--- a/src/HOL/Tools/ATP/atp_reconstruct.ML Mon Jan 23 17:40:31 2012 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,951 +0,0 @@
-(* Title: HOL/Tools/ATP/atp_reconstruct.ML
- Author: Lawrence C. Paulson, Cambridge University Computer Laboratory
- Author: Claire Quigley, Cambridge University Computer Laboratory
- Author: Jasmin Blanchette, TU Muenchen
-
-Proof reconstruction from ATP proofs.
-*)
-
-signature ATP_RECONSTRUCT =
-sig
- type ('a, 'b) ho_term = ('a, 'b) ATP_Problem.ho_term
- type ('a, 'b, 'c) formula = ('a, 'b, 'c) ATP_Problem.formula
- type 'a proof = 'a ATP_Proof.proof
- type locality = ATP_Translate.locality
-
- datatype reconstructor =
- Metis of string * string |
- SMT
-
- datatype play =
- Played of reconstructor * Time.time |
- Trust_Playable of reconstructor * Time.time option |
- Failed_to_Play of reconstructor
-
- type minimize_command = string list -> string
- type one_line_params =
- play * string * (string * locality) list * minimize_command * int * int
- type isar_params =
- bool * int * string Symtab.table * (string * locality) list vector
- * int Symtab.table * string proof * thm
-
- val metisN : string
- val smtN : string
- val full_typesN : string
- val partial_typesN : string
- val no_typesN : string
- val really_full_type_enc : string
- val full_type_enc : string
- val partial_type_enc : string
- val no_type_enc : string
- val full_type_encs : string list
- val partial_type_encs : string list
- val metis_default_lam_trans : string
- val metis_call : string -> string -> string
- val string_for_reconstructor : reconstructor -> string
- val used_facts_in_atp_proof :
- Proof.context -> (string * locality) list vector -> string proof
- -> (string * locality) list
- val lam_trans_from_atp_proof : string proof -> string -> string
- val is_typed_helper_used_in_atp_proof : string proof -> bool
- val used_facts_in_unsound_atp_proof :
- Proof.context -> (string * locality) list vector -> 'a proof
- -> string list option
- val unalias_type_enc : string -> string list
- val one_line_proof_text : one_line_params -> string
- val make_tvar : string -> typ
- val make_tfree : Proof.context -> string -> typ
- val term_from_atp :
- Proof.context -> bool -> int Symtab.table -> typ option
- -> (string, string) ho_term -> term
- val prop_from_atp :
- Proof.context -> bool -> int Symtab.table
- -> (string, string, (string, string) ho_term) formula -> term
- val isar_proof_text :
- Proof.context -> bool -> isar_params -> one_line_params -> string
- val proof_text :
- Proof.context -> bool -> isar_params -> one_line_params -> string
-end;
-
-structure ATP_Reconstruct : ATP_RECONSTRUCT =
-struct
-
-open ATP_Util
-open ATP_Problem
-open ATP_Proof
-open ATP_Translate
-
-structure String_Redirect = ATP_Redirect(
- type key = step_name
- val ord = fn ((s, _ : string list), (s', _)) => fast_string_ord (s, s')
- val string_of = fst)
-
-open String_Redirect
-
-datatype reconstructor =
- Metis of string * string |
- SMT
-
-datatype play =
- Played of reconstructor * Time.time |
- Trust_Playable of reconstructor * Time.time option |
- Failed_to_Play of reconstructor
-
-type minimize_command = string list -> string
-type one_line_params =
- play * string * (string * locality) list * minimize_command * int * int
-type isar_params =
- bool * int * string Symtab.table * (string * locality) list vector
- * int Symtab.table * string proof * thm
-
-val metisN = "metis"
-val smtN = "smt"
-
-val full_typesN = "full_types"
-val partial_typesN = "partial_types"
-val no_typesN = "no_types"
-
-val really_full_type_enc = "mono_tags"
-val full_type_enc = "poly_guards_query"
-val partial_type_enc = "poly_args"
-val no_type_enc = "erased"
-
-val full_type_encs = [full_type_enc, really_full_type_enc]
-val partial_type_encs = partial_type_enc :: full_type_encs
-
-val type_enc_aliases =
- [(full_typesN, full_type_encs),
- (partial_typesN, partial_type_encs),
- (no_typesN, [no_type_enc])]
-
-fun unalias_type_enc s =
- AList.lookup (op =) type_enc_aliases s |> the_default [s]
-
-val metis_default_lam_trans = combinatorsN
-
-fun metis_call type_enc lam_trans =
- let
- val type_enc =
- case AList.find (fn (enc, encs) => enc = hd encs) type_enc_aliases
- type_enc of
- [alias] => alias
- | _ => type_enc
- val opts = [] |> type_enc <> partial_typesN ? cons type_enc
- |> lam_trans <> metis_default_lam_trans ? cons lam_trans
- in metisN ^ (if null opts then "" else " (" ^ commas opts ^ ")") end
-
-fun string_for_reconstructor (Metis (type_enc, lam_trans)) =
- metis_call type_enc lam_trans
- | string_for_reconstructor SMT = smtN
-
-fun find_first_in_list_vector vec key =
- Vector.foldl (fn (ps, NONE) => AList.lookup (op =) ps key
- | (_, value) => value) NONE vec
-
-val unprefix_fact_number = space_implode "_" o tl o space_explode "_"
-
-fun resolve_one_named_fact fact_names s =
- case try (unprefix fact_prefix) s of
- SOME s' =>
- let val s' = s' |> unprefix_fact_number |> unascii_of in
- s' |> find_first_in_list_vector fact_names |> Option.map (pair s')
- end
- | NONE => NONE
-fun resolve_fact fact_names = map_filter (resolve_one_named_fact fact_names)
-fun is_fact fact_names = not o null o resolve_fact fact_names
-
-fun resolve_one_named_conjecture s =
- case try (unprefix conjecture_prefix) s of
- SOME s' => Int.fromString s'
- | NONE => NONE
-
-val resolve_conjecture = map_filter resolve_one_named_conjecture
-val is_conjecture = not o null o resolve_conjecture
-
-fun is_axiom_used_in_proof pred =
- exists (fn Inference ((_, ss), _, _, []) => exists pred ss | _ => false)
-
-val is_combinator_def = String.isPrefix (helper_prefix ^ combinator_prefix)
-
-val ascii_of_lam_fact_prefix = ascii_of lam_fact_prefix
-
-(* overapproximation (good enough) *)
-fun is_lam_lifted s =
- String.isPrefix fact_prefix s andalso
- String.isSubstring ascii_of_lam_fact_prefix s
-
-fun lam_trans_from_atp_proof atp_proof default =
- if is_axiom_used_in_proof is_combinator_def atp_proof then combinatorsN
- else if is_axiom_used_in_proof is_lam_lifted atp_proof then lam_liftingN
- else default
-
-val is_typed_helper_name =
- String.isPrefix helper_prefix andf String.isSuffix typed_helper_suffix
-fun is_typed_helper_used_in_atp_proof atp_proof =
- is_axiom_used_in_proof is_typed_helper_name atp_proof
-
-val leo2_ext = "extcnf_equal_neg"
-val isa_ext = Thm.get_name_hint @{thm ext}
-val isa_short_ext = Long_Name.base_name isa_ext
-
-fun ext_name ctxt =
- if Thm.eq_thm_prop (@{thm ext},
- singleton (Attrib.eval_thms ctxt) (Facts.named isa_short_ext, [])) then
- isa_short_ext
- else
- isa_ext
-
-fun add_fact _ fact_names (Inference ((_, ss), _, _, [])) =
- union (op =) (resolve_fact fact_names ss)
- | add_fact ctxt _ (Inference (_, _, rule, _)) =
- if rule = leo2_ext then insert (op =) (ext_name ctxt, General) else I
- | add_fact _ _ _ = I
-
-fun used_facts_in_atp_proof ctxt fact_names atp_proof =
- if null atp_proof then Vector.foldl (uncurry (union (op =))) [] fact_names
- else fold (add_fact ctxt fact_names) atp_proof []
-
-(* (quasi-)underapproximation of the truth *)
-fun is_locality_global Local = false
- | is_locality_global Assum = false
- | is_locality_global Chained = false
- | is_locality_global _ = true
-
-fun used_facts_in_unsound_atp_proof _ _ [] = NONE
- | used_facts_in_unsound_atp_proof ctxt fact_names atp_proof =
- let
- val used_facts = used_facts_in_atp_proof ctxt fact_names atp_proof
- in
- if forall (is_locality_global o snd) used_facts andalso
- not (is_axiom_used_in_proof (is_conjecture o single) atp_proof) then
- SOME (map fst used_facts)
- else
- NONE
- end
-
-
-(** Soft-core proof reconstruction: one-liners **)
-
-fun string_for_label (s, num) = s ^ string_of_int num
-
-fun show_time NONE = ""
- | show_time (SOME ext_time) = " (" ^ string_from_ext_time ext_time ^ ")"
-
-fun apply_on_subgoal _ 1 = "by "
- | apply_on_subgoal 1 _ = "apply "
- | apply_on_subgoal i n =
- "prefer " ^ string_of_int i ^ " " ^ apply_on_subgoal 1 n
-fun command_call name [] =
- name |> not (Lexicon.is_identifier name) ? enclose "(" ")"
- | command_call name args = "(" ^ name ^ " " ^ space_implode " " args ^ ")"
-fun try_command_line banner time command =
- banner ^ ": " ^ Markup.markup Isabelle_Markup.sendback command ^ show_time time ^ "."
-fun using_labels [] = ""
- | using_labels ls =
- "using " ^ space_implode " " (map string_for_label ls) ^ " "
-fun reconstructor_command reconstr i n (ls, ss) =
- using_labels ls ^ apply_on_subgoal i n ^
- command_call (string_for_reconstructor reconstr) ss
-fun minimize_line _ [] = ""
- | minimize_line minimize_command ss =
- case minimize_command ss of
- "" => ""
- | command => "\nTo minimize: " ^ Markup.markup Isabelle_Markup.sendback command ^ "."
-
-val split_used_facts =
- List.partition (curry (op =) Chained o snd)
- #> pairself (sort_distinct (string_ord o pairself fst))
-
-fun one_line_proof_text (preplay, banner, used_facts, minimize_command,
- subgoal, subgoal_count) =
- let
- val (chained, extra) = split_used_facts used_facts
- val (failed, reconstr, ext_time) =
- case preplay of
- Played (reconstr, time) => (false, reconstr, (SOME (false, time)))
- | Trust_Playable (reconstr, time) =>
- (false, reconstr,
- case time of
- NONE => NONE
- | SOME time =>
- if time = Time.zeroTime then NONE else SOME (true, time))
- | Failed_to_Play reconstr => (true, reconstr, NONE)
- val try_line =
- ([], map fst extra)
- |> reconstructor_command reconstr subgoal subgoal_count
- |> (if failed then enclose "One-line proof reconstruction failed: " "."
- else try_command_line banner ext_time)
- in try_line ^ minimize_line minimize_command (map fst (extra @ chained)) end
-
-(** Hard-core proof reconstruction: structured Isar proofs **)
-
-fun forall_of v t = HOLogic.all_const (fastype_of v) $ lambda v t
-fun exists_of v t = HOLogic.exists_const (fastype_of v) $ lambda v t
-
-fun make_tvar s = TVar (("'" ^ s, 0), HOLogic.typeS)
-fun make_tfree ctxt w =
- let val ww = "'" ^ w in
- TFree (ww, the_default HOLogic.typeS (Variable.def_sort ctxt (ww, ~1)))
- end
-
-val indent_size = 2
-val no_label = ("", ~1)
-
-val raw_prefix = "x"
-val assum_prefix = "a"
-val have_prefix = "f"
-
-fun raw_label_for_name (num, ss) =
- case resolve_conjecture ss of
- [j] => (conjecture_prefix, j)
- | _ => case Int.fromString num of
- SOME j => (raw_prefix, j)
- | NONE => (raw_prefix ^ num, 0)
-
-(**** INTERPRETATION OF TSTP SYNTAX TREES ****)
-
-exception HO_TERM of (string, string) ho_term list
-exception FORMULA of (string, string, (string, string) ho_term) formula list
-exception SAME of unit
-
-(* Type variables are given the basic sort "HOL.type". Some will later be
- constrained by information from type literals, or by type inference. *)
-fun typ_from_atp ctxt (u as ATerm (a, us)) =
- let val Ts = map (typ_from_atp ctxt) us in
- case unprefix_and_unascii type_const_prefix a of
- SOME b => Type (invert_const b, Ts)
- | NONE =>
- if not (null us) then
- raise HO_TERM [u] (* only "tconst"s have type arguments *)
- else case unprefix_and_unascii tfree_prefix a of
- SOME b => make_tfree ctxt b
- | NONE =>
- (* Could be an Isabelle variable or a variable from the ATP, say "X1"
- or "_5018". Sometimes variables from the ATP are indistinguishable
- from Isabelle variables, which forces us to use a type parameter in
- all cases. *)
- (a |> perhaps (unprefix_and_unascii tvar_prefix), HOLogic.typeS)
- |> Type_Infer.param 0
- end
-
-(* Type class literal applied to a type. Returns triple of polarity, class,
- type. *)
-fun type_constraint_from_term ctxt (u as ATerm (a, us)) =
- case (unprefix_and_unascii class_prefix a, map (typ_from_atp ctxt) us) of
- (SOME b, [T]) => (b, T)
- | _ => raise HO_TERM [u]
-
-(* Accumulate type constraints in a formula: negative type literals. *)
-fun add_var (key, z) = Vartab.map_default (key, []) (cons z)
-fun add_type_constraint false (cl, TFree (a ,_)) = add_var ((a, ~1), cl)
- | add_type_constraint false (cl, TVar (ix, _)) = add_var (ix, cl)
- | add_type_constraint _ _ = I
-
-fun repair_variable_name f s =
- let
- fun subscript_name s n = s ^ nat_subscript n
- val s = String.map f s
- in
- case space_explode "_" s of
- [_] => (case take_suffix Char.isDigit (String.explode s) of
- (cs1 as _ :: _, cs2 as _ :: _) =>
- subscript_name (String.implode cs1)
- (the (Int.fromString (String.implode cs2)))
- | (_, _) => s)
- | [s1, s2] => (case Int.fromString s2 of
- SOME n => subscript_name s1 n
- | NONE => s)
- | _ => s
- end
-
-(* The number of type arguments of a constant, zero if it's monomorphic. For
- (instances of) Skolem pseudoconstants, this information is encoded in the
- constant name. *)
-fun num_type_args thy s =
- if String.isPrefix skolem_const_prefix s then
- s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
- else if String.isPrefix lam_lifted_prefix s then
- if String.isPrefix lam_lifted_poly_prefix s then 2 else 0
- else
- (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
-
-fun slack_fastype_of t = fastype_of t handle TERM _ => HOLogic.typeT
-
-(* First-order translation. No types are known for variables. "HOLogic.typeT"
- should allow them to be inferred. *)
-fun term_from_atp ctxt textual sym_tab =
- let
- val thy = Proof_Context.theory_of ctxt
- (* For Metis, we use 1 rather than 0 because variable references in clauses
- may otherwise conflict with variable constraints in the goal. At least,
- type inference often fails otherwise. See also "axiom_inference" in
- "Metis_Reconstruct". *)
- val var_index = if textual then 0 else 1
- fun do_term extra_ts opt_T u =
- case u of
- ATerm (s, us) =>
- if String.isPrefix simple_type_prefix s then
- @{const True} (* ignore TPTP type information *)
- else if s = tptp_equal then
- let val ts = map (do_term [] NONE) us in
- if textual andalso length ts = 2 andalso
- hd ts aconv List.last ts then
- (* Vampire is keen on producing these. *)
- @{const True}
- else
- list_comb (Const (@{const_name HOL.eq}, HOLogic.typeT), ts)
- end
- else case unprefix_and_unascii const_prefix s of
- SOME s' =>
- let
- val ((s', s''), mangled_us) =
- s' |> unmangled_const |>> `invert_const
- in
- if s' = type_tag_name then
- case mangled_us @ us of
- [typ_u, term_u] =>
- do_term extra_ts (SOME (typ_from_atp ctxt typ_u)) term_u
- | _ => raise HO_TERM us
- else if s' = predicator_name then
- do_term [] (SOME @{typ bool}) (hd us)
- else if s' = app_op_name then
- let val extra_t = do_term [] NONE (List.last us) in
- do_term (extra_t :: extra_ts)
- (case opt_T of
- SOME T => SOME (slack_fastype_of extra_t --> T)
- | NONE => NONE)
- (nth us (length us - 2))
- end
- else if s' = type_guard_name then
- @{const True} (* ignore type predicates *)
- else
- let
- val new_skolem = String.isPrefix new_skolem_const_prefix s''
- val num_ty_args =
- length us - the_default 0 (Symtab.lookup sym_tab s)
- val (type_us, term_us) =
- chop num_ty_args us |>> append mangled_us
- val term_ts = map (do_term [] NONE) term_us
- val T =
- (if not (null type_us) andalso
- num_type_args thy s' = length type_us then
- let val Ts = type_us |> map (typ_from_atp ctxt) in
- if new_skolem then
- SOME (Type_Infer.paramify_vars (tl Ts ---> hd Ts))
- else if textual then
- try (Sign.const_instance thy) (s', Ts)
- else
- NONE
- end
- else
- NONE)
- |> (fn SOME T => T
- | NONE => map slack_fastype_of term_ts --->
- (case opt_T of
- SOME T => T
- | NONE => HOLogic.typeT))
- val t =
- if new_skolem then
- Var ((new_skolem_var_name_from_const s'', var_index), T)
- else
- Const (unproxify_const s', T)
- in list_comb (t, term_ts @ extra_ts) end
- end
- | NONE => (* a free or schematic variable *)
- let
- val term_ts = map (do_term [] NONE) us
- val ts = term_ts @ extra_ts
- val T =
- case opt_T of
- SOME T => map slack_fastype_of term_ts ---> T
- | NONE => map slack_fastype_of ts ---> HOLogic.typeT
- val t =
- case unprefix_and_unascii fixed_var_prefix s of
- SOME s => Free (s, T)
- | NONE =>
- case unprefix_and_unascii schematic_var_prefix s of
- SOME s => Var ((s, var_index), T)
- | NONE =>
- Var ((s |> textual ? repair_variable_name Char.toLower,
- var_index), T)
- in list_comb (t, ts) end
- in do_term [] end
-
-fun term_from_atom ctxt textual sym_tab pos (u as ATerm (s, _)) =
- if String.isPrefix class_prefix s then
- add_type_constraint pos (type_constraint_from_term ctxt u)
- #> pair @{const True}
- else
- pair (term_from_atp ctxt textual sym_tab (SOME @{typ bool}) u)
-
-val combinator_table =
- [(@{const_name Meson.COMBI}, @{thm Meson.COMBI_def_raw}),
- (@{const_name Meson.COMBK}, @{thm Meson.COMBK_def_raw}),
- (@{const_name Meson.COMBB}, @{thm Meson.COMBB_def_raw}),
- (@{const_name Meson.COMBC}, @{thm Meson.COMBC_def_raw}),
- (@{const_name Meson.COMBS}, @{thm Meson.COMBS_def_raw})]
-
-fun uncombine_term thy =
- let
- fun aux (t1 $ t2) = betapply (pairself aux (t1, t2))
- | aux (Abs (s, T, t')) = Abs (s, T, aux t')
- | aux (t as Const (x as (s, _))) =
- (case AList.lookup (op =) combinator_table s of
- SOME thm => thm |> prop_of |> specialize_type thy x
- |> Logic.dest_equals |> snd
- | NONE => t)
- | aux t = t
- in aux end
-
-(* Update schematic type variables with detected sort constraints. It's not
- totally clear whether this code is necessary. *)
-fun repair_tvar_sorts (t, tvar_tab) =
- let
- fun do_type (Type (a, Ts)) = Type (a, map do_type Ts)
- | do_type (TVar (xi, s)) =
- TVar (xi, the_default s (Vartab.lookup tvar_tab xi))
- | do_type (TFree z) = TFree z
- fun do_term (Const (a, T)) = Const (a, do_type T)
- | do_term (Free (a, T)) = Free (a, do_type T)
- | do_term (Var (xi, T)) = Var (xi, do_type T)
- | do_term (t as Bound _) = t
- | do_term (Abs (a, T, t)) = Abs (a, do_type T, do_term t)
- | do_term (t1 $ t2) = do_term t1 $ do_term t2
- in t |> not (Vartab.is_empty tvar_tab) ? do_term end
-
-fun quantify_over_var quant_of var_s t =
- let
- val vars = [] |> Term.add_vars t |> filter (fn ((s, _), _) => s = var_s)
- |> map Var
- in fold_rev quant_of vars t end
-
-(* Interpret an ATP formula as a HOL term, extracting sort constraints as they
- appear in the formula. *)
-fun prop_from_atp ctxt textual sym_tab phi =
- let
- fun do_formula pos phi =
- case phi of
- AQuant (_, [], phi) => do_formula pos phi
- | AQuant (q, (s, _) :: xs, phi') =>
- do_formula pos (AQuant (q, xs, phi'))
- (* FIXME: TFF *)
- #>> quantify_over_var (case q of
- AForall => forall_of
- | AExists => exists_of)
- (s |> textual ? repair_variable_name Char.toLower)
- | AConn (ANot, [phi']) => do_formula (not pos) phi' #>> s_not
- | AConn (c, [phi1, phi2]) =>
- do_formula (pos |> c = AImplies ? not) phi1
- ##>> do_formula pos phi2
- #>> (case c of
- AAnd => s_conj
- | AOr => s_disj
- | AImplies => s_imp
- | AIff => s_iff
- | ANot => raise Fail "impossible connective")
- | AAtom tm => term_from_atom ctxt textual sym_tab pos tm
- | _ => raise FORMULA [phi]
- in repair_tvar_sorts (do_formula true phi Vartab.empty) end
-
-fun infer_formula_types ctxt =
- Type.constraint HOLogic.boolT
- #> Syntax.check_term
- (Proof_Context.set_mode Proof_Context.mode_schematic ctxt)
-
-fun uncombined_etc_prop_from_atp ctxt textual sym_tab =
- let val thy = Proof_Context.theory_of ctxt in
- prop_from_atp ctxt textual sym_tab
- #> textual ? uncombine_term thy #> infer_formula_types ctxt
- end
-
-(**** Translation of TSTP files to Isar proofs ****)
-
-fun unvarify_term (Var ((s, 0), T)) = Free (s, T)
- | unvarify_term t = raise TERM ("unvarify_term: non-Var", [t])
-
-fun decode_line sym_tab (Definition (name, phi1, phi2)) ctxt =
- let
- val thy = Proof_Context.theory_of ctxt
- val t1 = prop_from_atp ctxt true sym_tab phi1
- val vars = snd (strip_comb t1)
- val frees = map unvarify_term vars
- val unvarify_args = subst_atomic (vars ~~ frees)
- val t2 = prop_from_atp ctxt true sym_tab phi2
- val (t1, t2) =
- HOLogic.eq_const HOLogic.typeT $ t1 $ t2
- |> unvarify_args |> uncombine_term thy |> infer_formula_types ctxt
- |> HOLogic.dest_eq
- in
- (Definition (name, t1, t2),
- fold Variable.declare_term (maps Misc_Legacy.term_frees [t1, t2]) ctxt)
- end
- | decode_line sym_tab (Inference (name, u, rule, deps)) ctxt =
- let val t = u |> uncombined_etc_prop_from_atp ctxt true sym_tab in
- (Inference (name, t, rule, deps),
- fold Variable.declare_term (Misc_Legacy.term_frees t) ctxt)
- end
-fun decode_lines ctxt sym_tab lines =
- fst (fold_map (decode_line sym_tab) lines ctxt)
-
-fun is_same_inference _ (Definition _) = false
- | is_same_inference t (Inference (_, t', _, _)) = t aconv t'
-
-(* No "real" literals means only type information (tfree_tcs, clsrel, or
- clsarity). *)
-val is_only_type_information = curry (op aconv) @{term True}
-
-fun replace_one_dependency (old, new) dep =
- if is_same_atp_step dep old then new else [dep]
-fun replace_dependencies_in_line _ (line as Definition _) = line
- | replace_dependencies_in_line p (Inference (name, t, rule, deps)) =
- Inference (name, t, rule,
- fold (union (op =) o replace_one_dependency p) deps [])
-
-(* Discard facts; consolidate adjacent lines that prove the same formula, since
- they differ only in type information.*)
-fun add_line _ (line as Definition _) lines = line :: lines
- | add_line fact_names (Inference (name as (_, ss), t, rule, [])) lines =
- (* No dependencies: fact, conjecture, or (for Vampire) internal facts or
- definitions. *)
- if is_fact fact_names ss then
- (* Facts are not proof lines. *)
- if is_only_type_information t then
- map (replace_dependencies_in_line (name, [])) lines
- (* Is there a repetition? If so, replace later line by earlier one. *)
- else case take_prefix (not o is_same_inference t) lines of
- (_, []) => lines (* no repetition of proof line *)
- | (pre, Inference (name', _, _, _) :: post) =>
- pre @ map (replace_dependencies_in_line (name', [name])) post
- | _ => raise Fail "unexpected inference"
- else if is_conjecture ss then
- Inference (name, s_not t, rule, []) :: lines
- else
- map (replace_dependencies_in_line (name, [])) lines
- | add_line _ (Inference (name, t, rule, deps)) lines =
- (* Type information will be deleted later; skip repetition test. *)
- if is_only_type_information t then
- Inference (name, t, rule, deps) :: lines
- (* Is there a repetition? If so, replace later line by earlier one. *)
- else case take_prefix (not o is_same_inference t) lines of
- (* FIXME: Doesn't this code risk conflating proofs involving different
- types? *)
- (_, []) => Inference (name, t, rule, deps) :: lines
- | (pre, Inference (name', t', rule, _) :: post) =>
- Inference (name, t', rule, deps) ::
- pre @ map (replace_dependencies_in_line (name', [name])) post
- | _ => raise Fail "unexpected inference"
-
-(* Recursively delete empty lines (type information) from the proof. *)
-fun add_nontrivial_line (line as Inference (name, t, _, [])) lines =
- if is_only_type_information t then delete_dependency name lines
- else line :: lines
- | add_nontrivial_line line lines = line :: lines
-and delete_dependency name lines =
- fold_rev add_nontrivial_line
- (map (replace_dependencies_in_line (name, [])) lines) []
-
-(* ATPs sometimes reuse free variable names in the strangest ways. Removing
- offending lines often does the trick. *)
-fun is_bad_free frees (Free x) = not (member (op =) frees x)
- | is_bad_free _ _ = false
-
-fun add_desired_line _ _ _ (line as Definition (name, _, _)) (j, lines) =
- (j, line :: map (replace_dependencies_in_line (name, [])) lines)
- | add_desired_line isar_shrink_factor fact_names frees
- (Inference (name as (_, ss), t, rule, deps)) (j, lines) =
- (j + 1,
- if is_fact fact_names ss orelse
- is_conjecture ss orelse
- (* the last line must be kept *)
- j = 0 orelse
- (not (is_only_type_information t) andalso
- null (Term.add_tvars t []) andalso
- not (exists_subterm (is_bad_free frees) t) andalso
- length deps >= 2 andalso j mod isar_shrink_factor = 0 andalso
- (* kill next to last line, which usually results in a trivial step *)
- j <> 1) then
- Inference (name, t, rule, deps) :: lines (* keep line *)
- else
- map (replace_dependencies_in_line (name, deps)) lines) (* drop line *)
-
-(** Isar proof construction and manipulation **)
-
-type label = string * int
-type facts = label list * string list
-
-datatype isar_qualifier = Show | Then | Moreover | Ultimately
-
-datatype isar_step =
- Fix of (string * typ) list |
- Let of term * term |
- Assume of label * term |
- Prove of isar_qualifier list * label * term * byline
-and byline =
- By_Metis of facts |
- Case_Split of isar_step list list * facts
-
-fun add_fact_from_dependency fact_names (name as (_, ss)) =
- if is_fact fact_names ss then
- apsnd (union (op =) (map fst (resolve_fact fact_names ss)))
- else
- apfst (insert (op =) (raw_label_for_name name))
-
-fun repair_name "$true" = "c_True"
- | repair_name "$false" = "c_False"
- | repair_name "$$e" = tptp_equal (* seen in Vampire proofs *)
- | repair_name s =
- if is_tptp_equal s orelse
- (* seen in Vampire proofs *)
- (String.isPrefix "sQ" s andalso String.isSuffix "_eqProxy" s) then
- tptp_equal
- else
- s
-
-(* FIXME: Still needed? Try with SPASS proofs perhaps. *)
-val kill_duplicate_assumptions_in_proof =
- let
- fun relabel_facts subst =
- apfst (map (fn l => AList.lookup (op =) subst l |> the_default l))
- fun do_step (step as Assume (l, t)) (proof, subst, assums) =
- (case AList.lookup (op aconv) assums t of
- SOME l' => (proof, (l, l') :: subst, assums)
- | NONE => (step :: proof, subst, (t, l) :: assums))
- | do_step (Prove (qs, l, t, by)) (proof, subst, assums) =
- (Prove (qs, l, t,
- case by of
- By_Metis facts => By_Metis (relabel_facts subst facts)
- | Case_Split (proofs, facts) =>
- Case_Split (map do_proof proofs,
- relabel_facts subst facts)) ::
- proof, subst, assums)
- | do_step step (proof, subst, assums) = (step :: proof, subst, assums)
- and do_proof proof = fold do_step proof ([], [], []) |> #1 |> rev
- in do_proof end
-
-fun used_labels_of_step (Prove (_, _, _, by)) =
- (case by of
- By_Metis (ls, _) => ls
- | Case_Split (proofs, (ls, _)) =>
- fold (union (op =) o used_labels_of) proofs ls)
- | used_labels_of_step _ = []
-and used_labels_of proof = fold (union (op =) o used_labels_of_step) proof []
-
-fun kill_useless_labels_in_proof proof =
- let
- val used_ls = used_labels_of proof
- fun do_label l = if member (op =) used_ls l then l else no_label
- fun do_step (Assume (l, t)) = Assume (do_label l, t)
- | do_step (Prove (qs, l, t, by)) =
- Prove (qs, do_label l, t,
- case by of
- Case_Split (proofs, facts) =>
- Case_Split (map (map do_step) proofs, facts)
- | _ => by)
- | do_step step = step
- in map do_step proof end
-
-fun prefix_for_depth n = replicate_string (n + 1)
-
-val relabel_proof =
- let
- fun aux _ _ _ [] = []
- | aux subst depth (next_assum, next_fact) (Assume (l, t) :: proof) =
- if l = no_label then
- Assume (l, t) :: aux subst depth (next_assum, next_fact) proof
- else
- let val l' = (prefix_for_depth depth assum_prefix, next_assum) in
- Assume (l', t) ::
- aux ((l, l') :: subst) depth (next_assum + 1, next_fact) proof
- end
- | aux subst depth (next_assum, next_fact)
- (Prove (qs, l, t, by) :: proof) =
- let
- val (l', subst, next_fact) =
- if l = no_label then
- (l, subst, next_fact)
- else
- let
- val l' = (prefix_for_depth depth have_prefix, next_fact)
- in (l', (l, l') :: subst, next_fact + 1) end
- val relabel_facts =
- apfst (maps (the_list o AList.lookup (op =) subst))
- val by =
- case by of
- By_Metis facts => By_Metis (relabel_facts facts)
- | Case_Split (proofs, facts) =>
- Case_Split (map (aux subst (depth + 1) (1, 1)) proofs,
- relabel_facts facts)
- in
- Prove (qs, l', t, by) :: aux subst depth (next_assum, next_fact) proof
- end
- | aux subst depth nextp (step :: proof) =
- step :: aux subst depth nextp proof
- in aux [] 0 (1, 1) end
-
-fun string_for_proof ctxt0 type_enc lam_trans i n =
- let
- val ctxt =
- ctxt0 |> Config.put show_free_types false
- |> Config.put show_types true
- |> Config.put show_sorts true
- fun fix_print_mode f x =
- Print_Mode.setmp (filter (curry (op =) Symbol.xsymbolsN)
- (print_mode_value ())) f x
- fun do_indent ind = replicate_string (ind * indent_size) " "
- fun do_free (s, T) =
- maybe_quote s ^ " :: " ^
- maybe_quote (fix_print_mode (Syntax.string_of_typ ctxt) T)
- fun do_label l = if l = no_label then "" else string_for_label l ^ ": "
- fun do_have qs =
- (if member (op =) qs Moreover then "moreover " else "") ^
- (if member (op =) qs Ultimately then "ultimately " else "") ^
- (if member (op =) qs Then then
- if member (op =) qs Show then "thus" else "hence"
- else
- if member (op =) qs Show then "show" else "have")
- val do_term = maybe_quote o fix_print_mode (Syntax.string_of_term ctxt)
- val reconstr = Metis (type_enc, lam_trans)
- fun do_facts (ls, ss) =
- reconstructor_command reconstr 1 1
- (ls |> sort_distinct (prod_ord string_ord int_ord),
- ss |> sort_distinct string_ord)
- and do_step ind (Fix xs) =
- do_indent ind ^ "fix " ^ space_implode " and " (map do_free xs) ^ "\n"
- | do_step ind (Let (t1, t2)) =
- do_indent ind ^ "let " ^ do_term t1 ^ " = " ^ do_term t2 ^ "\n"
- | do_step ind (Assume (l, t)) =
- do_indent ind ^ "assume " ^ do_label l ^ do_term t ^ "\n"
- | do_step ind (Prove (qs, l, t, By_Metis facts)) =
- do_indent ind ^ do_have qs ^ " " ^
- do_label l ^ do_term t ^ " " ^ do_facts facts ^ "\n"
- | do_step ind (Prove (qs, l, t, Case_Split (proofs, facts))) =
- implode (map (prefix (do_indent ind ^ "moreover\n") o do_block ind)
- proofs) ^
- do_indent ind ^ do_have qs ^ " " ^ do_label l ^ do_term t ^ " " ^
- do_facts facts ^ "\n"
- and do_steps prefix suffix ind steps =
- let val s = implode (map (do_step ind) steps) in
- replicate_string (ind * indent_size - size prefix) " " ^ prefix ^
- String.extract (s, ind * indent_size,
- SOME (size s - ind * indent_size - 1)) ^
- suffix ^ "\n"
- end
- and do_block ind proof = do_steps "{ " " }" (ind + 1) proof
- (* One-step proofs are pointless; better use the Metis one-liner
- directly. *)
- and do_proof [Prove (_, _, _, By_Metis _)] = ""
- | do_proof proof =
- (if i <> 1 then "prefer " ^ string_of_int i ^ "\n" else "") ^
- do_indent 0 ^ "proof -\n" ^ do_steps "" "" 1 proof ^ do_indent 0 ^
- (if n <> 1 then "next" else "qed")
- in do_proof end
-
-fun isar_proof_text ctxt isar_proof_requested
- (debug, isar_shrink_factor, pool, fact_names, sym_tab, atp_proof, goal)
- (one_line_params as (_, _, _, _, subgoal, subgoal_count)) =
- let
- val isar_shrink_factor =
- (if isar_proof_requested then 1 else 2) * isar_shrink_factor
- val (params, hyp_ts, concl_t) = strip_subgoal ctxt goal subgoal
- val frees = fold Term.add_frees (concl_t :: hyp_ts) []
- val one_line_proof = one_line_proof_text one_line_params
- val type_enc =
- if is_typed_helper_used_in_atp_proof atp_proof then full_typesN
- else partial_typesN
- val lam_trans = lam_trans_from_atp_proof atp_proof metis_default_lam_trans
-
- fun isar_proof_of () =
- let
- val atp_proof =
- atp_proof
- |> clean_up_atp_proof_dependencies
- |> nasty_atp_proof pool
- |> map_term_names_in_atp_proof repair_name
- |> decode_lines ctxt sym_tab
- |> rpair [] |-> fold_rev (add_line fact_names)
- |> rpair [] |-> fold_rev add_nontrivial_line
- |> rpair (0, [])
- |-> fold_rev (add_desired_line isar_shrink_factor fact_names frees)
- |> snd
- val conj_name = conjecture_prefix ^ string_of_int (length hyp_ts)
- val conjs =
- atp_proof
- |> map_filter (fn Inference (name as (_, ss), _, _, []) =>
- if member (op =) ss conj_name then SOME name else NONE
- | _ => NONE)
- fun dep_of_step (Definition _) = NONE
- | dep_of_step (Inference (name, _, _, from)) = SOME (from, name)
- val ref_graph = atp_proof |> map_filter dep_of_step |> make_ref_graph
- val axioms = axioms_of_ref_graph ref_graph conjs
- val tainted = tainted_atoms_of_ref_graph ref_graph conjs
- val props =
- Symtab.empty
- |> fold (fn Definition _ => I (* FIXME *)
- | Inference ((s, _), t, _, _) =>
- Symtab.update_new (s,
- t |> member (op = o apsnd fst) tainted s ? s_not))
- atp_proof
- (* FIXME: add "fold_rev forall_of (map Var (Term.add_vars t []))"? *)
- fun prop_of_clause c =
- fold (curry s_disj) (map_filter (Symtab.lookup props o fst) c)
- @{term False}
- fun label_of_clause c = (space_implode "___" (map fst c), 0)
- fun maybe_show outer c =
- (outer andalso length c = 1 andalso subset (op =) (c, conjs))
- ? cons Show
- fun do_have outer qs (gamma, c) =
- Prove (maybe_show outer c qs, label_of_clause c, prop_of_clause c,
- By_Metis (fold (add_fact_from_dependency fact_names
- o the_single) gamma ([], [])))
- fun do_inf outer (Have z) = do_have outer [] z
- | do_inf outer (Hence z) = do_have outer [Then] z
- | do_inf outer (Cases cases) =
- let val c = succedent_of_cases cases in
- Prove (maybe_show outer c [Ultimately], label_of_clause c,
- prop_of_clause c,
- Case_Split (map (do_case false) cases, ([], [])))
- end
- and do_case outer (c, infs) =
- Assume (label_of_clause c, prop_of_clause c) ::
- map (do_inf outer) infs
- val isar_proof =
- (if null params then [] else [Fix params]) @
- (ref_graph
- |> redirect_graph axioms tainted
- |> chain_direct_proof
- |> map (do_inf true)
- |> kill_duplicate_assumptions_in_proof
- |> kill_useless_labels_in_proof
- |> relabel_proof)
- |> string_for_proof ctxt type_enc lam_trans subgoal subgoal_count
- in
- case isar_proof of
- "" =>
- if isar_proof_requested then
- "\nNo structured proof available (proof too short)."
- else
- ""
- | _ =>
- "\n\n" ^ (if isar_proof_requested then "Structured proof"
- else "Perhaps this will work") ^
- ":\n" ^ Markup.markup Isabelle_Markup.sendback isar_proof
- end
- val isar_proof =
- if debug then
- isar_proof_of ()
- else case try isar_proof_of () of
- SOME s => s
- | NONE => if isar_proof_requested then
- "\nWarning: The Isar proof construction failed."
- else
- ""
- in one_line_proof ^ isar_proof end
-
-fun proof_text ctxt isar_proof isar_params
- (one_line_params as (preplay, _, _, _, _, _)) =
- (if case preplay of Failed_to_Play _ => true | _ => isar_proof then
- isar_proof_text ctxt isar_proof isar_params
- else
- one_line_proof_text) one_line_params
-
-end;