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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
open Context.Named.Declaration
let map_const_entry_body (f:Term.constr->Term.constr) (x:Safe_typing.private_constants Entries.const_entry_body)
: Safe_typing.private_constants Entries.const_entry_body =
Future.chain ~pure:true x begin fun ((b,ctx),fx) ->
(f b , ctx) , fx
end
(** [start_deriving f suchthat lemma] starts a proof of [suchthat]
(which can contain references to [f]) in the context extended by
[f:=?x]. When the proof ends, [f] is defined as the value of [?x]
and [lemma] as the proof. *)
let start_deriving f suchthat lemma =
let env = Global.env () in
let sigma = Evd.from_env env in
let kind = Decl_kinds.(Global,false,DefinitionBody Definition) in
(** create a sort variable for the type of [f] *)
(* spiwack: I don't know what the rigidity flag does, picked the one
that looked the most general. *)
let (sigma,f_type_sort) = Evd.new_sort_variable Evd.univ_flexible_alg sigma in
let f_type_type = Term.mkSort f_type_sort in
(** create the initial goals for the proof: |- Type ; |- ?1 ; f:=?2 |- suchthat *)
let goals =
let open Proofview in
TCons ( env , sigma , f_type_type , (fun sigma f_type ->
TCons ( env , sigma , f_type , (fun sigma ef ->
let env' = Environ.push_named (LocalDef (f, ef, f_type)) env in
let evdref = ref sigma in
let suchthat = Constrintern.interp_type_evars env' evdref suchthat in
TCons ( env' , !evdref , suchthat , (fun sigma _ ->
TNil sigma))))))
in
(** The terminator handles the registering of constants when the proof is closed. *)
let terminator com =
let open Proof_global in
(** Extracts the relevant information from the proof. [Admitted]
and [Save] result in user errors. [opaque] is [true] if the
proof was concluded by [Qed], and [false] if [Defined]. [f_def]
and [lemma_def] correspond to the proof of [f] and of
[suchthat], respectively. *)
let (opaque,f_def,lemma_def) =
match com with
| Admitted _ -> Errors.error"Admitted isn't supported in Derive."
| Proved (_,Some _,_) ->
Errors.error"Cannot save a proof of Derive with an explicit name."
| Proved (opaque, None, obj) ->
match Proof_global.(obj.entries) with
| [_;f_def;lemma_def] ->
opaque <> Vernacexpr.Transparent , f_def , lemma_def
| _ -> assert false
in
(** The opacity of [f_def] is adjusted to be [false], as it
must. Then [f] is declared in the global environment. *)
let f_def = { f_def with Entries.const_entry_opaque = false } in
let f_def = Entries.DefinitionEntry f_def , Decl_kinds.(IsDefinition Definition) in
let f_kn = Declare.declare_constant f f_def in
let f_kn_term = Term.mkConst f_kn in
(** In the type and body of the proof of [suchthat] there can be
references to the variable [f]. It needs to be replaced by
references to the constant [f] declared above. This substitution
performs this precise action. *)
let substf c = Vars.replace_vars [f,f_kn_term] c in
(** Extracts the type of the proof of [suchthat]. *)
let lemma_pretype =
match Entries.(lemma_def.const_entry_type) with
| Some t -> t
| None -> assert false (* Proof_global always sets type here. *)
in
(** The references of [f] are subsituted appropriately. *)
let lemma_type = substf lemma_pretype in
(** The same is done in the body of the proof. *)
let lemma_body =
map_const_entry_body substf Entries.(lemma_def.const_entry_body)
in
let lemma_def = let open Entries in { lemma_def with
const_entry_body = lemma_body ;
const_entry_type = Some lemma_type ;
const_entry_opaque = opaque ; }
in
let lemma_def =
Entries.DefinitionEntry lemma_def ,
Decl_kinds.(IsProof Proposition)
in
ignore (Declare.declare_constant lemma lemma_def)
in
let terminator = Proof_global.make_terminator terminator in
let () = Proof_global.start_dependent_proof lemma kind goals terminator in
let _ = Proof_global.with_current_proof begin fun _ p ->
Proof.run_tactic env Proofview.(tclFOCUS 1 2 shelve) p
end in
()
|
