -> dangerous_inert arities showstoppers x args num_more_args
- | `I((x,_),args') -> dangerous_inert arities showstoppers x (Listx.to_list args' @ args) num_more_args
+ | `Var(x,_) -> dangerous_inert arities showstoppers x args 2
+ | `I((x,_),args') -> dangerous_inert arities showstoppers x (Listx.to_list args' @ args) 2
)
| `I((k,_),args) -> dangerous_inert arities showstoppers k (Listx.to_list args) 0
Not_found -> ()
(* cut & paste from above *)
-let rec dangerous_conv arities showstoppers =
+let rec dangerous_conv p arities showstoppers =
function
- `N _
+ | `N _
| `Var _
| `Lam _
- | `Pacman -> []
- | `Match(t,_,liftno,bs,args) ->
+ | `Pacman -> ()
+ | `Match(t,_,liftno,bs,args) -> (
(* CSC: XXX partial dependency on the encoding *)
- (match t with
- `N _ -> concat_map (dangerous_conv arities showstoppers) args
- | `Match _ as t -> dangerous_conv arities showstoppers t @ concat_map (dangerous_conv arities showstoppers) args
- | `Var(x,_) -> dangerous_inert_conv arities showstoppers x [] args 2
- | `I((x,_),args') -> dangerous_inert_conv arities showstoppers x (Listx.to_list args') args 2
- )
- | `I((k,_),args) -> dangerous_inert_conv arities showstoppers k (Listx.to_list args) [] 0
-
-and dangerous_inert_conv arities showstoppers k args match_args more_args =
+ try (match t with
+ | `N _ -> List.iter (dangerous_conv p arities showstoppers) args
+ | `Match _ as t -> dangerous_conv p arities showstoppers t; List.iter (dangerous_conv p arities showstoppers) args
+ | `Var(x,_) -> dangerous_inert_conv p arities showstoppers x [] args 2
+ | `I((x,_),args') -> dangerous_inert_conv p arities showstoppers x (Listx.to_list args') args 2
+ ) with TriggerMatchReduction x -> (
+ match Util.find_opt (fun (n, t) -> if hd_of (List.nth p.ps n) = Some x then Some t else None) !bs with
+ | None -> ()
+ | Some t -> (
+ match t with
+ | `Bottom -> raise Dangerous
+ | #nf_nob as t -> dangerous_conv p arities showstoppers t
+ )
+ )
+ )
+ | `I((k,_),args) -> dangerous_inert_conv p arities showstoppers k (Listx.to_list args) [] 0
+
+and dangerous_inert_conv p arities showstoppers k args match_args more_args =
let all_args = args @ match_args in
- let dangerous_args = concat_map (dangerous_conv arities showstoppers) all_args in
+ List.iter (dangerous_conv p arities showstoppers) all_args;
let all_args = (all_args :> nf list) in
- if dangerous_args = [] then (
- if List.mem k showstoppers then k :: concat_map free_vars all_args else
- try
- let arity = arity_of arities k in
-prerr_endline ("dangerous_inert_conv: ar=" ^ string_of_int arity ^ " k="^string_of_var k ^ " listlenargs=" ^ (string_of_int (List.length args)) ^ " more_args=" ^ string_of_int more_args);
- if more_args > 0 (* match argument*) && List.length args = arity then []
- else if List.length all_args + more_args > arity then k :: concat_map free_vars all_args else []
- with
- Not_found -> []
- ) else k :: concat_map free_vars all_args
+ if List.mem k showstoppers then raise Dangerous else
+ try
+ let arity = arity_of arities k in
+(* prerr_endline ("dangerous_inert_conv: ar=" ^ string_of_int arity ^ " k="^string_of_var p.var_names k ^ " listlenargs=" ^ (string_of_int (List.length args)) ^ " more_args=" ^ string_of_int more_args); *)
+ if more_args > 0 (* match argument*) && List.length args = arity then raise (TriggerMatchReduction k)
+ else if List.length all_args + more_args > arity then raise Dangerous else ()
+ with
+ Not_found -> ()
(* inefficient algorithm *)
-let rec edible arities div ps conv showstoppers =
- let rec aux showstoppers =
- function
- [] -> showstoppers
+let rec edible p arities showstoppers =
+ let rec aux f showstoppers tms = function
+ | [] -> showstoppers
| x::xs when List.exists (fun y -> hd_of x = Some y) showstoppers ->
(* se la testa di x e' uno show-stopper *)
let new_showstoppers = sort_uniq (showstoppers @ free_vars (x :> nf)) in
(* aggiungi tutte le variabili libere di x *)
if List.length showstoppers <> List.length new_showstoppers then
- aux new_showstoppers ps
+ aux f new_showstoppers tms tms
else
- aux showstoppers xs
+ aux f showstoppers tms xs
| x::xs ->
match hd_of x with
- None -> aux showstoppers xs
+ None -> aux f showstoppers tms xs
| Some h ->
try
- dangerous arities showstoppers (x : i_n_var :> nf_nob) ;
- aux showstoppers xs
+ f showstoppers (x :> nf_nob) ;
+ aux f showstoppers tms xs
with
Dangerous ->
- aux (sort_uniq (h::showstoppers)) ps
+ aux f (sort_uniq (h::showstoppers)) tms tms
in
- let showstoppers = sort_uniq (aux showstoppers ps) in
- let dangerous_conv =
- List.map (dangerous_conv arities showstoppers) conv in
-
-prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv));
-List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))) dangerous_conv;
+ let showstoppers = sort_uniq (aux (dangerous arities) showstoppers p.ps p.ps) in
+ let dangerous_conv = sort_uniq (aux (dangerous_conv p arities) showstoppers p.conv p.conv) in
- let showstoppers' = showstoppers @ List.concat dangerous_conv in
- let showstoppers' = sort_uniq (match div with
+ let showstoppers' = showstoppers @ dangerous_conv in
+ let showstoppers' = sort_uniq (match p.div with
| None -> showstoppers'
| Some div ->
if List.exists ((=) (hd_of_i_var div)) showstoppers'
then showstoppers' @ free_vars (div :> nf) else showstoppers') in
- if showstoppers <> showstoppers' then edible arities div ps conv showstoppers' else showstoppers', dangerous_conv
+ if showstoppers <> showstoppers' then edible p arities showstoppers' else showstoppers'
;;
let precompute_edible_data {ps; div} xs =
- (match div with None -> [] | Some div -> [hd_of_i_var div, -1, (div :> i_n_var)]) @
- List.map (fun hd ->
+ let aux t = match t with `Var _ -> 0 | `I(_, args) -> Listx.length args | `N _ -> assert false in
+ (fun l -> match div with
+ | None -> l
+ | Some div -> (-1, hd_of_i_var div, aux div) :: l)
+ (List.map (fun hd ->
let i, tm = Util.findi (fun y -> hd_of y = Some hd) ps in
- hd, i, tm
- ) xs
+ i, hd, aux tm
+ ) xs)
;;
+(** Returns (p, showstoppers_step, showstoppers_eat) where:
+ - showstoppers_step are the heads occurring twice
+ in the same discriminating set
+ - showstoppers_eat are the heads in ps having different number
+ of arguments *)
let critical_showstoppers p =
let p = super_simplify p in
let hd_of_div = match p.div with None -> [] | Some t -> [hd_of_i_var t] in
let showstoppers_eat = List.filter
(fun x -> not (List.mem x showstoppers_step))
showstoppers_eat in
- List.iter (fun v -> prerr_endline ("DANGEROUS STEP: " ^ string_of_var v)) showstoppers_step;
- List.iter (fun v -> prerr_endline ("DANGEROUS EAT: " ^ string_of_var v)) showstoppers_eat;
+prerr_endline ("DANGEROUS STEP: " ^ String.concat " " (List.map (string_of_var p.var_names) showstoppers_step));
+prerr_endline ("DANGEROUS EAT: " ^ String.concat " " (List.map (string_of_var p.var_names) showstoppers_eat));
p, showstoppers_step, showstoppers_eat
;;
let showstoppers = showstoppers_step @ showstoppers_eat in
let heads = List.sort compare (filter_map hd_of ps) in
let arities = precompute_edible_data p (uniq heads) in
- let showstoppers, showstoppers_conv =
- edible arities p.div ps (p.conv :> nf_nob list) showstoppers in
- let l = List.filter (fun (x,_,_) -> not (List.mem x showstoppers)) arities in
- let p =
- List.fold_left (fun p (x,pos,(xx : i_n_var)) -> if pos = -1 then p else
- let n = match xx with `I(_,args) -> Listx.length args | _ -> 0 in
- let v = `N(pos) in
- let inst = make_lams v n in
-(let l = Array.to_list (Array.init (p.freshno + 1) string_of_var) in
-prerr_endline ("# INST_IN_EAT: " ^ string_of_var x ^ " := " ^ print ~l inst));
- { p with sigma = p.sigma @ [x,inst] }
- ) p l in
+ let inedible = edible p arities showstoppers in
+ prerr_endline ("showstoppers (in eat)" ^ String.concat " " (List.map (string_of_var p.var_names) inedible));
+ let l = List.filter (fun (_,hd,_) -> not (List.mem hd inedible)) arities in
+ let new_sigma = List.map (fun (pos,hd,nargs) ->
+ let v = if pos = -1 then `Bottom else `N pos in
+ let inst = make_lams v nargs in
+prerr_endline ("# [INST_IN_EAT] eating: " ^ string_of_var p.var_names hd ^ " := " ^ string_of_term p inst);
+ hd,inst
+ ) l in
(* to avoid applied numbers in safe positions that
trigger assert failures subst_in_problem x inst p*)
let ps =
List.map (fun t ->
try
- let _,j,_ = List.find (fun (h,_,_) -> hd_of t = Some h) l in
+ let j,_,_ = List.find (fun (_,hd,_) -> hd_of t = Some hd) l in
`N j
with Not_found -> t
) ps in
- let p = match p.div with
- | None -> p
- | Some div ->
- if List.mem (hd_of_i_var div) showstoppers
- then p
- else
- let n = match div with `I(_,args) -> Listx.length args | `Var _ -> 0 in
- let x = hd_of_i_var div in
- let inst = make_lams `Bottom n in
- subst_in_problem x inst p in
- let dangerous_conv = showstoppers_conv in
-let _ = prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv));
-List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))) dangerous_conv; in
+(*let dangerous_conv = showstoppers_conv in
+prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv));
+List.iter (fun l -> prerr_endline (String.concat " " (List.map (string_of_var p.var_names) l))) dangerous_conv; *)
let conv =
- List.map (function s,t ->
+ List.map (function t ->
try
- if s <> [] then t else (
(match t with | `Var _ -> raise Not_found | _ -> ());
- let _ = List.find (fun h -> hd_of t = Some h) showstoppers in
- t)
- with Not_found -> match hd_of t with
- | None -> assert (t = `N ~-1); t
- | Some h ->
- prerr_endline ("FREEZING " ^ string_of_var h);
- `N ~-1 (* convergent dummy*)
- ) (List.combine showstoppers_conv p.conv) in
+ let _ = List.find (fun h -> hd_of t = Some h) inedible in t
+ with Not_found -> (
+ (match hd_of t with
+ | None -> assert (t = convergent_dummy)
+ | Some h -> prerr_endline ("FREEZING " ^ string_of_var p.var_names h));
+ convergent_dummy)
+ ) p.conv in
List.iter
(fun bs ->
bs :=
) p.deltas ;
let old_conv = p.conv in
let p = { p with ps; conv } in
+ (* In case (match x ... with ...) and we are eating x,
+ so we need to substitute *)
+ let p = List.fold_left (fun p (x,inst) -> subst_in_problem x inst p) p new_sigma in
if l <> [] || old_conv <> conv
then prerr_endline (string_of_problem "eat" p);
if List.for_all (function `N _ -> true | _ -> false) ps && p.div = None then
else
`Continue p
-let instantiate p x perm n =
- let arity_of_x = max_arity_tms x (all_terms p) in
- (if arity_of_x = None then failwithProblem p "step on var non occurring in problem");
- let arity_of_x = Util.option_get(arity_of_x) in
- (if arity_of_x = min_int then failwithProblem p "step on fake variable");
- (if arity_of_x <= 0 then failwithProblem p "step on var of non-positive arity");
- (if perm < 1 || perm > arity_of_x then
- failwithProblem p ("Tried to permutate variable "^ string_of_var x ^" beyond its max arity"));
- let n = (prerr_endline "WARNING: using constant initialSpecialK"); p.initialSpecialK in
+
+let safe_arity_of_var p x =
+ (* Compute the minimum number of arguments when x is in head
+ position at p.div or p.ps *)
+ let aux = function
+ | `Var(y,_) -> if x = y then 0 else max_int
+ | `I((y,_),args) -> if x = y then Listx.length args else max_int
+ | _ -> max_int in
+ let tms = ((match p.div with None -> [] | Some t -> [(t :> i_n_var)]) @ p.ps) in
+ List.fold_left (fun acc t -> Pervasives.min acc (aux t)) max_int tms
+;;
+
+let instantiate p x perm =
+ let n = (prerr_endline ("WARNING: using constant initialSpecialK=" ^ string_of_int p.initialSpecialK)); p.initialSpecialK in
let arities = Array.to_list (Array.make (n+1) min_int) in
let p,vars = make_fresh_vars p arities in
(* manual lifting of vars by perm in next line *)
| `Bottom
| `Pacman
| `Var _ -> 0
- ) in Listx.max (Listx.map (aux 0) tms)
+ ) in
+ let rec aux' top t = match t with
+ | `Lam(_,t) -> aux' false t
+ | `I((_,ar), tms) -> max ar
+ (Listx.max (Listx.map (aux' false) (tms :> nf Listx.listx)))
+ | `Match(t, _, liftno, bs, args) ->
+ List.fold_left max 0 (List.map (aux' false) ((t :> nf)::(args :> nf list)@List.map snd !bs))
+ | `N _
+ | `Bottom
+ | `Pacman
+ | `Var _ -> 0 in
+ Listx.max (Listx.map (aux 0) tms) + Listx.max (Listx.map (aux' true) tms)
;;
-let choose_step (n,p) =
+let choose_step p =
let p, showstoppers_step, showstoppers_eat = critical_showstoppers p in
let x =
match showstoppers_step, showstoppers_eat with
| [], y::_ ->
- prerr_endline ("INSTANTIATING CRITICAL TO EAT " ^ string_of_var y); y
+ prerr_endline ("INSTANTIATING (critical eat) : " ^ string_of_var p.var_names y); y
+ | x::_, _ ->
+ prerr_endline ("INSTANTIATING (critical step): " ^ string_of_var p.var_names x); x
| [], [] ->
let heads =
(* Choose only variables still alive (with arity > 0) *)
with
Not_found -> assert false)
| x::_ ->
- prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
- x)
- | x::_, _ ->
- prerr_endline ("INSTANTIATING " ^ string_of_var x);
- x in
-(* Strategy that decreases the special_k to 0 first (round robin)
-1:11m42 2:14m5 3:11m16s 4:14m46s 5:12m7s 6:6m31s *)
- let x =
- try
- match
- hd_of (List.find (fun t ->
- compute_special_k (Listx.Nil (t :> nf)) > 0 && arity_of_hd t > 0
- ) (all_terms p))
- with
- | None -> assert false
- | Some x ->
- prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
- x
- with
- Not_found -> x in
-(* Instantiate in decreasing order of compute_special_k
-1:15m14s 2:13m14s 3:4m55s 4:4m43s 5:4m34s 6:6m28s 7:3m31s
-let x =
- try
- (match hd_of (snd (List.hd (List.sort (fun c1 c2 -> - compare (fst c1) (fst c2)) (filter_map (function `I _ as t -> Some (compute_special_k (Listx.Nil (t :> nf)),t) | _ -> None) (all_terms p))))) with
- None -> assert false
- | Some x ->
- prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
- x)
- with
- Not_found -> x
-in*)
- let special_k =
- compute_special_k (Listx.from_list (all_terms p :> nf list) )in
- if special_k < n then
- prerr_endline ("@@@@ NEW INSTANTIATE PHASE (" ^ string_of_int special_k ^ ") @@@@");
+ prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var p.var_names x);
+ x) in
let arity_of_x = Util.option_get (max_arity_tms x (all_terms p)) in
- x,arity_of_x,special_k
+ let safe_arity_of_x = safe_arity_of_var p x in
+ x, min arity_of_x safe_arity_of_x
+;;
-let rec auto_eat (n,p) =
- prerr_endline "{{{{{{{{ Computing measure before auto_instantiate }}}}}}";
+let rec auto_eat p =
+(* prerr_endline "{{{{{{{{ Computing measure before auto_instantiate }}}}}}"; *)
let m = problem_measure p in
- let x, arity_of, n = choose_step (n,p) in
+ let x, arity_of = choose_step p in
first arity_of p x (fun p j ->
- let p' = instantiate p x j n in
+ let p' = instantiate p x j in
+ prerr_endline (string_of_problem "after instantiate" p');
match eat p' with
| `Finished p -> p
| `Continue p ->
- prerr_endline "{{{{{{{{ Computing measure inafter auto_instantiate }}}}}}";
+(* prerr_endline "{{{{{{{{ Computing measure inafter auto_instantiate }}}}}}"; *)
let delta = problem_measure p - m in
- (* let delta = m - problem_measure p' in *)
if delta >= 0
then
(failwith
("Measure did not decrease (+=" ^ string_of_int delta ^ ")"))
- else prerr_endline ("$ Measure decreased of " ^ string_of_int delta);
- auto_eat (n,p))
+ else prerr_endline ("$ Measure decreased: " ^ string_of_int delta);
+ auto_eat p)
;;
let auto p n =
- prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
+prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
match eat p with
| `Finished p -> p
- | `Continue p -> auto_eat (n,p)
+ | `Continue p -> auto_eat p
;;
-(*
-0 = snd
-
- x y = y 0 a y = k k z = z 0 c y = k y u = u h1 h2 0 h2 a = h3
-1 x a c 1 a 0 c 1 k c 1 c 0 1 k 1 k 1 k
-2 x a y 2 a 0 y 2 k y 2 y 0 2 y 0 2 h2 0 2 h3
-3 x b y 3 b 0 y 3 b 0 y 3 b 0 y 3 b 0 y 3 b 0 (\u. u h1 h2 0) 3 b 0 (\u. u h1 (\w.h3) 0)
-4 x b c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c
-5 x (b e) 5 b e 0 5 b e 0 5 b e 0 5 b e 0 5 b e 0 5 b e 0
-6 y y 6 y y 6 y y 6 y y 6 y y 6 h1 h1 h2 0 h2 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0
-
- l2 _ = l3
-b u = u l1 l2 0 e _ _ _ _ = f l3 n = n j 0
-1 k 1 k 1 k
-2 h3 2 h3 2 h3
-3 l2 0 (\u. u h1 (\w. h3) 0) 3 l3 (\u. u h1 (\w. h3) 0) 3 j h1 (\w. h3) 0 0
-4 l2 0 c 4 l3 c 4 c j 0
-5 e l1 l2 0 0 5 f 5 f
-6 h1 h1 (\w. h3) 0 (\w. h3) 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0
-*)
-
-(*
- x n = n 0 ?
-x a (b (a c)) a 0 = 1 ? (b (a c)) 8
-x a (b d') a 0 = 1 ? (b d') 7
-x b (a c) b 0 = 1 ? (a c) 4
-x b (a c') b 0 = 1 ? (a c') 5
-
-c = 2
-c' = 3
-a 2 = 4 (* a c *)
-a 3 = 5 (* a c' *)
-d' = 6
-b 6 = 7 (* b d' *)
-b 4 = 8 (* b (a c) *)
-b 0 = 1
-a 0 = 1
-*)
-
-(************** Tests ************************)
+
+(******************************************************************************)
let optimize_numerals p =
let replace_in_sigma perm =
Not_found -> ([],Pure.V n,[]))::e
in aux 0
;;
+(* ************************************************************************** *)
+
+type response = [
+ | `CompleteSeparable of string
+ | `CompleteUnseparable of string
+ | `Uncomplete
+]
+
+type result = [
+ `Complete | `Uncomplete
+] * [
+ | `Separable of (int * Num.nf) list
+ | `Unseparable of string
+]
+
+let run p =
+ Console.print_hline();
+ prerr_endline (string_of_problem "main" p);
+ let p_finale = auto p p.initialSpecialK in
+ let freshno,sigma = p_finale.freshno, p_finale.sigma in
+ prerr_endline ("------- <DONE> ------ measure=. \n ");
+ List.iter (fun (x,inst) -> prerr_endline (string_of_var p_finale.var_names x ^ " := " ^ string_of_term p_finale inst)) sigma;
+
+ prerr_endline "---------<OPT>----------";
+ let sigma = optimize_numerals p_finale in (* optimize numerals *)
+ List.iter (fun (x,inst) -> prerr_endline (string_of_var p_finale.var_names x ^ " := " ^ string_of_term p_finale inst)) sigma;
+
+ prerr_endline "---------<PURE>---------";
+ let scott_of_nf t = ToScott.scott_of_nf (t :> nf) in
+ let div = option_map scott_of_nf p.div in
+ let conv = List.map scott_of_nf p.conv in
+ let ps = List.map scott_of_nf p.ps in
+
+ let sigma' = List.map (fun (x,inst) -> x, ToScott.scott_of_nf inst) sigma in
+ let e' = env_of_sigma freshno sigma' in
+
+ prerr_endline "--------<REDUCE>---------";
+ (function Some div ->
+ print_endline (Pure.print div);
+ let t = Pure.mwhd (e',div,[]) in
+ prerr_endline ("*:: " ^ (Pure.print t));
+ assert (t = Pure.B)
+ | None -> ()) div;
+ List.iter (fun n ->
+ verbose ("_::: " ^ (Pure.print n));
+ let t = Pure.mwhd (e',n,[]) in
+ verbose ("_:: " ^ (Pure.print t));
+ assert (t <> Pure.B)
+ ) conv ;
+ List.iteri (fun i n ->
+ verbose ((string_of_int i) ^ "::: " ^ (Pure.print n));
+ let t = Pure.mwhd (e',n,[]) in
+ verbose ((string_of_int i) ^ ":: " ^ (Pure.print t));
+ assert (t = Scott.mk_n i)
+ ) ps ;
+ prerr_endline "-------- </DONE> --------";
+ p_finale.sigma
+;;
-prerr_endline "########## main ##########";;
-
-(* Commands:
- v ==> v := \a. a k1 .. kn \^m.0
- + ==> v := \^k. numero for every v such that ...
- * ==> tries v as long as possible and then +v as long as possible
-*)
-let main problems =
- let rec aux ({ps} as p) n l =
- if List.for_all (function `N _ -> true | _ -> false) ps && p.div = None then begin
- p
- end else
- let _ = prerr_endline (string_of_problem "main" p) in
- let x,l =
- match l with
- | cmd::l -> cmd,l
- | [] -> read_line (),[] in
- let cmd =
- if x = "+" then
- `DoneWith
- else if x = "*" then
- `Auto
- else
- `Step x in
- match cmd with
- | `DoneWith -> assert false (*aux (eat p) n l*) (* CSC: TODO *)
- | `Step x -> assert false
- (* let x = var_of_string x in
- aux (instantiate p x 1 n) n l *)
- | `Auto -> aux (auto p n) n l
- in
- List.iter
- (fun (p,n,cmds) ->
- Console.print_hline();
- let p_finale = aux p n cmds in
- let freshno,sigma = p_finale.freshno, p_finale.sigma in
- prerr_endline ("------- <DONE> ------\n ");
- (* prerr_endline (string_of_problem "Original problem" p); *)
- prerr_endline "---------------------";
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- prerr_endline "---------------------";
- List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
-(*
- prerr_endline "----------------------";
- let ps =
- List.fold_left (fun ps (x,inst) ->
- (* CSC: XXXX Is the subst always sorted correctly? Otherwise, implement a recursive subst *)
- (* In this non-recursive version, the intermediate states may containt Matchs *)
- List.map (fun t -> let t = subst false x inst (t :> nf) in cast_to_i_num_var t) ps)
- (p.ps :> i_num_var list) sigma in
- prerr_endline (string_of_problem {p with ps= List.map (function t -> cast_to_i_n_var t) ps; freshno});
- List.iteri (fun i (n,more_args) -> assert (more_args = 0 && n = `N i)) ps ;
-*)
- prerr_endline "---------<OPT>----------";
- let sigma = optimize_numerals p_finale in (* optimize numerals *)
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
- prerr_endline "---------<PURE>---------";
-
- let div = option_map (fun div -> ToScott.scott_of_nf (div :> nf)) p.div in
- let conv = List.map (fun t -> ToScott.scott_of_nf (t :> nf)) p.conv in
- let ps = List.map (fun t -> ToScott.scott_of_nf (t :> nf)) p.ps in
-
- let sigma' = List.map (fun (x,inst) -> x, ToScott.scott_of_nf inst) sigma in
- let e' = env_of_sigma freshno sigma' in
-
-(*
- prerr_endline "---------<PPP>---------";
-let rec print_e e =
- "[" ^ String.concat ";" (List.map (fun (e,t,[]) -> print_e e ^ ":" ^ Pure.print t) e) ^ "]"
-in
- prerr_endline (print_e e);
- List.iter (fun (t,t_ok) ->
- prerr_endline ("T0= " ^ Pure.print t ^ "\nTM= " ^ Pure.print (Pure.unwind (e,t,[])) ^ "\nOM= " ^ Pure.print t_ok);
- (*assert (Pure.unwind (e,t,[]) = t_ok)*)
- ) (List.combine ps ps_ok);
-*)
- prerr_endline "--------<REDUCE>---------";
- (function Some div ->
- print_endline (Pure.print div);
- let t = Pure.mwhd (e',div,[]) in
- prerr_endline ("*:: " ^ (Pure.print t));
- assert (t = Pure.B)
- | None -> ()) div;
- List.iter (fun n ->
- prerr_endline ("_::: " ^ (Pure.print n));
- let t = Pure.mwhd (e',n,[]) in
- prerr_endline ("_:: " ^ (Pure.print t))
- ) conv ;
- List.iteri (fun i n ->
- prerr_endline ((string_of_int i) ^ "::: " ^ (Pure.print n));
- let t = Pure.mwhd (e',n,[]) in
- prerr_endline ((string_of_int i) ^ ":: " ^ (Pure.print t));
- assert (t = Scott.mk_n i)
- ) ps ;
- prerr_endline "-------- </DONE> --------"
- ) problems
-
-(********************** problems *******************)
-
-let zero = `Var(0,0);;
-
-let append_zero =
- function
- | `I _
- | `Var _ as i -> cast_to_i_n_var (mk_app i zero)
- | _ -> assert false
+let solve (p, todo) =
+ let completeness, to_run =
+ match todo with
+ | `CompleteUnseparable s -> `Complete, `False s
+ | `CompleteSeparable _ -> `Complete, `True
+ | `Uncomplete -> `Uncomplete, `True in
+ completeness, match to_run with
+ | `False s -> `Unseparable s
+ | `True ->
+ try
+ `Separable (run p)
+ with
+ Backtrack _ -> `Unseparable "backtrack"
;;
-type t = problem * int * string list;;
-
-let magic_conv ~div ~conv ~nums cmds =
- let all_tms = (match div with None -> [] | Some div -> [div]) @ nums @ conv in
- let all_tms, var_names = parse' all_tms in
- let div, (tms, conv) = match div with
- | None -> None, list_cut (List.length nums, all_tms)
- | Some _ -> Some (List.hd all_tms), list_cut (List.length nums, List.tl all_tms) in
-
- if match div with None -> false | Some div -> List.exists (eta_subterm div) (tms@conv)
- then (
- prerr_endline "--- TEST SKIPPED ---";
- {freshno=0; div=None; conv=[]; ps=[]; sigma=[]; deltas=[]; initialSpecialK=0; trail=[]}, 0, []
- ) else
- let tms = sort_uniq ~compare:eta_compare tms in
- let special_k = compute_special_k (Listx.from_list all_tms) in (* compute initial special K *)
- (* casts *)
- let div = option_map cast_to_i_var div in
- let conv = Util.filter_map (function #i_n_var as t -> Some (cast_to_i_n_var t) | _ -> None) conv in
- let tms = List.map cast_to_i_n_var tms in
-
- let ps = List.map append_zero tms in (* crea lista applicando zeri o dummies *)
- let freshno = List.length var_names in
- let deltas =
- let dummy = `Var (max_int / 2, -666) in
- [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
- let trail = [] in
- {freshno; div; conv; ps; sigma=[] ; deltas; initialSpecialK=special_k; trail}, special_k, cmds
+let no_bombs_pacmans p =
+ not (List.exists (eta_subterm `Bottom) (p.ps@p.conv))
+ && not (List.exists (eta_subterm `Pacman) p.ps)
+ && Util.option_map (eta_subterm `Pacman) p.div <> Some true
;;
-let magic strings cmds = magic_conv None [] strings cmds;;
+let check p =
+ if (let rec f = function
+ | [] -> false
+ | hd::tl -> List.exists (eta_eq hd) tl || f tl in
+ f p.ps) (* FIXME what about initial fragments of numbers? *)
+ then `CompleteUnseparable "ps contains duplicates"
+ (* check if div occurs somewhere in ps@conv *)
+ else if (match p.div with
+ | None -> true
+ | Some div -> not (List.exists (eta_subterm div) (p.ps@p.conv))
+ ) && no_bombs_pacmans p
+ then `CompleteSeparable "no bombs, pacmans and div"
+ (* il check seguente e' spostato nel parser e lancia un ParsingError *)
+ (* else if false (* TODO bombs or div fuori da lambda in ps@conv *)
+ then `CompleteUnseparable "bombs or div fuori da lambda in ps@conv" *)
+ else if p.div = None
+ then `CompleteSeparable "no div"
+ else `Uncomplete
+;;
+
+let problem_of (label, div, conv, ps, var_names) =
+ (* TODO: replace div with bottom in problem??? *)
+ let all_tms = (match div with None -> [] | Some div -> [(div :> i_n_var)]) @ ps @ conv in
+ if all_tms = [] then failwith "problem_of: empty problem";
+ let initialSpecialK = compute_special_k (Listx.from_list (all_tms :> nf list)) in
+ let freshno = List.length var_names in
+ let deltas =
+ let dummy = `Var (max_int / 2, -666) in
+ [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
+ let trail = [] in
+ let sigma = [] in
+ let p = {freshno; div; conv; ps; sigma; deltas; initialSpecialK; trail; var_names; label} in
+ p, check p
+;;
projects / fireball-separation.git / blobdiff