(******************)
(* complete later *)
(******************)
fun not_newline ch = not (ch = "\n");
(* Versions that include type information *)
fun string_of_thm thm = let val _ = set show_sorts
val str = Sign.string_of_term Mainsign (prop_of thm)
val no_returns =List.filter not_newline (explode str)
val _ = reset show_sorts
in
implode no_returns
end
fun thm_of_string str = let val _ = set show_sorts
val term = read str
val propterm = mk_Trueprop term
val cterm = cterm_of Mainsign propterm
val _ = reset show_sorts
in
assume cterm
end
(* check separate args in the watcher program for separating strings with a * or ; or something *)
fun clause_strs_to_string [] str = str
| clause_strs_to_string (x::xs) str = clause_strs_to_string xs (str^x^"%")
fun thmvars_to_string [] str = str
| thmvars_to_string (x::xs) str = thmvars_to_string xs (str^x^"%")
fun proofstep_to_string Axiom = "Axiom()"
| proofstep_to_string (Binary ((a,b), (c,d)))= "Binary"^"("^"("^(string_of_int a)^","^(string_of_int b)^")"^","^"("^(string_of_int c)^","^(string_of_int d)^")"^")"
| proofstep_to_string (Factor (a,b,c)) = "Factor"^"("^(string_of_int a)^","^(string_of_int b)^","^(string_of_int c)^")"
| proofstep_to_string (Para ((a,b), (c,d)))= "Para"^"("^"("^(string_of_int a)^","^(string_of_int b)^")"^","^"("^(string_of_int c)^","^(string_of_int d)^")"^")"
| proofstep_to_string (MRR ((a,b), (c,d)))= "MRR"^"("^"("^(string_of_int a)^","^(string_of_int b)^")"^","^"("^(string_of_int c)^","^(string_of_int d)^")"^")"
| proofstep_to_string (Rewrite((a,b),(c,d))) = "Rewrite"^"("^"("^(string_of_int a)^","^(string_of_int b)^")"^","^"("^(string_of_int c)^","^(string_of_int d)^")"^")"
fun list_to_string [] liststr = liststr
| list_to_string (x::[]) liststr = liststr^(string_of_int x)
| list_to_string (x::xs) liststr = list_to_string xs (liststr^(string_of_int x)^",")
fun proof_to_string (num,(step,clause_strs, thmvars)) = (string_of_int num)^(proofstep_to_string step)^"["^(clause_strs_to_string clause_strs "")^"]"^"["^(thmvars_to_string thmvars "")^"]"
fun proofs_to_string [] str = str
| proofs_to_string (x::xs) str = let val newstr = proof_to_string x
in
proofs_to_string xs (str^newstr)
end
fun init_proofstep_to_string (num, step, clause_strs) = (string_of_int num)^" "^(proofstep_to_string step)^" "^(clause_strs_to_string clause_strs "")^" "
fun init_proofsteps_to_string [] str = str
| init_proofsteps_to_string (x::xs) str = let val newstr = init_proofstep_to_string x
in
init_proofsteps_to_string xs (str^newstr)
end
(*** get a string representing the Isabelle ordered axioms ***)
fun origAx_to_string (num,(meta,thmvars)) =let val clause_strs = get_meta_lits_bracket meta
in
(string_of_int num)^"OrigAxiom()"^"["^(clause_strs_to_string clause_strs "")^"]"^"["^(thmvars_to_string thmvars "")^"]"
end
fun origAxs_to_string [] str = str
| origAxs_to_string (x::xs) str = let val newstr = origAx_to_string x
in
origAxs_to_string xs (str^newstr)
end
(*** get a string representing the Isabelle ordered axioms not used in the spass proof***)
fun extraAx_to_string (num, (meta,thmvars)) = let val clause_strs = get_meta_lits_bracket meta
in
(string_of_int num)^"ExtraAxiom()"^"["^(clause_strs_to_string clause_strs "")^"]"^"["^(thmvars_to_string thmvars "")^"]"
end
fun extraAxs_to_string [] str = str
| extraAxs_to_string (x::xs) str = let val newstr = extraAx_to_string x
in
extraAxs_to_string xs (str^newstr)
end
fun is_axiom ( num:int,Axiom, str) = true
| is_axiom (num, _,_) = false
fun get_init_axioms xs = List.filter (is_axiom) ( xs)
fun get_step_nums [] nums = nums
| get_step_nums (( num:int,Axiom, str)::xs) nums = get_step_nums xs (nums@[num])
fun assoc_snd a [] = raise Noassoc
| assoc_snd a ((x, y)::t) = if a = y then x else assoc_snd a t;
(* change to be something using check_order instead of a = y --> returns true if ASSERTION not raised in checkorder, false otherwise *)
(*fun get_assoc_snds [] xs assocs= assocs
| get_assoc_snds (x::xs) ys assocs = get_assoc_snds xs ys (assocs@[((assoc_snd x ys))])
*)
(*FIX - should this have vars in it? *)
fun there_out_of_order xs ys = let val foo = (checkorder xs ys [] ([],[],[]))
in
true
end
handle EXCEP => false
fun assoc_out_of_order a [] = raise Noassoc
| assoc_out_of_order a ((b,c)::t) = if there_out_of_order a c then b else assoc_out_of_order a t;
fun get_assoc_snds [] xs assocs= assocs
| get_assoc_snds (x::xs) ys assocs = get_assoc_snds xs ys (assocs@[((assoc_out_of_order x ys))])
fun add_if_not_inlist [] xs newlist = newlist
| add_if_not_inlist (y::ys) xs newlist = if (not (inlist y xs)) then
add_if_not_inlist ys xs (y::newlist)
else add_if_not_inlist ys xs (newlist)
(*
fun is_alpha_space_neg_eq_colon ch = (ch = "~") orelse (is_alpha ch) orelse ( ch = " ")orelse ( ch = ";") orelse( ch = "=")
(* replace | by ; here *)
fun change_or [] = []
| change_or (x::xs) = if x = "|"
then
[";"]@(change_or xs)
else (x::(change_or xs))
fun clause_lit_string t = let val termstr = (Sign.string_of_term Mainsign ) t
val exp_term = explode termstr
val colon_term = change_or exp_term
in
implode(List.filter is_alpha_space_neg_eq_colon colon_term)
end
fun get_clause_lits thm = clause_lit_string (prop_of thm)
*)
fun onestr [] str = str
| onestr (x::xs) str = onestr xs (str^(concat x))
fun thmstrings [] str = str
| thmstrings (x::xs) str = thmstrings xs (str^(string_of_thm x))
fun onelist [] newlist = newlist
| onelist (x::xs) newlist = onelist xs (newlist@x)
(**** Code to support ordinary resolution, rather than Model Elimination ****)
(*Convert a list of clauses (disjunctions) to meta-level clauses (==>),
with no contrapositives, for ordinary resolution.*)
(*raises exception if no rules apply -- unlike RL*)
fun tryres (th, rl::rls) = (th RS rl handle THM _ => tryres(th,rls))
| tryres (th, []) = raise THM("tryres", 0, [th]);
val prop_of = #prop o rep_thm;
(*For ordinary resolution. *)
val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule'];
(*Use "theorem naming" to label the clauses*)
fun name_thms label =
let fun name1 (th, (k,ths)) =
(k-1, Thm.name_thm (label ^ string_of_int k, th) :: ths)
in fn ths => #2 (foldr name1 (length ths, []) ths) end;
(*Find an all-negative support clause*)
fun is_negative th = forall (not o #1) (literals (prop_of th));
val neg_clauses = List.filter is_negative;
(*True if the given type contains bool anywhere*)
fun has_bool (Type("bool",_)) = true
| has_bool (Type(_, Ts)) = exists has_bool Ts
| has_bool _ = false;
(*Create a meta-level Horn clause*)
fun make_horn crules th = make_horn crules (tryres(th,crules))
handle THM _ => th;
(*Raises an exception if any Vars in the theorem mention type bool. That would mean
they are higher-order, and in addition, they could cause make_horn to loop!*)
fun check_no_bool th =
if exists (has_bool o fastype_of) (term_vars (#prop (rep_thm th)))
then raise THM ("check_no_bool", 0, [th]) else th;
(*Rules to convert the head literal into a negated assumption. If the head
literal is already negated, then using notEfalse instead of notEfalse'
prevents a double negation.*)
val notEfalse = read_instantiate [("R","False")] notE;
val notEfalse' = rotate_prems 1 notEfalse;
fun negated_asm_of_head th =
th RS notEfalse handle THM _ => th RS notEfalse';
(*Converting one clause*)
fun make_meta_clause th =
negated_asm_of_head (make_horn resolution_clause_rules (check_no_bool th));
fun make_meta_clauses ths =
name_thms "MClause#"
(gen_distinct Drule.eq_thm_prop (map make_meta_clause ths));
(*Permute a rule's premises to move the i-th premise to the last position.*)
fun make_last i th =
let val n = nprems_of th
in if 1 <= i andalso i <= n
then Thm.permute_prems (i-1) 1 th
else raise THM("select_literal", i, [th])
end;
(*Maps a rule that ends "... ==> P ==> False" to "... ==> ~P" while suppressing
double-negations.*)
val negate_head = rewrite_rule [atomize_not, not_not RS eq_reflection];
(*Maps the clause [P1,...Pn]==>False to [P1,...,P(i-1),P(i+1),...Pn] ==> ~P*)
fun select_literal i cl = negate_head (make_last i cl);
fun get_axioms_used proof_steps thmstring = let
val outfile = TextIO.openOut("foo_ax_thmstr");
val _ = TextIO.output (outfile, thmstring)
val _ = TextIO.closeOut outfile
(* not sure why this is necessary again, but seems to be *)
val _= (print_mode := (Library.gen_rems (op =) (! print_mode, ["xsymbols", "symbols"])))
val axioms = get_init_axioms proof_steps
val step_nums = get_step_nums axioms []
val thm = thm_of_string thmstring
val clauses = make_clauses [thm]
val vars = map thm_vars clauses
val distvars = distinct (fold append vars [])
val clause_terms = map prop_of clauses
val clause_frees = onelist (map term_frees clause_terms) []
val frees = map lit_string_with_nums clause_frees;
val distfrees = distinct frees
val metas = map make_meta_clause clauses
val ax_strs = map (three_of_three ) axioms
(* literals of -all- axioms, not just those used by spass *)
val meta_strs = map get_meta_lits metas
val metas_and_strs = zip metas meta_strs
val outfile = TextIO.openOut("foo_clauses");
val _ = TextIO.output (outfile, (onestr ax_strs ""))
val _ = TextIO.closeOut outfile
val outfile = TextIO.openOut("foo_metastrs");
val _ = TextIO.output (outfile, (onestr meta_strs ""))
val _ = TextIO.closeOut outfile
(* get list of axioms as thms with their variables *)
val ax_metas = get_assoc_snds ax_strs metas_and_strs []
val ax_vars = map thm_vars ax_metas
val ax_with_vars = zip ax_metas ax_vars
(* get list of extra axioms as thms with their variables *)
val extra_metas = add_if_not_inlist metas ax_metas []
val extra_vars = map thm_vars extra_metas
val extra_with_vars = if (not (extra_metas = []) )
then
zip extra_metas extra_vars
else
[]
(* val _= (print_mode := (Library.gen_rems (op =) (! print_mode, ["xsymbols", "symbols"])))
val outfile = TextIO.openOut("foo_metas")
val _ = TextIO.output (outfile, ((thmstrings ax_metas "")))
val _ = TextIO.closeOut outfile
val execperl = Unix.execute("/usr/bin/perl", ["remchars2.pl <foo_metas >foo_metas2"])
val infile = TextIO.openIn("foo_metas2")
val ax_metas_str = TextIO.inputLine (infile)
val _ = TextIO.closeIn infile
val _= (print_mode := (["xsymbols", "symbols"] @ ! print_mode))*)
in
(distfrees,distvars, extra_with_vars,ax_with_vars, (zip step_nums ax_metas))
end
fun thmstrings [] str = str
| thmstrings (x::xs) str = thmstrings xs (str^(string_of_thm x))
fun numclstr (vars, []) str = str
| numclstr ( vars, ((num, thm)::rest)) str = let val newstr = str^(string_of_int num)^" "^(string_of_thm thm)^" "
in
numclstr (vars,rest) newstr
end
(*
val proofstr = "Did parsing on Here is a proof with depth 4, length 9 :\
\1[0:Inp] || v_P(tconst_fun(typ__da_a,tconst_bool),v_x)*+ -> v_P(tconst_fun(typ__da_a,tconst_bool),U)*.\
\3[0:Inp] || v_P(tconst_fun(typ__da_a,tconst_bool),U)*+ -> v_P(tconst_fun(typ__da_a,tconst_bool),v_x)*.\
\5[0:Inp] || -> v_P(tconst_fun(typ__da_a,tconst_bool),U)* v_P(tconst_fun(typ__da_a,tconst_bool),v_xa)*.\
\7[0:Inp] || v_P(tconst_fun(typ__da_a,tconst_bool),U)*+ v_P(tconst_fun(typ__da_a,tconst_bool),v_xb)* -> .\
\9[0:Fac:5.0,5.1] || -> v_P(tconst_fun(typ__da_a,tconst_bool),v_xa)*.\
\10[0:Res:9.0,3.0] || -> v_P(tconst_fun(typ__da_a,tconst_bool),v_x)*.\
\11[0:Res:10.0,1.0] || -> v_P(tconst_fun(typ__da_a,tconst_bool),U)*.\
\12[0:Fac:7.0,7.1] || v_P(tconst_fun(typ__da_a,tconst_bool),v_xb)* -> .\
\14[0:Res:11.0,12.0] || -> .\
\Formulae used in the proof :"
*)
fun addvars c (a,b) = (a,b,c)
(*********************************************************************)
(* Pass in spass string of proof and string version of isabelle goal *)
(* Get out reconstruction steps as a string to be sent to Isabelle *)
(*********************************************************************)
(*
val proofstr = "Here is a proof with depth 2, length 5 :\
\1[0:Inp] || -> v_P(tconst_fun(typ__asc39_a,tconst_bool),U)*.\
\3[0:Inp] || v_Q(tconst_fun(typ__asc39_a,tconst_bool),U)* -> .\
\5[0:Inp] || v_P(tconst_fun(typ__asc39_a,tconst_bool),v_x)* -> v_Q(tconst_fun(typ__asc39_a,tconst_bool),v_xa).\
\7[0:Res:1.0,5.0] || -> v_Q(tconst_fun(typ__asc39_a,tconst_bool),v_xa)*.\
\9[0:Res:7.0,3.0] || -> .\
\Formulae used in the proof :"
val proofstr = "Here is a proof with depth 4, length 9 :\
\1[0:Inp] || v_P(tconst_fun(typ__asc39_a,tconst_bool),v_x)*+ -> v_P(tconst_fun(typ__asc39_a,tconst_bool),U)*.\
\3[0:Inp] || v_P(tconst_fun(typ__asc39_a,tconst_bool),U)*+ -> v_P(tconst_fun(typ__asc39_a,tconst_bool),v_x)*.\
\5[0:Inp] || -> v_P(tconst_fun(typ__asc39_a,tconst_bool),U)* v_P(tconst_fun(typ__asc39_a,tconst_bool),v_xa)*.\
\7[0:Inp] || v_P(tconst_fun(typ__asc39_a,tconst_bool),U)*+ v_P(tconst_fun(typ__asc39_a,tconst_bool),v_xb)* -> .\
\9[0:Fac:5.0,5.1] || -> v_P(tconst_fun(typ__asc39_a,tconst_bool),v_xa)*.\
\10[0:Res:9.0,3.0] || -> v_P(tconst_fun(typ__asc39_a,tconst_bool),v_x)*.\
\11[0:Res:10.0,1.0] || -> v_P(tconst_fun(typ__asc39_a,tconst_bool),U)*.\
\12[0:Fac:7.0,7.1] || v_P(tconst_fun(typ__asc39_a,tconst_bool),v_xb)* -> .\
\14[0:Res:11.0,12.0] || -> .\
\Formulae used in the proof :";
val thmstring = " (~ (P::'a::type => bool) (x::'a::type) | P (U::'a::type)) & (~ (P::'a::type => bool) (U::'a::type) | P (x::'a::type)) & ((P::'a::type => bool) (xa::'a::type) | P (U::'a::type)) & (~ (P::'a::type => bool) (U::'a::type) | ~ P (xb::'a::type))";
val thmstring = "(ALL xb::'a::type. (~ (P::'a::type => bool) ((x::'a::type => 'a::type) xb) | (Q::'a::type => bool) ((xa::'a::type => 'a::type) xb)) & P xb & ~ Q xb)"
val thmstring ="(ALL xb::'a::type. (~ (P::'a::type => bool) ((x::'a::type => 'a::type) xb) | (Q::'a::type => bool) ((xa::'a::type => 'a::type) xb)) & P xb & ~ Q xb)"
val proofstr = "Did parsing on Here is a proof with depth 2, length 5 :\
\1[0:Inp] || -> v_P(tconst_fun(typ__asc39_a,tconst_bool),U)*.\
\3[0:Inp] || v_Q(tconst_fun(typ__asc39_a,tconst_bool),U)* -> .\
\5[0:Inp] || v_P(tconst_fun(typ__asc39_a,tconst_bool),v_x(tconst_fun(typ__asc39_a,typ__asc39_a),U))* -> v_Q(tconst_fun(typ__asc39_a,tconst_bool),v_xa(tconst_fun(typ__asc39_a,typ__asc39_a),U)).\
\7[0:Res:1.0,5.0] || -> v_Q(tconst_fun(typ__asc39_a,tconst_bool),v_xa(tconst_fun(typ__asc39_a,typ__asc39_a),U))*.\
\9[0:Res:7.0,3.0] || -> .\
\Formulae used in the proof :";
*)
fun spassString_to_reconString proofstr thmstring =
let val outfile = TextIO.openOut("thmstringfile"); val _= warning("proofstr is: "^proofstr);
val _ = warning ("thmstring is: "^thmstring);
val _ = TextIO.output (outfile, (thmstring))
val _ = TextIO.closeOut outfile
val proofextract = extract_proof proofstr
val tokens = fst(lex proofextract)
(***********************************)
(* parse spass proof into datatype *)
(***********************************)
val proof_steps1 = parse tokens
val proof_steps = just_change_space proof_steps1
val outfile = TextIO.openOut("foo_parse"); val _ = TextIO.output (outfile, ("Did parsing on "^proofstr))
val _ = TextIO.closeOut outfile
val outfile = TextIO.openOut("foo_thmstring_at_parse"); val _ = TextIO.output (outfile, ("Parsing for thmstring: "^thmstring))
val _ = TextIO.closeOut outfile
(************************************)
(* recreate original subgoal as thm *)
(************************************)
(* get axioms as correctly numbered clauses w.r.t. the Spass proof *)
val (frees,vars,extra_with_vars ,ax_with_vars,numcls) = get_axioms_used proof_steps thmstring
(*val numcls_string = numclstr ( vars, numcls) ""*)
val outfile = TextIO.openOut("foo_axiom"); val _ = TextIO.output (outfile,"got axioms")
val _ = TextIO.closeOut outfile
(************************************)
(* translate proof *)
(************************************)
val outfile = TextIO.openOut("foo_steps"); val _ = TextIO.output (outfile, ("about to translate proof, steps: "^(init_proofsteps_to_string proof_steps "")))
val _ = TextIO.closeOut outfile
val (newthm,proof) = translate_proof numcls proof_steps vars
val outfile = TextIO.openOut("foo_steps2"); val _ = TextIO.output (outfile, ("translated proof, steps: "^(init_proofsteps_to_string proof_steps "")))
val _ = TextIO.closeOut outfile
(***************************************************)
(* transfer necessary steps as strings to Isabelle *)
(***************************************************)
(* turn the proof into a string *)
val reconProofStr = proofs_to_string proof ""
(* do the bit for the Isabelle ordered axioms at the top *)
val ax_nums = map fst numcls
val ax_strs = map get_meta_lits_bracket (map snd numcls)
val numcls_strs = zip ax_nums ax_strs
val num_cls_vars = map (addvars vars) numcls_strs;
val reconIsaAxStr = origAxs_to_string (zip ax_nums ax_with_vars) ""
val extra_nums = if (not (extra_with_vars = [])) then (1 upto (length extra_with_vars)) else []
val reconExtraAxStr = extraAxs_to_string ( zip extra_nums extra_with_vars) ""
val frees_str = "["^(thmvars_to_string frees "")^"]"
val outfile = TextIO.openOut("reconstringfile");
val _ = TextIO.output (outfile, (frees_str^reconExtraAxStr^reconIsaAxStr^reconProofStr))
val _ = TextIO.closeOut outfile
in
(frees_str^reconExtraAxStr^reconIsaAxStr^reconProofStr)
end
handle _ => (let val outfile = TextIO.openOut("foo_handler");
val _ = TextIO.output (outfile, ("In exception handler"));
val _ = TextIO.closeOut outfile
in
"Proof found but translation failed!"
end)
(**********************************************************************************)
(* At other end, want to turn back into datatype so can apply reconstruct_proof. *)
(* This will be done by the signal handler *)
(**********************************************************************************)
(* Parse in the string version of the proof steps for reconstruction *)
(* Isar format: cl1 [BINARY 0 cl2 0];cl1 [PARAMOD 0 cl2 0]; cl1 [DEMOD 0 cl2];cl1 [FACTOR 1 2];*)
val term_numstep =
(number ++ (a (Other ",")) ++ number) >> (fn (a, (_, c)) => (a, c))
val extraaxiomstep = (a (Word "ExtraAxiom"))++ (a (Other "(")) ++(a (Other ")"))
>> (fn (_) => ExtraAxiom)
val origaxiomstep = (a (Word "OrigAxiom"))++ (a (Other "(")) ++(a (Other ")"))
>> (fn (_) => OrigAxiom)
val axiomstep = (a (Word "Axiom"))++ (a (Other "(")) ++(a (Other ")"))
>> (fn (_) => Axiom)
val binarystep = (a (Word "Binary")) ++ (a (Other "(")) ++ (a (Other "("))
++ term_numstep ++ (a (Other ")")) ++ (a (Other ","))
++ (a (Other "(")) ++ term_numstep ++ (a (Other ")")) ++ (a (Other ")"))
>> (fn (_, (_, (_, (c, (_,(_,(_, (e,(_,_))))))))) => Binary (c,e))
val parastep = (a (Word "Para")) ++ (a (Other "(")) ++ (a (Other "("))
++ term_numstep ++ (a (Other ")")) ++ (a (Other ","))
++ (a (Other "(")) ++ term_numstep ++ (a (Other ")")) ++ (a (Other ")"))
>> (fn (_, (_, (_, (c, (_,(_,(_, (e,(_,_))))))))) => Para(c, e))
val mrrstep = (a (Word "MRR")) ++ (a (Other "(")) ++ (a (Other "("))
++ term_numstep ++ (a (Other ")")) ++ (a (Other ","))
++ (a (Other "(")) ++ term_numstep ++ (a (Other ")")) ++ (a (Other ")"))
>> (fn (_, (_, (_, (c, (_,(_,(_, (e,(_,_))))))))) => MRR(c, e))
val factorstep = (a (Word "Factor")) ++ (a (Other "("))
++ number ++ (a (Other ","))
++ number ++ (a (Other ","))
++ number ++ (a (Other ")"))
>> (fn (_, (_, (c, (_, (e,(_,(f,_))))))) => Factor (c,e,f))
val rewritestep = (a (Word "Rewrite")) ++ (a (Other "(")) ++ (a (Other "("))
++ term_numstep ++ (a (Other ")")) ++ (a (Other ","))
++ (a (Other "(")) ++ term_numstep ++ (a (Other ")")) ++ (a (Other ")"))
>> (fn (_, (_, (_, (c, (_,(_,(_, (e,(_,_))))))))) => Rewrite (c,e))
val obviousstep = (a (Word "Obvious")) ++ (a (Other "("))
++ term_numstep ++ (a (Other ")"))
>> (fn (_, (_, (c,_))) => Obvious (c))
val methodstep = extraaxiomstep || origaxiomstep || axiomstep ||binarystep || factorstep|| parastep || mrrstep || rewritestep || obviousstep
val number_list_step =
( number ++ many ((a (Other ",") ++ number)>> snd))
>> (fn (a,b) => (a::b))
val numberlist_step = a (Other "[") ++ a (Other "]")
>>(fn (_,_) => ([]:int list))
|| a (Other "[") ++ number_list_step ++ a (Other "]")
>>(fn (_,(a,_)) => a)
(** change this to allow P (x U) *)
fun arglist_step input = ( word ++ many word >> (fn (a, b) => (a^" "^(implode_with_space b)))
||word >> (fn (a) => (a)))input
fun literal_step input = (word ++ a (Other "(") ++ arglist_step ++ a (Other ")")
>>(fn (a, (b, (c,d))) => (a^" ("^(c)^")"))
|| arglist_step >> (fn (a) => (a)))input
(* fun term_step input = (a (Other "~") ++ arglist_step ++ a (Other "%")>> (fn (a,(b,c)) => ("~ "^b))
|| arglist_step ++ a (Other "%")>> (fn (a,b) => a ))input
*)
fun term_step input = (a (Other "~") ++ literal_step ++ a (Other "%")>> (fn (a,(b,c)) => ("~ "^b))
|| literal_step ++ a (Other "%")>> (fn (a,b) => a ))input
val term_list_step =
( term_step ++ many ( term_step))
>> (fn (a,b) => (a::b))
val term_lists_step = a (Other "[") ++ a (Other "]")
>>(fn (_,_) => ([]:string list))
|| a (Other "[") ++ term_list_step ++ a (Other "]")
>>(fn (_,(a,_)) => a)
fun anytoken_step input = (word>> (fn (a) => a) ) input
handle NOPARSE_WORD => (number>> (fn (a) => string_of_int a) ) input
handle NOPARSE_NUMBER => (other_char >> (fn(a) => a)) input
fun goalstring_step input= (anytoken_step ++ many (anytoken_step )
>> (fn (a,b) => (a^" "^(implode b)))) input
val linestep = number ++ methodstep ++ term_lists_step ++ term_lists_step
>> (fn (a, (b, (c,d))) => (a,(b,c,d)))
val lines_step = many linestep
val alllines_step = (term_lists_step ++ lines_step ) ++ finished >> fst
val parse_step = fst o alllines_step
(*
val reconstr ="[P%x%xa%xb%]1OrigAxiom()[P x%~ P U%][U%]3OrigAxiom()[P U%~ P x%][U%]5OrigAxiom()[~ P xa%~ P U%][U%]7OrigAxiom()[P U%P xb%][U%]1Axiom()[P x%~ P U%][U%]3Axiom()[P U%~ P x%][U%]5Axiom()[~ P U%~ P xa%][U%]7Axiom()[P U%P xb%][U%]9Factor(5,0,1)[~ P xa%][]10Binary((9,0),(3,0))[~ P x%][]11Binary((10,0),(1,0))[~ P U%][U%]12Factor(7,0,1)[P xb%][]14Binary((11,0),(12,0))[][]%(EX x::'a::type. ALL y::'a::type. (P::'a::type => bool) x = P y) -->(EX x::'a::type. P x) = (ALL y::'a::type. P y)"
*)
(************************************************************)
(* Construct an Isar style proof from a list of proof steps *)
(************************************************************)
(* want to assume all axioms, then do haves for the other clauses*)
(* then show for the last step *)
fun one_of_three (a,b,c) = a;
fun two_of_three (a,b,c) = b;
fun three_of_three (a,b,c) = c;
(* replace ~ by not here *)
fun change_nots [] = []
| change_nots (x::xs) = if x = "~"
then
["\\", "<", "n", "o", "t", ">"]@(change_nots xs)
else (x::(change_nots xs))
(*
fun clstrs_to_string [] str = str
| clstrs_to_string (x::[]) str = str^x
| clstrs_to_string (x::xs) str = clstrs_to_string xs (str^(x^"; "))
*)
fun clstrs_to_string [] str = implode (change_nots (explode str))
| clstrs_to_string (x::[]) str = implode (change_nots (explode (str^x)))
| clstrs_to_string (x::xs) str = implode (change_nots (explode (clstrs_to_string xs (str^(x^"; ")))))
fun thmvars_to_quantstring [] str = str
| thmvars_to_quantstring (x::[]) str =str^x^". "
| thmvars_to_quantstring (x::xs) str = thmvars_to_quantstring xs (str^(x^" "))
fun clause_strs_to_isar clstrs [] = "\"\\<lbrakk>"^(clstrs_to_string clstrs "")^"\\<rbrakk> "^" \\<Longrightarrow> False\""
| clause_strs_to_isar clstrs thmvars = "\"\\<And>"^(thmvars_to_quantstring thmvars "")^"\\<lbrakk>"^(clstrs_to_string clstrs "")^"\\<rbrakk> "^"\\<Longrightarrow> False\""
fun frees_to_string [] str = implode (change_nots (explode str))
| frees_to_string (x::[]) str = implode (change_nots (explode (str^x)))
| frees_to_string (x::xs) str = implode (change_nots (explode (frees_to_string xs (str^(x^" ")))))
fun frees_to_isar_str [] = ""
| frees_to_isar_str clstrs = (frees_to_string clstrs "")
(***********************************************************************)
(* functions for producing assumptions for the Isabelle ordered axioms *)
(***********************************************************************)
(*val str = "[P%x%xa%xb%]1OrigAxiom()[P x%~ P U%][U%]3OrigAxiom()[P U%~ P x%][U%]5OrigAxiom()[~ P xa%~ P U%][U%]7OrigAxiom()[P U%P xb%][U%]1Axiom()[P x%~ P U%][U%]3Axiom()[P U%~ P x%][U%]5Axiom()[~ P U%~ P xa%][U%]7Axiom()[P U%P xb%][U%]9Factor(5,0,1)[~ P xa%][]10Binary((9,0),(3,0))[~ P x%][]11Binary((10,0),(1,0))[~ P U%][U%]12Factor(7,0,1)[P xb%][]14Binary((11,0),(12,0))[][]";
num, rule, clausestrs, vars*)
(* assume the extra clauses - not used in Spass proof *)
fun is_extraaxiom_step ( num:int,(ExtraAxiom, str, tstr)) = true
| is_extraaxiom_step (num, _) = false
fun get_extraaxioms xs = List.filter (is_extraaxiom_step) ( xs)
fun assume_isar_extraaxiom [] str = str
| assume_isar_extraaxiom ((numb,(step, clstr, thmvars))::xs) str = assume_isar_extraaxiom xs (str^"and cl"^(string_of_int numb)^"': "^(clause_strs_to_isar clstr thmvars)^"\n " )
fun assume_isar_extraaxioms [] = ""
|assume_isar_extraaxioms ((numb,(step, clstrs, thmstrs))::xs) = let val str = "assume cl"^(string_of_int numb)^"': "^(clause_strs_to_isar clstrs thmstrs)^"\n"
in
assume_isar_extraaxiom xs str
end
(* assume the Isabelle ordered clauses *)
fun is_origaxiom_step ( num:int,(OrigAxiom, str, tstr)) = true
| is_origaxiom_step (num, _) = false
fun get_origaxioms xs = List.filter (is_origaxiom_step) ( xs)
fun assume_isar_origaxiom [] str = str
| assume_isar_origaxiom ((numb,(step, clstr, thmvars))::xs) str = assume_isar_origaxiom xs (str^"and cl"^(string_of_int numb)^"': "^(clause_strs_to_isar clstr thmvars)^"\n " )
fun assume_isar_origaxioms ((numb,(step, clstrs, thmstrs))::xs) = let val str = "assume cl"^(string_of_int numb)^"': "^(clause_strs_to_isar clstrs thmstrs)^"\n"
in
assume_isar_origaxiom xs str
end
fun is_axiom_step ( num:int,(Axiom, str, tstr)) = true
| is_axiom_step (num, _) = false
fun get_axioms xs = List.filter (is_axiom_step) ( xs)
fun have_isar_axiomline (numb,(step, clstrs, thmstrs))="have cl"^(string_of_int numb)^": "^(clause_strs_to_isar clstrs thmstrs)^"\n"
fun by_isar_axiomline (numb,(step, clstrs, thmstrs))="by (rule cl"^ (string_of_int numb)^"') \n"
fun isar_axiomline (numb, (step, clstrs, thmstrs)) = (have_isar_axiomline (numb,(step,clstrs, thmstrs )))^( by_isar_axiomline(numb,(step,clstrs, thmstrs )) )
fun isar_axiomlines [] str = str
| isar_axiomlines (x::xs) str = isar_axiomlines xs (str^(isar_axiomline x))
fun have_isar_line (numb,(step, clstrs, thmstrs))="have cl"^(string_of_int numb)^": "^(clause_strs_to_isar clstrs thmstrs)^"\n"
fun by_isar_line ((Binary ((a,b), (c,d))))="by(rule cl"^
(string_of_int a)^" [BINARY "^(string_of_int b)^" "^"cl"^
(string_of_int c)^" "^(string_of_int d)^"])"^"\n"
| by_isar_line ( (Para ((a,b), (c,d)))) ="by (rule cl"^
(string_of_int a)^" [PARAMOD "^(string_of_int b)^" "^"cl"^
(string_of_int c)^" "^(string_of_int d)^"])"^"\n"
| by_isar_line ((Factor ((a,b,c)))) = "by (rule cl"^(string_of_int a)^" [FACTOR "^(string_of_int b)^" "^
(string_of_int c)^" "^"])"^"\n"
| by_isar_line ( (Rewrite ((a,b),(c,d)))) = "by (rule cl"^(string_of_int a)^" [DEMOD "^(string_of_int b)^" "^
(string_of_int c)^" "^(string_of_int d)^" "^"])"^"\n"
| by_isar_line ( (Obvious ((a,b)))) = "by (rule cl"^(string_of_int a)^" [OBVIOUS "^(string_of_int b)^" ])"^"\n"
fun isar_line (numb, (step, clstrs, thmstrs)) = (have_isar_line (numb,(step,clstrs, thmstrs )))^( by_isar_line step)
fun isar_lines [] str = str
| isar_lines (x::xs) str = isar_lines xs (str^(isar_line x))
fun last_isar_line (numb,( step, clstrs,thmstrs)) = "show \"False\"\n"^(by_isar_line step)
fun to_isar_proof (frees, xs, goalstring) = let val extraaxioms = get_extraaxioms xs
val extraax_num = length extraaxioms
val origaxioms_and_steps = drop (extraax_num) xs
val origaxioms = get_origaxioms origaxioms_and_steps
val origax_num = length origaxioms
val axioms_and_steps = drop (origax_num + extraax_num) xs
val axioms = get_axioms axioms_and_steps
val steps = drop origax_num axioms_and_steps
val firststeps = butlast steps
val laststep = last steps
val goalstring = implode(butlast(explode goalstring))
val isar_proof =
("show \""^goalstring^"\"\n")^
("proof (rule ccontr,skolemize, make_clauses) \n")^
("fix "^(frees_to_isar_str frees)^"\n")^
(assume_isar_extraaxioms extraaxioms)^
(assume_isar_origaxioms origaxioms)^
(isar_axiomlines axioms "")^
(isar_lines firststeps "")^
(last_isar_line laststep)^
("qed")
val outfile = TextIO.openOut("isar_proof_file");
val _ = TextIO.output (outfile, isar_proof)
val _ = TextIO.closeOut outfile
in
isar_proof
end
(* get fix vars from axioms - all Frees *)
(* check each clause for meta-vars and /\ over them at each step*)
(*******************************************************)
(* This assumes the thm list "numcls" is still there *)
(* In reality, should probably label it with an *)
(* ID number identifying the subgoal. This could *)
(* be passed over to the watcher, e.g. numcls25 *)
(*******************************************************)
(* val str = "[S%x%P%R%Q%]1ExtraAxiom()[~ Q U%~ R U%][U%]2ExtraAxiom()[~ Q U%~ P U%][U%]3ExtraAxiom()[Q U%R U%][U%]1OrigAxiom()[S x%][]2OrigAxiom()[P U%R U%][U%]6OrigAxiom()[~ S U%~ P U%][U%]7OrigAxiom()[~ S U%~ R U%][U%]1Axiom()[S x%][]2Axiom()[R U%P U%][U%]6Axiom()[~ P U%~ S U%][U%]7Axiom()[~ R U%~ S U%][U%]8Binary((6,1),(1,0))[~ P x%][]9Binary((7,1),(1,0))[~ R x%][]19Binary((9,0),(2,0))[P x%][]25Binary((8,0),(19,0))[][]";
val str = "[P%x%xa%xb%]1OrigAxiom()[P x%~ P U%][U%]3OrigAxiom()[P U%~ P x%][U%]5OrigAxiom()[~ P xa%~ P U%][U%]7OrigAxiom()[P U%P xb%][U%]1Axiom()[P x%~ P U%][U%]3Axiom()[P U%~ P x%][U%]5Axiom()[~ P U%~ P xa%][U%]7Axiom()[P U%P xb%][U%]9Factor(5,0,1)[~ P xa%][]10Binary((9,0),(3,0))[~ P x%][]11Binary((10,0),(1,0))[~ P U%][U%]12Factor(7,0,1)[P xb%][]14Binary((11,0),(12,0))[][]";
val reconstr = "[P%Q%x%xa%]1OrigAxiom()[~ P U%][U%]3OrigAxiom()[Q U%][U%]5OrigAxiom()[P (x U)%~ Q (xa U)%][U%]9Binary((7,0),(3,0))[][]7Binary((1,0),(5,0))[~ Q (xa U)%][U%]5Axiom()[P (x U)%~ Q (xa U)%][U%]3Axiom()[Q U%][U%]1Axiom()[~ P U%][U%](ALL xb::'a::type. (~ (P::'a::type => bool) ((x::'a::type => 'a::type) xb) | (Q::'a::type => bool) ((xa::'a::type => 'a::type) xb)) & P xb & ~ Q xb)";
val reconstr = "[P%x%xa%xb%]1OrigAxiom()[P x%~ P U%][U%]3OrigAxiom()[P U%~ P x%][U%]5OrigAxiom()[~ P xa%~ P U%][U%]7OrigAxiom()[P U%P xb%][U%]1Axiom()[P x%~ P U%][U%]3Axiom()[P U%~ P x%][U%]5Axiom()[~ P U%~ P xa%][U%]7Axiom()[P U%P xb%][U%]9Factor(5,0,1)[~ P xa%][]10Binary((9,0),(3,0))[~ P x%][]11Binary((10,0),(1,0))[~ P U%][U%]12Factor(7,0,1)[P xb%][]14Binary((11,0),(12,0))[][]";
val thmstring = " (ALL xa::'a::type. (~ (P::'a::type => bool) (x::'a::type) | P xa) & (~ P xa | P x)) & (((P::'a::type => bool) (xa::'a::type) | (ALL x::'a::type. P x)) &((ALL x::'a::type. ~ P x) | ~ P (xb::'a::type)))";
*)
fun apply_res_thm str goalstring = let val tokens = fst (lex str);
val (frees,recon_steps) = parse_step tokens
val isar_str = to_isar_proof (frees, recon_steps, goalstring)
val foo = TextIO.openOut "foobar";
in
TextIO.output(foo,(isar_str));TextIO.closeOut foo;Pretty.writeln(Pretty.str isar_str); ()
end