| 'nf i_n_var_
| `Match of 'nf i_num_var_ * (* originating var *) var * (*lift*) int * (*branches*)(int * 'nf) list ref * (*args*)'nf list
]
-type 'nf nf_ = [ `Lam of (* was_unpacked *) bool * 'nf nf_ | 'nf i_num_var_ ]
+type 'nf nf_ = [ `Lam of (* was_unpacked *) bool * 'nf nf_ * ('nf nf_) list | 'nf i_num_var_ ]
type nf = nf nf_
type i_var = nf i_var_;;
type i_n_var = nf i_n_var_;;
and aux l =
function
#i_num_var as x -> (aux_i_num_var l x :> nf)
- | `Lam(b,nf) -> `Lam (b, aux (l+1) nf)
+ | `Lam(b,nf,g) -> `Lam (b, aux (l+1) nf, List.map (aux (l+1)) g)
in
(aux 0 t : nf)
;;
let rec make_lams t =
function
0 -> t
- | n when n > 0 -> `Lam (false, lift 1 (make_lams t (n-1)))
+ | n when n > 0 -> `Lam (false, lift 1 (make_lams t (n-1)), [])
| _ -> assert false
let free_vars' =
| `I((x,ar),args) ->
(if x < n then [] else [(x-n,ar)]) @
List.concat (List.map (aux n) (Listx.to_list args))
- | `Lam(_,t) -> aux (n+1) t
+ | `Lam(_,t,g) -> List.concat (List.map (aux (n+1)) (t::g))
| `Match(t,_,liftno,bs,args) ->
aux n (t :> nf) @
List.concat (List.map (fun (_,t) -> aux (n-liftno) t) !bs) @
module ToScott =
struct
+let delta = let open Pure in L(A(V 0, V 0))
+
+let bomb = ref(`Var(-1, -666));;
+
let rec t_of_i_num_var =
function
| `N n -> Scott.mk_n n
- | `Var(v,_) -> Pure.V v
+ | `Var(v,_) as x -> assert (x <> !bomb); Pure.V v
| `Match(t,_,liftno,bs,args) ->
- let bs = List.map (fun (n,t) -> n, t_of_nf (lift liftno t)) !bs in
+ let bs = List.map (
+ function (n,t) -> n,
+ (if t = !bomb then delta
+ else Pure.L (t_of_nf (lift (liftno+1) t)))
+ ) !bs in
let t = t_of_i_num_var t in
let m = Scott.mk_match t bs in
+ let m = Pure.A(m,delta) in
List.fold_left (fun acc t -> Pure.A(acc,t_of_nf t)) m args
| `I((v,_), args) -> Listx.fold_left (fun acc t -> Pure.A(acc,t_of_nf t)) (Pure.V v) args
and t_of_nf =
function
| #i_num_var as x -> t_of_i_num_var x
- | `Lam(b,f) -> Pure.L (t_of_nf f)
+ | `Lam(b,f,g) ->
+ let t = t_of_nf (lift (List.length g) f) in
+ let t = List.fold_left (fun t g -> Pure.A(Pure.L t, t_of_nf g)) t g in
+ Pure.L t
end
(* let rec string_of_term l = fun _ -> "";; *)
-let rec string_of_term =
+let string_of_term =
let boundvar x = "v" ^ string_of_int x in
let varname lev l n =
if n < lev then boundvar (lev-n-1)
- else if n < List.length l then List.nth l (n-lev)
+ else if n - lev < List.length l then List.nth l (n-lev)
else "`" ^ string_of_int (n-lev) in
let rec string_of_term_w_pars lev l = function
| `Var(n,ar) -> varname lev l n ^ (if debug_display_arities then ":" ^ string_of_int ar else "")
| `Lam _ as t -> "(" ^ string_of_term_no_pars_lam lev l t ^ ")"
| `Match(t,(v,ar),bs_lift,bs,args) ->
(* assert (bs_lift = lev); *)
- "(["^ varname lev l v ^ (if debug_display_arities then ":"^ string_of_int ar else "") ^",match " ^ string_of_term_no_pars lev l (t :> nf) ^
+ "(["^ varname 0 l v ^ (if debug_display_arities then ":"^ string_of_int ar else "") ^",match " ^ string_of_term_no_pars lev l (t :> nf) ^
" with " ^ String.concat " | " (List.map (fun (n,t) -> string_of_int n ^ " => " ^ string_of_term l (t :> nf)) !bs) ^ "] " ^
String.concat " " (List.map (string_of_term l) (args :> nf list)) ^ ")"
and string_of_term_no_pars_app lev l = function
| `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))
| #nf as t -> string_of_term_w_pars lev l t
and string_of_term_no_pars_lam lev l = function
- | `Lam(_,t) -> "λ" ^ boundvar lev ^ ". " ^ (string_of_term_no_pars_lam (lev+1) l t)
+ | `Lam(_,t,g) -> "λ" ^ boundvar lev ^ ". " ^ (string_of_term_no_pars_lam (lev+1) l t)
+ ^ (if g = [] then "" else String.concat ", " ("" :: List.map (string_of_term_no_pars (lev+1) l) g))
| _ as t -> string_of_term_no_pars lev l t
and string_of_term_no_pars lev l = function
| `Lam _ as t -> string_of_term_no_pars_lam lev l t
| #nf as t -> string_of_term_no_pars_app lev l t
- in string_of_term_no_pars 0
+ and string_of_term t = string_of_term_no_pars 0 t in
+ string_of_term
;;
let print ?(l=[]) = string_of_term l;;
(* FIXME because onlt variables should be in branches of matches, one day *)
| `Var(n,_) -> `Var(n,arity)
| `N _ as t -> t
-| `Lam(false, t) -> `Lam(false, set_arity arity t)
+| `Lam(false, t, []) -> `Lam(false, set_arity arity t, [])
| `Match(t,(n,_),bs_lift,bs,args) -> `Match(t,(n,arity),bs_lift,bs,args)
| `I _ | `Lam _ -> assert false
match h with
`I(v,args) -> `I(v,Listx.append (Listx.Nil arg) args)
| `Var v -> `I(v, Listx.Nil arg)
- | `Lam(truelam,nf) -> subst truelam true 0 arg (nf : nf) (* AC FIXME sanity check on arity *)
+ | `Lam(truelam,nf,g) -> assert (g = []); subst truelam true 0 arg (nf : nf) (* AC FIXME sanity check on arity *)
| `Match(t,v,lift,bs,args) -> `Match(t,v,lift,bs,List.append args [arg])
| `N _ -> assert false (* Numbers cannot be applied *)
(*in let l = ["v0";"v1";"v2"] in
and subst truelam delift_by_one what (with_what : nf) (where : nf) =
let rec aux_propagate_arity ar = function
- | `Lam(false, t) when not delift_by_one -> `Lam(false, aux_propagate_arity ar t)
+ | `Lam(false,t,g) when not delift_by_one -> assert (g = []); `Lam(false,aux_propagate_arity ar t,[])
| `Match(`I(v,args),(x,_),liftno,bs,args') when not delift_by_one ->
`Match(`I(v,args),(x,ar),liftno,bs,args')
| `Var(i,oldar) -> `Var(i, if truelam then (assert (oldar = min_int); ar) else oldar)
| `N _ as x -> x
| `Match(t,v,bs_lift,bs,args) ->
let bs_lift = bs_lift + if delift_by_one then -1 else 0 in
- (* let l' = l - bs_lift in *)
- (* let with_what' = lift l' (with_what :> nf) in *)
+ (* Warning! It now applies again the substitution in branches of matches.
+ But careful, it does it many times, for every occurrence of
+ the match. This is okay because what does not occur in with_what. *)
+ let l' = l - bs_lift in
+ let with_what' = lift l' (with_what :> nf) in
(* The following line should be the identity when delift_by_one = true because we
are assuming the ts to not contain lambda-bound variables. *)
- (* bs := List.map (fun (n,t) -> n,subst truelam false what with_what' t) !bs ; *)
+ bs := List.map (fun (n,t) -> n,subst truelam false what with_what' t) !bs ;
let body = cast_to_i_num_var (aux_i_num_var l t) in
- mk_match body v bs_lift bs (List.map (aux l) args)
+ mk_match body v bs_lift bs (List.map (aux l) (args :> nf list))
and aux l(*lift*) =
(*function iii -> let res = match iii with*)
function
| #i_num_var as x -> aux_i_num_var l x
- | `Lam(b, nf) -> `Lam(b, aux (l+1) nf)
+ | `Lam(b, nf, g) -> `Lam(b, aux (l+1) nf, List.map (aux (l+1)) g)
(*in let ll = ["v0";"v1";"v2"] in
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*)
in
clex compare (lex aux) (n1, Listx.to_list l1) (n2, Listx.to_list l2)
| `Lam _, `N _ -> -1
| `N _, `Lam _ -> 1
- | `Lam(_,t1), `Lam(_,t2) -> aux t1 t2
- | `Lam(_,t1), t2 -> - aux t1 (mk_app (lift 1 t2) (`Var(0,-666)))
- | t2, `Lam(_,t1) -> aux t1 (mk_app (lift 1 t2) (`Var(0,-666)))
+ | `Lam(_,t1,_), `Lam(_,t2,_) -> aux t1 t2
+ | `Lam(_,t1,_), t2 -> - aux t1 (mk_app (lift 1 t2) (`Var(0,-666)))
+ | t2, `Lam(_,t1,_) -> aux t1 (mk_app (lift 1 t2) (`Var(0,-666)))
| `N n1, `N n2 -> compare n1 n2
| `Match(u,_,bs_lift,bs,args), `Match(u',_,bs_lift',bs',args') ->
let bs = List.sort (fun (n,_) (m,_) -> compare n m) !bs in
let rec eta_subterm sub t =
if eta_eq sub t then true else
match t with
- | `Lam(_,t') -> eta_subterm (lift 1 sub) t'
+ | `Lam(_,t,g) -> List.exists (eta_subterm (lift 1 sub)) (t::g)
| `Match(u,ar,liftno,bs,args) ->
eta_subterm sub (u :> nf)
|| List.exists (fun (_, t) -> eta_subterm sub (lift liftno t)) !bs
let rec aux l = function
| `Var v -> aux_var l v
| `I(v,tms) -> max (aux_var l v) (aux_tms l (Listx.to_list tms))
- | `Lam(_,t) -> aux (l+1) t
+ | `Lam(_,t, g) -> List.fold_left (fun n t -> max n (aux (l+1) t)) None (t::g)
| `Match(u,_,_,bs,args) -> max (max (aux l (u :> nf)) (aux_tms l args)) (aux_tms l (List.map snd !bs))
| `N _ -> None
and aux_tms l =
let get_first_args var =
let rec aux l = function
-| `Lam(_,t) -> aux (l+1) t
+| `Lam(_,t,_) -> aux (l+1) t
| `Match(u,orig,liftno,bs,args) -> Util.concat_map (aux l) args
| `I((n,_), args) -> if n = var + l then [Listx.last args] else []
| `N _
if n = 0
then []
else
- let tms = Util.filter_map (function `Lam(_,t) -> Some t | _ -> None ) tms in
+ let tms = Util.filter_map (function `Lam(_,t,_) -> Some t | _ -> None ) tms in
let arity = match max_arity_tms (m-n) tms with None -> -666 | Some x -> x in
arity :: (aux (n-1) tms)
in fun tms -> List.rev (aux m tms)