6 let debug_display_arities = false;;
8 (************ Syntax ************************************)
12 (* Var n = n-th De Bruijn index, 0-based *)
21 type var = int * (* arity of variable*) int;;
22 type 'nf_nob i_var_ = [ `I of var * 'nf_nob Listx.listx | `Var of var ]
23 type 'nf_nob i_n_var_ = [ `N of int | 'nf_nob i_var_ ]
24 type ('nf_nob,'nf) i_num_var_ = [
26 | `Match of ('nf_nob,'nf) i_num_var_ * (* originating var *) var * (*lift*) int * (*branches*)(int * 'nf) list ref * (*args*)'nf_nob list
28 type 'nf nf_nob_ = [ `Lam of (* was_unpacked *) bool * 'nf | `Pacman | ('nf nf_nob_,'nf) i_num_var_ ]
29 type nf = [ nf nf_nob_ | `Bottom ]
30 type nf_nob = nf nf_nob_
31 type i_var = nf_nob i_var_;;
32 type i_n_var = nf_nob i_n_var_;;
33 type i_num_var = (nf_nob,nf) i_num_var_;;
45 | `Match _ -> assert false
54 let aux_var l (n, ar) = (if n < l then n else n+m), ar in
55 let rec aux_i_num_var l =
57 `I(v,args) -> `I(aux_var l v, Listx.map (aux_nob l) args)
58 | `Var v -> `Var(aux_var l v)
60 | `Match(t,v,lift,bs,args) ->
61 `Match(aux_i_num_var l t, v, lift + m, bs, List.map (aux_nob l) args)
64 #i_num_var as x -> (aux_i_num_var l x :> nf_nob)
65 | `Lam(b,nf) -> `Lam (b, aux (l+1) nf)
69 #nf_nob as x -> (aux_nob l x :> nf)
75 (* put t under n lambdas, lifting t accordingtly *)
79 | n when n > 0 -> `Lam (false, lift 1 (make_lams t (n-1)))
83 let rec aux n = function
85 | `Var(x,ar) -> if x < n then [] else [(x-n,ar)]
87 (if x < n then [] else [(x-n,ar)]) @
88 List.concat (List.map (aux n) (Listx.to_list args :> nf list))
89 | `Lam(_,t) -> aux (n+1) t
90 | `Match(t,_,liftno,bs,args) ->
92 List.concat (List.map (fun (_,t) -> aux (n-liftno) t) !bs) @
93 List.concat (List.map (aux n) (args :> nf list))
94 | `Bottom | `Pacman -> []
97 let free_vars = (List.map fst) ++ free_vars';;
102 let rec scott_of_nf = function
103 | `N n -> Scott.mk_n n
104 | `Var(v,_) -> Pure.V v
105 | `Match(t,_,liftno,bs,args) ->
106 let bs = List.map (fun (n,t) -> n, scott_of_nf (lift liftno (t :> nf))) !bs in
107 let t = scott_of_nf (t :> nf) in
108 let m = Scott.mk_match t bs in
109 List.fold_left (fun acc t -> Pure.A(acc,scott_of_nf t)) m (args :> nf list)
110 | `I((v,_), args) -> Listx.fold_left (fun acc t -> Pure.A(acc,scott_of_nf t)) (Pure.V v) (args :> nf Listx.listx)
111 | `Lam(_,t) -> Pure.L (scott_of_nf t)
113 | `Pacman -> let f x = Pure.A (x,x) in f (Pure.L (Pure.L (f (Pure.V 0))))
117 (************ Pretty-printing ************************************)
119 (* let rec string_of_term l = fun _ -> "";; *)
121 let rec string_of_term =
122 let boundvar x = "v" ^ string_of_int x in
123 let varname lev l n =
124 if n < lev then boundvar (lev-n-1)
125 else if n < List.length l then List.nth l (n-lev)
126 else "`" ^ string_of_int (n-lev) in
127 let rec string_of_term_w_pars lev l = function
128 | `Var(n,ar) -> varname lev l n ^ (if debug_display_arities then ":" ^ string_of_int ar else "")
129 | `N n -> string_of_int n
130 | `I _ as t -> "(" ^ string_of_term_no_pars_app lev l t ^ ")"
131 | `Lam(_,`Bottom) -> "BOMB"
132 | `Lam _ as t -> "(" ^ string_of_term_no_pars_lam lev l t ^ ")"
133 | `Match(t,(v,ar),bs_lift,bs,args) ->
134 (* assert (bs_lift = lev); *)
135 "(["^ varname lev l v ^ (if debug_display_arities then ":"^ string_of_int ar else "") ^",match " ^ string_of_term_no_pars lev l (t :> nf) ^
136 " with " ^ String.concat " | " (List.map (fun (n,t) -> string_of_int n ^ " => " ^ string_of_term l (t :> nf)) !bs) ^ "] " ^
137 String.concat " " (List.map (string_of_term l) (args :> nf list)) ^ ")"
140 and string_of_term_no_pars_app lev l = function
141 | `I((n,ar), args) -> varname lev l n ^ (if debug_display_arities then ":" ^ string_of_int ar else "") ^ " " ^ String.concat " " (List.map (string_of_term_w_pars lev l) (Listx.to_list args :> nf list))
142 | #nf as t -> string_of_term_w_pars lev l t
143 and string_of_term_no_pars_lam lev l = function
144 | `Lam(_,`Bottom) -> "BOMB"
145 | `Lam(_,t) -> "λ" ^ boundvar lev ^ ". " ^ (string_of_term_no_pars_lam (lev+1) l t)
146 | _ as t -> string_of_term_no_pars lev l t
147 and string_of_term_no_pars lev l = function
148 | `Lam _ as t -> string_of_term_no_pars_lam lev l t
149 | #nf as t -> string_of_term_no_pars_app lev l t
150 in string_of_term_no_pars 0
153 let print ?(l=[]) = string_of_term l;;
154 let string_of_nf t = string_of_term [] (t :> nf);;
156 (************ Hereditary substitutions ************************************)
160 #i_var as y -> (y : i_var)
162 prerr_endline (print (t :> nf));
163 assert false (* algorithm failed *)
165 let cast_to_i_n_var =
167 #i_n_var as y -> (y : i_n_var)
169 prerr_endline (print (t :> nf));
170 assert false (* algorithm failed *)
172 let cast_to_i_num_var =
174 #i_num_var as y -> (y : i_num_var)
176 prerr_endline (print (t :> nf));
177 assert false (* algorithm failed *)
179 let rec set_arity arity = function
180 (* FIXME because onlt variables should be in branches of matches, one day *)
181 | `Var(n,_) -> `Var(n,arity)
182 | `N _ | `Bottom | `Pacman as t -> t
183 | `Lam(false, t) -> `Lam(false, set_arity arity t)
184 | `Match(t,(n,_),bs_lift,bs,args) -> `Match(t,(n,arity),bs_lift,bs,args)
185 | `I _ | `Lam _ -> assert false
187 let minus1 n = if n = min_int then n else n - 1;;
189 let rec mk_app (h : nf) (arg : nf) =
194 | `I(v,args) -> `I(v,Listx.append (Listx.Nil arg) args)
195 | `Var v -> `I(v, Listx.Nil arg)
196 | `Lam(truelam,nf) -> subst truelam true 0 arg (nf : nf) (* AC FIXME sanity check on arity *)
197 | `Match(t,v,lift,bs,args) -> `Match(t,v,lift,bs,List.append args [arg])
198 | `Bottom | `Pacman as t -> t
199 | `N _ -> assert false (* Numbers cannot be applied *)
200 (*in let l = ["v0";"v1";"v2"] in
201 prerr_endline ("mk_app h:" ^ print ~l h ^ " arg:" ^ print ~l:l arg ^ " res:" ^ print ~l:l res); res*)
204 (*prerr_endline ("MK_APPL: " ^ print h ^ " " ^ String.concat " " (List.map print args));*)
205 List.fold_left mk_app h args
207 and mk_appx h args = Listx.fold_left mk_app h args
209 and mk_match t (n,ar) bs_lift bs args =
210 (*prerr_endline ("MK_MATCH: ([" ^ print t ^ "] " ^ String.concat " " (Listx.to_list (Listx.map (fun (n,t) -> string_of_int n ^ " => " ^ print t) bs)) ^ ") " ^ String.concat " " (List.map print args));*)
215 let h = List.assoc m !bs in
216 let h = set_arity (minus1 ar) h in
217 let h = lift bs_lift h in
220 `Match (t,(n,ar),bs_lift,bs,[]))
221 (* We are assuming that the econding of matches is s.t.:
222 - match PAC.. --> PAC
223 - match BOT.. --> BOT *)
226 | `Lam _ -> assert false
227 | `I _ | `Var _ | `Match _ as t -> `Match(t,(n,ar),bs_lift,bs,[]) in
230 and subst truelam delift_by_one what (with_what : nf(*_nob*)) (where : nf) =
231 let rec aux_propagate_arity ar = function
232 | `Lam(false, t) when not delift_by_one -> `Lam(false, aux_propagate_arity ar t)
233 | `Match(`I(v,args),(x,_),liftno,bs,args') when not delift_by_one ->
234 `Match(`I(v,args),(x,ar),liftno,bs,args')
235 | `Var(i,oldar) -> `Var(i, if truelam then (assert (oldar = min_int); ar) else oldar)
237 let rec aux_i_num_var l =
241 let args = Listx.map (aux l) (args :> nf Listx.listx) in
242 mk_appx (lift l (aux_propagate_arity ar (with_what :> nf))) args
244 mk_appl (`Var ((if delift_by_one && n >= l then n-1 else n), ar)) (List.map (aux l) (Listx.to_list (args :> nf Listx.listx)))
247 lift l (aux_propagate_arity ar (with_what :> nf))
249 `Var((if delift_by_one && n >= l then n-1 else n), ar)
251 | `Match(t,v,bs_lift,bs,args) ->
252 let bs_lift = bs_lift + if delift_by_one then -1 else 0 in
253 (* let l' = l - bs_lift in *)
254 (* let with_what' = lift l' (with_what :> nf) in *)
255 (* The following line should be the identity when delift_by_one = true because we
256 are assuming the ts to not contain lambda-bound variables. *)
257 (* bs := List.map (fun (n,t) -> n,subst truelam false what with_what' t) !bs ; *)
258 let body = aux_i_num_var l t in
259 mk_match body v bs_lift bs (List.map (aux l) (args :> nf list))
261 (*function iii -> let res = match iii with*)
263 | #i_num_var as x -> aux_i_num_var l x
264 | `Lam(b, nf) -> `Lam(b, aux (l+1) nf)
267 (*in let ll = ["v0";"v1";"v2"] in
268 prerr_endline ("subst l:" ^ string_of_int l ^ " delift_by_one:" ^ string_of_bool delift_by_one ^ " what:" ^ (List.nth ll what) ^ " with_what:" ^ print ~l:ll with_what ^ " where:" ^ print ~l:ll iii ^ " res:" ^ print ~l:ll res); res*)
273 (************ Parsing ************************************)
275 (************** Algorithm(s) ************************)
277 let eta_compare x y =
278 (* let clex a b = let diff = ? a b in if diff = 0 then cont () else 0 in *)
279 let clex aux1 aux2 (a1,a2) (b1,b2) =
280 let diff = aux1 a1 b1 in if diff = 0 then aux2 a2 b2 else diff in
281 let rec lex aux l1 l2 =
286 | x::xs, y::ys -> clex aux (lex aux) (x,xs) (y,ys) in
287 let rec aux t1 t2 = match t1, t2 with
288 | `Var(n,_) , `Var(m,_) -> compare n m
289 | `I((n1,_), l1), `I((n2,_), l2) ->
290 clex compare (lex aux) (n1, (Listx.to_list l1 :> nf list)) (n2, (Listx.to_list l2 :> nf list))
292 | `Pacman, `Pacman -> 0
296 | `Lam _, `Bottom -> assert false (* TO BE UNDERSTOOD *)
297 | `Lam(_,t1), `Lam(_,t2) -> aux t1 t2
298 | `Lam(_,t1), t2 -> - aux t1 (mk_app (lift 1 t2) (`Var(0,-666)))
299 | t2, `Lam(_,t1) -> aux t1 (mk_app (lift 1 t2) (`Var(0,-666)))
300 | `N n1, `N n2 -> compare n1 n2
301 | `Match(u,_,bs_lift,bs,args), `Match(u',_,bs_lift',bs',args') ->
302 let bs = List.sort (fun (n,_) (m,_) -> compare n m) !bs in
303 let bs' = List.sort (fun (n,_) (m,_) -> compare n m) !bs' in
304 clex aux (clex (lex (clex compare aux)) (lex aux)) ((u :> nf), (bs, (args :> nf list))) ((u' :> nf), (bs', (args' :> nf list)))
318 let eta_eq (#nf as x) (#nf as y) = 0 = eta_compare x y ;;
320 let rec eta_subterm sub t =
321 if eta_eq sub t then true else
323 | `Lam(_,t') -> eta_subterm (lift 1 sub) t'
326 | `Match(u,ar,liftno,bs,args) ->
327 eta_subterm sub (u :> nf)
328 || List.exists (fun (_, t) -> eta_subterm sub (lift liftno t)) !bs
329 || List.exists (eta_subterm sub) (args :> nf list)
330 | `I((v,_), args) -> List.exists (eta_subterm sub) ((Listx.to_list args) :> nf list) || (match sub with
331 | `Var(v',_) -> v = v'
332 | `I((v',_), args') -> v = v'
333 && Listx.length args' < Listx.length args
334 && List.for_all (fun (x,y) -> eta_eq x y) (List.combine (Util.take (Listx.length args') (Listx.to_list args :> nf list)) (Listx.to_list args' :> nf list))
337 | `N _ | `Var _ -> false
340 let eta_subterm (#nf as x) (#nf as y) = eta_subterm x y;;
342 let max_arity_tms n =
343 let max a b = match a, b with
346 | Some x, None -> Some x
347 | Some x, Some y -> Some (Pervasives.max x y) in
348 let aux_var l (m,a) = if n + l = m then Some a else None in
349 let rec aux l = function
350 | `Var v -> aux_var l v
351 | `I(v,tms) -> max (aux_var l v) (aux_tms l (Listx.to_list tms :> nf list))
352 | `Lam(_,t) -> aux (l+1) t
353 | `Match(u,_,_,bs,args) -> max (max (aux l (u :> nf)) (aux_tms l (args :> nf list))) (aux_tms l (List.map snd !bs))
354 | `N _ | `Bottom | `Pacman -> None
356 List.fold_left (fun acc t -> max acc (aux l t)) None in
357 fun tms -> aux_tms 0 (tms :> nf list)