adpated the checker to handle coomutative cuts and lazyness

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13365 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 194 insertions, 157 deletions

diff --git a/checker/inductive.ml b/checker/inductive.ml
index c1cee60639..756f434104 100644
--- a/checker/inductive.ml
+++ b/checker/inductive.ml
@@ -402,8 +402,10 @@ type subterm_spec =
   | Dead_code
   | Not_subterm
 
-let spec_of_tree t =
-  if Rtree.eq_rtree (=) t mk_norec then Not_subterm else Subterm(Strict,t)
+let spec_of_tree t = lazy
+  (if Rtree.eq_rtree (=) (Lazy.force t) mk_norec
+   then Not_subterm
+   else Subterm(Strict,Lazy.force t))
 
 let subterm_spec_glb =
   let glb2 s1 s2 =
@@ -427,7 +429,7 @@ type guard_env =
     (* the recarg information of inductive family *)
     recvec  : wf_paths array;
     (* dB of variables denoting subterms *)
-    genv    : subterm_spec list;
+    genv    : subterm_spec Lazy.t list;
   }
 
 let make_renv env minds recarg (kn,tyi) =
@@ -438,7 +440,7 @@ let make_renv env minds recarg (kn,tyi) =
     rel_min = recarg+2;
     inds = minds;
     recvec = mind_recvec;
-    genv = [Subterm(Large,mind_recvec.(tyi))] }
+    genv = [Lazy.lazy_from_val(Subterm(Large,mind_recvec.(tyi)))] }
 
 let push_var renv (x,ty,spec) =
   { renv with
@@ -450,11 +452,11 @@ let assign_var_spec renv (i,spec) =
   { renv with genv = list_assign renv.genv (i-1) spec }
 
 let push_var_renv renv (x,ty) =
-  push_var renv (x,ty,Not_subterm)
+  push_var renv (x,ty,Lazy.lazy_from_val Not_subterm)
 
 (* Fetch recursive information about a variable p *)
 let subterm_var p renv =
-  try List.nth renv.genv (p-1)
+  try Lazy.force (List.nth renv.genv (p-1))
   with Failure _ | Invalid_argument _ -> Not_subterm
 
 (* Add a variable and mark it as strictly smaller with information [spec]. *)
@@ -466,16 +468,25 @@ let push_ctxt_renv renv ctxt =
   { renv with
     env = push_rel_context ctxt renv.env;
     rel_min = renv.rel_min+n;
-    genv = iterate (fun ge -> Not_subterm::ge) n renv.genv }
+    genv = iterate (fun ge -> Lazy.lazy_from_val Not_subterm::ge) n renv.genv }
 
 let push_fix_renv renv (_,v,_ as recdef) =
   let n = Array.length v in
   { renv with
     env = push_rec_types recdef renv.env;
     rel_min = renv.rel_min+n;
-    genv = iterate (fun ge -> Not_subterm::ge) n renv.genv }
+    genv = iterate (fun ge -> Lazy.lazy_from_val Not_subterm::ge) n renv.genv }
 
 
+(* Definition and manipulation of the stack *)
+type stack_element = |SClosure of guard_env*constr |SArg of subterm_spec Lazy.t
+
+let push_stack_closures renv l stack = 
+  List.fold_right (fun h b -> (SClosure (renv,h))::b) l stack
+
+let push_stack_args l stack = 
+  List.fold_right (fun h b -> (SArg h)::b) l stack
+
 (******************************)
 (* Computing the recursive subterms of a term (propagation of size
    information through Cases). *)
@@ -495,36 +506,38 @@ let lookup_subterms env ind =
   let (_,mip) = lookup_mind_specif env ind in
   mip.mind_recargs
 
-(*********************************)
-
-(* Propagation of size information through Cases: if the matched
-   object is a recursive subterm then compute the information
-   associated to its own subterms.
-   Rq: if branch is not eta-long, then the recursive information
-   is not propagated to the missing abstractions *)
-let case_branches_specif renv c_spec ind lbr =
-  let rec push_branch_args renv lrec c =
-    match lrec with
-        ra::lr ->
-          let c' = whd_betadeltaiota renv.env c in
-          (match c' with
-              Lambda(x,a,b) ->
-                let renv' = push_var renv (x,a,ra) in
-                push_branch_args renv' lr b
-            | _ -> (* branch not in eta-long form: cannot perform rec. calls *)
-                (renv,c'))
-      | [] -> (renv, c) in
-  match c_spec with
-      Subterm (_,t) ->
-        let sub_spec = Array.map (List.map spec_of_tree) (dest_subterms t) in
-        assert (Array.length sub_spec = Array.length lbr);
-        array_map2 (push_branch_args renv) sub_spec lbr
-    | Dead_code ->
-        let t = dest_subterms (lookup_subterms renv.env ind) in
-        let sub_spec = Array.map (List.map (fun _ -> Dead_code)) t in
-        assert (Array.length sub_spec = Array.length lbr);
-        array_map2 (push_branch_args renv) sub_spec lbr
-    | Not_subterm -> Array.map (fun c -> (renv,c)) lbr
+let match_inductive ind ra =
+  match ra with
+    | (Mrec i | Imbr i) -> eq_ind ind i
+    | Norec -> false
+
+(* In {match c as z in ci y_s return P with |C_i x_s => t end}
+   [branches_specif renv c_spec ci] returns an array of x_s specs knowing
+   c_spec. *)
+let branches_specif renv c_spec ci =
+  let car = 
+    (* We fetch the regular tree associated to the inductive of the match.
+       This is just to get the number of constructors (and constructor
+       arities) that fit the match branches without forcing c_spec.
+       Note that c_spec might be more precise than [v] below, because of
+       nested inductive types. *)
+    let (_,mip) = lookup_mind_specif renv.env ci.ci_ind in
+    let v = dest_subterms mip.mind_recargs in
+      Array.map List.length v in
+    Array.mapi
+      (fun i nca -> (* i+1-th cstructor has arity nca *)
+	 let lvra = lazy 
+	   (match Lazy.force c_spec with
+		Subterm (_,t) when match_inductive ci.ci_ind (dest_recarg t) ->
+		  let vra = Array.of_list (dest_subterms t).(i) in
+		  assert (nca = Array.length vra);
+		  Array.map
+		    (fun t -> Lazy.force (spec_of_tree (lazy t)))
+		    vra
+	      | Dead_code -> Array.create nca Dead_code
+	      | _ -> Array.create nca Not_subterm) in
+	 list_tabulate (fun j -> lazy (Lazy.force lvra).(j)) nca)
+      car 
 
 (* [subterm_specif renv t] computes the recursive structure of [t] and
    compare its size with the size of the initial recursive argument of
@@ -532,72 +545,88 @@ let case_branches_specif renv c_spec ind lbr =
    about variables.
 *)
 
-let rec subterm_specif renv t =
+
+let rec subterm_specif renv stack t =
   (* maybe reduction is not always necessary! *)
   let f,l = decompose_app (whd_betadeltaiota renv.env t) in
-  match f with
-    | Rel k -> subterm_var k renv
-
-    | Case (ci,_,c,lbr) ->
-        if Array.length lbr = 0 then Dead_code
-        else
-          let c_spec = subterm_specif renv c in
-          let lbr_spec = case_branches_specif renv c_spec ci.ci_ind lbr in
-          let stl  =
-            Array.map (fun (renv',br') -> subterm_specif renv' br')
-              lbr_spec in
-          subterm_spec_glb stl
-
-    | Fix ((recindxs,i),(_,typarray,bodies as recdef)) ->
-(* when proving that the fixpoint f(x)=e is less than n, it is enough
-   to prove that e is less than n assuming f is less than n
-   furthermore when f is applied to a term which is strictly less than
-   n, one may assume that x itself is strictly less than n
-*)
-        let (ctxt,clfix) = dest_prod renv.env typarray.(i) in
-        let oind =
-          let env' = push_rel_context ctxt renv.env in
-          try Some(fst(find_inductive env' clfix))
-          with Not_found -> None in
-        (match oind with
-            None -> Not_subterm (* happens if fix is polymorphic *)
-          | Some ind ->
-              let nbfix = Array.length typarray in
-              let recargs = lookup_subterms renv.env ind in
-              (* pushing the fixpoints *)
-              let renv' = push_fix_renv renv recdef in
-              let renv' =
-                (* Why Strict here ? To be general, it could also be
-                   Large... *)
-                assign_var_spec renv' (nbfix-i, Subterm(Strict,recargs)) in
-              let decrArg = recindxs.(i) in
-              let theBody = bodies.(i)   in
-              let nbOfAbst = decrArg+1 in
-              let sign,strippedBody = decompose_lam_n_assum nbOfAbst theBody in
-              (* pushing the fix parameters *)
-              let renv'' = push_ctxt_renv renv' sign in
-              let renv'' =
-                if List.length l < nbOfAbst then renv''
-                else
-                  let theDecrArg  = List.nth l decrArg in
-	          let arg_spec    = subterm_specif renv theDecrArg in
-                  assign_var_spec renv'' (1, arg_spec) in
-	      subterm_specif renv'' strippedBody)
-
-    | Lambda (x,a,b) ->
-        assert (l=[]);
-        subterm_specif (push_var_renv renv (x,a)) b
-
-    (* Metas and evars are considered OK *)
-    | (Meta _|Evar _) -> Dead_code
+    match f with
+      | Rel k -> subterm_var k renv
 
-    (* Other terms are not subterms *)
-    | _ -> Not_subterm
-
-
-(* Check term c can be applied to one of the mutual fixpoints. *)
-let check_is_subterm renv c =
-  match subterm_specif renv c with
+      | Case (ci,_,c,lbr) ->
+	  let stack' = push_stack_closures renv l stack in
+          let cases_spec = branches_specif renv 
+	    (lazy_subterm_specif renv [] c) ci in
+          let stl  =
+            Array.mapi (fun i br' ->
+			  let stack_br = push_stack_args (cases_spec.(i)) stack' in
+			    subterm_specif renv stack_br br')
+              lbr in
+            subterm_spec_glb stl
+
+      | Fix ((recindxs,i),(_,typarray,bodies as recdef)) ->
+	  (* when proving that the fixpoint f(x)=e is less than n, it is enough
+	     to prove that e is less than n assuming f is less than n
+	     furthermore when f is applied to a term which is strictly less than
+	     n, one may assume that x itself is strictly less than n
+	  *)
+          let (ctxt,clfix) = dest_prod renv.env typarray.(i) in
+          let oind =
+            let env' = push_rel_context ctxt renv.env in
+              try Some(fst(find_inductive env' clfix))
+              with Not_found -> None in
+            (match oind with
+		 None -> Not_subterm (* happens if fix is polymorphic *)
+               | Some ind ->
+		   let nbfix = Array.length typarray in
+		   let recargs = lookup_subterms renv.env ind in
+		     (* pushing the fixpoints *)
+		   let renv' = push_fix_renv renv recdef in
+		   let renv' =
+                     (* Why Strict here ? To be general, it could also be
+			Large... *)
+                     assign_var_spec renv'
+		       (nbfix-i, lazy (Subterm(Strict,recargs))) in
+		   let decrArg = recindxs.(i) in
+		   let theBody = bodies.(i)   in
+		   let nbOfAbst = decrArg+1 in
+		   let sign,strippedBody = decompose_lam_n_assum nbOfAbst theBody in
+		     (* pushing the fix parameters *)
+		   let stack' = push_stack_closures renv l stack in
+		   let renv'' = push_ctxt_renv renv' sign in
+		   let renv'' =
+                     if List.length stack' < nbOfAbst then renv''
+                     else
+		       let decrArg = List.nth stack' decrArg in
+                       let arg_spec = stack_element_specif decrArg in
+			 assign_var_spec renv'' (1, arg_spec) in
+		     subterm_specif renv'' [] strippedBody)
+
+      | Lambda (x,a,b) ->
+          assert (l=[]);
+	  let spec,stack' = extract_stack renv a stack in
+	    subterm_specif (push_var renv (x,a,spec)) stack' b
+
+      (* Metas and evars are considered OK *)
+      | (Meta _|Evar _) -> Dead_code
+
+      (* Other terms are not subterms *)
+      | _ -> Not_subterm
+
+and lazy_subterm_specif renv stack t =
+  lazy (subterm_specif renv stack t)
+
+and stack_element_specif = function
+  |SClosure (h_renv,h) -> lazy_subterm_specif h_renv [] h
+  |SArg x -> x
+
+and extract_stack renv a = function
+  | [] -> Lazy.lazy_from_val Not_subterm , []
+  | h::t -> stack_element_specif h, t
+
+
+(* Check size x is a correct size for recursive calls. *)
+let check_is_subterm x =
+  match Lazy.force x with
     Subterm (Strict,_) | Dead_code -> true
   |  _ -> false
 
@@ -605,17 +634,18 @@ let check_is_subterm renv c =
 
 exception FixGuardError of env * guard_error
 
-let error_illegal_rec_call renv fx arg =
+let error_illegal_rec_call renv fx (arg_renv,arg) =
   let (_,le_vars,lt_vars) =
     List.fold_left
       (fun (i,le,lt) sbt ->
-        match sbt with
+        match Lazy.force sbt with
             (Subterm(Strict,_) | Dead_code) -> (i+1, le, i::lt)
           | (Subterm(Large,_)) -> (i+1, i::le, lt)
           | _ -> (i+1, le ,lt))
       (1,[],[]) renv.genv in
   raise (FixGuardError (renv.env,
-                        RecursionOnIllegalTerm(fx,arg,le_vars,lt_vars)))
+                        RecursionOnIllegalTerm(fx,(arg_renv.env, arg),
+					       le_vars,lt_vars)))
 
 let error_partial_apply renv fx =
   raise (FixGuardError (renv.env,NotEnoughArgumentsForFixCall fx))
@@ -627,49 +657,57 @@ let check_one_fix renv recpos def =
   let nfi = Array.length recpos in
 
   (* Checks if [t] only make valid recursive calls *)
-  let rec check_rec_call renv t =
+  let rec check_rec_call renv stack t =
     (* if [t] does not make recursive calls, it is guarded: *)
     if noccur_with_meta renv.rel_min nfi t then ()
     else
-      let (f,l) = decompose_app (whd_betaiotazeta renv.env t) in
+      let (f,l) = decompose_app (whd_betaiotazeta t) in
       match f with
         | Rel p ->
             (* Test if [p] is a fixpoint (recursive call) *)
 	    if renv.rel_min <= p & p < renv.rel_min+nfi then
               begin
-                List.iter (check_rec_call renv) l;
+                List.iter (check_rec_call renv []) l;
                 (* the position of the invoked fixpoint: *)
 	        let glob = renv.rel_min+nfi-1-p in
                 (* the decreasing arg of the rec call: *)
 	        let np = recpos.(glob) in
-                if List.length l <= np then error_partial_apply renv glob
+		let stack' = push_stack_closures renv l stack in
+                if List.length stack' <= np then error_partial_apply renv glob
                 else
                   (* Check the decreasing arg is smaller *)
-                  let z = List.nth l np in
-	          if not (check_is_subterm renv z) then
-                    error_illegal_rec_call renv glob z
+                  let z = List.nth stack' np in
+	          if not (check_is_subterm (stack_element_specif z)) then
+                    begin match z with
+		      |SClosure (z,z') -> error_illegal_rec_call renv glob (z,z') 
+		      |SArg _ -> error_partial_apply renv glob
+		    end
               end
             else
               begin
                 match pi2 (lookup_rel p renv.env) with
                 | None ->
-                    List.iter (check_rec_call renv) l
+                    List.iter (check_rec_call renv []) l
                 | Some c ->
-                    try List.iter (check_rec_call renv) l
-                    with FixGuardError _ -> check_rec_call renv (applist(c,l))
+                    try List.iter (check_rec_call renv []) l
+                    with FixGuardError _ ->
+                      check_rec_call renv stack (applist(lift p c,l))
               end
-
+		
         | Case (ci,p,c_0,lrest) ->
-            List.iter (check_rec_call renv) (c_0::p::l);
+            List.iter (check_rec_call renv []) (c_0::p::l);
             (* compute the recarg information for the arguments of
                each branch *)
-            let c_spec = subterm_specif renv c_0 in
-            let lbr = case_branches_specif renv c_spec ci.ci_ind lrest in
-            Array.iter (fun (renv',br') -> check_rec_call renv' br') lbr
+            let case_spec = branches_specif renv 
+	      (lazy_subterm_specif renv [] c_0) ci in
+	    let stack' = push_stack_closures renv l stack in
+              Array.iteri (fun k br' -> 
+			     let stack_br = push_stack_args case_spec.(k) stack' in
+			     check_rec_call renv stack_br br') lrest
 
         (* Enables to traverse Fixpoint definitions in a more intelligent
            way, ie, the rule :
-           if - g = Fix g/p := [y1:T1]...[yp:Tp]e &
+           if - g = fix g (y1:T1)...(yp:Tp) {struct yp} := e &
               - f is guarded with respect to the set of pattern variables S
                 in a1 ... am        &
               - f is guarded with respect to the set of pattern variables S
@@ -679,81 +717,80 @@ let check_one_fix renv recpos def =
                 S+{yp} in e
            then f is guarded with respect to S in (g a1 ... am).
            Eduardo 7/9/98 *)
-
         | Fix ((recindxs,i),(_,typarray,bodies as recdef)) ->
-            List.iter (check_rec_call renv) l;
-            Array.iter (check_rec_call renv) typarray;
+            List.iter (check_rec_call renv []) l;
+            Array.iter (check_rec_call renv []) typarray;
             let decrArg = recindxs.(i) in
             let renv' = push_fix_renv renv recdef in
-            if (List.length l < (decrArg+1)) then
-	      Array.iter (check_rec_call renv') bodies
-            else
+	    let stack' = push_stack_closures renv l stack in
               Array.iteri
                 (fun j body ->
-                  if i=j then
-                    let theDecrArg  = List.nth l decrArg in
-	            let arg_spec = subterm_specif renv theDecrArg in
-	            check_nested_fix_body renv' (decrArg+1) arg_spec body
-                  else check_rec_call renv' body)
+                   if i=j && (List.length stack' > decrArg) then
+		     let recArg = List.nth stack' decrArg in
+	             let arg_sp = stack_element_specif recArg in
+	             check_nested_fix_body renv' (decrArg+1) arg_sp body
+                   else check_rec_call renv' [] body)
                 bodies
 
         | Const kn ->
             if evaluable_constant kn renv.env then
-              try List.iter (check_rec_call renv) l
+              try List.iter (check_rec_call renv []) l
               with (FixGuardError _ ) ->
-	        check_rec_call renv(applist(constant_value renv.env kn, l))
-	    else List.iter (check_rec_call renv) l
-
-        (* The cases below simply check recursively the condition on the
-           subterms *)
-        | Cast (a,_, b) ->
-            List.iter (check_rec_call renv) (a::b::l)
+		let value = (applist(constant_value renv.env kn, l)) in
+	        check_rec_call renv stack value
+	    else List.iter (check_rec_call renv []) l
 
         | Lambda (x,a,b) ->
-            List.iter (check_rec_call renv) (a::l);
-            check_rec_call (push_var_renv renv (x,a)) b
+	    assert (l = []);
+	    check_rec_call renv [] a ;
+	    let spec, stack' = extract_stack renv a stack in
+	    check_rec_call (push_var renv (x,a,spec)) stack' b
 
         | Prod (x,a,b) ->
-            List.iter (check_rec_call renv) (a::l);
-            check_rec_call (push_var_renv renv (x,a)) b
+	    assert (l = [] && stack = []);
+            check_rec_call renv [] a;
+            check_rec_call (push_var_renv renv (x,a)) [] b
 
         | CoFix (i,(_,typarray,bodies as recdef)) ->
-            List.iter (check_rec_call renv) l;
-	    Array.iter (check_rec_call renv) typarray;
+            List.iter (check_rec_call renv []) l;
+	    Array.iter (check_rec_call renv []) typarray;
 	    let renv' = push_fix_renv renv recdef in
-	    Array.iter (check_rec_call renv') bodies
+	    Array.iter (check_rec_call renv' []) bodies
 
-        | (Ind _ | Construct _ | Sort _) ->
-            List.iter (check_rec_call renv) l
+        | (Ind _ | Construct _) ->
+            List.iter (check_rec_call renv []) l
 
         | Var id ->
             begin
               match pi2 (lookup_named id renv.env) with
               | None ->
-                  List.iter (check_rec_call renv) l
+                  List.iter (check_rec_call renv []) l
               | Some c ->
-                  try List.iter (check_rec_call renv) l
-                  with (FixGuardError _) -> check_rec_call renv (applist(c,l))
+                  try List.iter (check_rec_call renv []) l
+                  with (FixGuardError _) -> 
+		    check_rec_call renv stack (applist(c,l))
             end
 
+	| Sort _ -> assert (l = [])
+
         (* l is not checked because it is considered as the meta's context *)
         | (Evar _ | Meta _) -> ()
 
-        | (App _|LetIn _) -> assert false (* beta zeta reduction *)
+        | (App _ | LetIn _ | Cast _) -> assert false (* beta zeta reduction *)
 
   and check_nested_fix_body renv decr recArgsDecrArg body =
     if decr = 0 then
-      check_rec_call (assign_var_spec renv (1,recArgsDecrArg)) body
+      check_rec_call (assign_var_spec renv (1,recArgsDecrArg)) [] body
     else
       match body with
 	| Lambda (x,a,b) ->
-	    check_rec_call renv a;
+	    check_rec_call renv [] a;
             let renv' = push_var_renv renv (x,a) in
-	    check_nested_fix_body renv' (decr-1) recArgsDecrArg b
+	      check_nested_fix_body renv' (decr-1) recArgsDecrArg b
 	| _ -> anomaly "Not enough abstractions in fix body"
-
+	    
   in
-  check_rec_call renv def
+  check_rec_call renv [] def
 
 
 let inductive_of_mutfix env ((nvect,bodynum),(names,types,bodies as recdef)) =