path: root/proofs/proof.ml

(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

(* Module defining the last essential tiles of interactive proofs.
   The features of the Proof module are undoing and focusing.
   A proof is a mutable object, it contains a proofview, and some information
   to be able to undo actions, and to unfocus the current view. All three
   of these being meant to evolve.
   - Proofview: a proof is primarily the data of the current view.
     That which is shown to the user (as a remainder, a proofview
     is mainly the logical state of the proof, together with the
     currently focused goals).
   - Focus: a proof has a focus stack: the top of the stack contains
     the context in which to unfocus the current view to a view focused
     with the rest of the stack.
     In addition, this contains, for each of the focus context,  a 
     "focus kind" and a "focus condition" (in practice, and for modularity,
     the focus kind is actually stored inside the condition). To unfocus, one
     needs to know the focus kind, and the condition (for instance "no condition" or
     the proof under focused must be complete) must be met.
   - Undo: since proofviews and focus stacks are immutable objects, 
     it could suffice to hold the previous states, to allow to return to the past.
     However, we also allow other modules to do actions that can be undone.
     Therefore the undo stack stores action to be ran to undo.
*)

type _focus_kind = int
type 'a focus_kind = _focus_kind
type focus_info = Obj.t
type unfocusable =
  | Cannot of exn
  | Loose
  | Strict
type _focus_condition = 
    (_focus_kind -> Proofview.proofview -> unfocusable) *
    (_focus_kind -> bool)
type 'a focus_condition = _focus_condition

let next_kind = ref 0
let new_focus_kind () =
  let r = !next_kind in
  incr next_kind;
  r

(* Auxiliary function to define conditions. *)
let check kind1 kind2 = kind1=kind2

(* To be authorized to unfocus one must meet the condition prescribed by
    the action which focused.*)
(* spiwack: we could consider having a list of authorized focus_kind instead
    of just one, if anyone needs it *)
(* [no_cond] only checks that the unfocusing command uses the right
    [focus_kind]. *)

module Cond = struct
  (* first attempt at an algebra of condition *)
  (* semantics:
     - [Cannot] means that the condition is not met
     - [Strict] that the condition is met
     - [Loose] that the condition is not quite met
       but authorises to unfocus provided a condition
       of a previous focus on the stack is (strictly)
       met. [Loose] focuses are those, like bullets,
       which do not have a closing command and
       are hence closed by unfocusing actions unrelated
       to their focus_kind.
  *)
  let bool e b =
    if b then fun _ _ -> Strict
    else fun _ _ -> Cannot e
  let loose c k p = match c k p with
    | Cannot _ -> Loose
    | c -> c
  let cloose l c =
    if l then loose c
    else c
  let (&&&) c1 c2 k p=
    match c1 k p , c2 k p with
    | Cannot e , _ 
    | _ , Cannot e -> Cannot e
    | Strict, Strict -> Strict
    | _ , _ -> Loose
  let kind e k0 k p = bool e (k0=k) k p 
  let pdone e k p = bool e (Proofview.finished p) k p
end


(* Unfocus command.
   Fails if the proof is not focused. *)
exception CannotUnfocusThisWay
let _ = Errors.register_handler begin function
  | CannotUnfocusThisWay ->
    Errors.error "This proof is focused, but cannot be unfocused this way"
  | _ -> raise Errors.Unhandled
end

open Cond
let no_cond_gen e ~loose_end k0 =
  cloose loose_end (kind e k0)
let no_cond_gen e ?(loose_end=false) k = no_cond_gen e ~loose_end k , check k
let no_cond ?loose_end = no_cond_gen CannotUnfocusThisWay ?loose_end
(* [done_cond] checks that the unfocusing command uses the right [focus_kind]
    and that the focused proofview is complete. *)
let done_cond_gen e ~loose_end k0 =
  (cloose loose_end (kind e k0)) &&& pdone e
let done_cond_gen e ?(loose_end=false) k = done_cond_gen e ~loose_end k , check k
let done_cond ?loose_end = done_cond_gen CannotUnfocusThisWay ?loose_end


(* Subpart of the type of proofs. It contains the parts of the proof which
   are under control of the undo mechanism *)
type proof_state = {
  (* Current focused proofview *)
  proofview: Proofview.proofview;
  (* History of the focusings, provides information on how
     to unfocus the proof and the extra information stored while focusing.
     The list is empty when the proof is fully unfocused. *)
  focus_stack: (_focus_condition*focus_info*Proofview.focus_context) list;
}

type proof_info = {
  mutable endline_tactic : unit Proofview.tactic ;
  mutable section_vars : Sign.section_context option;
  initial_conclusions : Term.types list
}

type undo_action = 
  | State of proof_state
  | Effect of (unit -> unit)

type proof = { (* current proof_state *)
               mutable state : proof_state;
               (* The undo stack *)
               mutable undo_stack : undo_action list;
	       (* secondary undo stacks used for transactions *)
	       mutable transactions : undo_action list list;
	       info : proof_info
             }


(*** General proof functions ***)

let proof { state = p } =
  let (goals,sigma) = Proofview.proofview p.proofview in
  (* spiwack: beware, the bottom of the stack is used by [Proof]
     internally, and should not be exposed. *)
  let rec map_minus_one f = function
    | [] -> assert false
    | [_] -> []
    | a::l -> f a :: (map_minus_one f l)
  in
  let stack =
    map_minus_one (fun (_,_,c) -> Proofview.focus_context c) p.focus_stack
  in
  (goals,stack,sigma)

let rec unroll_focus pv = function
  | (_,_,ctx)::stk -> unroll_focus (Proofview.unfocus ctx pv) stk
  | [] -> pv

(* spiwack: a proof is considered completed even if its still focused, if the focus
   doesn't hide any goal.
   Unfocusing is handled in {!return}. *)
let is_done p =
  Proofview.finished p.state.proofview && 
  Proofview.finished (unroll_focus p.state.proofview p.state.focus_stack)

(* spiwack: for compatibility with <= 8.2 proof engine *)
let has_unresolved_evar p =
  Proofview.V82.has_unresolved_evar p.state.proofview

(* Returns the list of partial proofs to initial goals *)
let partial_proof p =
  List.map fst (Proofview.return p.state.proofview)



(*** The following functions implement the basic internal mechanisms
     of proofs, they are not meant to be exported in the .mli ***)

(* An auxiliary function to push a {!focus_context} on the focus stack. *)
let push_focus cond inf context pr =
  pr.state <- { pr.state with focus_stack = (cond,inf,context)::pr.state.focus_stack }

exception FullyUnfocused
let _ = Errors.register_handler begin function
  | FullyUnfocused -> Errors.error "The proof is not focused"
  | _ -> raise Errors.Unhandled
end
(* An auxiliary function to read the kind of the next focusing step *)
let cond_of_focus pr =
  match pr.state.focus_stack with
  | (cond,_,_)::_ -> cond
  | _ -> raise FullyUnfocused

(* An auxiliary function to pop and read the last {!Proofview.focus_context} 
   on the focus stack. *)
let pop_focus pr =
  match pr.state.focus_stack with
  | focus::other_focuses -> 
      pr.state <- { pr.state with focus_stack = other_focuses }; focus
  | _ -> 
      raise FullyUnfocused

(* Auxiliary function to push a [proof_state] onto the undo stack. *)
let push_undo save pr =
  match pr.transactions with
  | [] -> pr.undo_stack <- save::pr.undo_stack
  | stack::trans' -> pr.transactions <- (save::stack)::trans'

(* Auxiliary function to pop and read a [save_state] from the undo stack. *)
exception EmptyUndoStack
let _ = Errors.register_handler begin function
  | EmptyUndoStack -> Errors.error "Cannot undo: no more undo information"
  | _ -> raise Errors.Unhandled
end
let pop_undo pr =
  match pr.transactions , pr.undo_stack with
  | [] , state::stack -> pr.undo_stack <- stack; state
  | (state::stack)::trans', _ -> pr.transactions <- stack::trans'; state
  | _ -> raise EmptyUndoStack


(* This function focuses the proof [pr] between indices [i] and [j] *)
let _focus cond inf i j pr =
  let (focused,context) = Proofview.focus i j pr.state.proofview in
  push_focus cond inf context pr;
  pr.state <- { pr.state with proofview = focused }

(* This function unfocuses the proof [pr], it raises [FullyUnfocused],
   if the proof is already fully unfocused.
   This function does not care about the condition of the current focus. *)
let _unfocus pr =
  let (_,_,fc) = pop_focus pr in
  pr.state <- { pr.state with proofview = Proofview.unfocus fc pr.state.proofview }


let set_used_variables l p =
  p.info.section_vars <- Some l

let get_used_variables p = p.info.section_vars

(*** Endline tactic ***)

(* spiwack this is an information about the UI, it might be a good idea to move
   it to the Proof_global module *)

(* Sets the tactic to be used when a tactic line is closed with [...] *)
let set_endline_tactic tac p =
 p.info.endline_tactic <- tac

let with_end_tac pr tac =
  Proofview.tclTHEN tac pr.info.endline_tactic

(*** The following functions define the safety mechanism of the
     proof system, they may be unsafe if not used carefully. There is
     currently no reason to export them in the .mli ***)

(* This functions saves the current state into a [proof_state]. *)
let save_state { state = ps } = State ps

(* This function stores the current proof state in the undo stack. *)
let save pr =
  push_undo (save_state pr) pr

(* This function restores a state, presumably from the top of the undo stack. *)
let restore_state save pr =
  match save with
  | State save -> pr.state <- save
  | Effect undo -> undo ()

(* Interpretes the Undo command. *)
let undo pr =
  (* On a single line, since the effects commute *)
  restore_state (pop_undo pr) pr

(* Adds an undo effect to the undo stack. Use it with care, errors here might result
    in inconsistent states. *)
let add_undo effect pr =
  push_undo (Effect effect) pr



(*** Transactions ***)

let init_transaction pr =
  pr.transactions <- []::pr.transactions

let commit_stack pr stack =
  let push s = push_undo s pr in
  List.iter push (List.rev stack)

(* Invariant: [commit] should be called only when a transaction
   is open. It closes the current transaction. *)
let commit pr =
  match pr.transactions with
  | stack::trans' ->
    pr.transactions <- trans';
    commit_stack pr stack
  | [] -> assert false

(* Invariant: [rollback] should be called only when a transaction
   is open. It closes the current transaction. *)
let rec rollback pr =
  try
    undo pr;
    rollback pr
  with EmptyUndoStack ->
    match pr.transactions with
    | []::trans' -> pr.transactions <- trans'
    | _ -> assert false


let transaction pr t =
  init_transaction pr;
  try t (); commit pr
  with e -> rollback pr; raise e


(* Focus command (focuses on the [i]th subgoal) *)
(* spiwack: there could also, easily be a focus-on-a-range tactic, is there 
   a need for it? *)
let focus cond inf i pr =
  save pr;
  _focus cond (Obj.repr inf) i i pr

let rec unfocus kind pr () =
  let starting_point = save_state pr in
  let cond = cond_of_focus pr in
  match fst cond kind pr.state.proofview with
  | Cannot e -> raise e
  | Strict -> 
    (_unfocus pr;
     push_undo starting_point pr)
  | Loose ->
    begin try
	    _unfocus pr;
	    push_undo starting_point pr;
	    unfocus kind pr ()
      with FullyUnfocused -> raise CannotUnfocusThisWay
    end

let unfocus kind pr =
  transaction pr (unfocus kind pr)

exception NoSuchFocus
(* no handler: should not be allowed to reach toplevel. *)
let rec get_in_focus_stack kind stack =
  match stack with
  | ((_,check),inf,_)::stack ->
      if check kind then inf
      else get_in_focus_stack kind stack
  | [] -> raise NoSuchFocus
let get_at_focus kind pr =
  Obj.magic (get_in_focus_stack kind pr.state.focus_stack)

let is_last_focus kind pr =
  let ((_,check),_,_) = List.hd pr.state.focus_stack in
  check kind

let no_focused_goal p =
  Proofview.finished p.state.proofview

(*** Proof Creation/Termination ***)

(* [end_of_stack] is unfocused by return to close every loose focus. *)
let end_of_stack_kind = new_focus_kind ()
let end_of_stack = done_cond_gen FullyUnfocused end_of_stack_kind

let unfocused = is_last_focus end_of_stack_kind

let start goals =
  let pr =
    { state = { proofview = Proofview.init goals ;
	        focus_stack = [] };
      undo_stack = [] ;
      transactions = [] ;
      info = { endline_tactic = Proofview.tclUNIT ();
               initial_conclusions = List.map snd goals;
               section_vars = None }
    }
  in
  _focus end_of_stack (Obj.repr ()) 1 (List.length goals) pr;
  pr

exception UnfinishedProof
exception HasUnresolvedEvar
let _ = Errors.register_handler begin function
  | UnfinishedProof -> Errors.error "Some goals have not been solved."
  | HasUnresolvedEvar -> Errors.error "Some existential variables are uninstantiated."
  | _ -> raise Errors.Unhandled
end
let return p =
  if not (is_done p) then
    raise UnfinishedProof
  else if has_unresolved_evar p then 
    (* spiwack: for compatibility with <= 8.3 proof engine *)
    raise HasUnresolvedEvar
  else
    unfocus end_of_stack_kind p;
    Proofview.return p.state.proofview

(*** Tactics ***)

let run_tactic env tac pr =
  let starting_point = save_state pr in
  let sp = pr.state.proofview in
  try
    let tacticced_proofview = Proofview.apply env tac sp in
    pr.state <- { pr.state with proofview = tacticced_proofview };
    push_undo starting_point pr
  with e -> 
    restore_state starting_point pr;
    raise e

(*** Commands ***)

let in_proof p k =
  Proofview.in_proofview p.state.proofview k


(*** Compatibility layer with <=v8.2 ***)
module V82 = struct
  let subgoals p =
    Proofview.V82.goals p.state.proofview

  let background_subgoals p =
    Proofview.V82.goals (unroll_focus p.state.proofview p.state.focus_stack)

  let get_initial_conclusions p = 
    p.info.initial_conclusions

  let depth p = List.length p.undo_stack

  let top_goal p = 
    let { Evd.it=gls ; sigma=sigma } = 
	Proofview.V82.top_goals p.state.proofview
    in
    { Evd.it=List.hd gls ; sigma=sigma }

  let top_evars p =
    Proofview.V82.top_evars p.state.proofview

  let grab_evars p =
    if not (is_done p) then
      raise UnfinishedProof
    else
      save p;
      p.state <- { p.state with proofview = Proofview.V82.grab p.state.proofview }
    

    let instantiate_evar n com pr =
      let starting_point = save_state pr in
      let sp = pr.state.proofview in
      try
	let new_proofview = Proofview.V82.instantiate_evar n com sp in
	pr.state <- { pr.state with proofview = new_proofview };
	push_undo starting_point pr
      with e -> 
	restore_state starting_point pr;
	raise e
end