(* Title: HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML
Author: Lawrence C Paulson and Claire Quigley, Cambridge University Computer Laboratory
Transfer of proofs from external provers.
*)
signature SLEDGEHAMMER_PROOF_RECONSTRUCT =
sig
type minimize_command = string list -> string
val chained_hint: string
val invert_const: string -> string
val invert_type_const: string -> string
val num_typargs: theory -> string -> int
val make_tvar: string -> typ
val strip_prefix: string -> string -> string option
val metis_line: int -> int -> string list -> string
val metis_proof_text:
minimize_command * string * string vector * thm * int
-> string * string list
val isar_proof_text:
bool -> int -> bool -> Proof.context
-> minimize_command * string * string vector * thm * int
-> string * string list
val proof_text:
bool -> bool -> int -> bool -> Proof.context
-> minimize_command * string * string vector * thm * int
-> string * string list
end;
structure Sledgehammer_Proof_Reconstruct : SLEDGEHAMMER_PROOF_RECONSTRUCT =
struct
open Sledgehammer_FOL_Clause
open Sledgehammer_Fact_Preprocessor
type minimize_command = string list -> string
val trace_proof_path = Path.basic "atp_trace";
fun trace_proof_msg f =
if !trace then File.append (File.tmp_path trace_proof_path) (f ()) else ();
fun string_of_thm ctxt = PrintMode.setmp [] (Display.string_of_thm ctxt);
fun is_ident_char c = Char.isAlphaNum c orelse c = #"_"
fun is_axiom thm_names line_no = line_no <= Vector.length thm_names
(**** PARSING OF TSTP FORMAT ****)
(* Syntax trees, either term list or formulae *)
datatype stree = Int of int | Br of string * stree list;
fun atom x = Br(x,[]);
fun scons (x,y) = Br("cons", [x,y]);
val listof = List.foldl scons (atom "nil");
(*Strings enclosed in single quotes, e.g. filenames*)
val quoted = $$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'" >> implode;
(*Intended for $true and $false*)
fun tf s = "c_" ^ str (Char.toUpper (String.sub(s,0))) ^ String.extract(s,1,NONE);
val truefalse = $$ "$" |-- Symbol.scan_id >> (atom o tf);
(*Integer constants, typically proof line numbers*)
fun is_digit s = Char.isDigit (String.sub(s,0));
val integer = Scan.many1 is_digit >> (the o Int.fromString o implode);
(* needed for SPASS's output format *)
fun fix_symbol "equal" = "c_equal"
| fix_symbol s = s
(*Generalized FO terms, which include filenames, numbers, etc.*)
fun term x = (quoted >> atom || integer >> Int || truefalse
|| (Symbol.scan_id >> fix_symbol)
-- Scan.optional ($$ "(" |-- terms --| $$ ")") [] >> Br
|| $$ "(" |-- term --| $$ ")"
|| $$ "[" |-- Scan.optional terms [] --| $$ "]" >> listof) x
and terms x = (term ::: Scan.repeat ($$ "," |-- term)) x
fun negate t = Br ("c_Not", [t])
fun equate t1 t2 = Br ("c_equal", [t1, t2]);
(*Apply equal or not-equal to a term*)
fun syn_equal (t, NONE) = t
| syn_equal (t1, SOME (NONE, t2)) = equate t1 t2
| syn_equal (t1, SOME (SOME _, t2)) = negate (equate t1 t2)
(*Literals can involve negation, = and !=.*)
fun literal x =
($$ "~" |-- literal >> negate
|| (term -- Scan.option (Scan.option ($$ "!") --| $$ "=" -- term)
>> syn_equal)) x
val literals = literal ::: Scan.repeat ($$ "|" |-- literal);
(*Clause: a list of literals separated by the disjunction sign*)
val clause = $$ "(" |-- literals --| $$ ")" || Scan.single literal;
fun ints_of_stree (Int n) = cons n
| ints_of_stree (Br (_, ts)) = fold ints_of_stree ts
val tstp_annotations =
Scan.optional ($$ "," |-- term --| Scan.option ($$ "," |-- terms)
>> (fn source => ints_of_stree source [])) []
fun retuple_tstp_line ((name, ts), deps) = (name, ts, deps)
(* <cnf_annotated> ::= cnf(<name>, <formula_role>, <cnf_formula> <annotations>).
The <name> could be an identifier, but we assume integers. *)
val parse_tstp_line =
(Scan.this_string "cnf" -- $$ "(") |-- integer --| $$ "," --| Symbol.scan_id
--| $$ "," -- clause -- tstp_annotations --| $$ ")" --| $$ "."
>> retuple_tstp_line
(**** PARSING OF SPASS OUTPUT ****)
val dot_name = integer --| $$ "." --| integer
val spass_annotations =
Scan.optional ($$ ":" |-- Scan.repeat (dot_name --| Scan.option ($$ ","))) []
val starred_literal = literal --| Scan.repeat ($$ "*" || $$ " ")
val horn_clause =
Scan.repeat starred_literal --| $$ "-" --| $$ ">"
-- Scan.repeat starred_literal
>> (fn ([], []) => [atom (tf "false")]
| (clauses1, clauses2) => map negate clauses1 @ clauses2)
fun retuple_spass_proof_line ((name, deps), ts) = (name, ts, deps)
(* Syntax: <name>[0:<inference><annotations>] || -> <cnf_formula> **. *)
val parse_spass_proof_line =
integer --| $$ "[" --| $$ "0" --| $$ ":" --| Symbol.scan_id
-- spass_annotations --| $$ "]" --| $$ "|" --| $$ "|" -- horn_clause
--| $$ "."
>> retuple_spass_proof_line
val parse_proof_line = fst o (parse_tstp_line || parse_spass_proof_line)
(**** INTERPRETATION OF TSTP SYNTAX TREES ****)
exception STREE of stree;
(*If string s has the prefix s1, return the result of deleting it.*)
fun strip_prefix s1 s =
if String.isPrefix s1 s
then SOME (undo_ascii_of (String.extract (s, size s1, NONE)))
else NONE;
(*Invert the table of translations between Isabelle and ATPs*)
val type_const_trans_table_inv =
Symtab.make (map swap (Symtab.dest type_const_trans_table));
fun invert_type_const c =
case Symtab.lookup type_const_trans_table_inv c of
SOME c' => c'
| NONE => c;
fun make_tvar s = TVar (("'" ^ s, 0), HOLogic.typeS);
fun make_tparam s = TypeInfer.param 0 (s, HOLogic.typeS)
fun make_var (b,T) = Var((b,0),T);
(*Type variables are given the basic sort, HOL.type. Some will later be constrained
by information from type literals, or by type inference.*)
fun type_of_stree t =
case t of
Int _ => raise STREE t
| Br (a,ts) =>
let val Ts = map type_of_stree ts
in
case strip_prefix tconst_prefix a of
SOME b => Type(invert_type_const b, Ts)
| NONE =>
if not (null ts) then raise STREE t (*only tconsts have type arguments*)
else
case strip_prefix tfree_prefix a of
SOME b => TFree("'" ^ b, HOLogic.typeS)
| NONE =>
case strip_prefix tvar_prefix a of
SOME b => make_tvar b
| NONE => make_tparam a (* Variable from the ATP, say "X1" *)
end;
(*Invert the table of translations between Isabelle and ATPs*)
val const_trans_table_inv =
Symtab.update ("fequal", "op =")
(Symtab.make (map swap (Symtab.dest const_trans_table)));
fun invert_const c =
case Symtab.lookup const_trans_table_inv c of
SOME c' => c'
| NONE => c;
(*The number of type arguments of a constant, zero if it's monomorphic*)
fun num_typargs thy s = length (Sign.const_typargs thy (s, Sign.the_const_type thy s));
(*Generates a constant, given its type arguments*)
fun const_of thy (a,Ts) = Const(a, Sign.const_instance thy (a,Ts));
(*First-order translation. No types are known for variables. HOLogic.typeT should allow
them to be inferred.*)
fun term_of_stree args thy t =
case t of
Int _ => raise STREE t
| Br ("hBOOL",[t]) => term_of_stree [] thy t (*ignore hBOOL*)
| Br ("hAPP",[t,u]) => term_of_stree (u::args) thy t
| Br (a,ts) =>
case strip_prefix const_prefix a of
SOME "equal" =>
list_comb(Const (@{const_name "op ="}, HOLogic.typeT), List.map (term_of_stree [] thy) ts)
| SOME b =>
let val c = invert_const b
val nterms = length ts - num_typargs thy c
val us = List.map (term_of_stree [] thy) (List.take(ts,nterms) @ args)
(*Extra args from hAPP come AFTER any arguments given directly to the
constant.*)
val Ts = List.map type_of_stree (List.drop(ts,nterms))
in list_comb(const_of thy (c, Ts), us) end
| NONE => (*a variable, not a constant*)
let val T = HOLogic.typeT
val opr = (*a Free variable is typically a Skolem function*)
case strip_prefix fixed_var_prefix a of
SOME b => Free(b,T)
| NONE =>
case strip_prefix schematic_var_prefix a of
SOME b => make_var (b,T)
| NONE => make_var (a,T) (* Variable from the ATP, say "X1" *)
in list_comb (opr, List.map (term_of_stree [] thy) (ts@args)) end;
(*Type class literal applied to a type. Returns triple of polarity, class, type.*)
fun constraint_of_stree pol (Br("c_Not",[t])) = constraint_of_stree (not pol) t
| constraint_of_stree pol t = case t of
Int _ => raise STREE t
| Br (a,ts) =>
(case (strip_prefix class_prefix a, map type_of_stree ts) of
(SOME b, [T]) => (pol, b, T)
| _ => raise STREE t);
(** Accumulate type constraints in a clause: negative type literals **)
fun addix (key,z) = Vartab.map_default (key,[]) (cons z);
fun add_constraint ((false, cl, TFree(a,_)), vt) = addix ((a,~1),cl) vt
| add_constraint ((false, cl, TVar(ix,_)), vt) = addix (ix,cl) vt
| add_constraint (_, vt) = vt;
(*False literals (which E includes in its proofs) are deleted*)
val nofalses = filter (not o equal HOLogic.false_const);
(*Final treatment of the list of "real" literals from a clause.*)
fun finish [] = HOLogic.true_const (*No "real" literals means only type information*)
| finish lits =
case nofalses lits of
[] => HOLogic.false_const (*The empty clause, since we started with real literals*)
| xs => foldr1 HOLogic.mk_disj (rev xs);
(*Accumulate sort constraints in vt, with "real" literals in lits.*)
fun lits_of_strees _ (vt, lits) [] = (vt, finish lits)
| lits_of_strees ctxt (vt, lits) (t::ts) =
lits_of_strees ctxt (add_constraint (constraint_of_stree true t, vt), lits) ts
handle STREE _ =>
lits_of_strees ctxt (vt, term_of_stree [] (ProofContext.theory_of ctxt) t :: lits) ts;
(*Update TVars/TFrees with detected sort constraints.*)
fun fix_sorts vt =
let fun tysubst (Type (a, Ts)) = Type (a, map tysubst Ts)
| tysubst (TVar (xi, s)) = TVar (xi, the_default s (Vartab.lookup vt xi))
| tysubst (TFree (x, s)) = TFree (x, the_default s (Vartab.lookup vt (x, ~1)))
fun tmsubst (Const (a, T)) = Const (a, tysubst T)
| tmsubst (Free (a, T)) = Free (a, tysubst T)
| tmsubst (Var (xi, T)) = Var (xi, tysubst T)
| tmsubst (t as Bound _) = t
| tmsubst (Abs (a, T, t)) = Abs (a, tysubst T, tmsubst t)
| tmsubst (t $ u) = tmsubst t $ tmsubst u;
in not (Vartab.is_empty vt) ? tmsubst end;
(*Interpret a list of syntax trees as a clause, given by "real" literals and sort constraints.
vt0 holds the initial sort constraints, from the conjecture clauses.*)
fun clause_of_strees ctxt vt0 ts =
let val (vt, dt) = lits_of_strees ctxt (vt0,[]) ts in
singleton (Syntax.check_terms ctxt) (TypeInfer.constrain HOLogic.boolT (fix_sorts vt dt))
end
fun gen_all_vars t = fold_rev Logic.all (OldTerm.term_vars t) t;
fun decode_proof_step vt0 (name, ts, deps) ctxt =
let val cl = clause_of_strees ctxt vt0 ts in
((name, cl, deps), fold Variable.declare_term (OldTerm.term_frees cl) ctxt)
end
(** Global sort constraints on TFrees (from tfree_tcs) are positive unit clauses. **)
fun add_tfree_constraint ((true, cl, TFree(a,_)), vt) = addix ((a,~1),cl) vt
| add_tfree_constraint (_, vt) = vt;
fun tfree_constraints_of_clauses vt [] = vt
| tfree_constraints_of_clauses vt ([lit]::tss) =
(tfree_constraints_of_clauses (add_tfree_constraint (constraint_of_stree true lit, vt)) tss
handle STREE _ => (*not a positive type constraint: ignore*)
tfree_constraints_of_clauses vt tss)
| tfree_constraints_of_clauses vt (_::tss) = tfree_constraints_of_clauses vt tss;
(**** Translation of TSTP files to Isar Proofs ****)
fun decode_proof_steps ctxt tuples =
let val vt0 = tfree_constraints_of_clauses Vartab.empty (map #2 tuples) in
#1 (fold_map (decode_proof_step vt0) tuples ctxt)
end
(** Finding a matching assumption. The literals may be permuted, and variable names
may disagree. We must try all combinations of literals (quadratic!) and
match the variable names consistently. **)
fun strip_alls_aux n (Const(@{const_name all}, _)$Abs(a,T,t)) =
strip_alls_aux (n+1) (subst_bound (Var ((a,n), T), t))
| strip_alls_aux _ t = t;
val strip_alls = strip_alls_aux 0;
exception MATCH_LITERAL of unit
(* Remark 1: Ignore types. They are not to be trusted.
Remark 2: Ignore order of arguments for equality. SPASS sometimes swaps
them for no apparent reason. *)
fun match_literal (Const (@{const_name "op ="}, _) $ t1 $ u1)
(Const (@{const_name "op ="}, _) $ t2 $ u2) env =
(env |> match_literal t1 t2 |> match_literal u1 u2
handle MATCH_LITERAL () =>
env |> match_literal t1 u2 |> match_literal u1 t2)
| match_literal (t1 $ u1) (t2 $ u2) env =
env |> match_literal t1 t2 |> match_literal u1 u2
| match_literal (Abs (_,_,t1)) (Abs (_,_,t2)) env =
match_literal t1 t2 env
| match_literal (Bound i1) (Bound i2) env =
if i1=i2 then env else raise MATCH_LITERAL ()
| match_literal (Const(a1,_)) (Const(a2,_)) env =
if a1=a2 then env else raise MATCH_LITERAL ()
| match_literal (Free(a1,_)) (Free(a2,_)) env =
if a1=a2 then env else raise MATCH_LITERAL ()
| match_literal (Var(ix1,_)) (Var(ix2,_)) env = insert (op =) (ix1,ix2) env
| match_literal _ _ _ = raise MATCH_LITERAL ()
(* Checking that all variable associations are unique. The list "env" contains
no repetitions, but does it contain say (x, y) and (y, y)? *)
fun good env =
let val (xs,ys) = ListPair.unzip env
in not (has_duplicates (op=) xs orelse has_duplicates (op=) ys) end;
(*Match one list of literals against another, ignoring types and the order of
literals. Sorting is unreliable because we don't have types or variable names.*)
fun matches_aux _ [] [] = true
| matches_aux env (lit::lits) ts =
let fun match1 us [] = false
| match1 us (t::ts) =
let val env' = match_literal lit t env
in (good env' andalso matches_aux env' lits (us@ts)) orelse
match1 (t::us) ts
end
handle MATCH_LITERAL () => match1 (t::us) ts
in match1 [] ts end;
(*Is this length test useful?*)
fun matches (lits1,lits2) =
length lits1 = length lits2 andalso
matches_aux [] (map Envir.eta_contract lits1) (map Envir.eta_contract lits2);
fun permuted_clause t =
let val lits = HOLogic.disjuncts t
fun perm [] = NONE
| perm (ctm::ctms) =
if matches (lits, HOLogic.disjuncts (HOLogic.dest_Trueprop (strip_alls ctm)))
then SOME ctm else perm ctms
in perm end;
(*ctms is a list of conjecture clauses as yielded by Isabelle. Those returned by the
ATP may have their literals reordered.*)
fun isar_proof_body ctxt sorts ctms =
let
val _ = trace_proof_msg (K "\n\nisar_proof_body: start\n")
val string_of_term =
PrintMode.setmp (filter (curry (op =) Symbol.xsymbolsN)
(print_mode_value ()))
(Syntax.string_of_term ctxt)
fun have_or_show "show" _ = " show \""
| have_or_show have lname = " " ^ have ^ " " ^ lname ^ ": \""
fun do_line _ (lname, t, []) =
(* No depedencies: it's a conjecture clause, with no proof. *)
(case permuted_clause t ctms of
SOME u => " assume " ^ lname ^ ": \"" ^ string_of_term u ^ "\"\n"
| NONE => raise TERM ("Sledgehammer_Proof_Reconstruct.isar_proof_body",
[t]))
| do_line have (lname, t, deps) =
have_or_show have lname ^
string_of_term (gen_all_vars (HOLogic.mk_Trueprop t)) ^
"\"\n by (metis " ^ space_implode " " deps ^ ")\n"
fun do_lines [(lname, t, deps)] = [do_line "show" (lname, t, deps)]
| do_lines ((lname, t, deps) :: lines) =
do_line "have" (lname, t, deps) :: do_lines lines
in setmp_CRITICAL show_sorts sorts do_lines end;
fun unequal t (_, t', _) = not (t aconv t');
(*No "real" literals means only type information*)
fun eq_types t = t aconv HOLogic.true_const;
fun replace_dep (old:int, new) dep = if dep=old then new else [dep];
fun replace_deps (old:int, new) (lno, t, deps) =
(lno, t, List.foldl (uncurry (union (op =))) [] (map (replace_dep (old, new)) deps));
(*Discard axioms; consolidate adjacent lines that prove the same clause, since they differ
only in type information.*)
fun add_proof_line thm_names (lno, t, []) lines =
(* No dependencies: axiom or conjecture clause *)
if is_axiom thm_names lno then
(* Axioms are not proof lines *)
if eq_types t then
(* Must be clsrel/clsarity: type information, so delete refs to it *)
map (replace_deps (lno, [])) lines
else
(case take_prefix (unequal t) lines of
(_,[]) => lines (*no repetition of proof line*)
| (pre, (lno', _, _) :: post) => (*repetition: replace later line by earlier one*)
pre @ map (replace_deps (lno', [lno])) post)
else
(lno, t, []) :: lines
| add_proof_line _ (lno, t, deps) lines =
if eq_types t then (lno, t, deps) :: lines
(*Type information will be deleted later; skip repetition test.*)
else (*FIXME: Doesn't this code risk conflating proofs involving different types??*)
case take_prefix (unequal t) lines of
(_,[]) => (lno, t, deps) :: lines (*no repetition of proof line*)
| (pre, (lno', t', _) :: post) =>
(lno, t', deps) :: (*repetition: replace later line by earlier one*)
(pre @ map (replace_deps (lno', [lno])) post);
(*Recursively delete empty lines (type information) from the proof.*)
fun add_nonnull_prfline ((lno, t, []), lines) = (*no dependencies, so a conjecture clause*)
if eq_types t (*must be type information, tfree_tcs, clsrel, clsarity: delete refs to it*)
then delete_dep lno lines
else (lno, t, []) :: lines
| add_nonnull_prfline ((lno, t, deps), lines) = (lno, t, deps) :: lines
and delete_dep lno lines = List.foldr add_nonnull_prfline [] (map (replace_deps (lno, [])) lines);
fun bad_free (Free (a,_)) = String.isPrefix skolem_prefix a
| bad_free _ = false;
(*TVars are forbidden in goals. Also, we don't want lines with <2 dependencies.
To further compress proofs, setting modulus:=n deletes every nth line, and nlines
counts the number of proof lines processed so far.
Deleted lines are replaced by their own dependencies. Note that the "add_nonnull_prfline"
phase may delete some dependencies, hence this phase comes later.*)
fun add_wanted_prfline ctxt _ ((lno, t, []), (nlines, lines)) =
(nlines, (lno, t, []) :: lines) (*conjecture clauses must be kept*)
| add_wanted_prfline ctxt modulus ((lno, t, deps), (nlines, lines)) =
if eq_types t orelse not (null (Term.add_tvars t [])) orelse
exists_subterm bad_free t orelse
(not (null lines) andalso (*final line can't be deleted for these reasons*)
(length deps < 2 orelse nlines mod modulus <> 0))
then (nlines+1, map (replace_deps (lno, deps)) lines) (*Delete line*)
else (nlines+1, (lno, t, deps) :: lines);
(*Replace numeric proof lines by strings, either from thm_names or sequential line numbers*)
fun stringify_deps thm_names deps_map [] = []
| stringify_deps thm_names deps_map ((lno, t, deps) :: lines) =
if is_axiom thm_names lno then
(Vector.sub(thm_names,lno-1), t, []) :: stringify_deps thm_names deps_map lines
else let val lname = Int.toString (length deps_map)
fun fix lno = if is_axiom thm_names lno
then SOME(Vector.sub(thm_names,lno-1))
else AList.lookup (op =) deps_map lno;
in (lname, t, map_filter fix (distinct (op=) deps)) ::
stringify_deps thm_names ((lno,lname)::deps_map) lines
end;
fun isar_proof_start i =
(if i = 1 then "" else "prefer " ^ string_of_int i ^ "\n") ^
"proof (neg_clausify)\n";
fun isar_fixes [] = ""
| isar_fixes ts = " fix " ^ space_implode " " ts ^ "\n";
fun isar_proof_end 1 = "qed"
| isar_proof_end _ = "next"
fun isar_proof_from_atp_proof cnfs modulus sorts ctxt goal i thm_names =
let
val _ = trace_proof_msg (K "\nisar_proof_from_atp_proof: start\n")
val tuples = map (parse_proof_line o explode) cnfs
val _ = trace_proof_msg (fn () =>
Int.toString (length tuples) ^ " tuples extracted\n")
val ctxt = ProofContext.set_mode ProofContext.mode_schematic ctxt
val raw_lines =
fold_rev (add_proof_line thm_names) (decode_proof_steps ctxt tuples) []
val _ = trace_proof_msg (fn () =>
Int.toString (length raw_lines) ^ " raw_lines extracted\n")
val nonnull_lines = List.foldr add_nonnull_prfline [] raw_lines
val _ = trace_proof_msg (fn () =>
Int.toString (length nonnull_lines) ^ " nonnull_lines extracted\n")
val (_, lines) = List.foldr (add_wanted_prfline ctxt modulus) (0,[]) nonnull_lines
val _ = trace_proof_msg (fn () =>
Int.toString (length lines) ^ " lines extracted\n")
val (ccls, fixes) = neg_conjecture_clauses ctxt goal i
val _ = trace_proof_msg (fn () =>
Int.toString (length ccls) ^ " conjecture clauses\n")
val ccls = map forall_intr_vars ccls
val _ = app (fn th => trace_proof_msg
(fn () => "\nccl: " ^ string_of_thm ctxt th)) ccls
val body = isar_proof_body ctxt sorts (map prop_of ccls)
(stringify_deps thm_names [] lines)
val n = Logic.count_prems (prop_of goal)
val _ = trace_proof_msg (K "\nisar_proof_from_atp_proof: finishing\n")
in
isar_proof_start i ^ isar_fixes (map #1 fixes) ^ implode body ^
isar_proof_end n ^ "\n"
end
handle STREE _ => raise Fail "Cannot parse ATP output";
(* === EXTRACTING LEMMAS === *)
(* A list consisting of the first number in each line is returned.
TPTP: Interesting lines have the form "cnf(108, axiom, ...)", where the
number (108) is extracted.
DFG: Lines have the form "108[0:Inp] ...", where the first number (108) is
extracted. *)
fun get_step_nums proof =
let
val toks = String.tokens (not o is_ident_char)
fun inputno ("cnf" :: ntok :: "axiom" :: _) = Int.fromString ntok
| inputno ("cnf" :: ntok :: "negated_conjecture" :: _) =
Int.fromString ntok
| inputno (ntok :: "0" :: "Inp" :: _) =
Int.fromString ntok (* SPASS's output format *)
| inputno _ = NONE
in map_filter (inputno o toks) (split_lines proof) end
(*Used to label theorems chained into the sledgehammer call*)
val chained_hint = "CHAINED";
val kill_chained = filter_out (curry (op =) chained_hint)
fun apply_command _ 1 = "by "
| apply_command 1 _ = "apply "
| apply_command i _ = "prefer " ^ string_of_int i ^ " apply "
fun metis_command i n [] =
apply_command i n ^ "metis"
| metis_command i n xs =
apply_command i n ^ "(metis " ^ space_implode " " xs ^ ")"
fun metis_line i n xs =
"Try this command: " ^
Markup.markup Markup.sendback (metis_command i n xs) ^ ".\n"
fun minimize_line _ [] = ""
| minimize_line minimize_command facts =
case minimize_command facts of
"" => ""
| command =>
"To minimize the number of lemmas, try this command: " ^
Markup.markup Markup.sendback command ^ ".\n"
fun metis_proof_text (minimize_command, proof, thm_names, goal, i) =
let
val lemmas =
proof |> get_step_nums
|> filter (is_axiom thm_names)
|> map (fn i => Vector.sub (thm_names, i - 1))
|> filter (fn x => x <> "??.unknown")
|> sort_distinct string_ord
val n = Logic.count_prems (prop_of goal)
val xs = kill_chained lemmas
in
(metis_line i n xs ^ minimize_line minimize_command xs, kill_chained lemmas)
end
val is_proof_line = String.isPrefix "cnf(" orf String.isSubstring "||"
fun do_space c = if Char.isSpace c then "" else str c
fun strip_spaces_in_list [] = ""
| strip_spaces_in_list [c1] = do_space c1
| strip_spaces_in_list [c1, c2] = do_space c1 ^ do_space c2
| strip_spaces_in_list (c1 :: c2 :: c3 :: cs) =
if Char.isSpace c1 then
strip_spaces_in_list (c2 :: c3 :: cs)
else if Char.isSpace c2 then
if Char.isSpace c3 then
strip_spaces_in_list (c1 :: c3 :: cs)
else
str c1 ^
(if is_ident_char c1 andalso is_ident_char c3 then " " else "") ^
strip_spaces_in_list (c3 :: cs)
else
str c1 ^ strip_spaces_in_list (c2 :: c3 :: cs)
val strip_spaces = strip_spaces_in_list o String.explode
fun isar_proof_text debug modulus sorts ctxt
(minimize_command, proof, thm_names, goal, i) =
let
val cnfs = proof |> split_lines |> map strip_spaces |> filter is_proof_line
val (one_line_proof, lemma_names) =
metis_proof_text (minimize_command, proof, thm_names, goal, i)
val tokens = String.tokens (fn c => c = #" ") one_line_proof
fun isar_proof_for () =
case isar_proof_from_atp_proof cnfs modulus sorts ctxt goal i thm_names of
"" => ""
| isar_proof =>
"\nStructured proof:\n" ^ Markup.markup Markup.sendback isar_proof
val isar_proof =
if member (op =) tokens chained_hint then
""
else if debug then
isar_proof_for ()
else
try isar_proof_for ()
|> the_default "Warning: The Isar proof construction failed.\n"
in (one_line_proof ^ isar_proof, lemma_names) end
fun proof_text isar_proof debug modulus sorts ctxt =
if isar_proof then isar_proof_text debug modulus sorts ctxt
else metis_proof_text
end;