Source file zify.ml
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open Constr
open Names
open Pp
open Lazy
module NamedDecl = Context.Named.Declaration
let debug_zify = CDebug.create ~name:"zify" ()
let zify str =
EConstr.of_constr
(UnivGen.constr_of_monomorphic_global (Global.env ())
(Coqlib.lib_ref ("ZifyClasses." ^ str)))
(** classes *)
let coq_InjTyp = lazy (Coqlib.lib_ref "ZifyClasses.InjTyp")
let coq_BinOp = lazy (Coqlib.lib_ref "ZifyClasses.BinOp")
let coq_UnOp = lazy (Coqlib.lib_ref "ZifyClasses.UnOp")
let coq_CstOp = lazy (Coqlib.lib_ref "ZifyClasses.CstOp")
let coq_BinRel = lazy (Coqlib.lib_ref "ZifyClasses.BinRel")
let coq_PropBinOp = lazy (Coqlib.lib_ref "ZifyClasses.PropBinOp")
let coq_PropUOp = lazy (Coqlib.lib_ref "ZifyClasses.PropUOp")
let coq_BinOpSpec = lazy (Coqlib.lib_ref "ZifyClasses.BinOpSpec")
let coq_UnOpSpec = lazy (Coqlib.lib_ref "ZifyClasses.UnOpSpec")
let coq_Saturate = lazy (Coqlib.lib_ref "ZifyClasses.Saturate")
let mkapp2 = lazy (zify "mkapp2")
let mkapp = lazy (zify "mkapp")
let eq_refl = lazy (zify "eq_refl")
let eq = lazy (zify "eq")
let mkrel = lazy (zify "mkrel")
let iff_refl = lazy (zify "iff_refl")
let eq_iff = lazy (zify "eq_iff")
let rew_iff = lazy (zify "rew_iff")
let rew_iff_rev = lazy (zify "rew_iff_rev")
let op_and = lazy (zify "and")
let op_and_morph = lazy (zify "and_morph")
let op_or = lazy (zify "or")
let op_or_morph = lazy (zify "or_morph")
let op_impl_morph = lazy (zify "impl_morph")
let op_iff = lazy (zify "iff")
let op_iff_morph = lazy (zify "iff_morph")
let op_not = lazy (zify "not")
let op_not_morph = lazy (zify "not_morph")
let op_True = lazy (zify "True")
let op_I = lazy (zify "I")
(** [unsafe_to_constr c] returns a [Constr.t] without considering an evar_map.
This is useful for calling Constr.hash *)
let unsafe_to_constr = EConstr.Unsafe.to_constr
let pr_constr env evd e = Printer.pr_econstr_env env evd e
let gl_pr_constr e =
let genv = Global.env () in
let evd = Evd.from_env genv in
pr_constr genv evd e
let whd = Reductionops.clos_whd_flags CClosure.all
let is_convertible env evd t1 t2 = Reductionops.(is_conv env evd t1 t2)
(** [get_type_of] performs beta reduction ;
Is it ok for Retyping.get_type_of (Zpower_nat n q) to return (fun _ : nat => Z) q ? *)
let get_type_of env evd e =
Tacred.cbv_beta env evd (Retyping.get_type_of env evd e)
let rec find_option pred l =
match l with
| [] -> raise Not_found
| e :: l -> ( match pred e with Some r -> r | None -> find_option pred l )
module ConstrMap = struct
open Names.GlobRef
type 'a t = 'a list Map.t
let add gr e m =
Map.update gr (function None -> Some [e] | Some l -> Some (e :: l)) m
let empty = Map.empty
let find evd h m =
match Map.find (fst (EConstr.destRef evd h)) m with
| e :: _ -> e
| [] -> assert false
let find_all evd h m = Map.find (fst (EConstr.destRef evd h)) m
let fold f m acc =
Map.fold
(fun k l acc -> List.fold_left (fun acc e -> f k e acc) acc l)
m acc
end
module HConstr = struct
module M = Map.Make (struct
type t = EConstr.t
let compare c c' = Constr.compare (unsafe_to_constr c) (unsafe_to_constr c')
end)
type 'a t = 'a M.t
let add h e m = M.add h e m
let empty = M.empty
let find = M.find
end
(** [get_projections_from_constant (evd,c) ]
returns an array of constr [| a1,.. an|] such that [c] is defined as
Definition c := mk a1 .. an with mk a constructor.
ai is therefore either a type parameter or a projection.
*)
let get_projections_from_constant (evd, i) =
match EConstr.kind evd (whd (Global.env ()) evd i) with
| App (c, a) -> Some a
| _ ->
raise
(CErrors.user_err
Pp.(
str "The hnf of term "
++ pr_constr (Global.env ()) evd i
++ str " should be an application i.e. (c a1 ... an)"))
(** An instance of type, say T, is registered into a hashtable, say TableT. *)
type 'a decl =
{ decl : EConstr.t
;
deriv : 'a }
module EInjT = struct
type t =
{ isid : bool
;
source : EConstr.t
;
target : EConstr.t
;
inj : EConstr.t
;
pred : EConstr.t
;
cstr : EConstr.t option }
end
(** [classify_op] classify injected operators and detect special cases. *)
type classify_op =
| OpInj
| OpSame
| OpConv
| OpOther
let name x =
Context.make_annot (Name.mk_name (Names.Id.of_string x)) Sorts.Relevant
let mkconvert_unop i1 i2 op top =
let op =
EConstr.mkLambda
( name "x"
, i1.EInjT.source
, EConstr.mkApp (i2.EInjT.inj, [|EConstr.mkApp (op, [|EConstr.mkRel 1|])|])
)
in
let top =
EConstr.mkLambda
( name "x"
, i1.EInjT.source
, EConstr.mkApp
(top, [|EConstr.mkApp (i1.EInjT.inj, [|EConstr.mkRel 1|])|]) )
in
(op, top)
let mkconvert_binop i1 i2 i3 op top =
let op =
EConstr.mkLambda
( name "x"
, i1.EInjT.source
, EConstr.mkLambda
( name "y"
, i1.EInjT.source
, EConstr.mkApp
( i3.EInjT.inj
, [|EConstr.mkApp (op, [|EConstr.mkRel 2; EConstr.mkRel 1|])|] )
) )
in
let top =
EConstr.mkLambda
( name "x"
, i1.EInjT.source
, EConstr.mkLambda
( name "y"
, i2.EInjT.source
, EConstr.mkApp
( top
, [| EConstr.mkApp (i1.EInjT.inj, [|EConstr.mkRel 2|])
; EConstr.mkApp (i2.EInjT.inj, [|EConstr.mkRel 1|]) |] ) ) )
in
(op, top)
let mkconvert_rel i r tr =
let tr =
EConstr.mkLambda
( name "x"
, i.EInjT.source
, EConstr.mkLambda
( name "y"
, i.EInjT.source
, EConstr.mkApp
( tr
, [| EConstr.mkApp (i.EInjT.inj, [|EConstr.mkRel 2|])
; EConstr.mkApp (i.EInjT.inj, [|EConstr.mkRel 1|]) |] ) ) )
in
(r, tr)
(** [classify_op mkconvert op top] takes the injection [inj] for the origin operator [op]
and the destination operator [top] -- both [op] and [top] are closed terms *)
let classify_op mkconvert inj op top =
let env = Global.env () in
let evd = Evd.from_env env in
if is_convertible env evd inj op then OpInj
else if EConstr.eq_constr evd op top then OpSame
else
let op, top = mkconvert op top in
if is_convertible env evd op top then OpConv else OpOther
module EBinOpT = struct
type t =
{
source1 : EConstr.t
; source2 : EConstr.t
; source3 : EConstr.t
; target1 : EConstr.t
; target2 : EConstr.t
; target3 : EConstr.t
; inj1 : EInjT.t
; inj2 : EInjT.t
; inj3 : EInjT.t
; bop : EConstr.t
; tbop : EConstr.t
; tbopinj : EConstr.t
; classify_binop : classify_op }
end
module ECstOpT = struct
type t =
{ source : EConstr.t
; target : EConstr.t
; inj : EInjT.t
; cst : EConstr.t
; cstinj : EConstr.t
; is_construct : bool }
end
module EUnOpT = struct
type t =
{ source1 : EConstr.t
; source2 : EConstr.t
; target1 : EConstr.t
; target2 : EConstr.t
; uop : EConstr.t
; inj1_t : EInjT.t
; inj2_t : EInjT.t
; tuop : EConstr.t
; tuopinj : EConstr.t
; classify_unop : classify_op
; is_construct : bool }
end
module EBinRelT = struct
type t =
{ source : EConstr.t
; target : EConstr.t
; inj : EInjT.t
; brel : EConstr.t
; tbrel : EConstr.t
; brelinj : EConstr.t
; classify_rel : classify_op }
end
module EPropBinOpT = struct
type t = {op : EConstr.t; op_iff : EConstr.t}
end
module EPropUnOpT = struct
type t = {op : EConstr.t; op_iff : EConstr.t}
end
module ESatT = struct
type t = {parg1 : EConstr.t; parg2 : EConstr.t; satOK : EConstr.t}
end
module ESpecT = struct
type t = {spec : EConstr.t}
end
type decl_kind =
| PropOp of EPropBinOpT.t decl
| PropUnOp of EPropUnOpT.t decl
| InjTyp of EInjT.t decl
| BinRel of EBinRelT.t decl
| BinOp of EBinOpT.t decl
| UnOp of EUnOpT.t decl
| CstOp of ECstOpT.t decl
| Saturate of ESatT.t decl
| UnOpSpec of ESpecT.t decl
| BinOpSpec of ESpecT.t decl
type term_kind = Application of EConstr.constr | OtherTerm of EConstr.constr
module type Elt = sig
type elt
(** name *)
val name : string
val gref : GlobRef.t Lazy.t
val table : (term_kind * decl_kind) ConstrMap.t ref
val cast : elt decl -> decl_kind
val dest : decl_kind -> elt decl option
(** [get_key] is the type-index used as key for the instance *)
val get_key : int
(** [mk_elt evd i [a0,..,an] returns the element of the table
built from the type-instance i and the arguments (type indexes and projections)
of the type-class constructor. *)
val mk_elt : Evd.evar_map -> EConstr.t -> EConstr.t array -> elt
end
let table = Summary.ref ~name:"zify_table" ConstrMap.empty
let saturate = Summary.ref ~name:"zify_saturate" ConstrMap.empty
let specs = Summary.ref ~name:"zify_specs" ConstrMap.empty
let table_cache = ref ConstrMap.empty
let saturate_cache = ref ConstrMap.empty
let specs_cache = ref ConstrMap.empty
(** Each type-class gives rise to a different table.
They only differ on how projections are extracted. *)
module EInj = struct
open EInjT
type elt = EInjT.t
let name = "EInj"
let gref = coq_InjTyp
let table = table
let cast x = InjTyp x
let dest = function InjTyp x -> Some x | _ -> None
let is_cstr_true evd c =
match EConstr.kind evd c with
| Lambda (_, _, c) -> EConstr.eq_constr_nounivs evd c (Lazy.force op_True)
| _ -> false
let mk_elt evd i (a : EConstr.t array) =
let isid = EConstr.eq_constr_nounivs evd a.(0) a.(1) in
{ isid
; source = a.(0)
; target = a.(1)
; inj = a.(2)
; pred = a.(3)
; cstr = (if is_cstr_true evd a.(3) then None else Some a.(4)) }
let get_key = 0
end
let get_inj evd c =
match get_projections_from_constant (evd, c) with
| None ->
let env = Global.env () in
let t = string_of_ppcmds (pr_constr env evd c) in
failwith ("Cannot register term " ^ t)
| Some a -> EInj.mk_elt evd c a
let rec decomp_type evd ty =
match EConstr.kind_of_type evd ty with
| EConstr.ProdType (_, t1, rst) -> t1 :: decomp_type evd rst
| _ -> [ty]
let pp_type env evd l =
Pp.prlist_with_sep (fun _ -> Pp.str " -> ") (pr_constr env evd) l
let check_typ evd expty op =
let env = Global.env () in
let ty = Retyping.get_type_of env evd op in
let ty = decomp_type evd ty in
if List.for_all2 (EConstr.eq_constr_nounivs evd) ty expty then ()
else
raise
(CErrors.user_err
Pp.(
str ": Cannot register operator "
++ pr_constr env evd op ++ str ". It has type " ++ pp_type env evd ty
++ str " instead of expected type "
++ pp_type env evd expty))
module EBinOp = struct
type elt = EBinOpT.t
open EBinOpT
let name = "BinOp"
let gref = coq_BinOp
let table = table
let mk_elt evd i a =
let i1 = get_inj evd a.(7) in
let i2 = get_inj evd a.(8) in
let i3 = get_inj evd a.(9) in
let bop = a.(6) in
let tbop = a.(10) in
check_typ evd EInjT.[i1.source; i2.source; i3.source] bop;
{ source1 = a.(0)
; source2 = a.(1)
; source3 = a.(2)
; target1 = a.(3)
; target2 = a.(4)
; target3 = a.(5)
; inj1 = i1
; inj2 = i2
; inj3 = i3
; bop
; tbop
; tbopinj = a.(11)
; classify_binop =
classify_op (mkconvert_binop i1 i2 i3) i3.EInjT.inj a.(6) tbop }
let get_key = 6
let cast x = BinOp x
let dest = function BinOp x -> Some x | _ -> None
end
module ECstOp = struct
type elt = ECstOpT.t
open ECstOpT
let name = "CstOp"
let gref = coq_CstOp
let table = table
let cast x = CstOp x
let dest = function CstOp x -> Some x | _ -> None
let isConstruct evd c =
match EConstr.kind evd c with
| Construct _ | Int _ | Float _ -> true
| _ -> false
let mk_elt evd i a =
{ source = a.(0)
; target = a.(1)
; inj = get_inj evd a.(3)
; cst = a.(4)
; cstinj = a.(5)
; is_construct = isConstruct evd a.(2) }
let get_key = 2
end
module EUnOp = struct
type elt = EUnOpT.t
open EUnOpT
let name = "UnOp"
let gref = coq_UnOp
let table = table
let cast x = UnOp x
let dest = function UnOp x -> Some x | _ -> None
let mk_elt evd i a =
let i1 = get_inj evd a.(5) in
let i2 = get_inj evd a.(6) in
let uop = a.(4) in
check_typ evd EInjT.[i1.source; i2.source] uop;
let tuop = a.(7) in
{ source1 = a.(0)
; source2 = a.(1)
; target1 = a.(2)
; target2 = a.(3)
; uop
; inj1_t = i1
; inj2_t = i2
; tuop
; tuopinj = a.(8)
; is_construct = EConstr.isConstruct evd uop
; classify_unop = classify_op (mkconvert_unop i1 i2) i2.EInjT.inj uop tuop
}
let get_key = 4
end
module EBinRel = struct
type elt = EBinRelT.t
open EBinRelT
let name = "BinRel"
let gref = coq_BinRel
let table = table
let cast x = BinRel x
let dest = function BinRel x -> Some x | _ -> None
let mk_elt evd i a =
let i = get_inj evd a.(3) in
let brel = a.(2) in
let tbrel = a.(4) in
check_typ evd EInjT.[i.source; i.source; EConstr.mkProp] brel;
{ source = a.(0)
; target = a.(1)
; inj = get_inj evd a.(3)
; brel
; tbrel
; brelinj = a.(5)
; classify_rel = classify_op (mkconvert_rel i) i.EInjT.inj brel tbrel }
let get_key = 2
end
module EPropBinOp = struct
type elt = EPropBinOpT.t
open EPropBinOpT
let name = "PropBinOp"
let gref = coq_PropBinOp
let table = table
let cast x = PropOp x
let dest = function PropOp x -> Some x | _ -> None
let mk_elt evd i a = {op = a.(0); op_iff = a.(1)}
let get_key = 0
end
module EPropUnOp = struct
type elt = EPropUnOpT.t
open EPropUnOpT
let name = "PropUOp"
let gref = coq_PropUOp
let table = table
let cast x = PropUnOp x
let dest = function PropUnOp x -> Some x | _ -> None
let mk_elt evd i a = {op = a.(0); op_iff = a.(1)}
let get_key = 0
end
let constr_of_term_kind = function Application c -> c | OtherTerm c -> c
module type S = sig
val register : Libnames.qualid -> unit
val print : unit -> unit
end
module MakeTable (E : Elt) = struct
(** Given a term [c] and its arguments ai,
we construct a HConstr.t table that is
indexed by ai for i = E.get_key.
The elements of the table are built using E.mk_elt c [|a0,..,an|]
*)
let make_elt (evd, i) =
match get_projections_from_constant (evd, i) with
| None ->
let env = Global.env () in
let t = string_of_ppcmds (pr_constr env evd i) in
failwith ("Cannot register term " ^ t)
| Some a -> E.mk_elt evd i a
let safe_ref evd c =
try
fst (EConstr.destRef evd c)
with DestKO -> CErrors.user_err Pp.(str "Add Zify "++str E.name ++ str ": the term "++
gl_pr_constr c ++ str " should be a global reference")
let register_hint evd t elt =
match EConstr.kind evd t with
| App (c, _) ->
let gr = safe_ref evd c in
E.table := ConstrMap.add gr (Application t, E.cast elt) !E.table
| _ ->
let gr = safe_ref evd t in
E.table := ConstrMap.add gr (OtherTerm t, E.cast elt) !E.table
let register_constr env evd c =
let c = EConstr.of_constr c in
let t = get_type_of env evd c in
match EConstr.kind evd t with
| App (intyp, args) when EConstr.isRefX evd (Lazy.force E.gref) intyp ->
let styp = args.(E.get_key) in
let elt = {decl = c; deriv = make_elt (evd, c)} in
register_hint evd styp elt
| _ ->
let env = Global.env () in
raise
(CErrors.user_err
Pp.(
str "Cannot register " ++ pr_constr env evd c
++ str ". It has type " ++ pr_constr env evd t
++ str " instead of type "
++ Printer.pr_global (Lazy.force E.gref)
++ str " X1 ... Xn"))
let register_obj : Constr.constr -> Libobject.obj =
let cache_constr (_, c) =
let env = Global.env () in
let evd = Evd.from_env env in
register_constr env evd c
in
let subst_constr (subst, c) = Mod_subst.subst_mps subst c in
Libobject.declare_object
@@ Libobject.superglobal_object_nodischarge
("register-zify-" ^ E.name)
~cache:cache_constr ~subst:(Some subst_constr)
(** [register c] is called from the VERNACULAR ADD [name] reference(t).
The term [c] is interpreted and
registered as a [superglobal_object_nodischarge].
TODO: pre-compute [get_type_of] - [cache_constr] is using another environment.
*)
let register c =
try
let c = UnivGen.constr_of_monomorphic_global (Global.env ()) (Nametab.locate c) in
let _ = Lib.add_anonymous_leaf (register_obj c) in
()
with Not_found ->
raise
(CErrors.user_err Pp.(Libnames.pr_qualid c ++ str " does not exist."))
let pp_keys () =
let env = Global.env () in
let evd = Evd.from_env env in
ConstrMap.fold
(fun _ (k, d) acc ->
match E.dest d with
| None -> acc
| Some _ ->
Pp.(pr_constr env evd (constr_of_term_kind k) ++ str " " ++ acc))
!E.table (Pp.str "")
let print () = Feedback.msg_info (pp_keys ())
end
module InjTable = MakeTable (EInj)
module ESat = struct
type elt = ESatT.t
open ESatT
let name = "Saturate"
let gref = coq_Saturate
let table = saturate
let cast x = Saturate x
let dest = function Saturate x -> Some x | _ -> None
let mk_elt evd i a = {parg1 = a.(2); parg2 = a.(3); satOK = a.(5)}
let get_key = 1
end
module EUnopSpec = struct
open ESpecT
type elt = ESpecT.t
let name = "UnopSpec"
let gref = coq_UnOpSpec
let table = specs
let cast x = UnOpSpec x
let dest = function UnOpSpec x -> Some x | _ -> None
let mk_elt evd i a = {spec = a.(4)}
let get_key = 2
end
module EBinOpSpec = struct
open ESpecT
type elt = ESpecT.t
let name = "BinOpSpec"
let gref = coq_BinOpSpec
let table = specs
let cast x = BinOpSpec x
let dest = function BinOpSpec x -> Some x | _ -> None
let mk_elt evd i a = {spec = a.(5)}
let get_key = 3
end
module BinOp = MakeTable (EBinOp)
module UnOp = MakeTable (EUnOp)
module CstOp = MakeTable (ECstOp)
module BinRel = MakeTable (EBinRel)
module PropBinOp = MakeTable (EPropBinOp)
module PropUnOp = MakeTable (EPropUnOp)
module Saturate = MakeTable (ESat)
module UnOpSpec = MakeTable (EUnopSpec)
module BinOpSpec = MakeTable (EBinOpSpec)
let init_cache () =
table_cache := !table;
saturate_cache := !saturate;
specs_cache := !specs
open EInjT
(** Get constr of lemma and projections in ZifyClasses. *)
(** Module [CstrTable] records terms [x] injected into [inj x]
together with the corresponding type constraint.
The terms are stored by side-effect during the traversal
of the goal. It must therefore be cleared before calling
the main tactic.
*)
module CstrTable = struct
module HConstr = Hashtbl.Make (struct
type t = EConstr.t
let hash c = Constr.hash (unsafe_to_constr c)
let equal c c' = Constr.equal (unsafe_to_constr c) (unsafe_to_constr c')
end)
let table : EConstr.t HConstr.t = HConstr.create 10
let register evd t (i : EConstr.t) = HConstr.add table t i
let get () =
let l = HConstr.fold (fun k i acc -> (k, i) :: acc) table [] in
HConstr.clear table; l
(** [gen_cstr table] asserts (cstr k) for each element of the table (k,cstr).
NB: the constraint is only asserted if it does not already exist in the context.
*)
let gen_cstr table =
Proofview.Goal.enter (fun gl ->
let evd = Tacmach.project gl in
let has_hyp =
let hyps_table = HConstr.create 20 in
List.iter
(fun (_, (t : EConstr.types)) -> HConstr.add hyps_table t ())
(Tacmach.pf_hyps_types gl);
fun c ->
let m = HConstr.mem hyps_table c in
if not m then HConstr.add hyps_table c ();
m
in
let gen k cstr =
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let term = EConstr.mkApp (cstr, [|k|]) in
let types = get_type_of env evd term in
if has_hyp types then Tacticals.tclIDTAC
else
let n =
Tactics.fresh_id_in_env Id.Set.empty
(Names.Id.of_string "cstr")
env
in
Tactics.pose_proof (Names.Name n) term)
in
List.fold_left
(fun acc (k, i) -> Tacticals.tclTHEN (gen k i) acc)
Tacticals.tclIDTAC table)
end
type prf =
| Term
| Same
| Conv of EConstr.t
| Prf of EConstr.t * EConstr.t
(** [eq_proof typ source target] returns (target = target : source = target) *)
let eq_proof typ source target =
EConstr.mkCast
( EConstr.mkApp (force eq_refl, [|typ; target|])
, DEFAULTcast
, EConstr.mkApp (force eq, [|typ; source; target|]) )
let interp_prf evd inj source prf =
let inj_source =
if inj.EInjT.isid then source else EConstr.mkApp (inj.EInjT.inj, [|source|])
in
match prf with
| Term ->
let target = Tacred.compute (Global.env ()) evd inj_source in
(target, EConstr.mkApp (force eq_refl, [|inj.target; target|]))
| Same ->
(inj_source, EConstr.mkApp (force eq_refl, [|inj.target; inj_source|]))
| Conv trm -> (trm, eq_proof inj.target inj_source trm)
| Prf (target, prf) -> (target, prf)
let pp_prf prf =
match prf with
| Term -> Pp.str "Term"
| Same -> Pp.str "Same"
| Conv t -> Pp.(str "Conv " ++ gl_pr_constr t)
| Prf (_, _) -> Pp.str "Prf "
let interp_prf evd inj source prf =
let t, prf' = interp_prf evd inj source prf in
debug_zify (fun () ->
Pp.(
str "interp_prf " ++ gl_pr_constr inj.EInjT.inj ++ str " "
++ gl_pr_constr source ++ str " = " ++ gl_pr_constr t ++ str " by "
++ gl_pr_constr prf' ++ str " from " ++ pp_prf prf ++ fnl ()));
(t, prf')
let mkvar evd inj e =
(match inj.cstr with None -> () | Some ctr -> CstrTable.register evd e ctr);
Same
let pp_prf evd inj src prf =
let t, prf' = interp_prf evd inj src prf in
Pp.(
gl_pr_constr inj.EInjT.inj ++ str " " ++ gl_pr_constr src ++ str " = "
++ gl_pr_constr t ++ str " by "
++
match prf with
| Term -> Pp.str "Term"
| Same -> Pp.str "Same"
| Conv t -> Pp.str "Conv"
| Prf (_, p) -> Pp.str "Prf " ++ gl_pr_constr p)
let conv_of_term evd op isid arg =
Tacred.compute (Global.env ()) evd
(if isid then arg else EConstr.mkApp (op, [|arg|]))
let app_unop evd src unop arg prf =
let cunop = unop.EUnOpT.classify_unop in
let default a' prf' =
let target = EConstr.mkApp (unop.EUnOpT.tuop, [|a'|]) in
EUnOpT.(
Prf
( target
, EConstr.mkApp
( force mkapp
, [| unop.source1
; unop.source2
; unop.target1
; unop.target2
; unop.uop
; unop.inj1_t.EInjT.inj
; unop.inj2_t.EInjT.inj
; unop.tuop
; unop.tuopinj
; arg
; a'
; prf' |] ) ))
in
match prf with
| Term -> (
if unop.EUnOpT.is_construct then Term
else
match cunop with
| OpInj -> Conv (conv_of_term evd unop.EUnOpT.uop false arg)
| OpSame -> Same
| _ ->
let a', prf = interp_prf evd unop.EUnOpT.inj1_t arg prf in
default a' prf )
| Same -> (
match cunop with
| OpSame -> Same
| OpInj -> Same
| OpConv ->
Conv
(EConstr.mkApp
( unop.EUnOpT.tuop
, [|EConstr.mkApp (unop.EUnOpT.inj1_t.EInjT.inj, [|arg|])|] ))
| OpOther ->
let a', prf' = interp_prf evd unop.EUnOpT.inj1_t arg prf in
default a' prf' )
| Conv a' -> (
match cunop with
| OpSame | OpConv -> Conv (EConstr.mkApp (unop.EUnOpT.tuop, [|a'|]))
| OpInj -> Conv a'
| _ ->
let a', prf = interp_prf evd unop.EUnOpT.inj1_t arg prf in
default a' prf )
| Prf (a', prf') -> default a' prf'
let app_unop evd src unop arg prf =
let res = app_unop evd src unop arg prf in
debug_zify (fun () ->
Pp.(
str "\napp_unop "
++ pp_prf evd unop.EUnOpT.inj1_t arg prf
++ str " => "
++ pp_prf evd unop.EUnOpT.inj2_t src res));
res
let app_binop evd src binop arg1 prf1 arg2 prf2 =
EBinOpT.(
let mkApp a1 a2 = EConstr.mkApp (binop.tbop, [|a1; a2|]) in
let to_conv inj arg = function
| Term -> conv_of_term evd inj.EInjT.inj inj.EInjT.isid arg
| Same ->
if inj.EInjT.isid then arg else EConstr.mkApp (inj.EInjT.inj, [|arg|])
| Conv t -> t
| Prf _ -> failwith "Prf is not convertible"
in
let default a1 prf1 a2 prf2 =
let res = mkApp a1 a2 in
let prf =
EBinOpT.(
EConstr.mkApp
( force mkapp2
, [| binop.source1
; binop.source2
; binop.source3
; binop.target1
; binop.target2
; binop.target3
; binop.bop
; binop.inj1.EInjT.inj
; binop.inj2.EInjT.inj
; binop.inj3.EInjT.inj
; binop.tbop
; binop.tbopinj
; arg1
; a1
; prf1
; arg2
; a2
; prf2 |] ))
in
Prf (res, prf)
in
match (binop.EBinOpT.classify_binop, prf1, prf2) with
| OpSame, Same, Same -> Same
| OpSame, Term, Same | OpSame, Same, Term -> Same
| OpSame, (Term | Same | Conv _), (Term | Same | Conv _) ->
let t1 = to_conv binop.EBinOpT.inj1 arg1 prf1 in
let t2 = to_conv binop.EBinOpT.inj1 arg2 prf2 in
Conv (mkApp t1 t2)
| _, _, _ ->
let a1, prf1 = interp_prf evd binop.inj1 arg1 prf1 in
let a2, prf2 = interp_prf evd binop.inj2 arg2 prf2 in
default a1 prf1 a2 prf2)
type typed_constr = {constr : EConstr.t; typ : EConstr.t; inj : EInjT.t}
let get_injection env evd t =
try
match snd (ConstrMap.find evd t !table_cache) with
| InjTyp i -> i
| _ -> raise Not_found
with DestKO -> raise Not_found
let arrow =
let name x =
Context.make_annot (Name.mk_name (Names.Id.of_string x)) Sorts.Relevant
in
EConstr.mkLambda
( name "x"
, EConstr.mkProp
, EConstr.mkLambda
( name "y"
, EConstr.mkProp
, EConstr.mkProd
( Context.make_annot Names.Anonymous Sorts.Relevant
, EConstr.mkRel 2
, EConstr.mkRel 2 ) ) )
let is_prop env sigma term =
let sort = Retyping.get_sort_of env sigma term in
Sorts.is_prop sort
let is_arrow env evd a p1 p2 =
is_prop env evd p1
&& is_prop
(EConstr.push_rel (Context.Rel.Declaration.LocalAssum (a, p1)) env)
evd p2
&& (a.Context.binder_name = Names.Anonymous || EConstr.Vars.noccurn evd 1 p2)
(** [get_operator env evd e] expresses [e] as an application (c a)
where c is the head symbol and [a] is the array of arguments.
The function also transforms (x -> y) as (arrow x y) *)
let get_operator barrow env evd e =
let e' = EConstr.whd_evar evd e in
match EConstr.kind evd e' with
| Prod (a, p1, p2) ->
if barrow && is_arrow env evd a p1 p2 then (arrow, [|p1; p2|], false)
else raise Not_found
| App (c, a) -> (
let c' = EConstr.whd_evar evd c in
match EConstr.kind evd c' with
| Construct _ | Const _ | Proj _
|Lambda _ | Ind _ ->
(c', a, false)
| _ -> raise Not_found )
| Const _ -> (e', [||], false)
| Construct _ -> (e', [||], true)
| Int _ | Float _ -> (e', [||], true)
| _ -> raise Not_found
let decompose_app env evd e =
match EConstr.kind evd e with
| Prod (a, p1, p2) when is_arrow env evd a p1 p2 -> (arrow, [|p1; p2|])
| App (c, a) -> (c, a)
| _ -> (EConstr.whd_evar evd e, [||])
type 'op propop = {op : 'op; op_constr : EConstr.t; op_iff : EConstr.t}
let mk_propop op c1 c2 = {op; op_constr = c1; op_iff = c2}
type prop_binop = AND | OR | IFF | IMPL
type prop_unop = NOT
type prop_op =
| BINOP of prop_binop propop * EConstr.t * EConstr.t
| UNOP of prop_unop propop * EConstr.t
| OTHEROP of EConstr.t * EConstr.t array
let classify_prop env evd e =
match EConstr.kind evd e with
| Prod (a, p1, p2) when is_arrow env evd a p1 p2 ->
BINOP (mk_propop IMPL arrow (force op_impl_morph), p1, p2)
| App (c, a) -> (
match Array.length a with
| 1 ->
if EConstr.eq_constr_nounivs evd (force op_not) c then
UNOP (mk_propop NOT c (force op_not_morph), a.(0))
else OTHEROP (c, a)
| 2 ->
if EConstr.eq_constr_nounivs evd (force op_and) c then
BINOP (mk_propop AND c (force op_and_morph), a.(0), a.(1))
else if EConstr.eq_constr_nounivs evd (force op_or) c then
BINOP (mk_propop OR c (force op_or_morph), a.(0), a.(1))
else if EConstr.eq_constr_nounivs evd (force op_iff) c then
BINOP (mk_propop IFF c (force op_iff_morph), a.(0), a.(1))
else OTHEROP (c, a)
| _ -> OTHEROP (c, a) )
| _ -> OTHEROP (e, [||])
(** [match_operator env evd hd arg (t,d)]
- hd is head operator of t
- If t = OtherTerm _, then t = hd
- If t = Application _, then
we extract the relevant number of arguments from arg
and check for convertibility *)
let match_operator env evd hd args (t, d) =
let decomp t i =
let n = Array.length args in
let t' = EConstr.mkApp (hd, Array.sub args 0 (n - i)) in
if is_convertible env evd t' t then Some (d, t) else None
in
match t with
| OtherTerm t -> Some (d, t)
| Application t -> (
match d with
| CstOp _ -> decomp t 0
| UnOp _ -> decomp t 1
| BinOp _ -> decomp t 2
| BinRel _ -> decomp t 2
| PropOp _ -> decomp t 2
| PropUnOp _ -> decomp t 1
| _ -> None )
let pp_trans_expr env evd e res =
let {deriv = inj} = get_injection env evd e.typ in
debug_zify (fun () -> Pp.(str "\ntrans_expr " ++ pp_prf evd inj e.constr res));
res
let declared_term env evd hd args =
let match_operator (t, d) =
let decomp t i =
let n = Array.length args in
let t' = EConstr.mkApp (hd, Array.sub args 0 (n - i)) in
if is_convertible env evd t' t then Some (t, Array.sub args (n - i) i)
else None
in
match t with
| OtherTerm t -> ( match d with InjTyp _ -> None | _ -> Some (t, args) )
| Application t -> (
match d with
| CstOp _ -> decomp t 0
| UnOp _ -> decomp t 1
| BinOp _ -> decomp t 2
| BinRel _ -> decomp t 2
| PropOp _ -> decomp t 2
| PropUnOp _ -> decomp t 1
| _ -> None )
in
find_option match_operator (ConstrMap.find_all evd hd !table)
let rec trans_expr env evd e =
let inj = e.inj in
let e = e.constr in
try
let c, a, is_constant = get_operator false env evd e in
if is_constant then Term
else
let k, t =
find_option
(match_operator env evd c a)
(ConstrMap.find_all evd c !table_cache)
in
let n = Array.length a in
match k with
| CstOp {deriv = c'} ->
ECstOpT.(if c'.is_construct then Term else Prf (c'.cst, c'.cstinj))
| UnOp {deriv = unop} ->
let prf =
trans_expr env evd
{ constr = a.(n - 1)
; typ = unop.EUnOpT.source1
; inj = unop.EUnOpT.inj1_t }
in
app_unop evd e unop a.(n - 1) prf
| BinOp {deriv = binop} ->
let prf1 =
trans_expr env evd
{ constr = a.(n - 2)
; typ = binop.EBinOpT.source1
; inj = binop.EBinOpT.inj1 }
in
let prf2 =
trans_expr env evd
{ constr = a.(n - 1)
; typ = binop.EBinOpT.source2
; inj = binop.EBinOpT.inj2 }
in
app_binop evd e binop a.(n - 2) prf1 a.(n - 1) prf2
| d -> mkvar evd inj e
with Not_found | DestKO -> mkvar evd inj e
let trans_expr env evd e =
try pp_trans_expr env evd e (trans_expr env evd e)
with Not_found ->
raise
(CErrors.user_err
( Pp.str "Missing injection for type "
++ Printer.pr_leconstr_env env evd e.typ ))
type prfp =
| TProof of EConstr.t * EConstr.t (** Proof of tranformed proposition *)
| CProof of EConstr.t (** Transformed proposition is convertible *)
| IProof (** Transformed proposition is identical *)
let pp_prfp = function
| TProof (t, prf) ->
Pp.str "TProof " ++ gl_pr_constr t ++ Pp.str " by " ++ gl_pr_constr prf
| CProof t -> Pp.str "CProof " ++ gl_pr_constr t
| IProof -> Pp.str "IProof"
let trans_binrel evd src rop a1 prf1 a2 prf2 =
EBinRelT.(
match (rop.classify_rel, prf1, prf2) with
| OpSame, Same, Same -> IProof
| (OpSame | OpConv), Conv t1, Conv t2 ->
CProof (EConstr.mkApp (rop.tbrel, [|t1; t2|]))
| (OpSame | OpConv), (Same | Term | Conv _), (Same | Term | Conv _) ->
let a1', _ = interp_prf evd rop.inj a1 prf1 in
let a2', _ = interp_prf evd rop.inj a2 prf2 in
CProof (EConstr.mkApp (rop.tbrel, [|a1'; a2'|]))
| _, _, _ ->
let a1', prf1 = interp_prf evd rop.inj a1 prf1 in
let a2', prf2 = interp_prf evd rop.inj a2 prf2 in
TProof
( EConstr.mkApp (rop.EBinRelT.tbrel, [|a1'; a2'|])
, EConstr.mkApp
( force mkrel
, [| rop.source
; rop.target
; rop.brel
; rop.EBinRelT.inj.EInjT.inj
; rop.EBinRelT.tbrel
; rop.EBinRelT.brelinj
; a1
; a1'
; prf1
; a2
; a2'
; prf2 |] ) ))
let trans_binrel evd src rop a1 prf1 a2 prf2 =
let res = trans_binrel evd src rop a1 prf1 a2 prf2 in
debug_zify (fun () -> Pp.(str "\ntrans_binrel " ++ pp_prfp res));
res
let mkprf t p =
EConstr.(
match p with
| IProof -> (t, mkApp (force iff_refl, [|t|]))
| CProof t' -> (t', mkApp (force eq_iff, [|t; t'; eq_proof mkProp t t'|]))
| TProof (t', p) -> (t', p))
let mkprf t p =
let t', p = mkprf t p in
debug_zify (fun () ->
Pp.(
str "mkprf " ++ gl_pr_constr t ++ str " <-> " ++ gl_pr_constr t'
++ str " by " ++ gl_pr_constr p));
(t', p)
let trans_bin_prop op_constr op_iff t1 p1 t2 p2 =
match (p1, p2) with
| IProof, IProof -> IProof
| CProof t1', IProof -> CProof (EConstr.mkApp (op_constr, [|t1'; t2|]))
| IProof, CProof t2' -> CProof (EConstr.mkApp (op_constr, [|t1; t2'|]))
| CProof t1', CProof t2' -> CProof (EConstr.mkApp (op_constr, [|t1'; t2'|]))
| _, _ ->
let t1', p1 = mkprf t1 p1 in
let t2', p2 = mkprf t2 p2 in
TProof
( EConstr.mkApp (op_constr, [|t1'; t2'|])
, EConstr.mkApp (op_iff, [|t1; t2; t1'; t2'; p1; p2|]) )
let trans_bin_prop op_constr op_iff t1 p1 t2 p2 =
let prf = trans_bin_prop op_constr op_iff t1 p1 t2 p2 in
debug_zify (fun () -> pp_prfp prf);
prf
let trans_un_prop op_constr op_iff p1 prf1 =
match prf1 with
| IProof -> IProof
| CProof p1' -> CProof (EConstr.mkApp (op_constr, [|p1'|]))
| TProof (p1', prf) ->
TProof
( EConstr.mkApp (op_constr, [|p1'|])
, EConstr.mkApp (op_iff, [|p1; p1'; prf|]) )
let rec trans_prop env evd e =
match classify_prop env evd e with
| BINOP ({op_constr; op_iff}, p1, p2) ->
let prf1 = trans_prop env evd p1 in
let prf2 = trans_prop env evd p2 in
trans_bin_prop op_constr op_iff p1 prf1 p2 prf2
| UNOP ({op_constr; op_iff}, p1) ->
let prf1 = trans_prop env evd p1 in
trans_un_prop op_constr op_iff p1 prf1
| OTHEROP (c, a) -> (
try
let k, t =
find_option
(match_operator env evd c a)
(ConstrMap.find_all evd c !table_cache)
in
let n = Array.length a in
match k with
| BinRel {decl = br; deriv = rop} ->
let a1 =
trans_expr env evd
{ constr = a.(n - 2)
; typ = rop.EBinRelT.source
; inj = rop.EBinRelT.inj }
in
let a2 =
trans_expr env evd
{ constr = a.(n - 1)
; typ = rop.EBinRelT.source
; inj = rop.EBinRelT.inj }
in
trans_binrel evd e rop a.(n - 2) a1 a.(n - 1) a2
| _ -> IProof
with Not_found | DestKO -> IProof )
let trans_check_prop env evd t =
if is_prop env evd t then Some (trans_prop env evd t) else None
let get_hyp_typ = function
| NamedDecl.LocalDef (h, _, ty) | NamedDecl.LocalAssum (h, ty) ->
(h.Context.binder_name, EConstr.of_constr ty)
let trans_hyps env evd l =
List.fold_left
(fun acc decl ->
let h, ty = get_hyp_typ decl in
match trans_check_prop env evd ty with
| None -> acc
| Some p' -> (h, ty, p') :: acc)
[] l
let trans_hyp h t0 prfp =
debug_zify (fun () -> Pp.(str "trans_hyp: " ++ pp_prfp prfp ++ fnl ()));
match prfp with
| IProof -> Tacticals.tclIDTAC
| CProof t' ->
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let evd = Tacmach.project gl in
let t' = Reductionops.nf_betaiota env evd t' in
Tactics.change_in_hyp ~check:true None
(Tactics.make_change_arg t')
(h, Locus.InHypTypeOnly))
| TProof (t', prf) ->
Tacticals.(
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let evd = Tacmach.project gl in
let target = Reductionops.nf_betaiota env evd t' in
let h' = Tactics.fresh_id_in_env Id.Set.empty h env in
let prf =
EConstr.mkApp (force rew_iff, [|t0; target; prf; EConstr.mkVar h|])
in
tclTHEN
(Tactics.pose_proof (Name.Name h') prf)
(tclTRY
(tclTHEN (Tactics.clear [h]) (Tactics.rename_hyp [(h', h)])))))
let trans_concl prfp =
debug_zify (fun () -> Pp.(str "trans_concl: " ++ pp_prfp prfp ++ fnl ()));
match prfp with
| IProof -> Tacticals.tclIDTAC
| CProof t ->
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let evd = Tacmach.project gl in
let t' = Reductionops.nf_betaiota env evd t in
Tactics.change_concl t')
| TProof (t, prf) ->
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let evd = Tacmach.project gl in
let typ = get_type_of env evd prf in
match EConstr.kind evd typ with
| App (c, a) when Array.length a = 2 ->
Tactics.apply
(EConstr.mkApp (Lazy.force rew_iff_rev, [|a.(0); a.(1); prf|]))
| _ ->
raise (CErrors.anomaly Pp.(str "zify cannot transform conclusion")))
let tclTHENOpt e tac tac' =
match e with None -> tac' | Some e' -> Tacticals.tclTHEN (tac e') tac'
let assert_inj t =
init_cache ();
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let evd = Tacmach.project gl in
try
ignore (get_injection env evd t);
Tacticals.tclIDTAC
with Not_found ->
Tacticals.tclFAIL 0 (Pp.str " InjTyp does not exist"))
let elim_binding x t ty =
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let h =
Tactics.fresh_id_in_env Id.Set.empty (Nameops.add_prefix "heq_" x) env
in
Tacticals.tclTHEN
(Tactics.pose_proof (Name h) (eq_proof ty (EConstr.mkVar x) t))
(Tacticals.tclTRY (Tactics.clear_body [x])))
let do_let tac (h : Constr.named_declaration) =
match h with
| Context.Named.Declaration.LocalAssum _ -> Tacticals.tclIDTAC
| Context.Named.Declaration.LocalDef (id, t, ty) ->
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let evd = Tacmach.project gl in
try
let x = id.Context.binder_name in
ignore
(let eq = Lazy.force eq in
find_option
(match_operator env evd eq
[|EConstr.of_constr ty; EConstr.mkVar x; EConstr.of_constr t|])
(ConstrMap.find_all evd eq !table_cache));
tac x (EConstr.of_constr t) (EConstr.of_constr ty)
with Not_found -> Tacticals.tclIDTAC)
let iter_let_aux tac =
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let sign = Environ.named_context env in
init_cache ();
Tacticals.tclMAP (do_let tac) sign)
let iter_let (tac : Ltac_plugin.Tacinterp.Value.t) =
iter_let_aux (fun (id : Names.Id.t) t ty ->
Ltac_plugin.Tacinterp.Value.apply tac
[ Ltac_plugin.Tacinterp.Value.of_constr (EConstr.mkVar id)
; Ltac_plugin.Tacinterp.Value.of_constr t
; Ltac_plugin.Tacinterp.Value.of_constr ty ])
let elim_let = iter_let_aux elim_binding
let zify_tac =
Proofview.Goal.enter (fun gl ->
Coqlib.check_required_library ["Coq"; "micromega"; "ZifyClasses"];
Coqlib.check_required_library ["Coq"; "micromega"; "ZifyInst"];
init_cache ();
let evd = Tacmach.project gl in
let env = Tacmach.pf_env gl in
let sign = Environ.named_context env in
let concl = trans_check_prop env evd (Tacmach.pf_concl gl) in
let hyps = trans_hyps env evd sign in
let l = CstrTable.get () in
tclTHENOpt concl trans_concl
(Tacticals.tclTHEN
(Tacticals.tclTHENLIST
(List.rev_map (fun (h, p, t) -> trans_hyp h p t) hyps))
(CstrTable.gen_cstr l)))
type pscript = Set of Names.Id.t * EConstr.t | Pose of Names.Id.t * EConstr.t
type spec_env =
{ map : Names.Id.t HConstr.t
; spec_name : Names.Id.t
; term_name : Names.Id.t
; fresh : Nameops.Subscript.t
; proofs : pscript list }
let register_constr {map; spec_name; term_name; fresh; proofs} c thm =
let tname = Nameops.add_subscript term_name fresh in
let sname = Nameops.add_subscript spec_name fresh in
( EConstr.mkVar tname
, { map = HConstr.add c tname map
; spec_name
; term_name
; fresh = Nameops.Subscript.succ fresh
; proofs = Set (tname, c) :: Pose (sname, thm) :: proofs } )
let fresh_subscript env =
let ctx = (Environ.named_context_val env).Environ.env_named_map in
Nameops.Subscript.succ
(Names.Id.Map.fold
(fun id _ s ->
let _, s' = Nameops.get_subscript id in
let cmp = Nameops.Subscript.compare s s' in
if cmp = 0 then s else if cmp < 0 then s' else s)
ctx Nameops.Subscript.zero)
let init_env sname tname s =
{ map = HConstr.empty
; spec_name = sname
; term_name = tname
; fresh = s
; proofs = [] }
let rec spec_of_term env evd (senv : spec_env) t =
let get_name t env =
try EConstr.mkVar (HConstr.find t senv.map) with Not_found -> t
in
let c, a = decompose_app env evd t in
if a = [||] then
(get_name t senv, senv)
else
let a', senv' =
Array.fold_right
(fun e (l, senv) ->
let r, senv = spec_of_term env evd senv e in
(r :: l, senv))
a ([], senv)
in
let a' = Array.of_list a' in
let t' = EConstr.mkApp (c, a') in
try (EConstr.mkVar (HConstr.find t' senv'.map), senv')
with Not_found -> (
try
match snd (ConstrMap.find evd c !specs_cache) with
| UnOpSpec s | BinOpSpec s ->
let thm = EConstr.mkApp (s.deriv.ESpecT.spec, a') in
register_constr senv' t' thm
| _ -> (get_name t' senv', senv')
with Not_found | DestKO -> (t', senv') )
let interp_pscript s =
match s with
| Set (id, c) ->
Tacticals.tclTHEN
(Tactics.letin_tac None (Names.Name id) c None
{Locus.onhyps = None; Locus.concl_occs = Locus.AllOccurrences})
(Tactics.clear_body [id])
| Pose (id, c) -> Tactics.pose_proof (Names.Name id) c
let rec interp_pscripts l =
match l with
| [] -> Tacticals.tclIDTAC
| s :: l -> Tacticals.tclTHEN (interp_pscript s) (interp_pscripts l)
let spec_of_hyps =
Proofview.Goal.enter (fun gl ->
let terms =
Tacmach.pf_concl gl :: List.map snd (Tacmach.pf_hyps_types gl)
in
let env = Tacmach.pf_env gl in
let evd = Tacmach.project gl in
let s = fresh_subscript env in
let env =
List.fold_left
(fun acc t -> snd (spec_of_term env evd acc t))
(init_env (Names.Id.of_string "H") (Names.Id.of_string "z") s)
terms
in
interp_pscripts (List.rev env.proofs))
let iter_specs = spec_of_hyps
let find_hyp evd t l =
try
Some
(EConstr.mkVar
(fst (List.find (fun (h, t') -> EConstr.eq_constr evd t t') l)))
with Not_found -> None
let find_proof evd t l =
if EConstr.eq_constr evd t (Lazy.force op_True) then Some (Lazy.force op_I)
else find_hyp evd t l
(** [sat_constr env evd sub taclist hyps c d]= (sub',taclist',hyps') where
- sub' is a fresh subscript obtained from sub
- taclist' is obtained from taclist by posing the lemma 'd' applied to 'c'
- hyps' is obtained from hyps'
taclist and hyps are threaded to avoid adding duplicates
*)
let sat_constr env evd (sub,taclist, hyps) c d =
match EConstr.kind evd c with
| App (c, args) ->
if Array.length args = 2 then
let h1 =
Tacred.cbv_beta env evd
(EConstr.mkApp (d.ESatT.parg1, [|args.(0)|]))
in
let h2 =
Tacred.cbv_beta env evd
(EConstr.mkApp (d.ESatT.parg2, [|args.(1)|]))
in
let n = Nameops.add_subscript (Names.Id.of_string "__sat") sub in
let trm =
match (find_proof evd h1 hyps, find_proof evd h2 hyps) with
| Some h1, Some h2 ->
(EConstr.mkApp (d.ESatT.satOK, [|args.(0); args.(1); h1; h2|]))
| Some h1, _ ->
EConstr.mkApp (d.ESatT.satOK, [|args.(0); args.(1); h1|])
| _, _ -> EConstr.mkApp (d.ESatT.satOK, [|args.(0); args.(1)|])
in
let rtrm = Tacred.cbv_beta env evd trm in
let typ = Retyping.get_type_of env evd rtrm in
match find_hyp evd typ hyps with
| None -> (Nameops.Subscript.succ sub, (Tactics.pose_proof (Names.Name n) rtrm :: taclist) , (n,typ)::hyps)
| Some _ -> (sub, taclist, hyps)
else (sub,taclist,hyps)
| _ -> (sub,taclist,hyps)
let get_all_sat env evd c =
List.fold_left
(fun acc e -> match e with _, Saturate s -> s :: acc | _ -> acc)
[]
( try ConstrMap.find_all evd c !saturate_cache
with DestKO | Not_found -> [] )
let saturate =
Proofview.Goal.enter (fun gl ->
init_cache ();
let table = CstrTable.HConstr.create 20 in
let concl = Tacmach.pf_concl gl in
let hyps = Tacmach.pf_hyps_types gl in
let evd = Tacmach.project gl in
let env = Tacmach.pf_env gl in
let rec sat t =
match EConstr.kind evd t with
| App (c, args) ->
sat c;
Array.iter sat args;
if Array.length args = 2 then
let ds = get_all_sat env evd c in
if ds = [] || CstrTable.HConstr.mem table t
then ()
else List.iter (fun x ->
CstrTable.HConstr.add table t x.deriv) ds
else ()
| Prod (a, t1, t2) when a.Context.binder_name = Names.Anonymous ->
sat t1; sat t2
| _ -> ()
in
sat concl;
List.iter (fun (_, t) -> sat t) hyps;
let s0 = fresh_subscript env in
let (_,tacs,_) = CstrTable.HConstr.fold (fun c d acc -> sat_constr env evd acc c d) table (s0,[],hyps) in
Tacticals.tclTHENLIST tacs)