X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=ocaml%2Flambda4.ml;h=02ac1e018ff96f1cb1d9cacb8e85dc58be733adb;hb=f7a60345135a4032bf63a7dc650bcc9fe30aa30a;hp=f71f36005f220d09bdea65baf15aed2f181181bd;hpb=dc3d76330323f0eba348377062934481c763d450;p=fireball-separation.git
diff --git a/ocaml/lambda4.ml b/ocaml/lambda4.ml
index f71f360..02ac1e0 100644
--- a/ocaml/lambda4.ml
+++ b/ocaml/lambda4.ml
@@ -3,7 +3,21 @@ open Util.Vars
open Pure
open Num
-let bomb = ref(`Var(-1,-666));;
+(*
+ 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;;
+let _very_verbose = false;;
+
+let verbose s =
+ if _very_verbose then prerr_endline s
+;;
+
+let convergent_dummy = `N(-1);;
+
+type discriminating_set = (int * nf) list;;
type problem =
{ freshno: int
@@ -11,69 +25,80 @@ type problem =
; conv: i_n_var list (* the inerts that must converge *)
; ps: i_n_var list (* the n-th inert must become n *)
; sigma: (int * nf) list (* the computed substitution *)
- ; deltas: (int * nf) list ref list (* collection of all branches *)
- }
-
-
-(* let heads = Util.sort_uniq (List.map hd_of_i_var p.ps) in
-for all head
- List.map (fun (_, bs) -> List.map (fun (x,_) -> List.nth p.ps x) !bs) p.deltas *)
-
-(* let ($) f x = f x;; *)
-
-(* let subterms tms freshno =
- let apply_var =
- let no = ref freshno in
- function t -> incr no; mk_app t (`Var !no) in
- let applicative hd args = snd (
- List.fold_left (fun (hd, acc) t -> let hd = mk_app hd t in hd, hd::acc) (hd, []) args) in
- let rec aux t = match t with
- | `Var _ -> []
- | `I(v,ts) ->
- (* applicative (`Var v) (Listx.to_list ts) @ *)
- Util.concat_map aux (Listx.to_list ts) @ List.map apply_var (Listx.to_list ts)
- | `Lam(_,_,t) -> aux (lift ~-1 t)
- | `Match(u,_,bs_lift,bs,args) ->
- aux (u :> nf) @
- (* applicative (`Match(u,bs_lift,bs,[])) args @ *)
- Util.concat_map aux args @ List.map apply_var args
- (* @ Util.concat_map (aux ++ (lift bs_lift) ++ snd) !bs *)
- | `N _ -> []
- in let tms' = (* Util.sort_uniq ~compare:eta_compare*) (Util.concat_map aux tms) in
- tms @ tms'
- (* List.map (fun (t, v) -> match t with `N _ -> t | _ -> mk_app t v) (List.combine tms (List.mapi (fun i _ -> `Var(freshno+i)) tms)) *)
-;; *)
+ ; deltas: discriminating_set ref list (* collection of all branches *)
+ ; initialSpecialK: int
+ ; label : string
+ ; var_names : string list (* names of the original free variables *)
+
+ ; trail: discriminating_set list list
+};;
+
+let label_of_problem {label} = label;;
+
+(* exceptions *)
+exception Pacman
+exception Bottom
+exception Backtrack of string
+
+let first bound p var f =
+ let p = {p with trail = (List.map (!) p.deltas)::p.trail} in
+ let rec aux i =
+ if i > bound then
+ raise (Backtrack ("no more alternatives for " ^ string_of_var var))
+ else
+ try
+ f p i
+ with Backtrack s ->
+prerr_endline (">>>>>> BACKTRACK (reason: " ^ s ^") measure=$ ");
+ 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);
+ aux (i+1)
+ in
+ aux 1
+
let all_terms p =
-(match p.div with None -> [] | Some t -> [(t :> i_n_var)])
-@ p.conv
-@ p.ps
+ (match p.div with None -> [] | Some t -> [(t :> i_n_var)])
+ @ p.conv
+ @ p.ps
;;
-let problem_measure p = 0 ;;
-
-let print_problem label ({freshno; div; conv; ps; deltas} as p) =
+let sum_arities p =
+ 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)
+ and aux_many tms = List.fold_right ((+) ++ aux) tms 0 in
+ aux_many (all_terms p :> nf list)
+ ;;
+
+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_endline ("\n||||| Displaying 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
+ prerr_string ("\n(* DISPLAY PROBLEM (" ^ p.label ^ " - " ^ 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
- nl ^ "measure="^string_of_int(problem_measure p)^" freshno = " ^ string_of_int freshno
- ^ nl ^ "\b> DISCRIMINATING SETS (deltas)"
- ^ nl ^ deltas ^ (if deltas = "" then "" else nl)
- ^ "\b> DIVERGENT" ^ nl
- ^ "*: " ^ (match div with None -> "*" | Some div -> print ~l (div :> nf)) ^ "\n| "
- ^ "\b> CONVERGENT" ^ nl
- ^ String.concat "\n| " (List.map (fun t -> "_: " ^ (if t = `N (-1) then "_" else print ~l (t :> nf))) conv) ^
- (if conv = [] then "" else "\n| ")
- ^ "\b> NUMERIC" ^ nl
- ^ String.concat "\n| " (List.mapi (fun i t -> string_of_int i ^ ": " ^ print ~l (t :> nf)) ps)
- ^ nl
+ "measure="^string_of_measure(problem_measure p) (* ^ " freshno = " ^ string_of_int freshno*)
+ ^ nl ^ " Discriminating sets (deltas):"
+ ^ nl ^ " " ^ deltas ^ (if deltas = " " then "" else 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 = convergent_dummy 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 failwithProblem p reason =
- print_endline (print_problem "FAIL" p);
+ print_endline (string_of_problem "FAIL" p);
failwith reason
;;
@@ -84,94 +109,116 @@ let make_fresh_var p arity =
let make_fresh_vars p arities =
List.fold_right
- (* fold_left vs. fold_right hides/shows the bug in problem q7 *)
(fun arity (p, vars) -> let p, var = make_fresh_var p arity in p, var::vars)
arities
(p, [])
;;
let simple_expand_match ps =
- let rec aux level = function
- | #i_num_var as t -> aux_i_num_var level t
+ let rec aux_nob level = function
+ | #i_num_var as t -> (aux_i_num_var level t :> nf)
| `Lam(b,t) -> `Lam(b,aux (level+1) t)
- and aux_i_num_var level = function
+ | `Pacman as t -> t
+ and aux level = function
+ | `Bottom as t -> t
+ | #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 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 ->
- `Match(cast_to_i_num_var u,v,bs_lift,bs,List.map (aux level) args))
- | `I(v,args) -> `I(v,Listx.map (aux level) 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;;
+ in aux_i_num_var 0
+;;
let fixpoint f =
let rec aux x = let x' = f x in if x <> x' then aux x' else x in aux
;;
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}
-exception ExpandedToLambda;;
+let cast_to_ps_with_match =
+ function
+ #i_num_var as y -> (y : i_num_var)
+ | `Bottom | `Pacman -> raise (Backtrack "BOT/PAC in ps")
+ | t ->
+ prerr_endline (print (t :> nf));
+ assert false (* algorithm failed *)
let subst_in_problem x inst ({freshno; div; conv; ps; sigma} as p) =
let len_ps = List.length ps in
(*(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
- let rec aux ((freshno,acc_ps,acc_new_ps) as acc) =
+ let rec aux_ps ((freshno,acc_ps,acc_new_ps) as acc) =
function
| [] -> acc
| t::todo_ps ->
(*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
- let t = subst false x inst (t :> nf) in
+ 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 (freshno,acc_ps@[new_t],acc_new_ps) todo_ps
+ aux_ps (freshno,acc_ps@[new_t],acc_new_ps) todo_ps
(* cut&paste from aux above *)
- and aux' ps ((freshno,acc_conv,acc_new_ps) as acc) =
+ and aux_conv ps ((freshno,acc_conv,acc_new_ps) as acc) =
function
| [] -> acc
| t::todo_conv ->
-(*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
- (* try *)
- let t = subst false x inst (t :> nf) in
+ (*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
+ let t = subst false false x inst (t :> nf) in
(*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
- let freshno,new_t,acc_new_ps =
+ let freshno,new_t,acc_new_ps =
+ try
expand_match (freshno,ps,acc_new_ps) t
- in
- aux' ps (freshno,acc_conv@[new_t],acc_new_ps) todo_conv
- (* with ExpandedToLambda -> aux' ps (freshno,acc_conv@[`N(-1)],acc_new_ps) todo_conv *)
+ with Pacman -> 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 *)
- and aux'' ps (freshno,acc_new_ps) =
+ and aux_div ps (freshno,acc_new_ps) =
function
| None -> freshno, None, acc_new_ps
| Some t ->
- let t = subst false x inst (t :> nf) in
- let freshno,new_t,acc_new_ps =
- expand_match (freshno,ps,acc_new_ps) t
- in
- freshno,Some new_t,acc_new_ps
+ let t = subst false false x inst (t :> nf) in
+ try
+ let freshno,new_t,acc_new_ps = expand_match (freshno,ps,acc_new_ps) t in
+ (* 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
@@ -181,12 +228,12 @@ prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
match u with
| `N i -> acc_new_ps,i
| _ ->
- let ps = List.map (fun t -> cast_to_i_num_var (subst 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
@@ -194,22 +241,24 @@ List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplif
if List.exists (fun (j,_) -> i=j) !bs then
freshno
else
- let freshno,v = freshno+1, `Var (freshno+1, snd orig - 1) in (* make_fresh_var freshno in *)
+ let freshno,v = freshno+1, `Var (freshno+1, -666) in (* make_fresh_var freshno in *)
bs := !bs @ [i, v] ;
freshno in
(*prerr_endlie ("t DA RIDURRE:" ^ print (`Match(`N i,arity,bs_lift,bs,args) :> nf) ^ " more_args=" ^ string_of_int more_args);*)
- let t = mk_match (`N i) orig bs_lift bs args 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 _ -> raise ExpandedToLambda
+ | `Lam _ -> 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 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 freshno,old_ps,new_ps = aux (freshno,[],[]) (ps :> i_num_var list) in
- let freshno,conv,new_ps = aux' old_ps (freshno,[],new_ps) (conv :> i_num_var list) in
- let freshno,div,new_ps = aux'' old_ps (freshno,new_ps) (div :> i_num_var option) in
- let div = option_map cast_to_i_var div 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
@@ -217,11 +266,11 @@ prerr_endline ("# INST: " ^ string_of_var x ^ " := " ^ print ~l inst));
let p = {p with freshno; div; conv; ps} in
( (* check if double substituting a variable *)
if List.exists (fun (x',_) -> x = x') sigma
- then failwithProblem p "Variable replaced twice"
+ then failwithProblem p ("Variable "^ string_of_var x ^"replaced twice")
);
let p = {p with sigma = sigma@[x,inst]} in
let p = super_simplify p in
- prerr_endline (print_problem "instantiate" p);
+ prerr_endline (string_of_problem "instantiate" p);
p
;;
@@ -229,7 +278,7 @@ 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
+ let arity = match y with `Var _ -> 0 | `I(_,args) -> Listx.length args | `N _ -> assert false in
arity + if pos = -1 then - 1 else 0
;;
@@ -237,14 +286,15 @@ let rec dangerous arities showstoppers =
function
`N _
| `Var _
- | `Lam _ -> ()
+ | `Lam _
+ | `Pacman -> ()
| `Match(t,_,liftno,bs,args) ->
(* CSC: XXX partial dependency on the encoding *)
(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 2 (* 2 coming from Scott's encoding *)
- | `I((x,_),args') -> dangerous_inert arities showstoppers x (Listx.to_list args' @ args) 2 (* 2 coming from Scott's encoding *)
+ | `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
)
| `I((k,_),args) -> dangerous_inert arities showstoppers k (Listx.to_list args) 0
@@ -262,26 +312,32 @@ let rec dangerous_conv arities showstoppers =
function
`N _
| `Var _
- | `Lam _ -> []
+ | `Lam _
+ | `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 (* 2 coming from Scott's encoding *)
- | `I((x,_),args') -> dangerous_inert_conv arities showstoppers x (Listx.to_list args' @ args) 2 (* 2 coming from Scott's encoding *)
+ | `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 more_args =
- concat_map (dangerous_conv arities showstoppers) args @
- if List.mem k showstoppers then k :: concat_map free_vars args else
+ | `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 =
+ let all_args = args @ match_args in
+ let dangerous_args = concat_map (dangerous_conv arities showstoppers) all_args in
+ 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)) );
- if List.length args + more_args > arity then k :: concat_map free_vars args else []
+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
(* inefficient algorithm *)
let rec edible arities div ps conv showstoppers =
@@ -301,7 +357,7 @@ let rec edible arities div ps conv showstoppers =
None -> aux showstoppers xs
| Some h ->
try
- dangerous arities showstoppers (x : i_n_var :> nf) ;
+ dangerous arities showstoppers (x : i_n_var :> nf_nob) ;
aux showstoppers xs
with
Dangerous ->
@@ -309,10 +365,11 @@ let rec edible arities div ps conv showstoppers =
in
let showstoppers = sort_uniq (aux showstoppers ps) in
let dangerous_conv =
- List.map (dangerous_conv arities showstoppers) (conv :> nf list) in
+ 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;
- 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' = showstoppers @ List.concat dangerous_conv in
let showstoppers' = sort_uniq (match div with
| None -> showstoppers'
@@ -370,7 +427,7 @@ let eat p =
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 showstoppers in
+ 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
@@ -397,20 +454,10 @@ prerr_endline ("# INST_IN_EAT: " ^ string_of_var x ^ " := " ^ print ~l inst));
then p
else
let n = match div with `I(_,args) -> Listx.length args | `Var _ -> 0 in
- let p, bomb' = make_fresh_var p (-666) in
- (if !bomb <> `Var (-1,-666) then
- failwithProblem p
- ("Bomb was duplicated! It was " ^ string_of_nf !bomb ^
- ", tried to change it to " ^ string_of_nf bomb'));
- bomb := bomb';
- prerr_endline ("Just created bomb var: " ^ string_of_nf !bomb);
let x = hd_of_i_var div in
- let inst = make_lams !bomb n in
- prerr_endline ("# INST (div): " ^ string_of_var x ^ " := " ^ string_of_nf inst);
- let p = {p with div=None} in
- (* subst_in_problem (hd_of_i_var div) inst p in *)
- {p with sigma=p.sigma@[x,inst]} in
- let dangerous_conv = showstoppers_conv 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 conv =
@@ -421,10 +468,10 @@ List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))
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
+ | None -> assert (t = convergent_dummy); t
| Some h ->
prerr_endline ("FREEZING " ^ string_of_var h);
- `N ~-1 (* convergent dummy*)
+ convergent_dummy
) (List.combine showstoppers_conv p.conv) in
List.iter
(fun bs ->
@@ -439,69 +486,98 @@ List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))
let old_conv = p.conv in
let p = { p with ps; conv } in
if l <> [] || old_conv <> conv
- then prerr_endline (print_problem "eat" p);
+ then prerr_endline (string_of_problem "eat" p);
if List.for_all (function `N _ -> true | _ -> false) ps && p.div = None then
`Finished p
else
`Continue p
-let instantiate p x n =
- (if hd_of_i_var (cast_to_i_var !bomb) = x
- then failwithProblem p ("BOMB (" ^ string_of_nf !bomb ^ ") cannot be instantiated!"));
- (* ACL FIXME compute arity of x correctly below! *)
- let arity_of_x = -666 in
- (* AC: FIXME compute arities correctly below! *)
- let arities = Array.to_list (Array.make (n+1) 0) 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 n =
+ let n = (prerr_endline "WARNING: using constant 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
- (* let p,zero = make_fresh_var p in *)
- (* let zero = Listx.Nil zero in *)
- (* let args = if n = 0 then zero else Listx.append zero (Listx.from_list vars) in *)
- let args = Listx.from_list (vars :> nf list) in
+ (* manual lifting of vars by perm in next line *)
+ let vars = List.map (function `Var (n,ar) -> `Var (n+perm,ar)) vars in
+ let args = Listx.from_list vars in
let bs = ref [] in
- let inst = `Lam(false,`Match(`I((0,0),Listx.map (lift 1) args),(x,arity_of_x),1,bs,[])) in
+ (* other_vars are the variables which are delayed and re-applied to the match *)
+ let other_vars = Array.mapi (fun n () -> `Var(n+1,min_int)) (Array.make (perm-1) ()) in
+ let other_vars = Array.to_list other_vars in
+ (* 666, since it will be replaced anyway during subst: *)
+ let inst = `Match(`I((0,min_int),args),(x,-666),perm,bs,other_vars) in
+ (* Add a number of 'perm' leading lambdas *)
+ let inst = Array.fold_left (fun t () -> `Lam(false, t)) inst (Array.make perm ()) in
let p = {p with deltas=bs::p.deltas} in
subst_in_problem x inst p
;;
let compute_special_k tms =
- let rec aux k (t: nf) = Pervasives.max k (match t with
- | `Lam(b,t) -> aux (k + if b then 1 else 0) t
- | `I(n, tms) -> Listx.max (Listx.map (aux 0) tms)
- | `Match(t, _, liftno, bs, args) ->
- List.fold_left max 0 (List.map (aux 0) ((t :> nf)::args@List.map snd !bs))
- | `N _ -> 0
- | `Var _ -> 0
- ) in Listx.max (Listx.map (aux 0) tms)
+ let rec aux k (t: nf) = Pervasives.max k (match t with
+ | `Lam(b,t) -> aux (k + if b then 1 else 0) t
+ | `I(n, tms) -> Listx.max (Listx.map (aux 0) (tms :> nf Listx.listx))
+ | `Match(t, _, liftno, bs, args) ->
+ List.fold_left max 0 (List.map (aux 0) ((t :> nf)::(args :> nf list)@List.map snd !bs))
+ | `N _
+ | `Bottom
+ | `Pacman
+ | `Var _ -> 0
+ ) in Listx.max (Listx.map (aux 0) tms)
;;
-let auto_instantiate (n,p) =
- let p, showstoppers_step, showstoppers_eat = critical_showstoppers p in
+let choose_step (n,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
- | [], [] ->
- let heads = List.sort compare (filter_map (fun t -> match t with `Var _ -> None | x -> hd_of x) ((match p.div with Some t -> [(t :> i_n_var)] | _ -> []) @ p.ps)) in
+ | [], y::_ ->
+ prerr_endline ("INSTANTIATING CRITICAL TO EAT " ^ string_of_var y); y
+ | [], [] ->
+ let heads =
+ (* Choose only variables still alive (with arity > 0) *)
+ List.sort compare (filter_map (
+ fun t -> match t with `Var _ -> None | x -> if arity_of_hd x <= 0 then None else hd_of x
+ ) ((match p.div with Some t -> [(t :> i_n_var)] | _ -> []) @ p.ps)) in
(match heads with
- [] -> assert false
- | x::_ ->
- prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
- x)
+ | [] ->
+ (try
+ fst (List.find (((<) 0) ++ snd) (concat_map free_vars' (p.conv :> nf list)))
+ 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)
+(* 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) (all_terms p)) with
- None -> assert false
+ 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
+ with
+ Not_found ->
+ let arity_of_x = max_arity_tms x (all_terms p) in
+ assert (Util.option_get arity_of_x > 0);
+ 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 =
@@ -518,31 +594,34 @@ in*)
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 ^ ") @@@@");
- let p = instantiate p x special_k in
- special_k,p
+ let arity_of_x = Util.option_get (max_arity_tms x (all_terms p)) in
+ let safe_arity_of_x = safe_arity_of_var p x in
+ x, min arity_of_x safe_arity_of_x, special_k
-
-let rec auto_eat (n,({ps} as p)) =
+let rec auto_eat (n,p) =
prerr_endline "{{{{{{{{ Computing measure before auto_instantiate }}}}}}";
let m = problem_measure p in
- let (n,p') = auto_instantiate (n,p) in
- match eat p' with
- `Finished p -> p
- | `Continue p ->
- prerr_endline "{{{{{{{{ Computing measure inafter auto_instantiate }}}}}}";
- let delta = m - problem_measure p' in
- if delta <= 0 then (
- (* failwithProblem p' *)
- prerr_endline
- ("Measure did not decrease (delta=" ^ string_of_int delta ^ ")"))
- else prerr_endline ("$ Measure decreased by " ^ string_of_int delta);
- auto_eat (n,p)
+ let x, arity_of, n = choose_step (n,p) in
+ first arity_of p x (fun p j ->
+ let p' = instantiate p x j n in
+ match eat p' with
+ | `Finished p -> p
+ | `Continue p ->
+ 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))
;;
let auto p n =
prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
match eat p with
- `Finished p -> p
+ | `Finished p -> p
| `Continue p -> auto_eat (n,p)
;;
@@ -591,10 +670,12 @@ let optimize_numerals p =
let replace_in_sigma perm =
let rec aux = function
| `N n -> `N (List.nth perm n)
+ | `Pacman
| `I _ -> assert false
| `Var _ as t -> t
| `Lam(v,t) -> `Lam(v, aux t)
| `Match(_,_,_,bs,_) as t -> (bs := List.map (fun (n,t) -> (List.nth perm n, t)) !bs); t
+ | `Bottom as t -> t
in List.map (fun (n,t) -> (n,aux t))
in
let deltas' = List.mapi (fun n d -> (n, List.map fst !d)) p.deltas in
@@ -610,7 +691,7 @@ let optimize_numerals p =
replace_in_sigma (List.rev perm) p.sigma
;;
-let env_of_sigma freshno sigma should_explode =
+let env_of_sigma freshno sigma =
let rec aux n =
if n > freshno then
[]
@@ -619,154 +700,159 @@ let env_of_sigma freshno sigma should_explode =
(try
e,Pure.lift (-n-1) (snd (List.find (fun (i,_) -> i = n) sigma)),[]
with
- Not_found ->
- if should_explode && n = hd_of_i_var (cast_to_i_var !bomb)
- then ([], (let f t = Pure.A(t,t) in f (Pure.L (f (Pure.V 0)))), [])
- else ([],Pure.V n,[]))::e
+ 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 ("------- ------ measure=. \n ");
+ 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 "########## main ##########";;
+ prerr_endline "-------------------";
+ 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 "------------------";
+ 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 "-----------------";
+ (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 "-------- --------";
+ p_finale.sigma
+;;
-(* 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 (print_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 ->
- let x = var_of_string x in
- aux (instantiate p x n) n l
- | `Auto -> aux (auto p n) n l
- in
- List.iter
- (fun (p,n,cmds) ->
- Console.print_hline();
- bomb := `Var (-1,-666);
- let p_finale = aux p n cmds in
- let freshno,sigma = p_finale.freshno, p_finale.sigma in
- prerr_endline ("------- ------\n ");
- (* prerr_endline (print_problem "Original problem" p); *)
- prerr_endline "---------------------";
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- prerr_endline (" BOMB == " ^ print ~l !bomb);
- 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 (print_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 "-------------------";
- 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 "------------------";
- let div = option_map (fun div -> ToScott.t_of_nf (div :> nf)) p.div in
- let conv = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.conv in
- let ps = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.ps in
- let sigma = List.map (fun (x,inst) -> x, ToScott.t_of_nf inst) sigma in
- (*let ps_ok = List.fold_left (fun ps (x,inst) ->
- List.map (Pure.subst false x inst) ps) ps sigma in*)
- let e = env_of_sigma freshno sigma true in
- let e' = env_of_sigma freshno sigma false in
+let solve (p, todo) =
+ let completeness, to_run =
+ match todo with
+ | `CompleteUnseparable s -> `Complete, `False s
+ | `CompleteSeparable _ -> `Complete, `True
+ | `Uncomplete -> `Uncomplete, `True in
+ match to_run with
+ | `False s -> completeness, `Unseparable s
+ | `True ->
+ try
+ let sigma = run p in
+ completeness, `Separable sigma
+ with
+ | Backtrack _ -> completeness, `Unseparable "backtrack"
+;;
-(*
- prerr_endline "------------------";
-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 "-----------------";
- (function Some div ->
- print_endline (Pure.print div);
- let t = Pure.mwhd (e',div,[]) in
- prerr_endline ("*:: " ^ (Pure.print t));
- prerr_endline (print !bomb);
- assert (t = ToScott.t_of_nf (!bomb:>nf))
- | 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 "-------- --------"
- ) problems
-
-(********************** problems *******************)
-
-let zero = `Var(0,-1);;
+let check p =
+ (* check if there are duplicates in p.ps *)
+ (* FIXME what about initial fragments? *)
+ if (let rec f = function
+ | [] -> false
+ | hd::tl -> List.exists (eta_eq hd) tl || f tl in
+ f p.ps)
+ 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))
+ ) && false (* TODO no bombs && pacmans *)
+ then `CompleteSeparable "no bombs, pacmans and div"
+ 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 zero = `Var(0,0);;
let append_zero =
function
| `I _
- | `Var _ as i -> cast_to_i_n_var (mk_app i zero)
- | _ -> assert false
+ | `Var _ as i -> cast_to_i_n_var (mk_app i zero)
+ | `N _ -> raise (Parser.ParsingError " numbers in ps")
;;
-type t = problem * int * string list;;
+let tmp (label, div, conv, nums, var_names) =
+ (* DA SPOSTARE NEI TEST: *)
+ let ps = List.map append_zero nums in (* crea lista applicando zeri o dummies *)
+ let ps = sort_uniq ~compare:eta_compare (ps :> nf list) in
+ let ps = List.map (cast_to_i_n_var) ps in
+
+ (* TODO: *)
+ (* replace div with bottom in problem??? *)
+ let all_tms = (match div with None -> [] | Some div -> [(div :> i_n_var)]) @ nums @ conv in
+ if all_tms = [] then failwith "FIXME: 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
+;;
-let magic_conv ~div ~conv ~nums cmds =
+let problem_of ~div ~conv ~nums =
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=[]}, 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 = List.map cast_to_i_n_var 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
-
- {freshno; div; conv; ps; sigma=[] ; deltas}, special_k, cmds
+ let all_tms, var_names = Parser.parse' all_tms in
+ let div, (ps, 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
+
+ let div =
+ match div with
+ | None | Some `Bottom -> None
+ | Some (`I _ as t) -> Some t
+ | _ -> raise (Parser.ParsingError "div is not an inert or BOT in the initial problem") in
+ let conv = Util.filter_map (
+ function
+ | #i_n_var as t -> Some t
+ | `Lam _ -> None
+ | _ -> raise (Parser.ParsingError "A term in conv is not i_n_var")
+ ) conv in
+ let ps = List.map (
+ function
+ | #i_n_var as y -> y
+ | _ -> raise (Parser.ParsingError "A term in num is not i_n_var")
+ ) ps in
+ tmp("missing label", div, conv, ps, var_names)
;;
-
-let magic strings cmds = magic_conv None [] strings cmds;;