module C = Cic
module I = CicInspect
-module D = Deannotate
module S = CicSubstitution
module TC = CicTypeChecker
module Un = CicUniv
module A = Cic2acic
module Ut = CicUtil
module E = CicEnvironment
-module PEH = ProofEngineHelpers
module Pp = CicPp
+module PEH = ProofEngineHelpers
+module HEL = HExtlib
+module DTI = DoubleTypeInference
+module NU = CicNotationUtil
+module L = Librarian
module Cl = ProceduralClassify
module T = ProceduralTypes
module Cn = ProceduralConversion
+module H = ProceduralHelpers
type status = {
sorts : (C.id, A.sort_kind) Hashtbl.t;
types : (C.id, A.anntypes) Hashtbl.t;
- prefix: string;
max_depth: int option;
depth: int;
context: C.context;
- intros: string list
+ case: int list
}
-(* helpers ******************************************************************)
+let debug = ref false
-let cic = D.deannotate_term
+(* helpers ******************************************************************)
let split2_last l1 l2 =
try
let n = pred (List.length l1) in
- let before1, after1 = T.list_split n l1 in
- let before2, after2 = T.list_split n l2 in
+ let before1, after1 = HEL.split_nth n l1 in
+ let before2, after2 = HEL.split_nth n l2 in
before1, before2, List.hd after1, List.hd after2
with Invalid_argument _ -> failwith "A2P.split2_last"
-
+
let string_of_head = function
| C.ASort _ -> "sort"
| C.AConst _ -> "const"
| C.AMeta _ -> "meta"
| C.AImplicit _ -> "implict"
-let clear st = {st with intros = []}
+let next st = {st with depth = succ st.depth}
+
+let add st entry = {st with context = entry :: st.context}
+
+let push st = {st with case = 1 :: st.case}
-let next st = {(clear st) with depth = succ st.depth}
+let inc st =
+ {st with case = match st.case with
+ | [] -> []
+ | hd :: tl -> succ hd :: tl
+ }
-let add st entry intro =
- {st with context = entry :: st.context; intros = intro :: st.intros}
+let case st str =
+ let case = String.concat "." (List.rev_map string_of_int st.case) in
+ Printf.sprintf "case %s: %s" case str
let test_depth st =
try
| C.ARel _ -> true
| _ -> false
else false
-(*
-let get_ind_name uri tno xcno =
-try
- let ts = match E.get_obj Un.empty_ugraph uri with
- | C.InductiveDefinition (ts, _, _,_), _ -> ts
- | _ -> assert false
- in
- let tname, cs = match List.nth ts tno with
- | (name, _, _, cs) -> name, cs
- in
- match xcno with
- | None -> tname
- | Some cno -> fst (List.nth cs (pred cno))
-with Invalid_argument _ -> failwith "A2P.get_ind_name"
-*)
+
let get_inner_types st v =
try
let id = Ut.id_of_annterm v in
with Not_found -> `Type (CicUniv.fresh())
with Invalid_argument _ -> failwith "A2P.get_sort"
*)
-let get_type msg st bo =
-try
- let ty, _ = TC.type_of_aux' [] st.context (cic bo) Un.empty_ugraph in
- ty
-with e -> failwith (msg ^ ": " ^ Printexc.to_string e)
-
let get_entry st id =
let rec aux = function
| [] -> assert false
| _ :: tl -> aux tl
in
aux st.context
-
+
+let string_of_atomic = function
+ | C.ARel (_, _, _, s) -> s
+ | C.AVar (_, uri, _) -> H.name_of_uri uri None None
+ | C.AConst (_, uri, _) -> H.name_of_uri uri None None
+ | C.AMutInd (_, uri, i, _) -> H.name_of_uri uri (Some i) None
+ | C.AMutConstruct (_, uri, i, j, _) -> H.name_of_uri uri (Some i) (Some j)
+ | _ -> ""
+
+let get_sub_names head l =
+ let s = string_of_atomic head in
+ if s = "" then [] else
+ let map (names, i) _ =
+ let name = Printf.sprintf "%s_%u" s i in name :: names, succ i
+ in
+ let names, _ = List.fold_left map ([], 1) l in
+ List.rev names
+
+let get_type msg st t = H.get_type msg st.context (H.cic t)
+
+let clear_absts m =
+ let rec aux k n = function
+ | C.ALambda (id, s, v, t) when k > 0 ->
+ C.ALambda (id, s, v, aux (pred k) n t)
+ | C.ALambda (_, _, _, t) when n > 0 ->
+ aux 0 (pred n) (Cn.lift 1 (-1) t)
+ | t when n > 0 ->
+ Printf.eprintf "A2P.clear_absts: %u %s\n" n (Pp.ppterm (H.cic t));
+ assert false
+ | t -> t
+ in
+ aux m
+
(* proof construction *******************************************************)
-let unused_premise = "UNUSED"
+let anonymous_premise = C.Name "UNNAMED"
-let mk_exp_args hd tl classes =
+let mk_exp_args hd tl classes synth =
let meta id = C.AImplicit (id, None) in
let map v (cl, b) =
- if I.S.mem 0 cl && b then v else meta ""
+ if I.overlaps synth cl && b then v else meta ""
in
let rec aux = function
| [] -> []
| hd :: tl -> if hd = meta "" then aux tl else List.rev (hd :: tl)
in
- let args = List.rev_map2 map tl classes in
+ let args = T.list_rev_map2 map tl classes in
let args = aux args in
if args = [] then hd else C.AAppl ("", hd :: args)
+let mk_convert st ?name sty ety note =
+ let e = Cn.hole "" in
+ let csty, cety = H.cic sty, H.cic ety in
+ let script =
+ if !debug then
+ let sname = match name with None -> "" | Some (id, _) -> id in
+ let note = Printf.sprintf "%s: %s\nSINTH: %s\nEXP: %s"
+ note sname (Pp.ppterm csty) (Pp.ppterm cety)
+ in
+ [T.Note note]
+ else []
+ in
+ assert (Ut.is_sober st.context csty);
+ assert (Ut.is_sober st.context cety);
+ if Ut.alpha_equivalence csty cety then script else
+ let sty, ety = H.acic_bc st.context sty, H.acic_bc st.context ety in
+ match name with
+ | None -> T.Change (sty, ety, None, e, "") :: script
+ | Some (id, i) ->
+ begin match get_entry st id with
+ | C.Def _ -> assert false (* T.ClearBody (id, "") :: script *)
+ | C.Decl _ ->
+ T.Change (ety, sty, Some (id, Some id), e, "") :: script
+ end
+
let convert st ?name v =
match get_inner_types st v with
- | None -> []
- | Some (sty, ety) ->
- let e = Cn.mk_pattern 0 (T.mk_arel 1 "") in
- let csty, cety = cic sty, cic ety in
- if Ut.alpha_equivalence csty cety then [] else
- match name with
- | None -> [T.Change (sty, ety, None, e, "")]
- | Some (id, i) ->
- begin match get_entry st id with
- | C.Def _ -> [T.ClearBody (id, "")]
- | C.Decl w ->
- let w = S.lift i w in
- if Ut.alpha_equivalence csty w then []
- else
- [T.Note (Pp.ppterm csty); T.Note (Pp.ppterm w);
- T.Change (sty, ety, Some (id, id), e, "")]
- end
-
+ | None ->
+ if !debug then [T.Note "NORMAL: NO INNER TYPES"] else []
+ | Some (sty, ety) -> mk_convert st ?name sty ety "NORMAL"
+
let get_intro = function
- | C.Anonymous -> unused_premise
- | C.Name s -> s
+ | C.Anonymous -> None
+ | C.Name s -> Some s
-let mk_intros st script =
- if st.intros = [] then script else
- let count = List.length st.intros in
- T.Intros (Some count, List.rev st.intros, "") :: script
+let mk_preamble st what script =
+ convert st what @ script
let mk_arg st = function
| C.ARel (_, _, i, name) as what -> convert st ~name:(name, i) what
| _ -> []
-let mk_fwd_rewrite st dtext name tl direction =
+let mk_fwd_rewrite st dtext name tl direction v t ity =
+ let compare premise = function
+ | None -> true
+ | Some s -> s = premise
+ in
assert (List.length tl = 6);
let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
let e = Cn.mk_pattern 1 predicate in
+ if (Cn.does_not_occur e) then st, [] else
match where with
- | C.ARel (_, _, _, premise) ->
- let script = mk_arg st what in
- let where = Some (premise, name) in
- T.Rewrite (direction, what, where, e, dtext) :: script
+ | C.ARel (_, _, i, premise) as w ->
+ let script name =
+ let where = Some (premise, name) in
+ let script = mk_arg st what @ mk_arg st w in
+ T.Rewrite (direction, what, where, e, dtext) :: script
+ in
+ if DTI.does_not_occur (succ i) (H.cic t) || compare premise name then
+ {st with context = Cn.clear st.context premise}, script name
+ else begin
+ assert (Ut.is_sober st.context (H.cic ity));
+ let ity = H.acic_bc st.context ity in
+ let br1 = [T.Id ""] in
+ let br2 = List.rev (T.Apply (w, "assumption") :: script None) in
+ let text = "non-linear rewrite" in
+ st, [T.Branch ([br2; br1], ""); T.Cut (name, ity, text)]
+ end
| _ -> assert false
-let mk_rewrite st dtext what qs tl direction =
+let mk_rewrite st dtext where qs tl direction t =
assert (List.length tl = 5);
let predicate = List.nth tl 2 in
let e = Cn.mk_pattern 1 predicate in
- [T.Rewrite (direction, what, None, e, dtext); T.Branch (qs, "")]
-
-let rec proc_lambda st name v t =
- let entry = Some (name, C.Decl (cic v)) in
+ let script = [T.Branch (qs, "")] in
+ if (Cn.does_not_occur e) then script else
+ T.Rewrite (direction, where, None, e, dtext) :: script
+
+let rec proc_lambda st what name v t =
+ let name = match name with
+ | C.Anonymous -> H.mk_fresh_name st.context anonymous_premise
+ | name -> name
+ in
+ let entry = Some (name, C.Decl (H.cic v)) in
let intro = get_intro name in
- proc_proof (add st entry intro) t
+ let script = proc_proof (add st entry) t in
+ let script = T.Intros (Some 1, [intro], "") :: script in
+ mk_preamble st what script
-and proc_letin st what name v t =
+and proc_letin st what name v w t =
let intro = get_intro name in
let proceed, dtext = test_depth st in
let script = if proceed then
- let hyp, rqv = match get_inner_types st v with
+ let st, hyp, rqv = match get_inner_types st v with
| Some (ity, _) ->
- let rqv = match v with
+ let st, rqv = match v with
| C.AAppl (_, hd :: tl) when is_fwd_rewrite_right hd tl ->
- mk_fwd_rewrite st dtext intro tl true
+ mk_fwd_rewrite st dtext intro tl true v t ity
| C.AAppl (_, hd :: tl) when is_fwd_rewrite_left hd tl ->
- mk_fwd_rewrite st dtext intro tl false
+ mk_fwd_rewrite st dtext intro tl false v t ity
| v ->
- let qs = [[T.Id ""]; proc_proof (next st) v] in
- [T.Branch (qs, ""); T.Cut (intro, ity, dtext)]
+ assert (Ut.is_sober st.context (H.cic ity));
+ let ity = H.acic_bc st.context ity in
+ let qs = [proc_proof (next st) v; [T.Id ""]] in
+ st, [T.Branch (qs, ""); T.Cut (intro, ity, dtext)]
in
- C.Decl (cic ity), rqv
+ st, C.Decl (H.cic ity), rqv
| None ->
- C.Def (cic v, None), [T.LetIn (intro, v, dtext)]
+ st, C.Def (H.cic v, H.cic w), [T.LetIn (intro, v, dtext)]
in
let entry = Some (name, hyp) in
- let qt = proc_proof (next (add st entry intro)) t in
+ let qt = proc_proof (next (add st entry)) t in
List.rev_append rqv qt
else
[T.Apply (what, dtext)]
in
- mk_intros st script
+ mk_preamble st what script
and proc_rel st what =
let _, dtext = test_depth st in
let text = "assumption" in
let script = [T.Apply (what, dtext ^ text)] in
- mk_intros st script
+ mk_preamble st what script
and proc_mutconstruct st what =
let _, dtext = test_depth st in
let script = [T.Apply (what, dtext)] in
- mk_intros st script
+ mk_preamble st what script
+
+and proc_const st what =
+ let _, dtext = test_depth st in
+ let script = [T.Apply (what, dtext)] in
+ mk_preamble st what script
and proc_appl st what hd tl =
let proceed, dtext = test_depth st in
let script = if proceed then
- let ty = get_type "TC2" st hd in
- let (classes, rc) as h = Cl.classify st.context ty in
- let argsno = List.length classes in
- let diff = argsno - List.length tl in
- if diff <> 0 then failwith (Printf.sprintf "NOT TOTAL: %i %s |--- %s" diff (Pp.ppcontext st.context) (Pp.ppterm (cic hd)));
- let synth = I.S.singleton 0 in
- let text = Printf.sprintf "%u %s" argsno (Cl.to_string h) in
- let script = List.rev (mk_arg st hd) @ convert st what in
+ let ty = match get_inner_types st hd with
+ | Some (ity, _) -> H.cic ity
+ | None -> get_type "TC2" st hd
+ in
+ let classes, rc = Cl.classify st.context ty in
+ let goal_arity, goal = match get_inner_types st what with
+ | None -> 0, None
+ | Some (ity, ety) ->
+ snd (PEH.split_with_whd (st.context, H.cic ity)), Some (H.cic ety)
+ in
+ let parsno, argsno = List.length classes, List.length tl in
+ let decurry = parsno - argsno in
+ let diff = goal_arity - decurry in
+ if diff < 0 then failwith (Printf.sprintf "NOT TOTAL: %i %s |--- %s" diff (Pp.ppcontext st.context) (Pp.ppterm (H.cic hd)));
+ let classes = Cl.adjust st.context tl ?goal classes in
+ let rec mk_synth a n =
+ if n < 0 then a else mk_synth (I.S.add n a) (pred n)
+ in
+ let synth = mk_synth I.S.empty decurry in
+ let text = "" (* Printf.sprintf "%u %s" parsno (Cl.to_string h) *) in
+ let script = List.rev (mk_arg st hd) in
match rc with
- | Some (i, j) ->
- let classes, tl, _, where = split2_last classes tl in
- let script = List.rev (mk_arg st where) @ script in
- let synth = I.S.add 1 synth in
- let qs = proc_bkd_proofs (next st) synth classes tl in
- if is_rewrite_right hd then
- script @ mk_rewrite st dtext where qs tl false
+ | Some (i, j, uri, tyno) ->
+ let classes2, tl2, _, where = split2_last classes tl in
+ let script2 = List.rev (mk_arg st where) @ script in
+ let synth2 = I.S.add 1 synth in
+ let names = H.get_ind_names uri tyno in
+ let qs = proc_bkd_proofs (next st) synth2 names classes2 tl2 in
+ if List.length qs <> List.length names then
+ let qs = proc_bkd_proofs (next st) synth [] classes tl in
+ let hd = mk_exp_args hd tl classes synth in
+ script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
+ else if is_rewrite_right hd then
+ script2 @ mk_rewrite st dtext where qs tl2 false what
else if is_rewrite_left hd then
- script @ mk_rewrite st dtext where qs tl true
+ script2 @ mk_rewrite st dtext where qs tl2 true what
else
- let predicate = List.nth tl (argsno - i) in
- let e = Cn.mk_pattern 0 (T.mk_arel 1 "") (* j predicate *) in
+ let predicate = List.nth tl2 (parsno - i) in
+ let e = Cn.mk_pattern j predicate in
let using = Some hd in
- script @
+ script2 @
[T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
| None ->
- let qs = proc_bkd_proofs (next st) synth classes tl in
- let hd = mk_exp_args hd tl classes in
+ let names = get_sub_names hd tl in
+ let qs = proc_bkd_proofs (next st) synth names classes tl in
+ let hd = mk_exp_args hd tl classes synth in
script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
else
[T.Apply (what, dtext)]
in
- mk_intros st script
+ mk_preamble st what script
+
+and proc_case st what uri tyno u v ts =
+ let proceed, dtext = test_depth st in
+ let script = if proceed then
+ let synth, classes = I.S.empty, Cl.make ts in
+ let names = H.get_ind_names uri tyno in
+ let qs = proc_bkd_proofs (next st) synth names classes ts in
+ let lpsno, _ = H.get_ind_type uri tyno in
+ let ps, sort_disp = H.get_ind_parameters st.context (H.cic v) in
+ let _, rps = HEL.split_nth lpsno ps in
+ let rpsno = List.length rps in
+ let predicate = clear_absts rpsno (1 - sort_disp) u in
+ let e = Cn.mk_pattern rpsno predicate in
+ let text = "" in
+ let script = List.rev (mk_arg st v) in
+ script @ [T.Cases (v, e, dtext ^ text); T.Branch (qs, "")]
+ else
+ [T.Apply (what, dtext)]
+ in
+ mk_preamble st what script
and proc_other st what =
+ let _, dtext = test_depth st in
let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head what) in
- let script = [T.Note text] in
- mk_intros st script
-
-
-and proc_proof st = function
- | C.ALambda (_, name, w, t) -> proc_lambda st name w t
- | C.ALetIn (_, name, v, t) as what -> proc_letin st what name v t
- | C.ARel _ as what -> proc_rel st what
- | C.AMutConstruct _ as what -> proc_mutconstruct st what
- | C.AAppl (_, hd :: tl) as what -> proc_appl st what hd tl
- | what -> proc_other st what
-
-and proc_bkd_proofs st synth classes ts =
+ let script = [T.Apply (what, dtext ^ text)] in
+ mk_preamble st what script
+
+and proc_proof st t =
+ let f st =
+ let xtypes, note = match get_inner_types st t with
+ | Some (it, et) -> Some (H.cic it, H.cic et),
+ (Printf.sprintf "\nInferred: %s\nExpected: %s"
+ (Pp.ppterm (H.cic it)) (Pp.ppterm (H.cic et)))
+ | None -> None, "\nNo types"
+ in
+ let context, _clears = Cn.get_clears st.context (H.cic t) xtypes in
+ {st with context = context}
+ in
+ match t with
+ | C.ALambda (_, name, w, t) as what -> proc_lambda (f st) what name w t
+ | C.ALetIn (_, name, v, w, t) as what -> proc_letin (f st) what name v w t
+ | C.ARel _ as what -> proc_rel (f st) what
+ | C.AMutConstruct _ as what -> proc_mutconstruct (f st) what
+ | C.AConst _ as what -> proc_const (f st) what
+ | C.AAppl (_, hd :: tl) as what -> proc_appl (f st) what hd tl
+ | C.AMutCase (_, uri, i, u, v, ts) as what -> proc_case (f st) what uri i u v ts
+ | what -> proc_other (f st) what
+
+and proc_bkd_proofs st synth names classes ts =
try
+ let get_names b = ref (names, if b then push st else st) in
+ let get_note f b names =
+ match !names with
+ | [], st -> f st
+ | "" :: tl, st -> names := tl, st; f st
+ | hd :: tl, st ->
+ let note = case st hd in
+ names := tl, inc st;
+ if b then T.Note note :: f st else f st
+ in
let _, dtext = test_depth st in
let aux (inv, _) v =
if I.overlaps synth inv then None else
- if I.S.is_empty inv then Some (proc_proof st v) else
- Some [T.Apply (v, dtext ^ "dependent")]
- in
- T.list_map2_filter aux classes ts
-with Invalid_argument _ -> failwith "A2P.proc_bkd_proofs"
+ if I.S.is_empty inv then Some (get_note (fun st -> proc_proof st v)) else
+ Some (get_note (fun _ -> [T.Apply (v, dtext ^ "dependent")]))
+ in
+ let ps = T.list_map2_filter aux classes ts in
+ let b = List.length ps > 1 in
+ let names = get_names b in
+ List.rev_map (fun f -> f b names) ps
+
+with Invalid_argument s -> failwith ("A2P.proc_bkd_proofs: " ^ s)
(* object costruction *******************************************************)
-let is_theorem pars =
- List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars ||
- List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars
+let th_flavours = [`Theorem; `Lemma; `Remark; `Fact]
+
+let def_flavours = [`Definition]
-let proc_obj st = function
- | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
- let ast = proc_proof st v in
- let count = T.count_steps 0 ast in
- let text = Printf.sprintf "tactics: %u" count in
- T.Theorem (s, t, text) :: ast @ [T.Qed ""]
- | _ ->
- failwith "not a theorem"
+let get_flavour ?flavour attrs =
+ let rec aux = function
+ | [] -> List.hd th_flavours
+ | `Flavour fl :: _ -> fl
+ | _ :: tl -> aux tl
+ in
+ match flavour with
+ | Some fl -> fl
+ | None -> aux attrs
+
+let proc_obj ?flavour ?(info="") st = function
+ | C.AConstant (_, _, s, Some v, t, [], attrs) ->
+ begin match get_flavour ?flavour attrs with
+ | flavour when List.mem flavour th_flavours ->
+ let ast = proc_proof st v in
+ let steps, nodes = T.count_steps 0 ast, T.count_nodes 0 ast in
+ let text = Printf.sprintf "%s\n%s%s: %u\n%s: %u\n%s"
+ "COMMENTS" info "Tactics" steps "Final nodes" nodes "END"
+ in
+ T.Statement (flavour, Some s, t, None, "") :: ast @ [T.Qed text]
+ | flavour when List.mem flavour def_flavours ->
+ [T.Statement (flavour, Some s, t, Some v, "")]
+ | _ ->
+ failwith "not a theorem, definition, axiom or inductive type"
+ end
+ | C.AConstant (_, _, s, None, t, [], attrs) ->
+ [T.Statement (`Axiom, Some s, t, None, "")]
+ | C.AInductiveDefinition (_, types, [], lpsno, attrs) ->
+ [T.Inductive (types, lpsno, "")]
+ | _ ->
+ failwith "not a theorem, definition, axiom or inductive type"
(* interface functions ******************************************************)
-let acic2procedural ~ids_to_inner_sorts ~ids_to_inner_types ?depth prefix aobj =
+let procedural_of_acic_object ~ids_to_inner_sorts ~ids_to_inner_types
+ ?info ?depth ?flavour prefix anobj =
+ let st = {
+ sorts = ids_to_inner_sorts;
+ types = ids_to_inner_types;
+ max_depth = depth;
+ depth = 0;
+ context = [];
+ case = []
+ } in
+ L.time_stamp "P : LEVEL 2 ";
+ HLog.debug "Procedural: level 2 transformation";
+ let steps = proc_obj st ?flavour ?info anobj in
+ L.time_stamp "P : RENDERING";
+ HLog.debug "Procedural: grafite rendering";
+ let r = List.rev (T.render_steps [] steps) in
+ L.time_stamp "P : DONE "; r
+
+let procedural_of_acic_term ~ids_to_inner_sorts ~ids_to_inner_types ?depth
+ prefix context annterm =
let st = {
- sorts = ids_to_inner_sorts;
- types = ids_to_inner_types;
- prefix = prefix;
- max_depth = depth;
- depth = 0;
- context = [];
- intros = []
+ sorts = ids_to_inner_sorts;
+ types = ids_to_inner_types;
+ max_depth = depth;
+ depth = 0;
+ context = context;
+ case = []
} in
HLog.debug "Procedural: level 2 transformation";
- let steps = proc_obj st aobj in
+ let steps = proc_proof st annterm in
HLog.debug "Procedural: grafite rendering";
List.rev (T.render_steps [] steps)
projects / helm.git / blobdiff