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|
%=============================================================================%
% HOL 88 Version 2.1 %
% %
% FILE NAME: proof_rec.ml %
% %
% DESCRIPTION: function for recording and transforming proofs %
% %
% AUTHOR: Mike Gordon, Wai Wong %
% %
% USES FILES: hol-syn.ml %
% %
% University of Cambridge %
% Hardware Verification Group %
% Computer Laboratory %
% New Museums Site %
% Pembroke Street %
% Cambridge CB2 3QG %
% England %
% %
% COPYRIGHT: University of Edinburgh %
% COPYRIGHT: University of Cambridge %
% COPYRIGHT: INRIA %
% %
%=============================================================================%
%< --------------------------------------------------------------------------
Proof recording:
When proff recording is enabled, every inference step performed by
the system will be recorded in a list whose elements are of type step.
The low level functions for managing this feature are in the file
hol-syn.ml. They are reproduced below for easy reference.
The step list is then processed by the function MakeProof to become a
line list. This list can then be save into a disk file.
% We hide the flag and the list in local variables. Four functions are
provided for the users to control the recording of proof %
begin_section `record_proof`;;
letref steplist = [] : step list;;
letref record_proof_flag = false;;
letref suspended = false;;
let is_recording_proof (():void) = record_proof_flag;;
let record_proof b =
(if b then (steplist := [];());
record_proof_flag := b; ()) ;;
let suspend_recording () =
if record_proof_flag
then (record_proof_flag := false;
suspended := true; ());;
let resume_recording () =
if (suspended & (not record_proof_flag))
then (record_proof_flag := true;
suspended := false; ());;
let RecordStep step =
if record_proof_flag
then (steplist := (step.steplist); ());;
let get_steps (():void) = steplist;;
(record_proof,is_recording_proof,RecordStep,get_steps,
suspend_recording,resume_recording);;
end_section `record_proof`;;
let (record_proof,is_recording_proof,RecordStep,get_steps,
suspend_recording,resume_recording) = it;;
---------------------------------------------------------------------------->%
%----------------------------------------------------------------------------%
% Proof lines %
%----------------------------------------------------------------------------%
type justification =
Hypothesis
| Assume of term
| Refl of term
| Subst of (int#term)list # term # int
| BetaConv of term
| Abs of term # int
| InstType of (type#type)list # int
| Disch of term # int
| Mp of int # int
| MkComb of int # int
| MkAbs of int
| Alpha of term # term
| AddAssum of term # int
| Sym of int
| Trans of int # int
| ImpTrans of int # int
| ApTerm of term # int
| ApThm of int # term
| EqMp of int # int
| EqImpRuleR of int
| EqImpRuleL of int
| Spec of term # int
| EqtIntro of int
| Gen of term # int
| EtaConv of term
| Ext of int
| Exists of (term # term) # int
| Choose of (term # int) # int
| ImpAntisymRule of int # int
| MkExists of int
| Subs of int list # int
| SubsOccs of (int list # int) list # int
| SubstConv of (int # term) list # term # term
| Conj of int # int
| Conjunct1 of int
| Conjunct2 of int
| Disj1 of int # term
| Disj2 of term # int
| DisjCases of int # int # int
| NotIntro of int
| NotElim of int
| Contr of term # int
| Ccontr of term # int
| Inst of (term # term) list # int
| StoreDefinition of string # term
| Definition of string # string
| DefExistsRule of term
| NewAxiom of string # term
| Axiom of string # string
| Theorem of string # string
| NewConstant of string # type
| NewType of int # string
| NumConv of term;;
type line = Line of (int # thm # justification);;
%-------------------------------------------------------------------%
% MakeProof converts a step list into a line list. %
%-------------------------------------------------------------------%
let MakeProof steplst =
letref steps = rev steplst
and proof = [] : line list
and hyplist = [] : (int # thm) list
and thmlist = [] : (int # thm) list
and linecount = 1
and hypcount = 0
and thmcount = thm_count ()
in
let Pos th =
fst(rev_assoc th thmlist)
? fst(rev_assoc th hyplist)
? (hypcount := hypcount-1;
hyplist := (hypcount,th).hyplist;
hypcount)
and AddLine just th =
(proof := Line(linecount,th,just).proof;
thmlist := (linecount,th).thmlist;
linecount := linecount+1)
and AddHypLines () =
(proof := rev proof;
itlist (\(n,th) l. Line(n,th,Hypothesis).l) hyplist proof)
in
(suspend_recording ();
while not(null steps)
do ((case (hd steps) of
AssumeStep w .
AddLine (Assume w) (ASSUME w)
| ReflStep t .
AddLine (Refl t) (REFL t)
| SubstStep(thvars,w,lhsthm) .
AddLine (Subst(map (Pos # I) thvars, w, Pos lhsthm))
(SUBST thvars w lhsthm)
| BetaConvStep t .
AddLine (BetaConv t) (BETA_CONV t)
| AbsStep(x,th) .
AddLine (Abs(x,Pos th)) (ABS x th)
| InstTypeStep(inst_tylist,th) .
AddLine (InstType(inst_tylist,Pos th))
(INST_TYPE inst_tylist th)
| DischStep(w,th) .
AddLine (Disch(w,Pos th)) (DISCH w th)
| MpStep(thi,th) .
AddLine (Mp(Pos thi,Pos th)) (MP thi th)
| MkCombStep(funth,argth) .
AddLine (MkComb(Pos funth,Pos argth)) (MK_COMB(funth,argth))
| MkAbsStep th.
AddLine (MkAbs(Pos th)) (MK_ABS th)
| AlphaStep(t1,t2) .
AddLine (Alpha(t1,t2)) (ALPHA t1 t2)
| AddAssumStep(t,th) .
AddLine (AddAssum(t,Pos th)) (ADD_ASSUM t th)
| SymStep th .
AddLine (Sym(Pos th)) (SYM th)
| TransStep(th1,th2) .
AddLine (Trans(Pos th1,Pos th2)) (TRANS th1 th2)
| ImpTransStep(th1,th2) .
AddLine (ImpTrans(Pos th1,Pos th2)) (IMP_TRANS th1 th2)
| ApTermStep(tm,th) .
AddLine (ApTerm(tm,Pos th)) (AP_TERM tm th)
| ApThmStep(th,tm) .
AddLine (ApThm(Pos th,tm)) (AP_THM th tm)
| EqMpStep(th1,th2) .
AddLine (EqMp(Pos th1,Pos th2)) (EQ_MP th1 th2)
| EqImpRuleStep th .
(AddLine (EqImpRuleR(Pos th)) (fst(EQ_IMP_RULE th));
AddLine (EqImpRuleL(Pos th)) (snd(EQ_IMP_RULE th)))
| SpecStep(t,th) .
AddLine (Spec(t,Pos th)) (SPEC t th)
| EqtIntroStep th .
AddLine (EqtIntro(Pos th)) (EQT_INTRO th)
| GenStep(x,th) .
AddLine (Gen(x,Pos th)) (GEN x th)
| EtaConvStep tm .
AddLine (EtaConv tm) (ETA_CONV tm)
| ExtStep th .
AddLine (Ext(Pos th)) (EXT th)
| ExistsStep((w,t),th) .
AddLine (Exists((w,t),Pos th)) (EXISTS (w,t) th)
| ChooseStep((v,th1),th2) .
AddLine (Choose((v,Pos th1),Pos th2)) (CHOOSE (v,th1) th2)
| ImpAntisymRuleStep(th1,th2) .
AddLine (ImpAntisymRule(Pos th1,Pos th2))
(IMP_ANTISYM_RULE th1 th2)
| MkExistsStep bodyth .
AddLine (MkExists(Pos bodyth)) (MK_EXISTS bodyth)
| SubsStep(ths,th) .
AddLine (Subs(map Pos ths,Pos th)) (SUBS ths th)
| SubsOccsStep(nlths,th) .
AddLine (SubsOccs(map (I # Pos) nlths,Pos th))
(SUBS_OCCS nlths th)
| SubstConvStep(thvars,template,tm) .
AddLine (SubstConv(map (Pos # I) thvars, template, tm))
(SUBST_CONV thvars template tm)
| ConjStep(th1,th2) .
AddLine (Conj(Pos th1,Pos th2)) (CONJ th1 th2)
| Conjunct1Step th .
AddLine (Conjunct1(Pos th)) (CONJUNCT1 th)
| Conjunct2Step th .
AddLine (Conjunct2(Pos th)) (CONJUNCT2 th)
| Disj1Step(th,w) .
AddLine (Disj1(Pos th,w)) (DISJ1 th w)
| Disj2Step(w,th) .
AddLine (Disj2(w,Pos th)) (DISJ2 w th)
| DisjCasesStep(dth,ath,bth) .
AddLine (DisjCases(Pos dth,Pos ath,Pos bth))
(DISJ_CASES dth ath bth)
| NotIntroStep th .
AddLine (NotIntro(Pos th)) (NOT_INTRO th)
| NotElimStep th .
AddLine (NotElim(Pos th)) (NOT_ELIM th)
| ContrStep(w,fth) .
AddLine (Contr(w,Pos fth)) (CONTR w fth)
| CcontrStep(w,fth) .
AddLine (Ccontr(w,Pos fth)) (CCONTR w fth)
| InstStep(inst_list,th) .
AddLine (Inst(inst_list,Pos th)) (INST inst_list th)
| StoreDefinitionStep(name,t) .
AddLine (StoreDefinition(name,t)) (definition(current_theory()) name)
| DefinitionStep(thy,ax) .
AddLine (Definition(thy,ax)) (definition thy ax)
| DefExistsRuleStep tm .
AddLine (DefExistsRule tm) (DEF_EXISTS_RULE tm)
| NewAxiomStep(tk,tm) .
AddLine (NewAxiom(tk,tm)) (new_axiom(tk,tm))
| AxiomStep(thy,ax) .
AddLine (Axiom(thy,ax)) (axiom thy ax)
| TheoremStep(thy,factname) .
AddLine (Theorem(thy,factname)) (theorem thy factname)
| NewConstantStep(s,ty) .
AddLine (NewConstant(s,ty)) (TRUTH)
| NewTypeStep(arity,tok) .
AddLine (NewType(arity,tok)) (TRUTH)
| NumConvStep tm .
AddLine (NumConv tm) (num_CONV tm));
steps := tl steps);
resume_recording(); set_thm_count thmcount;
AddHypLines());;
% let ShowProof() = MakeProof (get_steps());; %
%-------------------------------------------------------------------%
% The functions below are for outputting proof lines to a disk file %
%-------------------------------------------------------------------%
begin_section `output_proof`;;
let output_strings port sl = % : (string -> string list -> void) %
do (map (\s. (write(port,s); write(port, `\L`))) sl);;
let write_pair port (fl,fr) =
\(l,r). (write(port, `{`);
(fl port l);
(fr port r);
write(port, `}`));;
let write_list port fn l =
(write(port, `[`);
(map (fn port) l);
write(port, `]`));;
letrec write_type port ty =
if (is_vartype ty)
then (write (port, (`(v `));
write(port, (dest_vartype ty));
write(port, `)`))
else (
let tyop,tyl = dest_type ty in
if null tyl
then (write (port, (`(c `));
write (port, tyop);
write (port, `)`))
else (write (port, (`(o `));
write (port, tyop);
write_list port write_type tyl;
write (port, `)`)));;
letrec write_term port tm =
let opt_delim s =
let lastchar s = (last o explode) s in
if (is_alphanum(lastchar s)) then () else write(port,` `) in
if (is_var tm)
then (let v,ty = dest_var tm in
(write(port, (`(V `));
write(port, (v)); opt_delim v;
write_type port ty;
write(port, `)`)))
else if (is_const tm)
then (let v,ty = dest_const tm in
(write(port, (`(C `));
write(port, (v)); opt_delim v;
write_type port ty;
write(port, `)`)))
else if (is_comb tm)
then (let ro,ra = dest_comb tm in
(write(port, (`(A `));
write_term port ro; write_term port ra;
write(port, `)`)))
else (let ro,ra = dest_abs tm in
(write(port, (`(L `));
write_term port ro; write_term port ra;
write(port, `)`)));;
let write_thm port thm =
(write_term port (concl thm);
write(port, `\L`));;
let write_all_thm port thm =
let asml,con = dest_thm thm in
(write(port, `(THM `);
write_list port write_term asml;
write_term port con;
write(port, `)\L`));;
let write_int port i =
(write(port, ` `);
write(port, (string_of_int i)));;
let write_just port j =
case j of
Hypothesis .
write(port, `(Hypothesis)`)
| (Assume tm) .
(write(port, `(Assume `);
write_term port tm;
write(port, `)`))
| (Refl tm) .
(write(port, `(Refl `);
write_term port tm;
write(port, `)`))
| (Subst (itl,tm,i)) .
(write(port, `(Subst `);
write_list port (\p. write_pair p (write_int,write_term)) itl;
write_term port tm;
write_int port i;
write(port, `)`))
| (BetaConv tm) .
(write(port, `(BetaConv `);
write_term port tm;
write(port, `)`))
| (Abs (tm,i)) .
(write(port, `(Abs `);
write_term port tm;
write_int port i;
write(port, `)`))
| (InstType (tyl,i)) .
(write(port, `(InstType `);
write_list port (\p. write_pair p (write_type,write_type)) tyl;
write_int port i;
write(port, `)`))
| (Disch (tm,i)) .
(write(port, `(Disch `);
write_term port tm;
write_int port i;
write(port, `)`))
| (Mp (i1,i2)) .
(write(port, `(Mp `);
write_int port i1;
write(port, ` `);
write_int port i2;
write(port, `)`))
| (MkComb (i1,i2)) .
(write(port, `(MkComb `);
write_int port i1;
write(port, ` `);
write_int port i2;
write(port, `)`))
| (MkAbs i) .
(write(port, `(MkAbs `);
write_int port i;
write(port, `)`))
| (Alpha (tm1,tm2)) .
(write(port, `(Alpha `);
write_term port tm1;
write_term port tm2;
write(port, `)`))
| (AddAssum (tm,i)) .
(write(port, `(AddAssum `);
write_term port tm;
write_int port i;
write(port, `)`))
| (Sym i) .
(write(port, `(Sym `);
write_int port i;
write(port, `)`))
| (Trans (i1,i2)) .
(write(port, `(Trans `);
write_int port i1;
write(port, ` `);
write_int port i2;
write(port, `)`))
| (ImpTrans (i1,i2)) .
(write(port, `(ImpTrans `);
write_int port i1;
write(port, ` `);
write_int port i2;
write(port, `)`))
| (ApTerm (tm,i)) .
(write(port, `(ApTerm `);
write_term port tm;
write_int port i;
write(port, `)`))
| (ApThm (i,tm)) .
(write(port, `(ApThm `);
write_int port i;
write_term port tm;
write(port, `)`))
| (EqMp (i1,i2)) .
(write(port, `(EqMp `);
write_int port i1;
write(port, ` `);
write_int port i2;
write(port, `)`))
| (EqImpRuleR i).
(write(port, `(EqImpRuleR `);
write_int port i;
write(port, `)`))
| (EqImpRuleL i).
(write(port, `(EqImpRuleL `);
write_int port i;
write(port, `)`))
| (Spec (tm,i)) .
(write(port, `(Spec `);
write_term port tm;
write_int port i;
write(port, `)`))
| (EqtIntro i) .
(write(port, `(EqtIntro `);
write_int port i;
write(port, `)`))
| (Gen (tm,i)) .
(write(port, `(Gen `);
write_term port tm;
write_int port i;
write(port, `)`))
| (EtaConv tm) .
(write(port, `(EtaConv `);
write_term port tm;
write(port, `)`))
| (Ext i) .
(write(port, `(Ext `);
write_int port i;
write(port, `)`))
| (Exists (tm,i)) .
(write(port, `(Exists `);
write_pair port (write_term,write_term) tm;
write_int port i;
write(port, `)`))
| (Choose (tmi,i)) .
(write(port, `(Choose `);
write_pair port (write_term,write_int) tmi;
write_int port i;
write(port, `)`))
| (ImpAntisymRule (i1,i2)) .
(write(port, `(ImpAntisymRule `);
write_int port i1;
write(port, ` `);
write_int port i2;
write(port, `)`))
| (MkExists i) .
(write(port, `(MkExists `);
write_int port i;
write(port, `)`))
| (Subs (il,i)) .
(write(port, `(Subs `);
write_list port write_int il;
write_int port i;
write(port, `)`))
| (SubsOccs (il,i)) .
(write(port, `(SubsOccs `);
write_list port
(\p (ill,ii). (write(p,`(`);
write_list p write_int ill;
write_int p ii;
write(p,`)`))) il;
write_int port i;
write(port, `)`))
| (SubstConv (itl, tm1, tm2)) .
(write(port, `(SubstConv `);
write_list port (\p. write_pair p (write_int,write_term)) itl;
write_term port tm1;
write_term port tm2;
write(port, `)`))
| (Conj (i1,i2)) .
(write(port, `(Conj `);
write_int port i1;
write(port, ` `);
write_int port i2;
write(port, `)`))
| (Conjunct1 i) .
(write(port, `(Conjunct1 `);
write_int port i;
write(port, `)`))
| (Conjunct2 i) .
(write(port, `(Conjunct2 `);
write_int port i;
write(port, `)`))
| (Disj1 (i,tm)) .
(write(port, `(Disj1 `);
write_int port i;
write_term port tm;
write(port, `)`))
| (Disj2 (tm,i)) .
(write(port, `(Disj2 `);
write_term port tm;
write_int port i;
write(port, `)`))
| (DisjCases (i1,i2,i3)) .
(write(port, `(DisjCases `);
write_int port i1;
write(port, ` `);
write_int port i2;
write(port, ` `);
write_int port i3;
write(port, `)`))
| (NotIntro i) .
(write(port, `(NotIntro `);
write_int port i;
write(port, `)`))
| (NotElim i) .
(write(port, `(NotElim `);
write_int port i;
write(port, `)`))
| (Contr (tm,i)) .
(write(port, `(Contr `);
write_term port tm;
write_int port i;
write(port, `)`))
| (Ccontr (tm,i)) .
(write(port, `(Ccontr `);
write_term port tm;
write_int port i;
write(port, `)`))
| (Inst (ttl,i)) .
(write(port, `(Inst `);
write_list port (\p. write_pair p (write_term,write_term)) ttl;
write_int port i;
write(port, `)`))
| (StoreDefinition (s,tm)) .
(write(port, (`(StoreDefinition `^s));
write_term port tm;
write(port, `)`))
| (Definition (s1,s2)) .
(write(port, (`(Definition `^s1^` `^s2^`)`)))
| (DefExistsRule tm) .
(write(port, (`(DefExistsRule `));
write_term port tm;
write(port, `)`))
| (NewAxiom (s,tm)) .
(write(port, (`(NewAxiom `^s));
write_term port tm;
write(port, `)`))
| (Axiom (s1,s2)) .
(write(port, (`(Axiom `^s1^` `^s2^`)`)))
| (Theorem (s1,s2)) .
(write(port, (`(Theorem `^s1^` `^s2^`)`)))
| (NewConstant (s,ty)) .
(write(port, (`(NewConstant `^s));
write_type port ty;
write(port, `)`))
| (NewType (i,s)) .
(write(port, (`(NewType `));
write_int port i;
write(port, (` `^s^`)`)))
| (NumConv tm) .
(write(port, `(NumConv `);
write_term port tm;
write(port, `)`));;
let write_line port (Line (ct, thm, just)) =
(write(port, `(LINE `);
write(port, (string_of_int ct));
write_just port just;
write(port,`\L`);
write_all_thm port thm;
write(port, `)\L\L`));;
let write_tyconst port (arity,tyname) =
(write_pair port ((\p s.write(p,s)), write_int) (tyname, arity));;
let write_sig port (cname, cty) =
(write_pair port ((\p s.write(p,s)), write_type) (cname, cty));;
let write_env ofile =
let holthy = `HOL` . (ancestors `HOL`) in
let thisthy = current_theory() in
let allthy = thisthy . (ancestors thisthy) in
let ths = subtract allthy holthy in
let tylst = flat (map types ths)
and conlst = map dest_const (flat (map constants ths)) in
(write(ofile, `(ENV `);
write(ofile, thisthy);
write_list ofile write_tyconst tylst;
write_list ofile write_sig conlst;
write(ofile, `)\L`));;
let write_thm_list port thml = write_list port write_all_thm thml;;
(write_line,write_thm_list,write_env);;
end_section `output_proof`;;
let (write_line,write_thm_list,write_env) = it;;
%-------------------------------------------------------------------%
% The functions below are the user level functions for recording %
% proofs %
%-------------------------------------------------------------------%
begin_section `proof_interface`;;
let format_version = `(VERSION PRF FORMAT 1.0 EXTENDED)\L`;;
let write_proof_add_to =
let format_name = (explode format_version) in
let read_line port =
letref ls = [] in
letref c = read port in
(if (c = `nil`) then (c := ``; ())
if not(c = `\L`) loop (ls := (c. ls); c := read port);
(ls := c.ls);
rev ls) in
let check_file fname =
let path = search_path() in
(set_search_path [``] ;
let fname' = find_file fname ?
(let ofile = openw fname in
(write(ofile, format_version);
write_env ofile;
close ofile; fname)) in
let ifile = openi fname' in
let fformat = read_line ifile in
(set_search_path path;
(fformat = format_name))) in
\file name thms prf.
if check_file file then
(let ofile = append_openw file in
(write(ofile, (`\L(PROOF `^name^`\L`));
write_thm_list ofile thms;
write(ofile, `\L[\L`);
map (write_line ofile) prf;
write(ofile, `])\L`);
close ofile))
else failwith
(`write_proof_add_to: ` ^file ^ ` not in the correct format`);;
let write_proof_to file pname thms prf =
let ofile = openw file in
(write(ofile, format_version);
write_env ofile;
write(ofile, (`(PROOF `^pname^`\L`));
write_thm_list ofile thms;
write(ofile, `\L[\L`);
map (write_line ofile) (prf);
write(ofile, `])\L`);
close ofile);;
letref proof_file_name = ``;;
letref proof_file_port = ``;;
letref proof_name = ``;;
letref proof_count = 0;;
letref current_goals = []:thm list;;
let write_last_proof =
\name thms.
(if (proof_file_port = ``) then failwith `no proof file`
else (
write(proof_file_port, (`\L(PROOF `^name^`\L`));
write_thm_list proof_file_port thms;
write(proof_file_port, `\L[\L`);
map (write_line proof_file_port) (MakeProof (get_steps()));
write(proof_file_port, `])\L`)))
?\s failwith (`write_last_proof: `^s);;
let current_proof_file (():void) = proof_file_name;;
let current_proof (():void) = proof_name;;
let close_proof_file (():void) =
(close proof_file_port;
proof_file_port := ``;
let c = system (`gzip `^ proof_file_name) in
if not(c = 0) then
tty_write(`WARNING: cannot compress proof file (gzip error `^
(string_of_int c) ^`)`)
else ();
proof_file_name := ``;
proof_count := 0; ());;
let new_proof_file name =
(if not(proof_file_name = ``) then(
close_proof_file();
failwith `a proof file is already opened`)
else(
proof_file_name := name;
proof_count := 0;
let ofile = openw proof_file_name in
(write(ofile, format_version);
write_env ofile);
proof_file_port := ofile; ()))
?\s failwith (`new_proof_file: `^s);;
let begin_proof name =
(if not(proof_name = ``) then failwith (`last proof is not saved yet`)
else (proof_name := name;
proof_count := proof_count + 1;
current_goals := [];
record_proof true; ()))
?\s failwith (`begin_proof: `^s);;
let end_proof name =
(if (proof_name = ``) then ()
else
(write_last_proof proof_name current_goals;
record_proof false;
proof_name := ``;
current_goals := []; ()))
?\s failwith (`end_proof: `^s);;
%-------------------------------------------------------------------%
% The functions below are the user level functions for recording %
% tactical proofs %
%-------------------------------------------------------------------%
let sanitise str =
let sps = explode `.;,:"!@#$^&*()|\\` in
let c' = `_` in
let san c = if (mem c sps) then c' else c in
letrec sani sl =
if (null sl) then []
else let h = san (hd sl) in (h . (sani (tl sl))) in
implode (sani (explode str));;
let TAC_PROOF (gl,tac) =
(let thm = TAC_PROOF(gl,tac) in
(current_goals := (mk_thm gl) . current_goals;
thm));;
let PROVE (tm,tac) =
(let thm = PROVE(tm,tac) in
(current_goals := (mk_thm([],tm)) . current_goals;
thm));;
let prove = \(t,tac). TAC_PROOF(([],t), tac);;
let prove_thm (name,tm,tac) =
(let thm = prove_thm(name,tm,tac) in
(current_goals := (mk_thm([],tm)) . current_goals;
thm));;
(write_proof_add_to, write_proof_to, write_last_proof,
current_proof, current_proof_file,
new_proof_file, close_proof_file, begin_proof, end_proof,
TAC_PROOF, PROVE, prove, prove_thm);;
end_section `proof_interface`;;
let (write_proof_add_to, write_proof_to, write_last_proof,
current_proof, current_proof_file,
new_proof_file, close_proof_file, begin_proof, end_proof,
TAC_PROOF, PROVE, prove, prove_thm) = it;;
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