module C = Cic
module I = CicInspect
module D = Deannotate
-module DTI = DoubleTypeInference
+module S = CicSubstitution
module TC = CicTypeChecker
module Un = CicUniv
module UM = UriManager
module A = Cic2acic
module Ut = CicUtil
module E = CicEnvironment
-module PER = ProofEngineReduction
+module PEH = ProofEngineHelpers
+module Pp = CicPp
-module P = ProceduralPreprocess
module Cl = ProceduralClassify
-module M = ProceduralMode
module T = ProceduralTypes
module Cn = ProceduralConversion
(* helpers ******************************************************************)
-let identity x = x
-
-let comp f g x = f (g x)
-
let cic = D.deannotate_term
let split2_last l1 l2 =
| {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"
-
+*)
+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
+ | Some (C.Name name, e) :: _ when name = id -> e
+ | _ :: tl -> aux tl
+ in
+ aux st.context
+
(* proof construction *******************************************************)
let unused_premise = "UNUSED"
-let defined_premise = "DEFINED"
-
-let expanded_premise = "EXPANDED"
+let mk_exp_args hd tl classes =
+ let meta id = C.AImplicit (id, None) in
+ let map v (cl, b) =
+ if I.S.mem 0 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 = aux args in
+ if args = [] then hd else C.AAppl ("", hd :: args)
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
+ | 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 (st, et, None, e, "")]
- | Some id -> [T.Change (st, et, Some (id, id), e, ""); T.ClearBody (id, "")]
-
-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)
- 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
+ | 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
+
+let get_intro = function
| 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"
+ | C.Name s -> s
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
+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 =
+ 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
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
+ let script = mk_arg st what in
+ let where = Some (premise, name) in
+ T.Rewrite (direction, what, where, 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)]
- 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
- end
- | C.ACast (_, v, _) ->
- mk_fwd_proof st dtext name v
- | v ->
- match get_inner_types st v with
+let mk_rewrite st dtext what qs tl direction =
+ 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 intro = get_intro name in
+ proc_proof (add st entry intro) t
+
+and proc_letin st what name v 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
| 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)]
+ let rqv = match v with
+ | C.AAppl (_, hd :: tl) when is_fwd_rewrite_right hd tl ->
+ mk_fwd_rewrite st dtext intro tl true
+ | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left hd tl ->
+ mk_fwd_rewrite st dtext intro tl false
+ | v ->
+ let qs = [[T.Id ""]; proc_proof (next st) v] in
+ [T.Branch (qs, ""); T.Cut (intro, ity, dtext)]
+ in
+ C.Decl (cic ity), rqv
+ | None ->
+ C.Def (cic v, None), [T.LetIn (intro, v, 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, _ = P.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 =
+ let entry = Some (name, hyp) in
+ let qt = proc_proof (next (add st entry intro)) t in
+ List.rev_append rqv qt
+ else
+ [T.Apply (what, dtext)]
+ in
+ mk_intros st 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
+
+and proc_mutconstruct st what =
+ let _, dtext = test_depth st in
+ let script = [T.Apply (what, dtext)] in
+ mk_intros st 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
+ 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
+ else if is_rewrite_left hd then
+ script @ mk_rewrite st dtext where qs tl true
+ else
+ let predicate = List.nth tl (argsno - i) in
+ let e = Cn.mk_pattern 0 (T.mk_arel 1 "") (* j predicate *) in
+ let using = Some hd in
+ script @
+ [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
+ script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
+ else
+ [T.Apply (what, dtext)]
+ in
+ mk_intros st script
+
+and proc_other st what =
+ 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 =
try
let _, dtext = test_depth st in
- let aux inv v =
+ 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
+ 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.mk_bkd_proofs"
+with Invalid_argument _ -> failwith "A2P.proc_bkd_proofs"
(* object costruction *******************************************************)
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
+let proc_obj st = function
| C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
- let ast = mk_proof st v in
+ 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 ""]
context = [];
intros = []
} in
- HLog.debug "Level 2 transformation";
- let steps = mk_obj st aobj in
- HLog.debug "grafite rendering";
+ HLog.debug "Procedural: level 2 transformation";
+ let steps = proc_obj st aobj in
+ HLog.debug "Procedural: grafite rendering";
List.rev (T.render_steps [] steps)
projects / helm.git / blobdiff