open NTacStatus
open Continuationals.Stack
-let debug = false
+let debug = false
let pp =
if debug then (fun x -> prerr_endline (Lazy.force x)) else (fun _ -> ())
(* input: nome della variabile riscritta
* output: lista dei nomi delle variabili il cui tipo dipende dall'input *)
-let cascade_select_in_ctx ~subst ctx iname =
+let cascade_select_in_ctx ~subst ctx skip iname =
let lctx, rctx = HExtlib.split_nth (iname - 1) ctx in
let lctx = List.rev lctx in
let rec rm_last = function
(fun (acc,context) item ->
match item with
| n,(NCic.Decl s | NCic.Def (s,_))
- when not (List.for_all (fun x -> NCicTypeChecker.does_not_occur ~subst context (x-1) x s) acc) ->
+ when (not (List.for_all (fun x -> NCicTypeChecker.does_not_occur ~subst context (x-1) x s) acc)
+ && not (List.mem n skip)) ->
List.iter (fun m -> pp (lazy ("acc has " ^ (string_of_int m)))) acc;
pp (lazy ("acc occurs in the type of " ^ n));
(1::List.map ((+) 1) acc, item::context)
let default_pattern = "",0,(None,[],Some CicNotationPt.UserInput);;
(* returns the discrimination = injection+contradiction principle *)
-(* FIXME: mi riservo di considerare tipi con parametri sx alla fine *)
-let mk_discriminator it nleft status =
+let mk_discriminator it ~use_jmeq nleft xyty status =
let _,indname,_,cl = it in
let mk_eq tys ts us es n =
+ if use_jmeq then
+ mk_appl [mk_id "jmeq";
+ CicNotationPt.Implicit `JustOne; List.nth ts n;
+ CicNotationPt.Implicit `JustOne; List.nth us n]
+ else
(* eqty = Tn u0 e0...un-1 en-1 *)
let eqty = mk_appl
(List.nth tys n :: iter (fun i acc ->
List.nth es i:: acc) (n-1) []) in
mk_appl [mk_id "eq"; eqty;
mk_appl (mk_id ("R" ^ string_of_int n) :: params);
- List.nth us n]
+ List.nth us n]
+
in
let kname it j =
let nargs = nargs it nleft i in
let es = List.map (fun x -> mk_id ("e" ^ string_of_int x)) (HExtlib.list_seq 0 nargs) in
let tys = List.map
- (fun x -> CicNotationPt.Implicit (`Tagged ("T" ^ (string_of_int x))))
- (HExtlib.list_seq 0 nargs) in
+ (fun x -> iter
+ (fun i acc ->
+ CicNotationPt.Binder (`Lambda, (mk_id ("x" ^ string_of_int i), None),
+ CicNotationPt.Binder (`Lambda, (mk_id ("p" ^ string_of_int i), None),
+ acc))) (x-1)
+ (CicNotationPt.Implicit (`Tagged ("T" ^ (string_of_int x)))))
+ (HExtlib.list_seq 0 nargs) in
let tys = tys @
[iter (fun i acc ->
CicNotationPt.Binder (`Lambda, (mk_id ("x" ^ string_of_int i), None),
List.combine ts nones),
inner i ts)
(HExtlib.list_seq 0 (List.length cl))) in
- let principle = CicNotationPt.Binder (`Lambda, (mk_id "x", (*Some (mk_id indname)*) None),
- CicNotationPt.Binder (`Lambda, (mk_id "y", (*Some (mk_id indname)*) None), outer))
+ let principle = CicNotationPt.Binder (`Lambda, (mk_id "x", Some xyty),
+ CicNotationPt.Binder (`Lambda, (mk_id "y", Some xyty), outer))
in
pp (lazy ("discriminator = " ^ (CicNotationPp.pp_term principle)));
let discriminate_tac ~context cur_eq status =
pp (lazy (Printf.sprintf "discriminate: equation %s" (name_of_rel ~context cur_eq)));
- let dbranch it leftno consno =
+ let dbranch it ~use_jmeq leftno consno =
+ let refl_id = mk_id (if use_jmeq then "refl_jmeq" else "refl") in
pp (lazy (Printf.sprintf "dbranch %d %d" leftno consno));
let nlist = HExtlib.list_seq 0 (nargs it leftno consno) in
(* (\forall ...\forall P.\forall DH : ( ... = ... -> P). P) *)
NTactics.intro_tac "P";
NTactics.intro_tac "DH";
NTactics.apply_tac ("",0,mk_id "DH");
- NTactics.apply_tac ("",0,mk_id "refl");
+ NTactics.apply_tac ("",0,refl_id); (* well, it works even if no goal is selected after applying DH... *)
] in
- let dbranches it leftno =
+ let dbranches it ~use_jmeq leftno =
pp (lazy (Printf.sprintf "dbranches %d" leftno));
let _,_,_,cl = it in
let nbranches = List.length cl in
let branches = iter (fun n acc ->
let m = nbranches - n - 1 in
- if m = 0 then acc @ (dbranch it leftno m)
- else acc @ NTactics.shift_tac :: (dbranch it
+ if m = 0 then acc @ (dbranch it ~use_jmeq leftno m)
+ else acc @ NTactics.shift_tac :: (dbranch it ~use_jmeq
leftno m))
(nbranches-1) [] in
if nbranches > 1 then
let _,ctx' = HExtlib.split_nth cur_eq context in
let status, s = NTacStatus.whd status ctx' (mk_cic_term ctx' s) in
let status, s = term_of_cic_term status s ctx' in
- let status, leftno, it =
- let it, t1, t2 = match s with
- | NCic.Appl [_;it;t1;t2] -> it,t1,t2
+ let status, leftno, it, use_jmeq =
+ let it, t1, t2, use_jmeq = match s with
+ | NCic.Appl [_;it;t1;t2] -> it,t1,t2,false
+ | NCic.Appl [_;it;t1;_;t2] -> it,t1,t2,true
| _ -> assert false in
(* XXX: serve? ho giĆ fatto whd *)
let status, it = whd status ctx' (mk_cic_term ctx' it) in
| _ -> pp (lazy ("discriminate: indty =" ^ NCicPp.ppterm
~metasenv:[] ~subst:[] ~context:[] it)) ; assert false in
let _,leftno,its,_,_ = its in
- status, leftno, List.nth its indtyno
+ status, leftno, List.nth its indtyno, use_jmeq
in
let itnargs =
List.length (arg_list 0 arity) in
let _,itname,_,_ = it in
let params = List.map (fun x -> "a" ^ string_of_int x) (HExtlib.list_seq 1 (itnargs+1)) in
+ let xyty = mk_appl (List.map mk_id (itname::params)) in
let print_tac s status = pp s ; status in
NTactics.block_tac (
[(fun status ->
- let status, discr = mk_discriminator it leftno status in
- NTactics.cut_tac ("",0, mk_prods params (CicNotationPt.Binder (`Forall, (mk_id "x",
- Some (mk_appl (List.map mk_id (itname::params)))),
- CicNotationPt.Binder (`Forall, (mk_id "y", None),
+ let status, discr = mk_discriminator it ~use_jmeq leftno xyty status in
+ let cut_term = mk_prods params (CicNotationPt.Binder (`Forall, (mk_id "x",
+ Some xyty),
+ CicNotationPt.Binder (`Forall, (mk_id "y", Some xyty),
CicNotationPt.Binder (`Forall, (mk_id "e",
Some (mk_appl [mk_id "eq";CicNotationPt.Implicit `JustOne; mk_id "x"; mk_id "y"])),
- mk_appl [discr; mk_id "x"; mk_id "y"(*;mk_id "e"*)])))))
+ mk_appl [discr; mk_id "x"; mk_id "y"(*;mk_id "e"*)])))) in
+ let status = print_tac (lazy ("cut_term = "^ CicNotationPp.pp_term cut_term)) status in
+ NTactics.cut_tac ("",0, cut_term)
status);
NTactics.branch_tac;
print_tac (lazy "ci sono");
print_tac (lazy "ci sono 2");
NTactics.rewrite_tac ~dir:`RightToLeft ~what:("",0,mk_id "Deq") ~where:default_pattern;
NTactics.cases_tac ~what:("",0,mk_id "x") ~where:default_pattern]
- @ dbranches it leftno @
+ @ dbranches it ~use_jmeq leftno @
[NTactics.shift_tac;
print_tac (lazy "ci sono 3");
NTactics.intro_tac "#discriminate";
[mk_id eq_name ]));
NTactics.reduce_tac ~reduction:(`Normalize true) ~where:default_pattern;
NTactics.clear_tac ["#discriminate"];
- NTactics.merge_tac]
+ NTactics.merge_tac; print_tac (lazy "the end of discriminate")]
) status
;;
+
+let saturate_skip status context skip =
+ HExtlib.list_uniq
+ (List.fold_left
+ (fun acc x ->
+ let ix = HExtlib.list_index ((=) x) (List.map fst context)
+ in match ix with
+ | None -> acc
+ | Some (i,_) ->
+ fst (cascade_select_in_ctx ~subst:(get_subst status) context [] (i+1)) @ acc) skip skip)
+;;
-let subst_tac ~context ~dir cur_eq =
- fun status ->
+let subst_tac ~context ~dir skip cur_eq =
+ fun status as oldstatus ->
let eq_name,(NCic.Decl s | NCic.Def (s,_)) = List.nth context (cur_eq-1) in
let _,ctx' = HExtlib.split_nth cur_eq context in
let status, s = NTacStatus.whd status ctx' (mk_cic_term ctx' s) in
let status, s = term_of_cic_term status s ctx' in
+ let skip = saturate_skip status context skip in
pp (lazy (Printf.sprintf "subst: equation %s" eq_name));
let l, r = match s with
- | NCic.Appl [_;_;t1;t2] -> t1,t2
+ | NCic.Appl [_;_;t1;t2] | NCic.Appl [_;_;t1;_;t2] -> t1,t2
| _ -> assert false in
let var = match dir with
| `LeftToRight -> l
| `RightToLeft -> r in
- let var = match var with
+ (* let var = match var with
| NCic.Rel i -> i
- | _ -> assert false in
+ | _ -> assert false in *)
let names_to_gen, _ =
- cascade_select_in_ctx ~subst:(get_subst status) context (var+cur_eq) in
- let names_to_gen = match names_to_gen with [] -> [] | _::tl -> tl in
+ match var with
+ | NCic.Rel var ->
+ cascade_select_in_ctx ~subst:(get_subst status) context skip (var+cur_eq)
+ | _ -> cascade_select_in_ctx ~subst:(get_subst status) context skip cur_eq in
+ let names_to_gen = List.filter (fun n -> n <> eq_name) names_to_gen in
+ if (List.exists (fun x -> List.mem x skip) names_to_gen)
+ then oldstatus
+ else
let gen_tac x =
NTactics.generalize_tac
~where:("",0,(Some (mk_id x),[], Some CicNotationPt.UserInput)) in
~what:("",0,mk_id eq_name) ~where:default_pattern;
NTactics.reduce_tac ~reduction:(`Normalize true)
~where:default_pattern;
- NTactics.clear_tac [eq_name]]@
+ NTactics.try_tac (NTactics.clear_tac [eq_name])]@
(List.map NTactics.intro_tac (List.rev names_to_gen))) status
;;
-let clearid_tac ~context cur_eq =
+let clearid_tac ~context skip cur_eq =
fun status ->
let eq_name,(NCic.Decl s | NCic.Def (s,_)) = List.nth context (cur_eq-1) in
let _,ctx' = HExtlib.split_nth cur_eq context in
let status, s = NTacStatus.whd status ctx' (mk_cic_term ctx' s) in
let status, s = term_of_cic_term status s ctx' in
+ let skip = saturate_skip status context skip in
+ (*
+ let streicher_id =
+ match s with
+ | NCic.Appl [_;_;_;_] -> mk_id "streicherK"
+ | NCic.Appl [_;_;_;_;_] -> mk_id "streicherKjmeq"
+ | _ -> assert false
+ in
pp (lazy (Printf.sprintf "clearid: equation %s" eq_name));
let names_to_gen, _ =
cascade_select_in_ctx ~subst:(get_subst status) context cur_eq in
~where:("",0,(Some (mk_id x),[], Some CicNotationPt.UserInput)) in
NTactics.block_tac ((List.map gen_tac names_to_gen)@
[NTactics.clear_tac names_to_gen;
- NTactics.apply_tac ("",0, mk_appl [mk_id "streicherK";
+ NTactics.apply_tac ("",0, mk_appl [streicher_id;
+ CicNotationPt.Implicit `JustOne;
+ CicNotationPt.Implicit `JustOne;
+ CicNotationPt.Implicit `JustOne;
+ CicNotationPt.Implicit `JustOne]);
+ NTactics.reduce_tac ~reduction:(`Normalize true)
+ ~where:default_pattern] @
+ (let names_to_intro =
+ match List.rev names_to_gen with
+ | [] -> []
+ | _::tl -> tl in
+ List.map NTactics.intro_tac names_to_intro)) status
+*)
+
+ pp (lazy (Printf.sprintf "clearid: equation %s" eq_name));
+ match s with
+ | NCic.Appl [_;_;_;_] ->
+ (* leibniz *)
+ let streicher_id = mk_id "streicherK"
+ in
+ let names_to_gen, _ =
+ cascade_select_in_ctx ~subst:(get_subst status) context skip cur_eq in
+ let names_to_gen = names_to_gen @ [eq_name] in
+ let gen_tac x =
+ NTactics.generalize_tac
+ ~where:("",0,(Some (mk_id x),[], Some CicNotationPt.UserInput)) in
+ NTactics.block_tac ((List.map gen_tac names_to_gen)@
+ [NTactics.clear_tac names_to_gen;
+ NTactics.apply_tac ("",0, mk_appl [streicher_id;
CicNotationPt.Implicit `JustOne;
CicNotationPt.Implicit `JustOne;
CicNotationPt.Implicit `JustOne;
| [] -> []
| _::tl -> tl in
List.map NTactics.intro_tac names_to_intro)) status
+ | NCic.Appl [_;_;_;_;_] ->
+ (* JMeq *)
+ let streicher_id = mk_id "streicherK"
+ in
+ let names_to_gen, _ =
+ cascade_select_in_ctx ~subst:(get_subst status) context skip cur_eq in
+ let names_to_gen = names_to_gen (* @ [eq_name]*) in
+ let gen_tac x =
+ NTactics.generalize_tac
+ ~where:("",0,(Some (mk_id x),[], Some CicNotationPt.UserInput)) in
+ let gen_eq = NTactics.generalize_tac
+ ~where:("",0,(Some (mk_appl [mk_id "jmeq_to_eq";
+ CicNotationPt.Implicit `JustOne;
+ CicNotationPt.Implicit `JustOne;
+ CicNotationPt.Implicit `JustOne;
+ mk_id eq_name]),[], Some CicNotationPt.UserInput)) in
+ NTactics.block_tac ((List.map gen_tac names_to_gen)@gen_eq::
+ [NTactics.clear_tac names_to_gen;
+ NTactics.try_tac (NTactics.clear_tac [eq_name]);
+ NTactics.apply_tac ("",0, mk_appl [streicher_id;
+ CicNotationPt.Implicit `JustOne;
+ CicNotationPt.Implicit `JustOne;
+ CicNotationPt.Implicit `JustOne;
+ CicNotationPt.Implicit `JustOne]);
+ NTactics.reduce_tac ~reduction:(`Normalize true)
+ ~where:default_pattern] @
+ (let names_to_intro = List.rev names_to_gen in
+ List.map NTactics.intro_tac names_to_intro)) status
+ | _ -> assert false
;;
let get_ctx st goal =
;;
(* = select + classify *)
-let select_eq ctx acc status goal =
+let select_eq ctx acc domain status goal =
let classify ~subst ctx' l r =
(* FIXME: metasenv *)
if NCicReduction.are_convertible ~metasenv:[] ~subst ctx' l r
let newprods = nargs it nleft (ki-1) in
`Discriminate (newprods, false)
| NCic.Rel j, _
- when NCicTypeChecker.does_not_occur ~subst ctx' (j-1) j r ->
- `Subst `LeftToRight
+ when NCicTypeChecker.does_not_occur ~subst ctx' (j-1) j r
+ && l = NCic.Rel j -> `Subst `LeftToRight
| _, NCic.Rel j
- when NCicTypeChecker.does_not_occur ~subst ctx' (j-1) j l ->
- `Subst `RightToLeft
- | (NCic.Rel _, _ | _, NCic.Rel _ ) -> `Cycle
+ when NCicTypeChecker.does_not_occur ~subst ctx' (j-1) j l
+ && r = NCic.Rel j -> `Subst `RightToLeft
+ | (NCic.Rel _, _ | _, NCic.Rel _ ) -> `Cycle (* could be a blob too... *)
| _ -> `Blob) in
let rec aux i =
try
let status, ty = NTacStatus.whd status ctx_ty (mk_cic_term ctx_ty ty) in
let status, ty = term_of_cic_term status ty ctx_ty in
pp (lazy (Printf.sprintf "select_eq tries %s" (NCicPp.ppterm ~context:ctx_ty ~subst:[] ~metasenv:[] ty)));
- match ty with
- | NCic.Appl [NCic.Const (NReference.Ref (u,_)) ;_;l;r] when NUri.name_of_uri u = "eq" ->
- (let status, kind = classify ~subst:(get_subst status) ctx_ty l r in
- match kind with
- | `Identity ->
- let status, goalty = term_of_cic_term status (get_goalty status goal) ctx in
- status, Some (List.length ctx - i), kind
- | `Cycle | `Blob -> aux (i+1) (* XXX: skip cyclic/blob equations for now *)
- | _ ->
- if (List.for_all (fun x -> x <> n) acc) then
- status, Some (List.length ctx - i), kind
- else aux (i+1))
- | _ -> aux (i+1))
+ let status, kind = match ty with
+ | NCic.Appl [NCic.Const (NReference.Ref (u,_)) ;_;l;r]
+ when NUri.name_of_uri u = "eq" ->
+ classify ~subst:(get_subst status) ctx_ty l r
+ | NCic.Appl [NCic.Const (NReference.Ref (u,_)) ;lty;l;rty;r]
+ when NUri.name_of_uri u = "jmeq" &&
+ NCicReduction.are_convertible ~metasenv:[]
+ ~subst:(get_subst status) ctx_ty lty rty
+ -> classify ~subst:(get_subst status) ctx_ty l r
+ | _ -> status, `NonEq
+ in match kind with
+ | `Identity ->
+ let status, goalty = term_of_cic_term status (get_goalty status goal) ctx in
+ status, Some (List.length ctx - i), kind
+ | `Cycle | `Blob | `NonEq -> aux (i+1) (* XXX: skip cyclic/blob equations for now *)
+ | _ ->
+ if (List.for_all (fun x -> x <> n) acc) &&
+ (List.exists (fun x -> x = n) domain)
+ then status, Some (List.length ctx - i), kind
+ else aux (i+1))
with Failure _ | Invalid_argument _ -> status, None, `Blob
in aux 0
;;
-let rec destruct_tac0 nprods acc status goal =
+let rec destruct_tac0 nprods acc domain skip status goal =
let ctx = get_ctx status goal in
let subst = get_subst status in
let get_newgoal os ns ogoal =
let go' = ([ogoal] @- gc) @+ go in
match go' with [] -> assert false | g::_ -> g
in
- let status, selection, kind = select_eq ctx acc status goal in
+ let status, selection, kind = select_eq ctx acc domain status goal in
pp (lazy ("destruct: acc is " ^ String.concat "," acc ));
match selection, kind with
| None, _ ->
pp (lazy (Printf.sprintf "destruct: nprods is %d, no selection, context is %s" nprods (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
- if nprods > 0 then
- let status' = NTactics.exec (NTactics.intro_tac (mk_fresh_name ctx 'e' 0)) status goal in
- destruct_tac0 (nprods-1) acc status' (get_newgoal status status' goal)
+ if nprods > 0 then
+ let fresh = mk_fresh_name ctx 'e' 0 in
+ let status' = NTactics.exec (NTactics.intro_tac fresh) status goal in
+ destruct_tac0 (nprods-1) acc (fresh::domain) skip status' (get_newgoal status status' goal)
else
status
| Some cur_eq, `Discriminate (newprods,conflict) ->
pp (lazy (Printf.sprintf "destruct: discriminate - nprods is %d, selection is %d, context is %s" nprods cur_eq (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
let status' = NTactics.exec (discriminate_tac ~context:ctx cur_eq) status goal in
if conflict then status'
- else destruct_tac0 (nprods+newprods)
- (name_of_rel ~context:ctx cur_eq::acc) status' (get_newgoal status status' goal)
+ else
+ destruct_tac0 (nprods+newprods)
+ (name_of_rel ~context:ctx cur_eq::acc)
+ (List.filter (fun x -> x <> name_of_rel ~context:ctx cur_eq) domain)
+ skip
+ status' (get_newgoal status status' goal)
| Some cur_eq, `Subst dir ->
pp (lazy (Printf.sprintf "destruct: subst - nprods is %d, selection is %d, context is %s" nprods cur_eq (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
- let status' = NTactics.exec (subst_tac ~context:ctx ~dir cur_eq) status goal in
+ let status' = NTactics.exec (subst_tac ~context:ctx ~dir skip cur_eq) status goal in
pp (lazy (Printf.sprintf " ctx after subst = %s" (NCicPp.ppcontext ~metasenv:[] ~subst (get_ctx status' (get_newgoal status status' goal)))));
let eq_name,_ = List.nth ctx (cur_eq-1) in
- destruct_tac0 nprods (List.filter (fun x -> x <> eq_name) acc) status' (get_newgoal status status' goal)
- | Some cur_eq, `Identity ->
+ let newgoal = get_newgoal status status' goal in
+ let has_cleared =
+ try
+ let _ = NTactics.find_in_context eq_name (get_ctx status' newgoal) in false
+ with _ -> true in
+ let rm_eq b l = if b then List.filter (fun x -> x <> eq_name) l else l in
+ let acc = rm_eq has_cleared acc in
+ let skip = rm_eq has_cleared skip in
+ let domain = rm_eq has_cleared domain in
+ destruct_tac0 nprods acc domain skip status' newgoal
+ | Some cur_eq, `Identity ->
pp (lazy (Printf.sprintf "destruct: identity - nprods is %d, selection is %d, context is %s" nprods cur_eq (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
let eq_name,_ = List.nth ctx (cur_eq-1) in
- let status' = NTactics.exec (clearid_tac ~context:ctx cur_eq) status goal in
- destruct_tac0 nprods (List.filter (fun x -> x <> eq_name) acc) status' (get_newgoal status status' goal)
+ let status' = NTactics.exec (clearid_tac ~context:ctx skip cur_eq) status goal in
+ let newgoal = get_newgoal status status' goal in
+ let has_cleared =
+ try
+ let _ = NTactics.find_in_context eq_name (get_ctx status' newgoal) in false
+ with _ -> true in
+ let rm_eq b l = if b then List.filter (fun x -> x <> eq_name) l else l in
+ let acc = rm_eq has_cleared acc in
+ let skip = rm_eq has_cleared skip in
+ let domain = rm_eq has_cleared domain in
+ destruct_tac0 nprods acc domain skip status' newgoal
| Some cur_eq, `Cycle -> (* TODO, should never happen *)
pp (lazy (Printf.sprintf "destruct: cycle - nprods is %d, selection is %d, context is %s" nprods cur_eq (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
assert false
| Some cur_eq, `Blob ->
pp (lazy (Printf.sprintf "destruct: blob - nprods is %d, selection is %d, context is %s" nprods cur_eq (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
assert false
+ | _ -> assert false
;;
-let destruct_tac s = NTactics.distribute_tac (destruct_tac0 0 []) s;;
+let destruct_tac dom skip s =
+ NTactics.distribute_tac
+ (fun s' g ->
+ let ctx = get_ctx s' g in
+ let domain = match dom with
+ | None -> List.map (fun (n,_) -> n) ctx
+ | Some l -> l
+ in
+ destruct_tac0 0 [] domain skip s' g) s;;