module C = Cic
module E = CicEnvironment
module Un = CicUniv
-module TC = CicTypeChecker
-module D = Deannotate
+module TC = CicTypeChecker
module UM = UriManager
+module Rd = CicReduction
+module PEH = ProofEngineHelpers
+module PT = PrimitiveTactics
+module DTI = DoubleTypeInference
-module T = ProceduralTypes
+module H = ProceduralHelpers
(* helpers ******************************************************************)
-let cic = D.deannotate_term
-
-let get_ind_type uri tyno =
- match E.get_obj Un.empty_ugraph uri with
- | C.InductiveDefinition (tys, _, lpsno, _), _ -> lpsno, List.nth tys tyno
- | _ -> assert false
-
-let get_default_eliminator context uri tyno ty =
- let _, (name, _, _, _) = get_ind_type uri tyno in
- let sort, _ = TC.type_of_aux' [] context ty Un.empty_ugraph in
- let ext = match sort with
- | C.Sort C.Prop -> "_ind"
- | C.Sort C.Set -> "_rec"
- | C.Sort C.CProp -> "_rec"
- | C.Sort (C.Type _) -> "_rect"
- | C.Meta (_,_) -> assert false
- | _ -> assert false
- in
- let buri = UM.buri_of_uri uri in
- let uri = UM.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con") in
- C.Const (uri, [])
-
+let rec list_sub start length = function
+ | _ :: tl when start > 0 -> list_sub (pred start) length tl
+ | hd :: tl when length > 0 -> hd :: list_sub start (pred length) tl
+ | _ -> []
+
(* proof construction *******************************************************)
-let rec need_whd i = function
- | C.ACast (_, t, _) -> need_whd i t
- | C.AProd (_, _, _, t) when i > 0 -> need_whd (pred i) t
- | _ when i > 0 -> true
- | _ -> false
-
-let lift k n =
- let rec lift_xns k (uri, t) = uri, lift_term k t
- and lift_ms k = function
+let iter f k =
+ let rec iter_xns k (uri, t) = uri, iter_term k t
+ and iter_ms k = function
| None -> None
- | Some t -> Some (lift_term k t)
- and lift_fix len k (id, name, i, ty, bo) =
- id, name, i, lift_term k ty, lift_term (k + len) bo
- and lift_cofix len k (id, name, ty, bo) =
- id, name, lift_term k ty, lift_term (k + len) bo
- and lift_term k = function
+ | Some t -> Some (iter_term k t)
+ and iter_fix len k (id, name, i, ty, bo) =
+ id, name, i, iter_term k ty, iter_term (k + len) bo
+ and iter_cofix len k (id, name, ty, bo) =
+ id, name, iter_term k ty, iter_term (k + len) bo
+ and iter_term k = function
| C.ASort _ as t -> t
| C.AImplicit _ as t -> t
- | C.ARel (id, rid, m, b) as t -> if m < k then t else C.ARel (id, rid, m + n, b)
- | C.AConst (id, uri, xnss) -> C.AConst (id, uri, List.map (lift_xns k) xnss)
- | C.AVar (id, uri, xnss) -> C.AVar (id, uri, List.map (lift_xns k) xnss)
- | C.AMutInd (id, uri, tyno, xnss) -> C.AMutInd (id, uri, tyno, List.map (lift_xns k) xnss)
- | C.AMutConstruct (id, uri, tyno, consno, xnss) -> C.AMutConstruct (id, uri,tyno,consno, List.map (lift_xns k) xnss)
- | C.AMeta (id, i, mss) -> C.AMeta(id, i, List.map (lift_ms k) mss)
- | C.AAppl (id, ts) -> C.AAppl (id, List.map (lift_term k) ts)
- | C.ACast (id, te, ty) -> C.ACast (id, lift_term k te, lift_term k ty)
- | C.AMutCase (id, sp, i, outty, t, pl) -> C.AMutCase (id, sp, i, lift_term k outty, lift_term k t, List.map (lift_term k) pl)
- | C.AProd (id, n, s, t) -> C.AProd (id, n, lift_term k s, lift_term (succ k) t)
- | C.ALambda (id, n, s, t) -> C.ALambda (id, n, lift_term k s, lift_term (succ k) t)
- | C.ALetIn (id, n, s, t) -> C.ALetIn (id, n, lift_term k s, lift_term (succ k) t)
- | C.AFix (id, i, fl) -> C.AFix (id, i, List.map (lift_fix (List.length fl) k) fl)
- | C.ACoFix (id, i, fl) -> C.ACoFix (id, i, List.map (lift_cofix (List.length fl) k) fl)
+ | C.ARel (id, rid, m, b) as t ->
+ if m < k then t else f k id rid m b
+ | C.AConst (id, uri, xnss) -> C.AConst (id, uri, List.map (iter_xns k) xnss)
+ | C.AVar (id, uri, xnss) -> C.AVar (id, uri, List.map (iter_xns k) xnss)
+ | C.AMutInd (id, uri, tyno, xnss) -> C.AMutInd (id, uri, tyno, List.map (iter_xns k) xnss)
+ | C.AMutConstruct (id, uri, tyno, consno, xnss) -> C.AMutConstruct (id, uri,tyno,consno, List.map (iter_xns k) xnss)
+ | C.AMeta (id, i, mss) -> C.AMeta(id, i, List.map (iter_ms k) mss)
+ | C.AAppl (id, ts) -> C.AAppl (id, List.map (iter_term k) ts)
+ | C.ACast (id, te, ty) -> C.ACast (id, iter_term k te, iter_term k ty)
+ | C.AMutCase (id, sp, i, outty, t, pl) -> C.AMutCase (id, sp, i, iter_term k outty, iter_term k t, List.map (iter_term k) pl)
+ | C.AProd (id, n, s, t) -> C.AProd (id, n, iter_term k s, iter_term (succ k) t)
+ | C.ALambda (id, n, s, t) -> C.ALambda (id, n, iter_term k s, iter_term (succ k) t)
+ | C.ALetIn (id, n, ty, s, t) -> C.ALetIn (id, n, iter_term k ty, iter_term k s, iter_term (succ k) t)
+ | C.AFix (id, i, fl) -> C.AFix (id, i, List.map (iter_fix (List.length fl) k) fl)
+ | C.ACoFix (id, i, fl) -> C.ACoFix (id, i, List.map (iter_cofix (List.length fl) k) fl)
in
- lift_term k
+ iter_term k
-let fake_annotate c =
+let lift k n =
+ let f _ id rid m b =
+ if m + n > 0 then C.ARel (id, rid, m + n, b) else
+ begin
+ HLog.error (Printf.sprintf "ProceduralConversion.lift: %i %i" m n);
+ assert false
+ end
+ in
+ iter f k
+
+let subst k v =
+ let f k id rid m b =
+ if m = k then lift 1 (pred k) v else C.ARel (id, rid, pred m, b)
+ in
+ iter f k
+
+let fake_annotate id c =
let get_binder c m =
try match List.nth c (pred m) with
- | Some (C.Name s, _) -> s
- | _ -> assert false
+ | Some (C.Name s, _) -> s
+ | _ -> assert false
with
- | Invalid_argument _ -> assert false
+ | Invalid_argument _ -> assert false
in
let mk_decl n v = Some (n, C.Decl v) in
- let mk_def n v = Some (n, C.Def (v, None)) in
- let mk_fix (name, _, _, bo) = mk_def (C.Name name) bo in
- let mk_cofix (name, _, bo) = mk_def (C.Name name) bo in
+ let mk_def n v ty = Some (n, C.Def (v, ty)) in
+ let mk_fix (name, _, ty, bo) = mk_def (C.Name name) bo ty in
+ let mk_cofix (name, ty, bo) = mk_def (C.Name name) bo ty in
let rec ann_xns c (uri, t) = uri, ann_term c t
and ann_ms c = function
- | None -> None
+ | None -> None
| Some t -> Some (ann_term c t)
and ann_fix newc c (name, i, ty, bo) =
- "", name, i, ann_term c ty, ann_term (List.rev_append newc c) bo
+ id, name, i, ann_term c ty, ann_term (List.rev_append newc c) bo
and ann_cofix newc c (name, ty, bo) =
- "", name, ann_term c ty, ann_term (List.rev_append newc c) bo
+ id, name, ann_term c ty, ann_term (List.rev_append newc c) bo
and ann_term c = function
- | C.Sort sort -> C.ASort ("", sort)
- | C.Implicit ann -> C.AImplicit ("", ann)
- | C.Rel m -> C.ARel ("", "", m, get_binder c m)
- | C.Const (uri, xnss) -> C.AConst ("", uri, List.map (ann_xns c) xnss)
- | C.Var (uri, xnss) -> C.AVar ("", uri, List.map (ann_xns c) xnss)
- | C.MutInd (uri, tyno, xnss) -> C.AMutInd ("", uri, tyno, List.map (ann_xns c) xnss)
- | C.MutConstruct (uri, tyno, consno, xnss) -> C.AMutConstruct ("", uri,tyno,consno, List.map (ann_xns c) xnss)
- | C.Meta (i, mss) -> C.AMeta("", i, List.map (ann_ms c) mss)
- | C.Appl ts -> C.AAppl ("", List.map (ann_term c) ts)
- | C.Cast (te, ty) -> C.ACast ("", ann_term c te, ann_term c ty)
- | C.MutCase (sp, i, outty, t, pl) -> C.AMutCase ("", sp, i, ann_term c outty, ann_term c t, List.map (ann_term c) pl)
- | C.Prod (n, s, t) -> C.AProd ("", n, ann_term c s, ann_term (mk_decl n s :: c) t)
- | C.Lambda (n, s, t) -> C.ALambda ("", n, ann_term c s, ann_term (mk_decl n s :: c) t)
- | C.LetIn (n, s, t) -> C.ALetIn ("", n, ann_term c s, ann_term (mk_def n s :: c) t)
- | C.Fix (i, fl) -> C.AFix ("", i, List.map (ann_fix (List.rev_map mk_fix fl) c) fl)
- | C.CoFix (i, fl) -> C.ACoFix ("", i, List.map (ann_cofix (List.rev_map mk_cofix fl) c) fl)
+ | C.Sort sort -> C.ASort (id, sort)
+ | C.Implicit ann -> C.AImplicit (id, ann)
+ | C.Rel m -> C.ARel (id, id, m, get_binder c m)
+ | C.Const (uri, xnss) -> C.AConst (id, uri, List.map (ann_xns c) xnss)
+ | C.Var (uri, xnss) -> C.AVar (id, uri, List.map (ann_xns c) xnss)
+ | C.MutInd (uri, tyno, xnss) -> C.AMutInd (id, uri, tyno, List.map (ann_xns c) xnss)
+ | C.MutConstruct (uri, tyno, consno, xnss) -> C.AMutConstruct (id, uri,tyno,consno, List.map (ann_xns c) xnss)
+ | C.Meta (i, mss) -> C.AMeta(id, i, List.map (ann_ms c) mss)
+ | C.Appl ts -> C.AAppl (id, List.map (ann_term c) ts)
+ | C.Cast (te, ty) -> C.ACast (id, ann_term c te, ann_term c ty)
+ | C.MutCase (sp, i, outty, t, pl) -> C.AMutCase (id, sp, i, ann_term c outty, ann_term c t, List.map (ann_term c) pl)
+ | C.Prod (n, s, t) -> C.AProd (id, n, ann_term c s, ann_term (mk_decl n s :: c) t)
+ | C.Lambda (n, s, t) -> C.ALambda (id, n, ann_term c s, ann_term (mk_decl n s :: c) t)
+ | C.LetIn (n, s, ty, t) -> C.ALetIn (id, n, ann_term c s, ann_term c ty, ann_term (mk_def n s ty :: c) t)
+ | C.Fix (i, fl) -> C.AFix (id, i, List.map (ann_fix (List.rev_map mk_fix fl) c) fl)
+ | C.CoFix (i, fl) -> C.ACoFix (id, i, List.map (ann_cofix (List.rev_map mk_cofix fl) c) fl)
in
ann_term c
-let rec add_abst n t =
- if n <= 0 then t else
- let t = C.ALambda ("", C.Anonymous, C.AImplicit ("", None), lift 0 1 t) in
- add_abst (pred n) t
-
-let mk_ind context id uri tyno outty arg cases =
- let lpsno, (_, _, arity, constructors) = get_ind_type uri tyno in
- let inty, _ = TC.type_of_aux' [] context (cic arg) Un.empty_ugraph in
- let ps = match inty with
- | C.MutInd _ -> []
- | C.Appl (C.MutInd _ :: args) -> List.map (fake_annotate context) args
- | _ -> assert false
+let mk_arel k = C.ARel ("", "", k, "")
+
+let mk_aappl ts = C.AAppl ("", ts)
+
+let rec clear_absts f n k = function
+ | t when n = 0 -> f k t
+ | C.ALambda (_, _, _, t) -> clear_absts f (pred n) (succ k) t
+ | t ->
+ let u = match mk_aappl [lift (succ k) 1 t; mk_arel (succ k)] with
+ | C.AAppl (_, [ C.AAppl (id, ts); t]) -> C.AAppl (id, ts @ [t])
+ | t -> t
+ in
+ clear_absts f (pred n) (succ k) u
+
+let hole id = C.AImplicit (id, Some `Hole)
+
+let meta id = C.AImplicit (id, None)
+
+let anon = C.Anonymous
+
+let generalize n =
+ let is_meta =
+ let map b = function
+ | C.AImplicit (_, None) when b -> b
+ | _ -> false
+ in
+ List.fold_left map true
+ in
+ let rec gen_fix len k (id, name, i, ty, bo) =
+ id, name, i, gen_term k ty, gen_term (k + len) bo
+ and gen_cofix len k (id, name, ty, bo) =
+ id, name, gen_term k ty, gen_term (k + len) bo
+ and gen_term k = function
+ | C.ASort (id, _)
+ | C.AImplicit (id, _)
+ | C.AConst (id, _, _)
+ | C.AVar (id, _, _)
+ | C.AMutInd (id, _, _, _)
+ | C.AMutConstruct (id, _, _, _, _)
+ | C.AMeta (id, _, _) -> meta id
+ | C.ARel (id, _, m, _) ->
+ if succ (k - n) <= m && m <= k then hole id else meta id
+ | C.AAppl (id, ts) ->
+ let ts = List.map (gen_term k) ts in
+ if is_meta ts then meta id else C.AAppl (id, ts)
+ | C.ACast (id, te, ty) ->
+ let te, ty = gen_term k te, gen_term k ty in
+ if is_meta [te; ty] then meta id else C.ACast (id, te, ty)
+ | C.AMutCase (id, sp, i, outty, t, pl) ->
+ let outty, t, pl = gen_term k outty, gen_term k t, List.map (gen_term k) pl in
+ if is_meta (outty :: t :: pl) then meta id else hole id (* C.AMutCase (id, sp, i, outty, t, pl) *)
+ | C.AProd (id, _, s, t) ->
+ let s, t = gen_term k s, gen_term (succ k) t in
+ if is_meta [s; t] then meta id else C.AProd (id, anon, s, t)
+ | C.ALambda (id, _, s, t) ->
+ let s, t = gen_term k s, gen_term (succ k) t in
+ if is_meta [s; t] then meta id else C.ALambda (id, anon, s, t)
+ | C.ALetIn (id, _, s, ty, t) ->
+ let s, ty, t = gen_term k s, gen_term k ty, gen_term (succ k) t in
+ if is_meta [s; t] then meta id else C.ALetIn (id, anon, s, ty, t)
+ | C.AFix (id, i, fl) -> C.AFix (id, i, List.map (gen_fix (List.length fl) k) fl)
+ | C.ACoFix (id, i, fl) -> C.ACoFix (id, i, List.map (gen_cofix (List.length fl) k) fl)
+ in
+ gen_term
+
+let convert g ity k predicate =
+ let rec aux = function
+ | C.ALambda (_, _, b, ity), C.ALambda (id, n, u, pred) ->
+ C.ALambda (id, n, aux (b, u), aux (ity, pred))
+ | C.AProd (_, _, b, ity), C.AProd (id, n, u, pred) ->
+ C.AProd (id, n, aux (b, u), aux (ity, pred))
+ | C.ALetIn (_, _, a, b, ity), C.ALetIn (id, n, v, u, pred) ->
+ C.ALetIn (id, n, aux (a, v), aux (b, u), aux (ity, pred))
+ | C.AAppl (_, bs), C.AAppl (id, us) when List.length bs = List.length us ->
+ let map b u = aux (b,u) in
+ C.AAppl (id, List.map2 map bs us)
+ | C.ACast (_, ity, b), C.ACast (id, pred, u) ->
+ C.ACast (id, aux (ity, pred), aux (b, u))
+ | ity, C.AAppl (_, C.ALambda (_, _, _, pred) :: v :: []) ->
+ aux (ity, subst 1 v pred)
+ | ity, C.AAppl (id, C.ALambda (_, _, _, pred) :: v :: vs) ->
+ aux (ity, C.AAppl (id, subst 1 v pred :: vs))
+ | _, pred -> pred
+ in
+ g k (aux (ity, predicate))
+
+let mk_pattern psno ity predicate =
+ clear_absts (convert (generalize psno) ity) psno 0 predicate
+
+let beta v = function
+ | C.ALambda (_, _, _, t) -> subst 1 v t
+ | _ -> assert false
+
+let get_clears c p xtypes =
+ let meta = C.Implicit None in
+ let rec aux c names p it et = function
+ | [] ->
+ List.rev c, List.rev names
+ | Some (C.Name name as n, C.Decl v) as hd :: tl ->
+ let hd, names, v =
+ if DTI.does_not_occur 1 p && DTI.does_not_occur 1 it && DTI.does_not_occur 1 et then
+ Some (C.Anonymous, C.Decl v), name :: names, meta
+ else
+ hd, names, v
+ in
+ let p = C.Lambda (n, v, p) in
+ let it = C.Prod (n, v, it) in
+ let et = C.Prod (n, v, et) in
+ aux (hd :: c) names p it et tl
+ | Some (C.Name name as n, C.Def (v, x)) as hd :: tl ->
+ let hd, names, v =
+ if DTI.does_not_occur 1 p && DTI.does_not_occur 1 it && DTI.does_not_occur 1 et then
+ Some (C.Anonymous, C.Def (v, x)), name :: names, meta
+ else
+ hd, names, v
+ in
+ let p = C.LetIn (n, v, x, p) in
+ let it = C.LetIn (n, v, x, it) in
+ let et = C.LetIn (n, v, x, et) in
+ aux (hd :: c) names p it et tl
+ | Some (C.Anonymous as n, C.Decl v) as hd :: tl ->
+ let p = C.Lambda (n, meta, p) in
+ let it = C.Lambda (n, meta, it) in
+ let et = C.Lambda (n, meta, et) in
+ aux (hd :: c) names p it et tl
+ | Some (C.Anonymous as n, C.Def (v, _)) as hd :: tl ->
+ let p = C.LetIn (n, meta, meta, p) in
+ let it = C.LetIn (n, meta, meta, it) in
+ let et = C.LetIn (n, meta, meta, et) in
+ aux (hd :: c) names p it et tl
+ | None :: tl -> assert false
+ in
+ match xtypes with
+ | Some (it, et) -> aux [] [] p it et c
+ | None -> c, []
+
+let clear c hyp =
+ let rec aux c = function
+ | [] -> List.rev c
+ | Some (C.Name name, entry) :: tail when name = hyp ->
+ aux (Some (C.Anonymous, entry) :: c) tail
+ | entry :: tail -> aux (entry :: c) tail
+ in
+ aux [] c
+(*
+let elim_inferred_type context goal arg using cpattern =
+ let metasenv, ugraph = [], Un.default_ugraph in
+ let ety = H.get_type "elim_inferred_type" context using in
+ let _splits, args_no = PEH.split_with_whd (context, ety) in
+ let _metasenv, _subst, predicate, _arg, actual_args =
+ PT.mk_predicate_for_elim
+ ~context ~metasenv ~subst:[] ~ugraph ~goal ~arg ~using ~cpattern ~args_no
in
- let lps, rps = T.list_split lpsno ps in
- let eliminator = get_default_eliminator context uri tyno inty in
- let arg_ref = T.mk_arel 0 "" in
- let body = C.AMutCase (id, uri, tyno, outty, arg_ref, cases) in
- let predicate = add_abst (succ (List.length rps)) body in
- None
+ let ty = C.Appl (predicate :: actual_args) in
+ let upto = List.length actual_args in
+ Rd.head_beta_reduce ~delta:false ~upto ty
+*)
+let does_not_occur = function
+ | C.AImplicit (_, None) -> true
+ | _ -> false
projects / helm.git / blobdiff