* http://cs.unibo.it/helm/.
*)
-module C = Cic
-module I = CicInspect
-module D = Deannotate
-module DTI = DoubleTypeInference
-module TC = CicTypeChecker
-module Un = CicUniv
-module UM = UriManager
-module Obj = LibraryObjects
-module HObj = HelmLibraryObjects
-module A = Cic2acic
-module Ut = CicUtil
-module E = CicEnvironment
-module PER = ProofEngineReduction
+module C = Cic
+module L = Librarian
+module G = GrafiteAst
-module Cl = ProceduralClassify
-module M = ProceduralMode
-module T = ProceduralTypes
-module Cn = ProceduralConversion
+module H = ProceduralHelpers
+module T = ProceduralTypes
+module P1 = Procedural1
+module P2 = Procedural2
+module X = ProceduralTeX
-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
-}
+let tex_formatter = ref None
-(* helpers ******************************************************************)
-
-let identity x = x
-
-let comp f g x = f (g x)
-
-let cic = D.deannotate_term
-
-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
- 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.AMutInd _ -> "mutind"
- | C.AMutConstruct _ -> "mutconstruct"
- | C.AVar _ -> "var"
- | C.ARel _ -> "rel"
- | C.AProd _ -> "prod"
- | C.ALambda _ -> "lambda"
- | C.ALetIn _ -> "letin"
- | C.AFix _ -> "fix"
- | C.ACoFix _ -> "cofix"
- | C.AAppl _ -> "appl"
- | C.ACast _ -> "cast"
- | C.AMutCase _ -> "mutcase"
- | C.AMeta _ -> "meta"
- | C.AImplicit _ -> "implict"
-
-let clear st = {st with intros = []}
-
-let next st = {(clear st) with depth = succ st.depth}
-
-let add st entry intro =
- {st with context = entry :: st.context; intros = intro :: st.intros}
-
-let test_depth st =
-try
- let msg = Printf.sprintf "Depth %u: " st.depth in
- match st.max_depth with
- | None -> true, ""
- | Some d -> if st.depth < d then true, msg else false, "DEPTH EXCEDED: "
-with Invalid_argument _ -> failwith "A2P.test_depth"
-
-let is_rewrite_right = function
- | C.AConst (_, uri, []) ->
- UM.eq uri HObj.Logic.eq_ind_r_URI || Obj.is_eq_ind_r_URI uri
- | _ -> false
-
-let is_rewrite_left = function
- | C.AConst (_, uri, []) ->
- UM.eq uri HObj.Logic.eq_ind_URI || Obj.is_eq_ind_URI uri
- | _ -> false
-
-let is_fwd_rewrite_right hd tl =
- if is_rewrite_right hd then match List.nth tl 3 with
- | C.ARel _ -> true
- | _ -> false
- else false
-
-let is_fwd_rewrite_left hd tl =
- if is_rewrite_left hd then match List.nth tl 3 with
- | 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
- try match Hashtbl.find st.types id with
- | {A.annsynthesized = st; A.annexpected = Some et} -> Some (st, et)
- | {A.annsynthesized = st; A.annexpected = None} -> Some (st, st)
- with Not_found -> None
-with Invalid_argument _ -> failwith "A2P.get_inner_types"
-
-let get_inner_sort st v =
-try
- let id = Ut.id_of_annterm v in
- try Hashtbl.find st.sorts id
- with Not_found -> `Type (CicUniv.fresh())
-with Invalid_argument _ -> failwith "A2P.get_sort"
-
-(* proof construction *******************************************************)
-
-let unused_premise = "UNUSED"
-
-let defined_premise = "DEFINED"
+(* object costruction *******************************************************)
-let expanded_premise = "EXPANDED"
+let th_flavours = [`Theorem; `Lemma; `Remark; `Fact]
-let convert st ?name v =
- match get_inner_types st v with
- | None -> []
- | Some (st, et) ->
- let cst, cet = cic st, cic et in
- if PER.alpha_equivalence cst cet then [] else
- let e = Cn.mk_pattern [] (T.mk_arel 1 "") in
- match name with
- | None -> [T.Change (st, et, None, e, "")]
- | Some id -> [T.Change (st, et, Some (id, id), e, ""); T.ClearBody (id, "")]
+let def_flavours = [`Definition; `Variant]
-let eta_expand n t =
- let id = Ut.id_of_annterm t in
- let ty = C.AImplicit ("", None) in
- let name i = Printf.sprintf "%s%u" expanded_premise i in
- let lambda i t = C.ALambda (id, C.Name (name i), ty, t) in
- let arg i n = T.mk_arel (n - i) (name (n - i - 1)) in
- let rec aux i f a =
- if i >= n then f, a else aux (succ i) (comp f (lambda i)) (arg i n :: a)
+let get_flavour sorts params context v attrs =
+ let rec aux = function
+ | [] ->
+ if H.is_acic_proof sorts context v then List.hd th_flavours
+ else List.hd def_flavours
+ | `Flavour fl :: _ -> fl
+ | _ :: tl -> aux tl
in
- let absts, args = aux 0 identity [] in
- match Cn.lift 1 n t with
- | C.AAppl (id, ts) -> absts (C.AAppl (id, ts @ args))
- | t -> absts (C.AAppl ("", t :: args))
-
-let appl_expand n = function
- | C.AAppl (id, ts) ->
- let before, after = T.list_split (List.length ts + n) ts in
- C.AAppl (id, C.AAppl ("", before) :: after)
- | _ -> assert false
-
-let get_intro name t =
-try
-match name with
- | C.Anonymous -> unused_premise
- | C.Name s ->
- if DTI.does_not_occur 1 (cic t) then unused_premise else s
-with Invalid_argument _ -> failwith "A2P.get_intro"
-
-let mk_intros st script =
-try
- if st.intros = [] then script else
- let count = List.length st.intros in
- T.Intros (Some count, List.rev st.intros, "") :: script
-with Invalid_argument _ -> failwith "A2P.mk_intros"
-
-let rec mk_atomic st dtext what =
- if T.is_atomic what then
- match what with
- | C.ARel (_, _, _, name) -> convert st ~name what, what
- | _ -> [], what
- else
- let name = defined_premise in
- let script = convert st ~name what in
- script @ mk_fwd_proof st dtext name what, T.mk_arel 0 name
-
-and mk_fwd_rewrite st dtext name tl direction =
- let what, where = List.nth tl 5, List.nth tl 3 in
- let rps, predicate = [List.nth tl 4], List.nth tl 2 in
- let e = Cn.mk_pattern rps predicate in
- match where with
- | C.ARel (_, _, _, premise) ->
- let script, what = mk_atomic st dtext what in
- T.Rewrite (direction, what, Some (premise, name), e, dtext) :: script
- | _ -> assert false
-
-and mk_fwd_proof st dtext name = function
- | C.ALetIn (_, n, v, t) ->
- let entry = Some (n, C.Def (cic v, None)) in
- let intro = get_intro n t in
- let qt = mk_fwd_proof (add st entry intro) dtext name t in
- let qv = mk_fwd_proof st "" intro v in
- List.append qt qv
- | C.AAppl (_, hd :: tl) as v ->
- if is_fwd_rewrite_right hd tl then mk_fwd_rewrite st dtext name tl true else
- if is_fwd_rewrite_left hd tl then mk_fwd_rewrite st dtext name tl false else
- let ty, _ = TC.type_of_aux' [] st.context (cic hd) Un.empty_ugraph in
- begin match get_inner_types st v with
- | Some (ity, _) when M.bkd st.context ty ->
- let qs = [[T.Id ""]; mk_proof (next st) v] in
- [T.Branch (qs, ""); T.Cut (name, ity, dtext)]
- | _ ->
- let (classes, rc) as h = Cl.classify st.context ty in
- let text = Printf.sprintf "%u %s" (List.length classes) (Cl.to_string h) in
- [T.LetIn (name, v, dtext ^ text)]
+ let flavour_map x y = match x, y with
+ | None, G.IPAs flavour -> Some flavour
+ | _ -> x
+ in
+ match List.fold_left flavour_map None params with
+ | Some fl -> fl
+ | None -> aux attrs
+
+let rec is_record = function
+ | [] -> None
+ | `Class (`Record fields) :: _ -> Some fields
+ | _ :: tl -> is_record tl
+
+let proc_obj ?(info="") proc_proof sorts params context = function
+ | C.AConstant (_, _, s, Some v, t, [], attrs) ->
+ begin match get_flavour sorts params context v attrs with
+ | flavour when List.mem flavour th_flavours ->
+ let ast = proc_proof v in
+ let steps, nodes = T.count_steps 0 ast, T.count_nodes 0 ast in
+ let text =
+ if List.mem G.IPComments params then
+ Printf.sprintf "%s\n%s%s: %u\n%s: %u\n%s"
+ "COMMENTS" info "Tactics" steps "Final nodes" nodes "END"
+ else
+ ""
+ 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.AMutCase (id, uri, tyno, outty, arg, cases) as v ->
- begin match Cn.mk_ind st.context id uri tyno outty arg cases with
- | None -> [T.LetIn (name, v, dtext)]
- | Some v -> mk_fwd_proof st dtext name v
+ | C.AConstant (_, _, s, None, t, [], attrs) ->
+ [T.Statement (`Axiom, Some s, t, None, "")]
+ | C.AInductiveDefinition (_, types, [], lpsno, attrs) ->
+ begin match is_record attrs with
+ | None -> [T.Inductive (types, lpsno, "")]
+ | Some fs -> [T.Record (types, lpsno, fs, "")]
end
- | C.ACast (_, v, _) ->
- mk_fwd_proof st dtext name v
- | v ->
- match get_inner_types st v with
- | Some (ity, _) ->
- let qs = [[T.Id ""]; mk_proof (next st) v] in
- [T.Branch (qs, ""); T.Cut (name, ity, dtext)]
- | _ ->
- [T.LetIn (name, v, dtext)]
-
-and mk_proof st = function
- | C.ALambda (_, name, v, t) ->
- let entry = Some (name, C.Decl (cic v)) in
- let intro = get_intro name t in
- mk_proof (add st entry intro) t
- | C.ALetIn (_, name, v, t) as what ->
- let proceed, dtext = test_depth st in
- let script = if proceed then
- let entry = Some (name, C.Def (cic v, None)) in
- let intro = get_intro name t in
- let q = mk_proof (next (add st entry intro)) t in
- List.rev_append (mk_fwd_proof st dtext intro v) q
- else
- [T.Apply (what, dtext)]
- in
- mk_intros st script
- | C.ARel _ as what ->
- let _, dtext = test_depth st in
- let text = "assumption" in
- let script = [T.Apply (what, dtext ^ text)] in
- mk_intros st script
- | C.AMutConstruct _ as what ->
- let _, dtext = test_depth st in
- let script = [T.Apply (what, dtext)] in
- mk_intros st script
- | C.AAppl (_, hd :: tl) as t ->
- let proceed, dtext = test_depth st in
- let script = if proceed then
- let ty, _ = TC.type_of_aux' [] st.context (cic hd) Un.empty_ugraph in
- let (classes, rc) as h = Cl.classify st.context ty in
- let premises, _ = Cl.split st.context ty in
- let decurry = List.length classes - List.length tl in
- if decurry < 0 then mk_proof (clear st) (appl_expand decurry t) else
- if decurry > 0 then mk_proof (clear st) (eta_expand decurry t) else
- let synth = I.S.singleton 0 in
- let text = Printf.sprintf "%u %s" (List.length classes) (Cl.to_string h) in
- match rc with
- | Some (i, j) when i > 1 && i <= List.length classes && M.is_eliminator premises ->
- let classes, tl, _, what = split2_last classes tl in
- let script, what = mk_atomic st dtext what in
- let synth = I.S.add 1 synth in
- let qs = mk_bkd_proofs (next st) synth classes tl in
- if is_rewrite_right hd then
- let rps, predicate = [List.nth tl 4], List.nth tl 2 in
- let e = Cn.mk_pattern rps predicate in
- List.rev script @ convert st t @
- [T.Rewrite (false, what, None, e, dtext); T.Branch (qs, "")]
- else if is_rewrite_left hd then
- let rps, predicate = [List.nth tl 4], List.nth tl 2 in
- let e = Cn.mk_pattern rps predicate in
- List.rev script @ convert st t @
- [T.Rewrite (true, what, None, e, dtext); T.Branch (qs, "")]
- else
- let using = Some hd in
- List.rev script @ convert st t @
- [T.Elim (what, using, dtext ^ text); T.Branch (qs, "")]
- | _ ->
- let qs = mk_bkd_proofs (next st) synth classes tl in
- let script, hd = mk_atomic st dtext hd in
- List.rev script @ convert st t @
- [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
- else
- [T.Apply (t, dtext)]
- in
- mk_intros st script
- | C.AMutCase (id, uri, tyno, outty, arg, cases) ->
- begin match Cn.mk_ind st.context id uri tyno outty arg cases with
- | _ (* None *) ->
- let text = Printf.sprintf "%s" "UNEXPANDED: mutcase" in
- let script = [T.Note text] in
- mk_intros st script
-(* | Some t -> mk_proof st t *)
- end
- | C.ACast (_, t, _) ->
- mk_proof st t
- | t ->
- let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head t) in
- let script = [T.Note text] in
- mk_intros st script
-
-and mk_bkd_proofs st synth classes ts =
-try
- 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 (mk_proof st v) else
- Some [T.Apply (v, dtext ^ "dependent")]
- in
- T.list_map2_filter aux classes ts
-with Invalid_argument _ -> failwith "A2P.mk_bkd_proofs"
-
-(* 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 mk_obj st = function
- | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
- let ast = mk_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"
+ | _ ->
+ 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 st = {
- sorts = ids_to_inner_sorts;
- types = ids_to_inner_types;
- prefix = prefix;
- max_depth = depth;
- depth = 0;
- context = [];
- intros = []
- } in
- HLog.debug "Level 2 transformation";
- let steps = mk_obj st aobj in
- HLog.debug "grafite rendering";
+let get_proc_proof ~ids_to_inner_sorts ~ids_to_inner_types params context =
+ let level_map x y = match x, y with
+ | None, G.IPLevel level -> Some level
+ | _ -> x
+ in
+ match List.fold_left level_map None params with
+ | None
+ | Some 2 ->
+ P2.proc_proof
+ (P2.init ~ids_to_inner_sorts ~ids_to_inner_types params context)
+ | Some 1 ->
+ P1.proc_proof
+ (P1.init ~ids_to_inner_sorts ~ids_to_inner_types params context)
+ | Some n ->
+ failwith (
+ "Procedural reconstruction level not supported: " ^
+ string_of_int n
+ )
+
+let procedural_of_acic_object ~ids_to_inner_sorts ~ids_to_inner_types
+ ?info params anobj =
+ let proc_proof =
+ get_proc_proof ~ids_to_inner_sorts ~ids_to_inner_types params []
+ in
+ L.time_stamp "P : LEVEL 2 ";
+ HLog.debug "Procedural: level 2 transformation";
+ let steps = proc_obj ?info proc_proof ids_to_inner_sorts params [] anobj in
+ let _ = match !tex_formatter with
+ | None -> ()
+ | Some frm -> X.tex_of_steps frm ids_to_inner_sorts steps
+ 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 params
+ context annterm =
+ let proc_proof =
+ get_proc_proof ~ids_to_inner_sorts ~ids_to_inner_types params context
+ in
+ HLog.debug "Procedural: level 2 transformation";
+ let steps = proc_proof annterm in
+ let _ = match !tex_formatter with
+ | None -> ()
+ | Some frm -> X.tex_of_steps frm ids_to_inner_sorts steps
+ in
+ HLog.debug "Procedural: grafite rendering";
List.rev (T.render_steps [] steps)
+
+let rec is_debug n = function
+ | [] -> false
+ | G.IPDebug debug :: _ -> n <= debug
+ | _ :: tl -> is_debug n tl
projects / helm.git / blobdiff