From: acondolu <andrea.condoluci@unibo.it>
Date: Sat, 9 Jun 2018 08:27:14 +0000 (+0200)
Subject: Added garbage to L
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=b532f22eeae82f364dbc533926ea657df765d1e8;p=fireball-separation.git

Added garbage to L

Note: eta_eq ignores garbage at the moment
---

diff --git a/ocaml/simple.ml b/ocaml/simple.ml
index 897d6b6..a028b1f 100644
--- a/ocaml/simple.ml
+++ b/ocaml/simple.ml
@@ -10,11 +10,11 @@ type var = int;;
 type t =
  | V of var
  | A of t * t
- | L of t
+ | L of (t * t list (*garbage*))
  | C (* constant *)
 ;;
 
-let delta = L(A(V 0, V 0));;
+let delta = L(A(V 0, V 0),[]);;
 
 let rec is_stuck = function
  | C -> true
@@ -25,9 +25,9 @@ let rec is_stuck = function
 let eta_eq' =
  let rec aux l1 l2 t1 t2 = match t1, t2 with
   | _, _ when is_stuck t1 || is_stuck t2 -> true
-  | L t1, L t2 -> aux l1 l2 t1 t2
-  | L t1, t2 -> aux l1 (l2+1) t1 t2
-  | t1, L t2 -> aux (l1+1) l2 t1 t2
+  | L t1, L t2 -> aux l1 l2 (fst t1) (fst t2)
+  | L t1, t2 -> aux l1 (l2+1) (fst t1) t2
+  | t1, L t2 -> aux (l1+1) l2 t1 (fst t2)
   | V a, V b -> a + l1 = b + l2
   | A(t1,t2), A(u1,u2) -> aux l1 l2 t1 u1 && aux l1 l2 t2 u2
   | _, _ -> false
@@ -37,14 +37,14 @@ let eta_eq = eta_eq' 0 0;;
 (* is arg1 eta-subterm of arg2 ? *)
 let eta_subterm u =
  let rec aux lev t = if t = C then false else (eta_eq' lev 0 u t || match t with
- | L t -> aux (lev+1) t
+ | L(t,g) -> List.exists (aux (lev+1)) (t::g)
  | A(t1, t2) -> aux lev t1 || aux lev t2
  | _ -> false) in
  aux 0
 ;;
 
 (* does NOT lift the argument *)
-let mk_lams = fold_nat (fun x _ -> L x) ;;
+let mk_lams = fold_nat (fun x _ -> L(x,[])) ;;
 
 let string_of_t =
   let string_of_bvar =
@@ -61,7 +61,8 @@ let string_of_t =
     | A(t1,t2) -> string_of_term_no_pars_app level t1 ^ " " ^ string_of_term_w_pars level t2
     | _ as t -> string_of_term_w_pars level t
   and string_of_term_no_pars level = function
-    | L t -> "λ" ^ string_of_bvar level ^ ". " ^ string_of_term_no_pars (level+1) t
+    | L(t,g) -> "λ" ^ string_of_bvar level ^ ". " ^ string_of_term_no_pars (level+1) t
+       ^ (if g = [] then "" else String.concat ", " ("" :: List.map (string_of_term_w_pars level) g))
     | _ as t -> string_of_term_no_pars_app level t
   in string_of_term_no_pars 0
 ;;
@@ -111,7 +112,7 @@ let rec is_constant =
     C -> true
   | V _ -> false
   | A(t,_)
-  | L t -> is_constant t
+  | L(t,_) -> is_constant t
 ;;
 
 let rec get_inert = function
@@ -133,7 +134,7 @@ let args_of_inert =
 (* precomputes the number of leading lambdas in a term,
    after replacing _v_ w/ a term starting with n lambdas *)
 let rec no_leading_lambdas v n = function
- | L t -> 1 + no_leading_lambdas (v+1) n t
+ | L(t,_) -> 1 + no_leading_lambdas (v+1) n t
  | A _ as t -> let v', m = get_inert t in if V v = v' then max 0 (n - m) else 0
  | V v' -> if v = v' then n else 0
  | C -> 0
@@ -141,22 +142,29 @@ let rec no_leading_lambdas v n = function
 
 let rec subst level delift sub =
  function
- | V v -> if v = level + fst sub then lift level (snd sub) else V (if delift && v > level then v-1 else v)
- | L t -> let t = subst (level + 1) delift sub t in if t = B then B else L t
+ | V v -> (if v = level + fst sub then lift level (snd sub) else V (if delift && v > level then v-1 else v)), []
+ | L x -> let t, g = subst_in_lam (level+1) delift sub x in L(t, g), []
  | A (t1,t2) ->
-  let t1 = subst level delift sub t1 in
-  let t2 = subst level delift sub t2 in
-  mk_app t1 t2
- | C -> C
+  let t1, g1 = subst level delift sub t1 in
+  let t2, g2 = subst level delift sub t2 in
+  let t3, g3 = mk_app t1 t2 in
+  t3, g1 @ g2 @ g3
+ | C -> C, []
+and subst_in_lam level delift sub (t, g) =
+  let t', g' = subst level delift sub t in
+  let g'' = List.fold_left
+   (fun xs t ->
+     let x,y = subst level delift sub t in
+     (x :: y @ xs)) g' g in t', g''
 and mk_app t1 t2 = if t1 = delta && t2 = delta then raise B
  else match t1 with
- | L t1 -> subst 0 true (0, t2) t1
- | _ -> A (t1, t2)
+ | L x -> subst_in_lam 0 true (0, t2) x
+ | _ -> A (t1, t2), []
 and lift n =
  let rec aux lev =
   function
   | V m -> V (if m >= lev then m + n else m)
-  | L t -> L (aux (lev+1) t)
+  | L(t,g) -> L (aux (lev+1) t, List.map (aux (lev+1)) g)
   | A (t1, t2) -> A (aux lev t1, aux lev t2)
   | C -> C
  in aux 0
@@ -165,29 +173,36 @@ let subst = subst 0 false;;
 
 let subst_in_problem ((v, t) as sub) p =
 print_endline ("-- SUBST " ^ string_of_t (V v) ^ " |-> " ^ string_of_t t);
- {p with
-  div=subst sub p.div;
-  conv=subst sub p.conv;
-  sigma=sub::p.sigma}
+ let sigma = sub :: p.sigma in
+ let div, g = try subst sub p.div with B -> raise (Done sigma) in
+ assert (g = []);
+ let conv, f = try subst sub p.conv with B -> raise (Fail(-1, "p.conv diverged")) in
+ assert (g = []);
+ {p with div; conv; sigma}
 ;;
 
 let get_subterms_with_head hd_var =
- let rec aux lev inert_done = function
- | L t -> aux (lev+1) false t
- | C | V _ -> []
+ let rec aux lev inert_done g = function
+ | L(t,g') -> List.fold_left (aux (lev+1) false) g (t::g')
+ | C | V _ -> g
  | A(t1,t2) as t ->
    let hd_var', n_args' = get_inert t1 in
    if not inert_done && hd_var' = V (hd_var + lev)
-    then lift ~-lev t :: aux lev true t1 @ aux lev false t2
-    else aux lev true t1 @ aux lev false t2
- in aux 0 false
+    then lift ~-lev t :: aux lev false (aux lev true g t1) t2
+    else                 aux lev false (aux lev true g t1) t2
+ in aux 0 false []
 ;;
 
-let rec purify = function
- | L t -> Pure.L (purify t)
- | A (t1,t2) -> Pure.A (purify t1, purify t2)
- | V n -> Pure.V n
+let purify =
+ let rec aux = function
+ | L(t,g) ->
+    let t = aux (lift (List.length g) t) in
+    let t = List.fold_left (fun t g -> Pure.A(Pure.L t, aux g)) t g in
+    Pure.L t
+ | A (t1,t2) -> Pure.A (aux t1, aux t2)
+ | V n -> Pure.V (n)
  | C -> Pure.V (min_int/2)
+ in aux
 ;;
 
 let check p sigma =
@@ -252,7 +267,7 @@ let compute_max_lambdas_at hd_var j =
         then let hd', j' = get_inert t2 in j - j'
         else no_leading_lambdas hd_var j t2)
       else id) (max (aux hd t1) (aux hd t2))
- | L t -> aux (hd+1) t
+ | L(t,_) -> aux (hd+1) t
  | V _ | C -> 0
  in aux hd_var
 ;;
@@ -296,7 +311,7 @@ let finish p =
  let compute_max_arity =
    let rec aux n = function
    | A(t1,t2) -> max (aux (n+1) t1) (aux 0 t2)
-   | L t -> max n (aux 0 t)
+   | L(t,g) -> List.fold_right (max ++ (aux 0)) (t::g) 0
    | _ -> n
  in aux 0 in
 print_cmd "FINISH" "";