--- a/src/HOL/IsaMakefile Tue Aug 31 23:43:23 2010 +0200
+++ b/src/HOL/IsaMakefile Tue Aug 31 23:46:23 2010 +0200
@@ -319,10 +319,10 @@
Tools/Sledgehammer/metis_clauses.ML \
Tools/Sledgehammer/metis_tactics.ML \
Tools/Sledgehammer/sledgehammer.ML \
- Tools/Sledgehammer/sledgehammer_fact_filter.ML \
- Tools/Sledgehammer/sledgehammer_fact_minimize.ML \
+ Tools/Sledgehammer/sledgehammer_filter.ML \
+ Tools/Sledgehammer/sledgehammer_minimize.ML \
Tools/Sledgehammer/sledgehammer_isar.ML \
- Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML \
+ Tools/Sledgehammer/sledgehammer_reconstruct.ML \
Tools/Sledgehammer/sledgehammer_translate.ML \
Tools/Sledgehammer/sledgehammer_util.ML \
Tools/SMT/cvc3_solver.ML \
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_fact_filter.ML Tue Aug 31 23:43:23 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,800 +0,0 @@
-(* Title: HOL/Tools/Sledgehammer/sledgehammer_fact_filter.ML
- Author: Jia Meng, Cambridge University Computer Laboratory and NICTA
- Author: Jasmin Blanchette, TU Muenchen
-*)
-
-signature SLEDGEHAMMER_FACT_FILTER =
-sig
- datatype locality = General | Intro | Elim | Simp | Local | Chained
-
- type relevance_override =
- {add: Facts.ref list,
- del: Facts.ref list,
- only: bool}
-
- val trace : bool Unsynchronized.ref
- val worse_irrel_freq : real Unsynchronized.ref
- val higher_order_irrel_weight : real Unsynchronized.ref
- val abs_rel_weight : real Unsynchronized.ref
- val abs_irrel_weight : real Unsynchronized.ref
- val skolem_irrel_weight : real Unsynchronized.ref
- val intro_bonus : real Unsynchronized.ref
- val elim_bonus : real Unsynchronized.ref
- val simp_bonus : real Unsynchronized.ref
- val local_bonus : real Unsynchronized.ref
- val chained_bonus : real Unsynchronized.ref
- val max_imperfect : real Unsynchronized.ref
- val max_imperfect_exp : real Unsynchronized.ref
- val threshold_divisor : real Unsynchronized.ref
- val ridiculous_threshold : real Unsynchronized.ref
- val name_thm_pairs_from_ref :
- Proof.context -> unit Symtab.table -> thm list -> Facts.ref
- -> ((string * locality) * thm) list
- val relevant_facts :
- Proof.context -> bool -> real * real -> int -> bool -> relevance_override
- -> thm list -> term list -> term -> ((string * locality) * thm) list
-end;
-
-structure Sledgehammer_Fact_Filter : SLEDGEHAMMER_FACT_FILTER =
-struct
-
-open Sledgehammer_Util
-
-val trace = Unsynchronized.ref false
-fun trace_msg msg = if !trace then tracing (msg ()) else ()
-
-(* experimental feature *)
-val term_patterns = false
-
-val respect_no_atp = true
-
-datatype locality = General | Intro | Elim | Simp | Local | Chained
-
-type relevance_override =
- {add: Facts.ref list,
- del: Facts.ref list,
- only: bool}
-
-val sledgehammer_prefix = "Sledgehammer" ^ Long_Name.separator
-
-fun repair_name reserved multi j name =
- (name |> Symtab.defined reserved name ? quote) ^
- (if multi then "(" ^ Int.toString j ^ ")" else "")
-
-fun name_thm_pairs_from_ref ctxt reserved chained_ths xref =
- let
- val ths = ProofContext.get_fact ctxt xref
- val name = Facts.string_of_ref xref
- val multi = length ths > 1
- in
- (ths, (1, []))
- |-> fold (fn th => fn (j, rest) =>
- (j + 1, ((repair_name reserved multi j name,
- if member Thm.eq_thm chained_ths th then Chained
- else General), th) :: rest))
- |> snd
- end
-
-(***************************************************************)
-(* Relevance Filtering *)
-(***************************************************************)
-
-(*** constants with types ***)
-
-fun order_of_type (Type (@{type_name fun}, [T1, @{typ bool}])) =
- order_of_type T1 (* cheat: pretend sets are first-order *)
- | order_of_type (Type (@{type_name fun}, [T1, T2])) =
- Int.max (order_of_type T1 + 1, order_of_type T2)
- | order_of_type (Type (_, Ts)) = fold (Integer.max o order_of_type) Ts 0
- | order_of_type _ = 0
-
-(* An abstraction of Isabelle types and first-order terms *)
-datatype pattern = PVar | PApp of string * pattern list
-datatype ptype = PType of int * pattern list
-
-fun string_for_pattern PVar = "_"
- | string_for_pattern (PApp (s, ps)) =
- if null ps then s else s ^ string_for_patterns ps
-and string_for_patterns ps = "(" ^ commas (map string_for_pattern ps) ^ ")"
-fun string_for_ptype (PType (_, ps)) = string_for_patterns ps
-
-(*Is the second type an instance of the first one?*)
-fun match_pattern (PVar, _) = true
- | match_pattern (PApp _, PVar) = false
- | match_pattern (PApp (s, ps), PApp (t, qs)) =
- s = t andalso match_patterns (ps, qs)
-and match_patterns (_, []) = true
- | match_patterns ([], _) = false
- | match_patterns (p :: ps, q :: qs) =
- match_pattern (p, q) andalso match_patterns (ps, qs)
-fun match_ptype (PType (_, ps), PType (_, qs)) = match_patterns (ps, qs)
-
-(* Is there a unifiable constant? *)
-fun pconst_mem f consts (s, ps) =
- exists (curry (match_ptype o f) ps)
- (map snd (filter (curry (op =) s o fst) consts))
-fun pconst_hyper_mem f const_tab (s, ps) =
- exists (curry (match_ptype o f) ps) (these (Symtab.lookup const_tab s))
-
-fun pattern_for_type (Type (s, Ts)) = PApp (s, map pattern_for_type Ts)
- | pattern_for_type (TFree (s, _)) = PApp (s, [])
- | pattern_for_type (TVar _) = PVar
-
-fun pterm thy t =
- case strip_comb t of
- (Const x, ts) => PApp (pconst thy true x ts)
- | (Free x, ts) => PApp (pconst thy false x ts)
- | (Var x, []) => PVar
- | _ => PApp ("?", []) (* equivalence class of higher-order constructs *)
-(* Pairs a constant with the list of its type instantiations. *)
-and ptype thy const x ts =
- (if const then map pattern_for_type (these (try (Sign.const_typargs thy) x))
- else []) @
- (if term_patterns then map (pterm thy) ts else [])
-and pconst thy const (s, T) ts = (s, ptype thy const (s, T) ts)
-and rich_ptype thy const (s, T) ts =
- PType (order_of_type T, ptype thy const (s, T) ts)
-and rich_pconst thy const (s, T) ts = (s, rich_ptype thy const (s, T) ts)
-
-fun string_for_hyper_pconst (s, ps) =
- s ^ "{" ^ commas (map string_for_ptype ps) ^ "}"
-
-val abs_name = "Sledgehammer.abs"
-val skolem_prefix = "Sledgehammer.sko"
-
-(* These are typically simplified away by "Meson.presimplify". Equality is
- handled specially via "fequal". *)
-val boring_consts =
- [@{const_name False}, @{const_name True}, @{const_name If}, @{const_name Let},
- @{const_name HOL.eq}]
-
-(* Add a pconstant to the table, but a [] entry means a standard
- connective, which we ignore.*)
-fun add_pconst_to_table also_skolem (c, p) =
- if member (op =) boring_consts c orelse
- (not also_skolem andalso String.isPrefix skolem_prefix c) then
- I
- else
- Symtab.map_default (c, [p]) (insert (op =) p)
-
-fun is_formula_type T = (T = HOLogic.boolT orelse T = propT)
-
-fun pconsts_in_terms thy also_skolems pos ts =
- let
- val flip = Option.map not
- (* We include free variables, as well as constants, to handle locales. For
- each quantifiers that must necessarily be skolemized by the ATP, we
- introduce a fresh constant to simulate the effect of Skolemization. *)
- fun do_const const (s, T) ts =
- add_pconst_to_table also_skolems (rich_pconst thy const (s, T) ts)
- #> fold do_term ts
- and do_term t =
- case strip_comb t of
- (Const x, ts) => do_const true x ts
- | (Free x, ts) => do_const false x ts
- | (Abs (_, T, t'), ts) =>
- (null ts
- ? add_pconst_to_table true (abs_name, PType (order_of_type T + 1, [])))
- #> fold do_term (t' :: ts)
- | (_, ts) => fold do_term ts
- fun do_quantifier will_surely_be_skolemized abs_T body_t =
- do_formula pos body_t
- #> (if also_skolems andalso will_surely_be_skolemized then
- add_pconst_to_table true
- (gensym skolem_prefix, PType (order_of_type abs_T, []))
- else
- I)
- and do_term_or_formula T =
- if is_formula_type T then do_formula NONE else do_term
- and do_formula pos t =
- case t of
- Const (@{const_name all}, _) $ Abs (_, T, t') =>
- do_quantifier (pos = SOME false) T t'
- | @{const "==>"} $ t1 $ t2 =>
- do_formula (flip pos) t1 #> do_formula pos t2
- | Const (@{const_name "=="}, Type (_, [T, _])) $ t1 $ t2 =>
- fold (do_term_or_formula T) [t1, t2]
- | @{const Trueprop} $ t1 => do_formula pos t1
- | @{const Not} $ t1 => do_formula (flip pos) t1
- | Const (@{const_name All}, _) $ Abs (_, T, t') =>
- do_quantifier (pos = SOME false) T t'
- | Const (@{const_name Ex}, _) $ Abs (_, T, t') =>
- do_quantifier (pos = SOME true) T t'
- | @{const HOL.conj} $ t1 $ t2 => fold (do_formula pos) [t1, t2]
- | @{const HOL.disj} $ t1 $ t2 => fold (do_formula pos) [t1, t2]
- | @{const HOL.implies} $ t1 $ t2 =>
- do_formula (flip pos) t1 #> do_formula pos t2
- | Const (@{const_name HOL.eq}, Type (_, [T, _])) $ t1 $ t2 =>
- fold (do_term_or_formula T) [t1, t2]
- | Const (@{const_name If}, Type (_, [_, Type (_, [T, _])]))
- $ t1 $ t2 $ t3 =>
- do_formula NONE t1 #> fold (do_term_or_formula T) [t2, t3]
- | Const (@{const_name Ex1}, _) $ Abs (_, T, t') =>
- do_quantifier (is_some pos) T t'
- | Const (@{const_name Ball}, _) $ t1 $ Abs (_, T, t') =>
- do_quantifier (pos = SOME false) T
- (HOLogic.mk_imp (incr_boundvars 1 t1 $ Bound 0, t'))
- | Const (@{const_name Bex}, _) $ t1 $ Abs (_, T, t') =>
- do_quantifier (pos = SOME true) T
- (HOLogic.mk_conj (incr_boundvars 1 t1 $ Bound 0, t'))
- | (t0 as Const (_, @{typ bool})) $ t1 =>
- do_term t0 #> do_formula pos t1 (* theory constant *)
- | _ => do_term t
- in Symtab.empty |> fold (do_formula pos) ts end
-
-(*Inserts a dummy "constant" referring to the theory name, so that relevance
- takes the given theory into account.*)
-fun theory_const_prop_of theory_relevant th =
- if theory_relevant then
- let
- val name = Context.theory_name (theory_of_thm th)
- val t = Const (name ^ ". 1", @{typ bool})
- in t $ prop_of th end
- else
- prop_of th
-
-(**** Constant / Type Frequencies ****)
-
-(* A two-dimensional symbol table counts frequencies of constants. It's keyed
- first by constant name and second by its list of type instantiations. For the
- latter, we need a linear ordering on "pattern list". *)
-
-fun pattern_ord p =
- case p of
- (PVar, PVar) => EQUAL
- | (PVar, PApp _) => LESS
- | (PApp _, PVar) => GREATER
- | (PApp q1, PApp q2) =>
- prod_ord fast_string_ord (dict_ord pattern_ord) (q1, q2)
-fun ptype_ord (PType p, PType q) =
- prod_ord (dict_ord pattern_ord) int_ord (swap p, swap q)
-
-structure PType_Tab = Table(type key = ptype val ord = ptype_ord)
-
-fun count_axiom_consts theory_relevant thy =
- let
- fun do_const const (s, T) ts =
- (* Two-dimensional table update. Constant maps to types maps to count. *)
- PType_Tab.map_default (rich_ptype thy const (s, T) ts, 0) (Integer.add 1)
- |> Symtab.map_default (s, PType_Tab.empty)
- #> fold do_term ts
- and do_term t =
- case strip_comb t of
- (Const x, ts) => do_const true x ts
- | (Free x, ts) => do_const false x ts
- | (Abs (_, _, t'), ts) => fold do_term (t' :: ts)
- | (_, ts) => fold do_term ts
- in do_term o theory_const_prop_of theory_relevant o snd end
-
-
-(**** Actual Filtering Code ****)
-
-fun pow_int x 0 = 1.0
- | pow_int x 1 = x
- | pow_int x n = if n > 0 then x * pow_int x (n - 1) else pow_int x (n + 1) / x
-
-(*The frequency of a constant is the sum of those of all instances of its type.*)
-fun pconst_freq match const_tab (c, ps) =
- PType_Tab.fold (fn (qs, m) => match (ps, qs) ? Integer.add m)
- (the (Symtab.lookup const_tab c)) 0
-
-
-(* A surprising number of theorems contain only a few significant constants.
- These include all induction rules, and other general theorems. *)
-
-(* "log" seems best in practice. A constant function of one ignores the constant
- frequencies. Rare constants give more points if they are relevant than less
- rare ones. *)
-fun rel_weight_for order freq = 1.0 + 2.0 / Math.ln (Real.fromInt freq + 1.0)
-
-(* FUDGE *)
-val worse_irrel_freq = Unsynchronized.ref 100.0
-val higher_order_irrel_weight = Unsynchronized.ref 1.05
-
-(* Irrelevant constants are treated differently. We associate lower penalties to
- very rare constants and very common ones -- the former because they can't
- lead to the inclusion of too many new facts, and the latter because they are
- so common as to be of little interest. *)
-fun irrel_weight_for order freq =
- let val (k, x) = !worse_irrel_freq |> `Real.ceil in
- (if freq < k then Math.ln (Real.fromInt (freq + 1)) / Math.ln x
- else rel_weight_for order freq / rel_weight_for order k)
- * pow_int (!higher_order_irrel_weight) (order - 1)
- end
-
-(* FUDGE *)
-val abs_rel_weight = Unsynchronized.ref 0.5
-val abs_irrel_weight = Unsynchronized.ref 2.0
-val skolem_irrel_weight = Unsynchronized.ref 0.75
-
-(* Computes a constant's weight, as determined by its frequency. *)
-fun generic_pconst_weight abs_weight skolem_weight weight_for f const_tab
- (c as (s, PType (m, _))) =
- if s = abs_name then abs_weight
- else if String.isPrefix skolem_prefix s then skolem_weight
- else weight_for m (pconst_freq (match_ptype o f) const_tab c)
-
-fun rel_pconst_weight const_tab =
- generic_pconst_weight (!abs_rel_weight) 0.0 rel_weight_for I const_tab
-fun irrel_pconst_weight const_tab =
- generic_pconst_weight (!abs_irrel_weight) (!skolem_irrel_weight)
- irrel_weight_for swap const_tab
-
-(* FUDGE *)
-val intro_bonus = Unsynchronized.ref 0.15
-val elim_bonus = Unsynchronized.ref 0.15
-val simp_bonus = Unsynchronized.ref 0.15
-val local_bonus = Unsynchronized.ref 0.55
-val chained_bonus = Unsynchronized.ref 1.5
-
-fun locality_bonus General = 0.0
- | locality_bonus Intro = !intro_bonus
- | locality_bonus Elim = !elim_bonus
- | locality_bonus Simp = !simp_bonus
- | locality_bonus Local = !local_bonus
- | locality_bonus Chained = !chained_bonus
-
-fun axiom_weight loc const_tab relevant_consts axiom_consts =
- case axiom_consts |> List.partition (pconst_hyper_mem I relevant_consts)
- ||> filter_out (pconst_hyper_mem swap relevant_consts) of
- ([], _) => 0.0
- | (rel, irrel) =>
- let
- val irrel = irrel |> filter_out (pconst_mem swap rel)
- val rel_weight =
- 0.0 |> fold (curry (op +) o rel_pconst_weight const_tab) rel
- val irrel_weight =
- ~ (locality_bonus loc)
- |> fold (curry (op +) o irrel_pconst_weight const_tab) irrel
- val res = rel_weight / (rel_weight + irrel_weight)
- in if Real.isFinite res then res else 0.0 end
-
-(* FIXME: experiment
-fun debug_axiom_weight loc const_tab relevant_consts axiom_consts =
- case axiom_consts |> List.partition (pconst_hyper_mem I relevant_consts)
- ||> filter_out (pconst_hyper_mem swap relevant_consts) of
- ([], _) => 0.0
- | (rel, irrel) =>
- let
- val irrel = irrel |> filter_out (pconst_mem swap rel)
- val rels_weight =
- 0.0 |> fold (curry (op +) o rel_pconst_weight const_tab) rel
- val irrels_weight =
- ~ (locality_bonus loc)
- |> fold (curry (op +) o irrel_pconst_weight const_tab) irrel
-val _ = tracing (PolyML.makestring ("REL: ", map (`(rel_pconst_weight const_tab)) rel))
-val _ = tracing (PolyML.makestring ("IRREL: ", map (`(irrel_pconst_weight const_tab)) irrel))
- val res = rels_weight / (rels_weight + irrels_weight)
- in if Real.isFinite res then res else 0.0 end
-*)
-
-fun pconsts_in_axiom thy t =
- Symtab.fold (fn (s, pss) => fold (cons o pair s) pss)
- (pconsts_in_terms thy true (SOME true) [t]) []
-fun pair_consts_axiom theory_relevant thy axiom =
- case axiom |> snd |> theory_const_prop_of theory_relevant
- |> pconsts_in_axiom thy of
- [] => NONE
- | consts => SOME ((axiom, consts), NONE)
-
-type annotated_thm =
- (((unit -> string) * locality) * thm) * (string * ptype) list
-
-(* FUDGE *)
-val max_imperfect = Unsynchronized.ref 11.5
-val max_imperfect_exp = Unsynchronized.ref 1.0
-
-fun take_most_relevant max_relevant remaining_max
- (candidates : (annotated_thm * real) list) =
- let
- val max_imperfect =
- Real.ceil (Math.pow (!max_imperfect,
- Math.pow (Real.fromInt remaining_max
- / Real.fromInt max_relevant, !max_imperfect_exp)))
- val (perfect, imperfect) =
- candidates |> sort (Real.compare o swap o pairself snd)
- |> take_prefix (fn (_, w) => w > 0.99999)
- val ((accepts, more_rejects), rejects) =
- chop max_imperfect imperfect |>> append perfect |>> chop remaining_max
- in
- trace_msg (fn () =>
- "Actually passed (" ^ Int.toString (length accepts) ^ " of " ^
- Int.toString (length candidates) ^ "): " ^
- (accepts |> map (fn ((((name, _), _), _), weight) =>
- name () ^ " [" ^ Real.toString weight ^ "]")
- |> commas));
- (accepts, more_rejects @ rejects)
- end
-
-fun if_empty_replace_with_locality thy axioms loc tab =
- if Symtab.is_empty tab then
- pconsts_in_terms thy false (SOME false)
- (map_filter (fn ((_, loc'), th) =>
- if loc' = loc then SOME (prop_of th) else NONE) axioms)
- else
- tab
-
-(* FUDGE *)
-val threshold_divisor = Unsynchronized.ref 2.0
-val ridiculous_threshold = Unsynchronized.ref 0.1
-
-fun relevance_filter ctxt threshold0 decay max_relevant theory_relevant
- ({add, del, ...} : relevance_override) axioms goal_ts =
- let
- val thy = ProofContext.theory_of ctxt
- val const_tab =
- fold (count_axiom_consts theory_relevant thy) axioms Symtab.empty
- val goal_const_tab =
- pconsts_in_terms thy false (SOME false) goal_ts
- |> fold (if_empty_replace_with_locality thy axioms) [Chained, Local]
- val add_thms = maps (ProofContext.get_fact ctxt) add
- val del_thms = maps (ProofContext.get_fact ctxt) del
- fun iter j remaining_max threshold rel_const_tab hopeless hopeful =
- let
- fun game_over rejects =
- (* Add "add:" facts. *)
- if null add_thms then
- []
- else
- map_filter (fn ((p as (_, th), _), _) =>
- if member Thm.eq_thm add_thms th then SOME p
- else NONE) rejects
- fun relevant [] rejects [] =
- (* Nothing has been added this iteration. *)
- if j = 0 andalso threshold >= !ridiculous_threshold then
- (* First iteration? Try again. *)
- iter 0 max_relevant (threshold / !threshold_divisor) rel_const_tab
- hopeless hopeful
- else
- game_over (rejects @ hopeless)
- | relevant candidates rejects [] =
- let
- val (accepts, more_rejects) =
- take_most_relevant max_relevant remaining_max candidates
- val rel_const_tab' =
- rel_const_tab
- |> fold (add_pconst_to_table false) (maps (snd o fst) accepts)
- fun is_dirty (c, _) =
- Symtab.lookup rel_const_tab' c <> Symtab.lookup rel_const_tab c
- val (hopeful_rejects, hopeless_rejects) =
- (rejects @ hopeless, ([], []))
- |-> fold (fn (ax as (_, consts), old_weight) =>
- if exists is_dirty consts then
- apfst (cons (ax, NONE))
- else
- apsnd (cons (ax, old_weight)))
- |>> append (more_rejects
- |> map (fn (ax as (_, consts), old_weight) =>
- (ax, if exists is_dirty consts then NONE
- else SOME old_weight)))
- val threshold =
- 1.0 - (1.0 - threshold)
- * Math.pow (decay, Real.fromInt (length accepts))
- val remaining_max = remaining_max - length accepts
- in
- trace_msg (fn () => "New or updated constants: " ^
- commas (rel_const_tab' |> Symtab.dest
- |> subtract (op =) (rel_const_tab |> Symtab.dest)
- |> map string_for_hyper_pconst));
- map (fst o fst) accepts @
- (if remaining_max = 0 then
- game_over (hopeful_rejects @ map (apsnd SOME) hopeless_rejects)
- else
- iter (j + 1) remaining_max threshold rel_const_tab'
- hopeless_rejects hopeful_rejects)
- end
- | relevant candidates rejects
- (((ax as (((_, loc), th), axiom_consts)), cached_weight)
- :: hopeful) =
- let
- val weight =
- case cached_weight of
- SOME w => w
- | NONE => axiom_weight loc const_tab rel_const_tab axiom_consts
-(* FIXME: experiment
-val name = fst (fst (fst ax)) ()
-val _ = if String.isSubstring "positive_minus" name orelse String.isSubstring "not_exp_le_zero" name then
-tracing ("*** " ^ name ^ PolyML.makestring (debug_axiom_weight loc const_tab rel_const_tab axiom_consts))
-else
-()
-*)
- in
- if weight >= threshold then
- relevant ((ax, weight) :: candidates) rejects hopeful
- else
- relevant candidates ((ax, weight) :: rejects) hopeful
- end
- in
- trace_msg (fn () =>
- "ITERATION " ^ string_of_int j ^ ": current threshold: " ^
- Real.toString threshold ^ ", constants: " ^
- commas (rel_const_tab |> Symtab.dest
- |> filter (curry (op <>) [] o snd)
- |> map string_for_hyper_pconst));
- relevant [] [] hopeful
- end
- in
- axioms |> filter_out (member Thm.eq_thm del_thms o snd)
- |> map_filter (pair_consts_axiom theory_relevant thy)
- |> iter 0 max_relevant threshold0 goal_const_tab []
- |> tap (fn res => trace_msg (fn () =>
- "Total relevant: " ^ Int.toString (length res)))
- end
-
-
-(***************************************************************)
-(* Retrieving and filtering lemmas *)
-(***************************************************************)
-
-(*** retrieve lemmas and filter them ***)
-
-(*Reject theorems with names like "List.filter.filter_list_def" or
- "Accessible_Part.acc.defs", as these are definitions arising from packages.*)
-fun is_package_def a =
- let val names = Long_Name.explode a
- in
- length names > 2 andalso
- not (hd names = "local") andalso
- String.isSuffix "_def" a orelse String.isSuffix "_defs" a
- end;
-
-fun mk_fact_table f xs =
- fold (Termtab.update o `(prop_of o f)) xs Termtab.empty
-fun uniquify xs = Termtab.fold (cons o snd) (mk_fact_table snd xs) []
-
-(* FIXME: put other record thms here, or declare as "no_atp" *)
-val multi_base_blacklist =
- ["defs", "select_defs", "update_defs", "induct", "inducts", "split", "splits",
- "split_asm", "cases", "ext_cases", "eq.simps", "eq.refl", "nchotomy",
- "case_cong", "weak_case_cong"]
- |> map (prefix ".")
-
-val max_lambda_nesting = 3
-
-fun term_has_too_many_lambdas max (t1 $ t2) =
- exists (term_has_too_many_lambdas max) [t1, t2]
- | term_has_too_many_lambdas max (Abs (_, _, t)) =
- max = 0 orelse term_has_too_many_lambdas (max - 1) t
- | term_has_too_many_lambdas _ _ = false
-
-(* Don't count nested lambdas at the level of formulas, since they are
- quantifiers. *)
-fun formula_has_too_many_lambdas Ts (Abs (_, T, t)) =
- formula_has_too_many_lambdas (T :: Ts) t
- | formula_has_too_many_lambdas Ts t =
- if is_formula_type (fastype_of1 (Ts, t)) then
- exists (formula_has_too_many_lambdas Ts) (#2 (strip_comb t))
- else
- term_has_too_many_lambdas max_lambda_nesting t
-
-(* The max apply depth of any "metis" call in "Metis_Examples" (on 2007-10-31)
- was 11. *)
-val max_apply_depth = 15
-
-fun apply_depth (f $ t) = Int.max (apply_depth f, apply_depth t + 1)
- | apply_depth (Abs (_, _, t)) = apply_depth t
- | apply_depth _ = 0
-
-fun is_formula_too_complex t =
- apply_depth t > max_apply_depth orelse formula_has_too_many_lambdas [] t
-
-val exists_sledgehammer_const =
- exists_Const (fn (s, _) => String.isPrefix sledgehammer_prefix s)
-
-(* FIXME: make more reliable *)
-val exists_low_level_class_const =
- exists_Const (fn (s, _) =>
- String.isSubstring (Long_Name.separator ^ "class" ^ Long_Name.separator) s)
-
-fun is_metastrange_theorem th =
- case head_of (concl_of th) of
- Const (a, _) => (a <> @{const_name Trueprop} andalso
- a <> @{const_name "=="})
- | _ => false
-
-fun is_that_fact th =
- String.isSuffix (Long_Name.separator ^ Obtain.thatN) (Thm.get_name_hint th)
- andalso exists_subterm (fn Free (s, _) => s = Name.skolem Auto_Bind.thesisN
- | _ => false) (prop_of th)
-
-val type_has_top_sort =
- exists_subtype (fn TFree (_, []) => true | TVar (_, []) => true | _ => false)
-
-(**** Predicates to detect unwanted facts (prolific or likely to cause
- unsoundness) ****)
-
-(* Too general means, positive equality literal with a variable X as one
- operand, when X does not occur properly in the other operand. This rules out
- clearly inconsistent facts such as X = a | X = b, though it by no means
- guarantees soundness. *)
-
-(* Unwanted equalities are those between a (bound or schematic) variable that
- does not properly occur in the second operand. *)
-val is_exhaustive_finite =
- let
- fun is_bad_equal (Var z) t =
- not (exists_subterm (fn Var z' => z = z' | _ => false) t)
- | is_bad_equal (Bound j) t = not (loose_bvar1 (t, j))
- | is_bad_equal _ _ = false
- fun do_equals t1 t2 = is_bad_equal t1 t2 orelse is_bad_equal t2 t1
- fun do_formula pos t =
- case (pos, t) of
- (_, @{const Trueprop} $ t1) => do_formula pos t1
- | (true, Const (@{const_name all}, _) $ Abs (_, _, t')) =>
- do_formula pos t'
- | (true, Const (@{const_name All}, _) $ Abs (_, _, t')) =>
- do_formula pos t'
- | (false, Const (@{const_name Ex}, _) $ Abs (_, _, t')) =>
- do_formula pos t'
- | (_, @{const "==>"} $ t1 $ t2) =>
- do_formula (not pos) t1 andalso
- (t2 = @{prop False} orelse do_formula pos t2)
- | (_, @{const HOL.implies} $ t1 $ t2) =>
- do_formula (not pos) t1 andalso
- (t2 = @{const False} orelse do_formula pos t2)
- | (_, @{const Not} $ t1) => do_formula (not pos) t1
- | (true, @{const HOL.disj} $ t1 $ t2) => forall (do_formula pos) [t1, t2]
- | (false, @{const HOL.conj} $ t1 $ t2) => forall (do_formula pos) [t1, t2]
- | (true, Const (@{const_name HOL.eq}, _) $ t1 $ t2) => do_equals t1 t2
- | (true, Const (@{const_name "=="}, _) $ t1 $ t2) => do_equals t1 t2
- | _ => false
- in do_formula true end
-
-fun has_bound_or_var_of_type tycons =
- exists_subterm (fn Var (_, Type (s, _)) => member (op =) tycons s
- | Abs (_, Type (s, _), _) => member (op =) tycons s
- | _ => false)
-
-(* Facts are forbidden to contain variables of these types. The typical reason
- is that they lead to unsoundness. Note that "unit" satisfies numerous
- equations like "?x = ()". The resulting clauses will have no type constraint,
- yielding false proofs. Even "bool" leads to many unsound proofs, though only
- for higher-order problems. *)
-val dangerous_types = [@{type_name unit}, @{type_name bool}, @{type_name prop}];
-
-(* Facts containing variables of type "unit" or "bool" or of the form
- "ALL x. x = A | x = B | x = C" are likely to lead to unsound proofs if types
- are omitted. *)
-fun is_dangerous_term full_types t =
- not full_types andalso
- let val t = transform_elim_term t in
- has_bound_or_var_of_type dangerous_types t orelse
- is_exhaustive_finite t
- end
-
-fun is_theorem_bad_for_atps full_types thm =
- let val t = prop_of thm in
- is_formula_too_complex t orelse exists_type type_has_top_sort t orelse
- is_dangerous_term full_types t orelse exists_sledgehammer_const t orelse
- exists_low_level_class_const t orelse is_metastrange_theorem thm orelse
- is_that_fact thm
- end
-
-fun clasimpset_rules_of ctxt =
- let
- val {safeIs, safeEs, hazIs, hazEs, ...} = ctxt |> claset_of |> rep_cs
- val intros = safeIs @ hazIs
- val elims = map Classical.classical_rule (safeEs @ hazEs)
- val simps = ctxt |> simpset_of |> dest_ss |> #simps |> map snd
- in (mk_fact_table I intros, mk_fact_table I elims, mk_fact_table I simps) end
-
-fun all_name_thms_pairs ctxt reserved full_types add_thms chained_ths =
- let
- val thy = ProofContext.theory_of ctxt
- val global_facts = PureThy.facts_of thy
- val local_facts = ProofContext.facts_of ctxt
- val named_locals = local_facts |> Facts.dest_static []
- val is_chained = member Thm.eq_thm chained_ths
- val (intros, elims, simps) =
- if exists (curry (op <) 0.0) [!intro_bonus, !elim_bonus, !simp_bonus] then
- clasimpset_rules_of ctxt
- else
- (Termtab.empty, Termtab.empty, Termtab.empty)
- (* Unnamed nonchained formulas with schematic variables are omitted, because
- they are rejected by the backticks (`...`) parser for some reason. *)
- fun is_good_unnamed_local th =
- not (Thm.has_name_hint th) andalso
- (not (exists_subterm is_Var (prop_of th)) orelse (is_chained th)) andalso
- forall (fn (_, ths) => not (member Thm.eq_thm ths th)) named_locals
- val unnamed_locals =
- union Thm.eq_thm (Facts.props local_facts) chained_ths
- |> filter is_good_unnamed_local |> map (pair "" o single)
- val full_space =
- Name_Space.merge (Facts.space_of global_facts, Facts.space_of local_facts)
- fun add_facts global foldx facts =
- foldx (fn (name0, ths) =>
- if name0 <> "" andalso
- forall (not o member Thm.eq_thm add_thms) ths andalso
- (Facts.is_concealed facts name0 orelse
- (respect_no_atp andalso is_package_def name0) orelse
- exists (fn s => String.isSuffix s name0) multi_base_blacklist orelse
- String.isSuffix "_def_raw" (* FIXME: crude hack *) name0) then
- I
- else
- let
- val multi = length ths > 1
- fun backquotify th =
- "`" ^ Print_Mode.setmp [Print_Mode.input]
- (Syntax.string_of_term ctxt) (prop_of th) ^ "`"
- |> String.translate (fn c => if Char.isPrint c then str c else "")
- |> simplify_spaces
- fun check_thms a =
- case try (ProofContext.get_thms ctxt) a of
- NONE => false
- | SOME ths' => Thm.eq_thms (ths, ths')
- in
- pair 1
- #> fold (fn th => fn (j, rest) =>
- (j + 1,
- if is_theorem_bad_for_atps full_types th andalso
- not (member Thm.eq_thm add_thms th) then
- rest
- else
- (((fn () =>
- if name0 = "" then
- th |> backquotify
- else
- let
- val name1 = Facts.extern facts name0
- val name2 = Name_Space.extern full_space name0
- in
- case find_first check_thms [name1, name2, name0] of
- SOME name => repair_name reserved multi j name
- | NONE => ""
- end),
- let val t = prop_of th in
- if is_chained th then Chained
- else if not global then Local
- else if Termtab.defined intros t then Intro
- else if Termtab.defined elims t then Elim
- else if Termtab.defined simps t then Simp
- else General
- end),
- (multi, th)) :: rest)) ths
- #> snd
- end)
- in
- [] |> add_facts false fold local_facts (unnamed_locals @ named_locals)
- |> add_facts true Facts.fold_static global_facts global_facts
- end
-
-(* The single-name theorems go after the multiple-name ones, so that single
- names are preferred when both are available. *)
-fun name_thm_pairs ctxt respect_no_atp =
- List.partition (fst o snd) #> op @ #> map (apsnd snd)
- #> respect_no_atp ? filter_out (No_ATPs.member ctxt o snd)
-
-(***************************************************************)
-(* ATP invocation methods setup *)
-(***************************************************************)
-
-fun relevant_facts ctxt full_types (threshold0, threshold1) max_relevant
- theory_relevant (relevance_override as {add, del, only})
- chained_ths hyp_ts concl_t =
- let
- val decay = Math.pow ((1.0 - threshold1) / (1.0 - threshold0),
- 1.0 / Real.fromInt (max_relevant + 1))
- val add_thms = maps (ProofContext.get_fact ctxt) add
- val reserved = reserved_isar_keyword_table ()
- val axioms =
- (if only then
- maps (map (fn ((name, loc), th) => ((K name, loc), (true, th)))
- o name_thm_pairs_from_ref ctxt reserved chained_ths) add
- else
- all_name_thms_pairs ctxt reserved full_types add_thms chained_ths)
- |> name_thm_pairs ctxt (respect_no_atp andalso not only)
- |> uniquify
- in
- trace_msg (fn () => "Considering " ^ Int.toString (length axioms) ^
- " theorems");
- (if threshold0 > 1.0 orelse threshold0 > threshold1 then
- []
- else if threshold0 < 0.0 then
- axioms
- else
- relevance_filter ctxt threshold0 decay max_relevant theory_relevant
- relevance_override axioms (concl_t :: hyp_ts))
- |> map (apfst (apfst (fn f => f ())))
- end
-
-end;
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_fact_minimize.ML Tue Aug 31 23:43:23 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,162 +0,0 @@
-(* Title: HOL/Tools/Sledgehammer/sledgehammer_fact_minimize.ML
- Author: Philipp Meyer, TU Muenchen
- Author: Jasmin Blanchette, TU Muenchen
-
-Minimization of theorem list for Metis using automatic theorem provers.
-*)
-
-signature SLEDGEHAMMER_FACT_MINIMIZE =
-sig
- type locality = Sledgehammer_Fact_Filter.locality
- type params = Sledgehammer.params
-
- val minimize_theorems :
- params -> int -> int -> Proof.state -> ((string * locality) * thm list) list
- -> ((string * locality) * thm list) list option * string
- val run_minimize : params -> int -> Facts.ref list -> Proof.state -> unit
-end;
-
-structure Sledgehammer_Fact_Minimize : SLEDGEHAMMER_FACT_MINIMIZE =
-struct
-
-open ATP_Systems
-open Sledgehammer_Util
-open Sledgehammer_Fact_Filter
-open Sledgehammer_Proof_Reconstruct
-open Sledgehammer
-
-(* wrapper for calling external prover *)
-
-fun string_for_failure Unprovable = "Unprovable."
- | string_for_failure TimedOut = "Timed out."
- | string_for_failure _ = "Unknown error."
-
-fun n_theorems names =
- let val n = length names in
- string_of_int n ^ " theorem" ^ plural_s n ^
- (if n > 0 then
- ": " ^ (names |> map fst
- |> sort_distinct string_ord |> space_implode " ")
- else
- "")
- end
-
-fun test_theorems ({debug, verbose, overlord, atps, full_types, isar_proof,
- isar_shrink_factor, ...} : params)
- (prover : prover) explicit_apply timeout subgoal state
- axioms =
- let
- val _ =
- priority ("Testing " ^ n_theorems (map fst axioms) ^ "...")
- val params =
- {blocking = true, debug = debug, verbose = verbose, overlord = overlord,
- atps = atps, full_types = full_types, explicit_apply = explicit_apply,
- relevance_thresholds = (1.01, 1.01), max_relevant = NONE,
- theory_relevant = NONE, isar_proof = isar_proof,
- isar_shrink_factor = isar_shrink_factor, timeout = timeout, expect = ""}
- val axioms = maps (fn (n, ths) => map (pair n) ths) axioms
- val {context = ctxt, facts, goal} = Proof.goal state
- val problem =
- {subgoal = subgoal, goal = (ctxt, (facts, goal)),
- relevance_override = {add = [], del = [], only = false},
- axioms = SOME axioms}
- val result as {outcome, used_thm_names, ...} = prover params (K "") problem
- in
- priority (case outcome of
- NONE =>
- if length used_thm_names = length axioms then
- "Found proof."
- else
- "Found proof with " ^ n_theorems used_thm_names ^ "."
- | SOME failure => string_for_failure failure);
- result
- end
-
-(* minimalization of thms *)
-
-fun filter_used_facts used = filter (member (op =) used o fst)
-
-fun sublinear_minimize _ [] p = p
- | sublinear_minimize test (x :: xs) (seen, result) =
- case test (xs @ seen) of
- result as {outcome = NONE, proof, used_thm_names, ...} : prover_result =>
- sublinear_minimize test (filter_used_facts used_thm_names xs)
- (filter_used_facts used_thm_names seen, result)
- | _ => sublinear_minimize test xs (x :: seen, result)
-
-(* Give the ATP some slack. The ATP gets further slack because the Sledgehammer
- preprocessing time is included in the estimate below but isn't part of the
- timeout. *)
-val fudge_msecs = 1000
-
-fun minimize_theorems {atps = [], ...} _ _ _ _ = error "No ATP is set."
- | minimize_theorems (params as {debug, atps = atp :: _, full_types,
- isar_proof, isar_shrink_factor, timeout, ...})
- i n state axioms =
- let
- val thy = Proof.theory_of state
- val prover = get_prover_fun thy atp
- val msecs = Time.toMilliseconds timeout
- val _ = priority ("Sledgehammer minimize: ATP " ^ quote atp ^ ".")
- val {context = ctxt, goal, ...} = Proof.goal state
- val (_, hyp_ts, concl_t) = strip_subgoal goal i
- val explicit_apply =
- not (forall (Meson.is_fol_term thy)
- (concl_t :: hyp_ts @ maps (map prop_of o snd) axioms))
- fun do_test timeout =
- test_theorems params prover explicit_apply timeout i state
- val timer = Timer.startRealTimer ()
- in
- (case do_test timeout axioms of
- result as {outcome = NONE, pool, used_thm_names,
- conjecture_shape, ...} =>
- let
- val time = Timer.checkRealTimer timer
- val new_timeout =
- Int.min (msecs, Time.toMilliseconds time + fudge_msecs)
- |> Time.fromMilliseconds
- val (min_thms, {proof, axiom_names, ...}) =
- sublinear_minimize (do_test new_timeout)
- (filter_used_facts used_thm_names axioms) ([], result)
- val n = length min_thms
- val _ = priority (cat_lines
- ["Minimized: " ^ string_of_int n ^ " theorem" ^ plural_s n] ^
- (case length (filter (curry (op =) Chained o snd o fst) min_thms) of
- 0 => ""
- | n => " (including " ^ Int.toString n ^ " chained)") ^ ".")
- in
- (SOME min_thms,
- proof_text isar_proof
- (pool, debug, isar_shrink_factor, ctxt, conjecture_shape)
- (full_types, K "", proof, axiom_names, goal, i) |> fst)
- end
- | {outcome = SOME TimedOut, ...} =>
- (NONE, "Timeout: You can increase the time limit using the \"timeout\" \
- \option (e.g., \"timeout = " ^
- string_of_int (10 + msecs div 1000) ^ " s\").")
- | {outcome = SOME UnknownError, ...} =>
- (* Failure sometimes mean timeout, unfortunately. *)
- (NONE, "Failure: No proof was found with the current time limit. You \
- \can increase the time limit using the \"timeout\" \
- \option (e.g., \"timeout = " ^
- string_of_int (10 + msecs div 1000) ^ " s\").")
- | {message, ...} => (NONE, "ATP error: " ^ message))
- handle ERROR msg => (NONE, "Error: " ^ msg)
- end
-
-fun run_minimize params i refs state =
- let
- val ctxt = Proof.context_of state
- val reserved = reserved_isar_keyword_table ()
- val chained_ths = #facts (Proof.goal state)
- val axioms =
- maps (map (apsnd single)
- o name_thm_pairs_from_ref ctxt reserved chained_ths) refs
- in
- case subgoal_count state of
- 0 => priority "No subgoal!"
- | n =>
- (kill_atps (); priority (#2 (minimize_theorems params i n state axioms)))
- end
-
-end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_filter.ML Tue Aug 31 23:46:23 2010 +0200
@@ -0,0 +1,800 @@
+(* Title: HOL/Tools/Sledgehammer/sledgehammer_fact_filter.ML
+ Author: Jia Meng, Cambridge University Computer Laboratory and NICTA
+ Author: Jasmin Blanchette, TU Muenchen
+*)
+
+signature SLEDGEHAMMER_FACT_FILTER =
+sig
+ datatype locality = General | Intro | Elim | Simp | Local | Chained
+
+ type relevance_override =
+ {add: Facts.ref list,
+ del: Facts.ref list,
+ only: bool}
+
+ val trace : bool Unsynchronized.ref
+ val worse_irrel_freq : real Unsynchronized.ref
+ val higher_order_irrel_weight : real Unsynchronized.ref
+ val abs_rel_weight : real Unsynchronized.ref
+ val abs_irrel_weight : real Unsynchronized.ref
+ val skolem_irrel_weight : real Unsynchronized.ref
+ val intro_bonus : real Unsynchronized.ref
+ val elim_bonus : real Unsynchronized.ref
+ val simp_bonus : real Unsynchronized.ref
+ val local_bonus : real Unsynchronized.ref
+ val chained_bonus : real Unsynchronized.ref
+ val max_imperfect : real Unsynchronized.ref
+ val max_imperfect_exp : real Unsynchronized.ref
+ val threshold_divisor : real Unsynchronized.ref
+ val ridiculous_threshold : real Unsynchronized.ref
+ val name_thm_pairs_from_ref :
+ Proof.context -> unit Symtab.table -> thm list -> Facts.ref
+ -> ((string * locality) * thm) list
+ val relevant_facts :
+ Proof.context -> bool -> real * real -> int -> bool -> relevance_override
+ -> thm list -> term list -> term -> ((string * locality) * thm) list
+end;
+
+structure Sledgehammer_Fact_Filter : SLEDGEHAMMER_FACT_FILTER =
+struct
+
+open Sledgehammer_Util
+
+val trace = Unsynchronized.ref false
+fun trace_msg msg = if !trace then tracing (msg ()) else ()
+
+(* experimental feature *)
+val term_patterns = false
+
+val respect_no_atp = true
+
+datatype locality = General | Intro | Elim | Simp | Local | Chained
+
+type relevance_override =
+ {add: Facts.ref list,
+ del: Facts.ref list,
+ only: bool}
+
+val sledgehammer_prefix = "Sledgehammer" ^ Long_Name.separator
+
+fun repair_name reserved multi j name =
+ (name |> Symtab.defined reserved name ? quote) ^
+ (if multi then "(" ^ Int.toString j ^ ")" else "")
+
+fun name_thm_pairs_from_ref ctxt reserved chained_ths xref =
+ let
+ val ths = ProofContext.get_fact ctxt xref
+ val name = Facts.string_of_ref xref
+ val multi = length ths > 1
+ in
+ (ths, (1, []))
+ |-> fold (fn th => fn (j, rest) =>
+ (j + 1, ((repair_name reserved multi j name,
+ if member Thm.eq_thm chained_ths th then Chained
+ else General), th) :: rest))
+ |> snd
+ end
+
+(***************************************************************)
+(* Relevance Filtering *)
+(***************************************************************)
+
+(*** constants with types ***)
+
+fun order_of_type (Type (@{type_name fun}, [T1, @{typ bool}])) =
+ order_of_type T1 (* cheat: pretend sets are first-order *)
+ | order_of_type (Type (@{type_name fun}, [T1, T2])) =
+ Int.max (order_of_type T1 + 1, order_of_type T2)
+ | order_of_type (Type (_, Ts)) = fold (Integer.max o order_of_type) Ts 0
+ | order_of_type _ = 0
+
+(* An abstraction of Isabelle types and first-order terms *)
+datatype pattern = PVar | PApp of string * pattern list
+datatype ptype = PType of int * pattern list
+
+fun string_for_pattern PVar = "_"
+ | string_for_pattern (PApp (s, ps)) =
+ if null ps then s else s ^ string_for_patterns ps
+and string_for_patterns ps = "(" ^ commas (map string_for_pattern ps) ^ ")"
+fun string_for_ptype (PType (_, ps)) = string_for_patterns ps
+
+(*Is the second type an instance of the first one?*)
+fun match_pattern (PVar, _) = true
+ | match_pattern (PApp _, PVar) = false
+ | match_pattern (PApp (s, ps), PApp (t, qs)) =
+ s = t andalso match_patterns (ps, qs)
+and match_patterns (_, []) = true
+ | match_patterns ([], _) = false
+ | match_patterns (p :: ps, q :: qs) =
+ match_pattern (p, q) andalso match_patterns (ps, qs)
+fun match_ptype (PType (_, ps), PType (_, qs)) = match_patterns (ps, qs)
+
+(* Is there a unifiable constant? *)
+fun pconst_mem f consts (s, ps) =
+ exists (curry (match_ptype o f) ps)
+ (map snd (filter (curry (op =) s o fst) consts))
+fun pconst_hyper_mem f const_tab (s, ps) =
+ exists (curry (match_ptype o f) ps) (these (Symtab.lookup const_tab s))
+
+fun pattern_for_type (Type (s, Ts)) = PApp (s, map pattern_for_type Ts)
+ | pattern_for_type (TFree (s, _)) = PApp (s, [])
+ | pattern_for_type (TVar _) = PVar
+
+fun pterm thy t =
+ case strip_comb t of
+ (Const x, ts) => PApp (pconst thy true x ts)
+ | (Free x, ts) => PApp (pconst thy false x ts)
+ | (Var x, []) => PVar
+ | _ => PApp ("?", []) (* equivalence class of higher-order constructs *)
+(* Pairs a constant with the list of its type instantiations. *)
+and ptype thy const x ts =
+ (if const then map pattern_for_type (these (try (Sign.const_typargs thy) x))
+ else []) @
+ (if term_patterns then map (pterm thy) ts else [])
+and pconst thy const (s, T) ts = (s, ptype thy const (s, T) ts)
+and rich_ptype thy const (s, T) ts =
+ PType (order_of_type T, ptype thy const (s, T) ts)
+and rich_pconst thy const (s, T) ts = (s, rich_ptype thy const (s, T) ts)
+
+fun string_for_hyper_pconst (s, ps) =
+ s ^ "{" ^ commas (map string_for_ptype ps) ^ "}"
+
+val abs_name = "Sledgehammer.abs"
+val skolem_prefix = "Sledgehammer.sko"
+
+(* These are typically simplified away by "Meson.presimplify". Equality is
+ handled specially via "fequal". *)
+val boring_consts =
+ [@{const_name False}, @{const_name True}, @{const_name If}, @{const_name Let},
+ @{const_name HOL.eq}]
+
+(* Add a pconstant to the table, but a [] entry means a standard
+ connective, which we ignore.*)
+fun add_pconst_to_table also_skolem (c, p) =
+ if member (op =) boring_consts c orelse
+ (not also_skolem andalso String.isPrefix skolem_prefix c) then
+ I
+ else
+ Symtab.map_default (c, [p]) (insert (op =) p)
+
+fun is_formula_type T = (T = HOLogic.boolT orelse T = propT)
+
+fun pconsts_in_terms thy also_skolems pos ts =
+ let
+ val flip = Option.map not
+ (* We include free variables, as well as constants, to handle locales. For
+ each quantifiers that must necessarily be skolemized by the ATP, we
+ introduce a fresh constant to simulate the effect of Skolemization. *)
+ fun do_const const (s, T) ts =
+ add_pconst_to_table also_skolems (rich_pconst thy const (s, T) ts)
+ #> fold do_term ts
+ and do_term t =
+ case strip_comb t of
+ (Const x, ts) => do_const true x ts
+ | (Free x, ts) => do_const false x ts
+ | (Abs (_, T, t'), ts) =>
+ (null ts
+ ? add_pconst_to_table true (abs_name, PType (order_of_type T + 1, [])))
+ #> fold do_term (t' :: ts)
+ | (_, ts) => fold do_term ts
+ fun do_quantifier will_surely_be_skolemized abs_T body_t =
+ do_formula pos body_t
+ #> (if also_skolems andalso will_surely_be_skolemized then
+ add_pconst_to_table true
+ (gensym skolem_prefix, PType (order_of_type abs_T, []))
+ else
+ I)
+ and do_term_or_formula T =
+ if is_formula_type T then do_formula NONE else do_term
+ and do_formula pos t =
+ case t of
+ Const (@{const_name all}, _) $ Abs (_, T, t') =>
+ do_quantifier (pos = SOME false) T t'
+ | @{const "==>"} $ t1 $ t2 =>
+ do_formula (flip pos) t1 #> do_formula pos t2
+ | Const (@{const_name "=="}, Type (_, [T, _])) $ t1 $ t2 =>
+ fold (do_term_or_formula T) [t1, t2]
+ | @{const Trueprop} $ t1 => do_formula pos t1
+ | @{const Not} $ t1 => do_formula (flip pos) t1
+ | Const (@{const_name All}, _) $ Abs (_, T, t') =>
+ do_quantifier (pos = SOME false) T t'
+ | Const (@{const_name Ex}, _) $ Abs (_, T, t') =>
+ do_quantifier (pos = SOME true) T t'
+ | @{const HOL.conj} $ t1 $ t2 => fold (do_formula pos) [t1, t2]
+ | @{const HOL.disj} $ t1 $ t2 => fold (do_formula pos) [t1, t2]
+ | @{const HOL.implies} $ t1 $ t2 =>
+ do_formula (flip pos) t1 #> do_formula pos t2
+ | Const (@{const_name HOL.eq}, Type (_, [T, _])) $ t1 $ t2 =>
+ fold (do_term_or_formula T) [t1, t2]
+ | Const (@{const_name If}, Type (_, [_, Type (_, [T, _])]))
+ $ t1 $ t2 $ t3 =>
+ do_formula NONE t1 #> fold (do_term_or_formula T) [t2, t3]
+ | Const (@{const_name Ex1}, _) $ Abs (_, T, t') =>
+ do_quantifier (is_some pos) T t'
+ | Const (@{const_name Ball}, _) $ t1 $ Abs (_, T, t') =>
+ do_quantifier (pos = SOME false) T
+ (HOLogic.mk_imp (incr_boundvars 1 t1 $ Bound 0, t'))
+ | Const (@{const_name Bex}, _) $ t1 $ Abs (_, T, t') =>
+ do_quantifier (pos = SOME true) T
+ (HOLogic.mk_conj (incr_boundvars 1 t1 $ Bound 0, t'))
+ | (t0 as Const (_, @{typ bool})) $ t1 =>
+ do_term t0 #> do_formula pos t1 (* theory constant *)
+ | _ => do_term t
+ in Symtab.empty |> fold (do_formula pos) ts end
+
+(*Inserts a dummy "constant" referring to the theory name, so that relevance
+ takes the given theory into account.*)
+fun theory_const_prop_of theory_relevant th =
+ if theory_relevant then
+ let
+ val name = Context.theory_name (theory_of_thm th)
+ val t = Const (name ^ ". 1", @{typ bool})
+ in t $ prop_of th end
+ else
+ prop_of th
+
+(**** Constant / Type Frequencies ****)
+
+(* A two-dimensional symbol table counts frequencies of constants. It's keyed
+ first by constant name and second by its list of type instantiations. For the
+ latter, we need a linear ordering on "pattern list". *)
+
+fun pattern_ord p =
+ case p of
+ (PVar, PVar) => EQUAL
+ | (PVar, PApp _) => LESS
+ | (PApp _, PVar) => GREATER
+ | (PApp q1, PApp q2) =>
+ prod_ord fast_string_ord (dict_ord pattern_ord) (q1, q2)
+fun ptype_ord (PType p, PType q) =
+ prod_ord (dict_ord pattern_ord) int_ord (swap p, swap q)
+
+structure PType_Tab = Table(type key = ptype val ord = ptype_ord)
+
+fun count_axiom_consts theory_relevant thy =
+ let
+ fun do_const const (s, T) ts =
+ (* Two-dimensional table update. Constant maps to types maps to count. *)
+ PType_Tab.map_default (rich_ptype thy const (s, T) ts, 0) (Integer.add 1)
+ |> Symtab.map_default (s, PType_Tab.empty)
+ #> fold do_term ts
+ and do_term t =
+ case strip_comb t of
+ (Const x, ts) => do_const true x ts
+ | (Free x, ts) => do_const false x ts
+ | (Abs (_, _, t'), ts) => fold do_term (t' :: ts)
+ | (_, ts) => fold do_term ts
+ in do_term o theory_const_prop_of theory_relevant o snd end
+
+
+(**** Actual Filtering Code ****)
+
+fun pow_int x 0 = 1.0
+ | pow_int x 1 = x
+ | pow_int x n = if n > 0 then x * pow_int x (n - 1) else pow_int x (n + 1) / x
+
+(*The frequency of a constant is the sum of those of all instances of its type.*)
+fun pconst_freq match const_tab (c, ps) =
+ PType_Tab.fold (fn (qs, m) => match (ps, qs) ? Integer.add m)
+ (the (Symtab.lookup const_tab c)) 0
+
+
+(* A surprising number of theorems contain only a few significant constants.
+ These include all induction rules, and other general theorems. *)
+
+(* "log" seems best in practice. A constant function of one ignores the constant
+ frequencies. Rare constants give more points if they are relevant than less
+ rare ones. *)
+fun rel_weight_for order freq = 1.0 + 2.0 / Math.ln (Real.fromInt freq + 1.0)
+
+(* FUDGE *)
+val worse_irrel_freq = Unsynchronized.ref 100.0
+val higher_order_irrel_weight = Unsynchronized.ref 1.05
+
+(* Irrelevant constants are treated differently. We associate lower penalties to
+ very rare constants and very common ones -- the former because they can't
+ lead to the inclusion of too many new facts, and the latter because they are
+ so common as to be of little interest. *)
+fun irrel_weight_for order freq =
+ let val (k, x) = !worse_irrel_freq |> `Real.ceil in
+ (if freq < k then Math.ln (Real.fromInt (freq + 1)) / Math.ln x
+ else rel_weight_for order freq / rel_weight_for order k)
+ * pow_int (!higher_order_irrel_weight) (order - 1)
+ end
+
+(* FUDGE *)
+val abs_rel_weight = Unsynchronized.ref 0.5
+val abs_irrel_weight = Unsynchronized.ref 2.0
+val skolem_irrel_weight = Unsynchronized.ref 0.75
+
+(* Computes a constant's weight, as determined by its frequency. *)
+fun generic_pconst_weight abs_weight skolem_weight weight_for f const_tab
+ (c as (s, PType (m, _))) =
+ if s = abs_name then abs_weight
+ else if String.isPrefix skolem_prefix s then skolem_weight
+ else weight_for m (pconst_freq (match_ptype o f) const_tab c)
+
+fun rel_pconst_weight const_tab =
+ generic_pconst_weight (!abs_rel_weight) 0.0 rel_weight_for I const_tab
+fun irrel_pconst_weight const_tab =
+ generic_pconst_weight (!abs_irrel_weight) (!skolem_irrel_weight)
+ irrel_weight_for swap const_tab
+
+(* FUDGE *)
+val intro_bonus = Unsynchronized.ref 0.15
+val elim_bonus = Unsynchronized.ref 0.15
+val simp_bonus = Unsynchronized.ref 0.15
+val local_bonus = Unsynchronized.ref 0.55
+val chained_bonus = Unsynchronized.ref 1.5
+
+fun locality_bonus General = 0.0
+ | locality_bonus Intro = !intro_bonus
+ | locality_bonus Elim = !elim_bonus
+ | locality_bonus Simp = !simp_bonus
+ | locality_bonus Local = !local_bonus
+ | locality_bonus Chained = !chained_bonus
+
+fun axiom_weight loc const_tab relevant_consts axiom_consts =
+ case axiom_consts |> List.partition (pconst_hyper_mem I relevant_consts)
+ ||> filter_out (pconst_hyper_mem swap relevant_consts) of
+ ([], _) => 0.0
+ | (rel, irrel) =>
+ let
+ val irrel = irrel |> filter_out (pconst_mem swap rel)
+ val rel_weight =
+ 0.0 |> fold (curry (op +) o rel_pconst_weight const_tab) rel
+ val irrel_weight =
+ ~ (locality_bonus loc)
+ |> fold (curry (op +) o irrel_pconst_weight const_tab) irrel
+ val res = rel_weight / (rel_weight + irrel_weight)
+ in if Real.isFinite res then res else 0.0 end
+
+(* FIXME: experiment
+fun debug_axiom_weight loc const_tab relevant_consts axiom_consts =
+ case axiom_consts |> List.partition (pconst_hyper_mem I relevant_consts)
+ ||> filter_out (pconst_hyper_mem swap relevant_consts) of
+ ([], _) => 0.0
+ | (rel, irrel) =>
+ let
+ val irrel = irrel |> filter_out (pconst_mem swap rel)
+ val rels_weight =
+ 0.0 |> fold (curry (op +) o rel_pconst_weight const_tab) rel
+ val irrels_weight =
+ ~ (locality_bonus loc)
+ |> fold (curry (op +) o irrel_pconst_weight const_tab) irrel
+val _ = tracing (PolyML.makestring ("REL: ", map (`(rel_pconst_weight const_tab)) rel))
+val _ = tracing (PolyML.makestring ("IRREL: ", map (`(irrel_pconst_weight const_tab)) irrel))
+ val res = rels_weight / (rels_weight + irrels_weight)
+ in if Real.isFinite res then res else 0.0 end
+*)
+
+fun pconsts_in_axiom thy t =
+ Symtab.fold (fn (s, pss) => fold (cons o pair s) pss)
+ (pconsts_in_terms thy true (SOME true) [t]) []
+fun pair_consts_axiom theory_relevant thy axiom =
+ case axiom |> snd |> theory_const_prop_of theory_relevant
+ |> pconsts_in_axiom thy of
+ [] => NONE
+ | consts => SOME ((axiom, consts), NONE)
+
+type annotated_thm =
+ (((unit -> string) * locality) * thm) * (string * ptype) list
+
+(* FUDGE *)
+val max_imperfect = Unsynchronized.ref 11.5
+val max_imperfect_exp = Unsynchronized.ref 1.0
+
+fun take_most_relevant max_relevant remaining_max
+ (candidates : (annotated_thm * real) list) =
+ let
+ val max_imperfect =
+ Real.ceil (Math.pow (!max_imperfect,
+ Math.pow (Real.fromInt remaining_max
+ / Real.fromInt max_relevant, !max_imperfect_exp)))
+ val (perfect, imperfect) =
+ candidates |> sort (Real.compare o swap o pairself snd)
+ |> take_prefix (fn (_, w) => w > 0.99999)
+ val ((accepts, more_rejects), rejects) =
+ chop max_imperfect imperfect |>> append perfect |>> chop remaining_max
+ in
+ trace_msg (fn () =>
+ "Actually passed (" ^ Int.toString (length accepts) ^ " of " ^
+ Int.toString (length candidates) ^ "): " ^
+ (accepts |> map (fn ((((name, _), _), _), weight) =>
+ name () ^ " [" ^ Real.toString weight ^ "]")
+ |> commas));
+ (accepts, more_rejects @ rejects)
+ end
+
+fun if_empty_replace_with_locality thy axioms loc tab =
+ if Symtab.is_empty tab then
+ pconsts_in_terms thy false (SOME false)
+ (map_filter (fn ((_, loc'), th) =>
+ if loc' = loc then SOME (prop_of th) else NONE) axioms)
+ else
+ tab
+
+(* FUDGE *)
+val threshold_divisor = Unsynchronized.ref 2.0
+val ridiculous_threshold = Unsynchronized.ref 0.1
+
+fun relevance_filter ctxt threshold0 decay max_relevant theory_relevant
+ ({add, del, ...} : relevance_override) axioms goal_ts =
+ let
+ val thy = ProofContext.theory_of ctxt
+ val const_tab =
+ fold (count_axiom_consts theory_relevant thy) axioms Symtab.empty
+ val goal_const_tab =
+ pconsts_in_terms thy false (SOME false) goal_ts
+ |> fold (if_empty_replace_with_locality thy axioms) [Chained, Local]
+ val add_thms = maps (ProofContext.get_fact ctxt) add
+ val del_thms = maps (ProofContext.get_fact ctxt) del
+ fun iter j remaining_max threshold rel_const_tab hopeless hopeful =
+ let
+ fun game_over rejects =
+ (* Add "add:" facts. *)
+ if null add_thms then
+ []
+ else
+ map_filter (fn ((p as (_, th), _), _) =>
+ if member Thm.eq_thm add_thms th then SOME p
+ else NONE) rejects
+ fun relevant [] rejects [] =
+ (* Nothing has been added this iteration. *)
+ if j = 0 andalso threshold >= !ridiculous_threshold then
+ (* First iteration? Try again. *)
+ iter 0 max_relevant (threshold / !threshold_divisor) rel_const_tab
+ hopeless hopeful
+ else
+ game_over (rejects @ hopeless)
+ | relevant candidates rejects [] =
+ let
+ val (accepts, more_rejects) =
+ take_most_relevant max_relevant remaining_max candidates
+ val rel_const_tab' =
+ rel_const_tab
+ |> fold (add_pconst_to_table false) (maps (snd o fst) accepts)
+ fun is_dirty (c, _) =
+ Symtab.lookup rel_const_tab' c <> Symtab.lookup rel_const_tab c
+ val (hopeful_rejects, hopeless_rejects) =
+ (rejects @ hopeless, ([], []))
+ |-> fold (fn (ax as (_, consts), old_weight) =>
+ if exists is_dirty consts then
+ apfst (cons (ax, NONE))
+ else
+ apsnd (cons (ax, old_weight)))
+ |>> append (more_rejects
+ |> map (fn (ax as (_, consts), old_weight) =>
+ (ax, if exists is_dirty consts then NONE
+ else SOME old_weight)))
+ val threshold =
+ 1.0 - (1.0 - threshold)
+ * Math.pow (decay, Real.fromInt (length accepts))
+ val remaining_max = remaining_max - length accepts
+ in
+ trace_msg (fn () => "New or updated constants: " ^
+ commas (rel_const_tab' |> Symtab.dest
+ |> subtract (op =) (rel_const_tab |> Symtab.dest)
+ |> map string_for_hyper_pconst));
+ map (fst o fst) accepts @
+ (if remaining_max = 0 then
+ game_over (hopeful_rejects @ map (apsnd SOME) hopeless_rejects)
+ else
+ iter (j + 1) remaining_max threshold rel_const_tab'
+ hopeless_rejects hopeful_rejects)
+ end
+ | relevant candidates rejects
+ (((ax as (((_, loc), th), axiom_consts)), cached_weight)
+ :: hopeful) =
+ let
+ val weight =
+ case cached_weight of
+ SOME w => w
+ | NONE => axiom_weight loc const_tab rel_const_tab axiom_consts
+(* FIXME: experiment
+val name = fst (fst (fst ax)) ()
+val _ = if String.isSubstring "positive_minus" name orelse String.isSubstring "not_exp_le_zero" name then
+tracing ("*** " ^ name ^ PolyML.makestring (debug_axiom_weight loc const_tab rel_const_tab axiom_consts))
+else
+()
+*)
+ in
+ if weight >= threshold then
+ relevant ((ax, weight) :: candidates) rejects hopeful
+ else
+ relevant candidates ((ax, weight) :: rejects) hopeful
+ end
+ in
+ trace_msg (fn () =>
+ "ITERATION " ^ string_of_int j ^ ": current threshold: " ^
+ Real.toString threshold ^ ", constants: " ^
+ commas (rel_const_tab |> Symtab.dest
+ |> filter (curry (op <>) [] o snd)
+ |> map string_for_hyper_pconst));
+ relevant [] [] hopeful
+ end
+ in
+ axioms |> filter_out (member Thm.eq_thm del_thms o snd)
+ |> map_filter (pair_consts_axiom theory_relevant thy)
+ |> iter 0 max_relevant threshold0 goal_const_tab []
+ |> tap (fn res => trace_msg (fn () =>
+ "Total relevant: " ^ Int.toString (length res)))
+ end
+
+
+(***************************************************************)
+(* Retrieving and filtering lemmas *)
+(***************************************************************)
+
+(*** retrieve lemmas and filter them ***)
+
+(*Reject theorems with names like "List.filter.filter_list_def" or
+ "Accessible_Part.acc.defs", as these are definitions arising from packages.*)
+fun is_package_def a =
+ let val names = Long_Name.explode a
+ in
+ length names > 2 andalso
+ not (hd names = "local") andalso
+ String.isSuffix "_def" a orelse String.isSuffix "_defs" a
+ end;
+
+fun mk_fact_table f xs =
+ fold (Termtab.update o `(prop_of o f)) xs Termtab.empty
+fun uniquify xs = Termtab.fold (cons o snd) (mk_fact_table snd xs) []
+
+(* FIXME: put other record thms here, or declare as "no_atp" *)
+val multi_base_blacklist =
+ ["defs", "select_defs", "update_defs", "induct", "inducts", "split", "splits",
+ "split_asm", "cases", "ext_cases", "eq.simps", "eq.refl", "nchotomy",
+ "case_cong", "weak_case_cong"]
+ |> map (prefix ".")
+
+val max_lambda_nesting = 3
+
+fun term_has_too_many_lambdas max (t1 $ t2) =
+ exists (term_has_too_many_lambdas max) [t1, t2]
+ | term_has_too_many_lambdas max (Abs (_, _, t)) =
+ max = 0 orelse term_has_too_many_lambdas (max - 1) t
+ | term_has_too_many_lambdas _ _ = false
+
+(* Don't count nested lambdas at the level of formulas, since they are
+ quantifiers. *)
+fun formula_has_too_many_lambdas Ts (Abs (_, T, t)) =
+ formula_has_too_many_lambdas (T :: Ts) t
+ | formula_has_too_many_lambdas Ts t =
+ if is_formula_type (fastype_of1 (Ts, t)) then
+ exists (formula_has_too_many_lambdas Ts) (#2 (strip_comb t))
+ else
+ term_has_too_many_lambdas max_lambda_nesting t
+
+(* The max apply depth of any "metis" call in "Metis_Examples" (on 2007-10-31)
+ was 11. *)
+val max_apply_depth = 15
+
+fun apply_depth (f $ t) = Int.max (apply_depth f, apply_depth t + 1)
+ | apply_depth (Abs (_, _, t)) = apply_depth t
+ | apply_depth _ = 0
+
+fun is_formula_too_complex t =
+ apply_depth t > max_apply_depth orelse formula_has_too_many_lambdas [] t
+
+val exists_sledgehammer_const =
+ exists_Const (fn (s, _) => String.isPrefix sledgehammer_prefix s)
+
+(* FIXME: make more reliable *)
+val exists_low_level_class_const =
+ exists_Const (fn (s, _) =>
+ String.isSubstring (Long_Name.separator ^ "class" ^ Long_Name.separator) s)
+
+fun is_metastrange_theorem th =
+ case head_of (concl_of th) of
+ Const (a, _) => (a <> @{const_name Trueprop} andalso
+ a <> @{const_name "=="})
+ | _ => false
+
+fun is_that_fact th =
+ String.isSuffix (Long_Name.separator ^ Obtain.thatN) (Thm.get_name_hint th)
+ andalso exists_subterm (fn Free (s, _) => s = Name.skolem Auto_Bind.thesisN
+ | _ => false) (prop_of th)
+
+val type_has_top_sort =
+ exists_subtype (fn TFree (_, []) => true | TVar (_, []) => true | _ => false)
+
+(**** Predicates to detect unwanted facts (prolific or likely to cause
+ unsoundness) ****)
+
+(* Too general means, positive equality literal with a variable X as one
+ operand, when X does not occur properly in the other operand. This rules out
+ clearly inconsistent facts such as X = a | X = b, though it by no means
+ guarantees soundness. *)
+
+(* Unwanted equalities are those between a (bound or schematic) variable that
+ does not properly occur in the second operand. *)
+val is_exhaustive_finite =
+ let
+ fun is_bad_equal (Var z) t =
+ not (exists_subterm (fn Var z' => z = z' | _ => false) t)
+ | is_bad_equal (Bound j) t = not (loose_bvar1 (t, j))
+ | is_bad_equal _ _ = false
+ fun do_equals t1 t2 = is_bad_equal t1 t2 orelse is_bad_equal t2 t1
+ fun do_formula pos t =
+ case (pos, t) of
+ (_, @{const Trueprop} $ t1) => do_formula pos t1
+ | (true, Const (@{const_name all}, _) $ Abs (_, _, t')) =>
+ do_formula pos t'
+ | (true, Const (@{const_name All}, _) $ Abs (_, _, t')) =>
+ do_formula pos t'
+ | (false, Const (@{const_name Ex}, _) $ Abs (_, _, t')) =>
+ do_formula pos t'
+ | (_, @{const "==>"} $ t1 $ t2) =>
+ do_formula (not pos) t1 andalso
+ (t2 = @{prop False} orelse do_formula pos t2)
+ | (_, @{const HOL.implies} $ t1 $ t2) =>
+ do_formula (not pos) t1 andalso
+ (t2 = @{const False} orelse do_formula pos t2)
+ | (_, @{const Not} $ t1) => do_formula (not pos) t1
+ | (true, @{const HOL.disj} $ t1 $ t2) => forall (do_formula pos) [t1, t2]
+ | (false, @{const HOL.conj} $ t1 $ t2) => forall (do_formula pos) [t1, t2]
+ | (true, Const (@{const_name HOL.eq}, _) $ t1 $ t2) => do_equals t1 t2
+ | (true, Const (@{const_name "=="}, _) $ t1 $ t2) => do_equals t1 t2
+ | _ => false
+ in do_formula true end
+
+fun has_bound_or_var_of_type tycons =
+ exists_subterm (fn Var (_, Type (s, _)) => member (op =) tycons s
+ | Abs (_, Type (s, _), _) => member (op =) tycons s
+ | _ => false)
+
+(* Facts are forbidden to contain variables of these types. The typical reason
+ is that they lead to unsoundness. Note that "unit" satisfies numerous
+ equations like "?x = ()". The resulting clauses will have no type constraint,
+ yielding false proofs. Even "bool" leads to many unsound proofs, though only
+ for higher-order problems. *)
+val dangerous_types = [@{type_name unit}, @{type_name bool}, @{type_name prop}];
+
+(* Facts containing variables of type "unit" or "bool" or of the form
+ "ALL x. x = A | x = B | x = C" are likely to lead to unsound proofs if types
+ are omitted. *)
+fun is_dangerous_term full_types t =
+ not full_types andalso
+ let val t = transform_elim_term t in
+ has_bound_or_var_of_type dangerous_types t orelse
+ is_exhaustive_finite t
+ end
+
+fun is_theorem_bad_for_atps full_types thm =
+ let val t = prop_of thm in
+ is_formula_too_complex t orelse exists_type type_has_top_sort t orelse
+ is_dangerous_term full_types t orelse exists_sledgehammer_const t orelse
+ exists_low_level_class_const t orelse is_metastrange_theorem thm orelse
+ is_that_fact thm
+ end
+
+fun clasimpset_rules_of ctxt =
+ let
+ val {safeIs, safeEs, hazIs, hazEs, ...} = ctxt |> claset_of |> rep_cs
+ val intros = safeIs @ hazIs
+ val elims = map Classical.classical_rule (safeEs @ hazEs)
+ val simps = ctxt |> simpset_of |> dest_ss |> #simps |> map snd
+ in (mk_fact_table I intros, mk_fact_table I elims, mk_fact_table I simps) end
+
+fun all_name_thms_pairs ctxt reserved full_types add_thms chained_ths =
+ let
+ val thy = ProofContext.theory_of ctxt
+ val global_facts = PureThy.facts_of thy
+ val local_facts = ProofContext.facts_of ctxt
+ val named_locals = local_facts |> Facts.dest_static []
+ val is_chained = member Thm.eq_thm chained_ths
+ val (intros, elims, simps) =
+ if exists (curry (op <) 0.0) [!intro_bonus, !elim_bonus, !simp_bonus] then
+ clasimpset_rules_of ctxt
+ else
+ (Termtab.empty, Termtab.empty, Termtab.empty)
+ (* Unnamed nonchained formulas with schematic variables are omitted, because
+ they are rejected by the backticks (`...`) parser for some reason. *)
+ fun is_good_unnamed_local th =
+ not (Thm.has_name_hint th) andalso
+ (not (exists_subterm is_Var (prop_of th)) orelse (is_chained th)) andalso
+ forall (fn (_, ths) => not (member Thm.eq_thm ths th)) named_locals
+ val unnamed_locals =
+ union Thm.eq_thm (Facts.props local_facts) chained_ths
+ |> filter is_good_unnamed_local |> map (pair "" o single)
+ val full_space =
+ Name_Space.merge (Facts.space_of global_facts, Facts.space_of local_facts)
+ fun add_facts global foldx facts =
+ foldx (fn (name0, ths) =>
+ if name0 <> "" andalso
+ forall (not o member Thm.eq_thm add_thms) ths andalso
+ (Facts.is_concealed facts name0 orelse
+ (respect_no_atp andalso is_package_def name0) orelse
+ exists (fn s => String.isSuffix s name0) multi_base_blacklist orelse
+ String.isSuffix "_def_raw" (* FIXME: crude hack *) name0) then
+ I
+ else
+ let
+ val multi = length ths > 1
+ fun backquotify th =
+ "`" ^ Print_Mode.setmp [Print_Mode.input]
+ (Syntax.string_of_term ctxt) (prop_of th) ^ "`"
+ |> String.translate (fn c => if Char.isPrint c then str c else "")
+ |> simplify_spaces
+ fun check_thms a =
+ case try (ProofContext.get_thms ctxt) a of
+ NONE => false
+ | SOME ths' => Thm.eq_thms (ths, ths')
+ in
+ pair 1
+ #> fold (fn th => fn (j, rest) =>
+ (j + 1,
+ if is_theorem_bad_for_atps full_types th andalso
+ not (member Thm.eq_thm add_thms th) then
+ rest
+ else
+ (((fn () =>
+ if name0 = "" then
+ th |> backquotify
+ else
+ let
+ val name1 = Facts.extern facts name0
+ val name2 = Name_Space.extern full_space name0
+ in
+ case find_first check_thms [name1, name2, name0] of
+ SOME name => repair_name reserved multi j name
+ | NONE => ""
+ end),
+ let val t = prop_of th in
+ if is_chained th then Chained
+ else if not global then Local
+ else if Termtab.defined intros t then Intro
+ else if Termtab.defined elims t then Elim
+ else if Termtab.defined simps t then Simp
+ else General
+ end),
+ (multi, th)) :: rest)) ths
+ #> snd
+ end)
+ in
+ [] |> add_facts false fold local_facts (unnamed_locals @ named_locals)
+ |> add_facts true Facts.fold_static global_facts global_facts
+ end
+
+(* The single-name theorems go after the multiple-name ones, so that single
+ names are preferred when both are available. *)
+fun name_thm_pairs ctxt respect_no_atp =
+ List.partition (fst o snd) #> op @ #> map (apsnd snd)
+ #> respect_no_atp ? filter_out (No_ATPs.member ctxt o snd)
+
+(***************************************************************)
+(* ATP invocation methods setup *)
+(***************************************************************)
+
+fun relevant_facts ctxt full_types (threshold0, threshold1) max_relevant
+ theory_relevant (relevance_override as {add, del, only})
+ chained_ths hyp_ts concl_t =
+ let
+ val decay = Math.pow ((1.0 - threshold1) / (1.0 - threshold0),
+ 1.0 / Real.fromInt (max_relevant + 1))
+ val add_thms = maps (ProofContext.get_fact ctxt) add
+ val reserved = reserved_isar_keyword_table ()
+ val axioms =
+ (if only then
+ maps (map (fn ((name, loc), th) => ((K name, loc), (true, th)))
+ o name_thm_pairs_from_ref ctxt reserved chained_ths) add
+ else
+ all_name_thms_pairs ctxt reserved full_types add_thms chained_ths)
+ |> name_thm_pairs ctxt (respect_no_atp andalso not only)
+ |> uniquify
+ in
+ trace_msg (fn () => "Considering " ^ Int.toString (length axioms) ^
+ " theorems");
+ (if threshold0 > 1.0 orelse threshold0 > threshold1 then
+ []
+ else if threshold0 < 0.0 then
+ axioms
+ else
+ relevance_filter ctxt threshold0 decay max_relevant theory_relevant
+ relevance_override axioms (concl_t :: hyp_ts))
+ |> map (apfst (apfst (fn f => f ())))
+ end
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_minimize.ML Tue Aug 31 23:46:23 2010 +0200
@@ -0,0 +1,162 @@
+(* Title: HOL/Tools/Sledgehammer/sledgehammer_fact_minimize.ML
+ Author: Philipp Meyer, TU Muenchen
+ Author: Jasmin Blanchette, TU Muenchen
+
+Minimization of theorem list for Metis using automatic theorem provers.
+*)
+
+signature SLEDGEHAMMER_FACT_MINIMIZE =
+sig
+ type locality = Sledgehammer_Fact_Filter.locality
+ type params = Sledgehammer.params
+
+ val minimize_theorems :
+ params -> int -> int -> Proof.state -> ((string * locality) * thm list) list
+ -> ((string * locality) * thm list) list option * string
+ val run_minimize : params -> int -> Facts.ref list -> Proof.state -> unit
+end;
+
+structure Sledgehammer_Fact_Minimize : SLEDGEHAMMER_FACT_MINIMIZE =
+struct
+
+open ATP_Systems
+open Sledgehammer_Util
+open Sledgehammer_Fact_Filter
+open Sledgehammer_Proof_Reconstruct
+open Sledgehammer
+
+(* wrapper for calling external prover *)
+
+fun string_for_failure Unprovable = "Unprovable."
+ | string_for_failure TimedOut = "Timed out."
+ | string_for_failure _ = "Unknown error."
+
+fun n_theorems names =
+ let val n = length names in
+ string_of_int n ^ " theorem" ^ plural_s n ^
+ (if n > 0 then
+ ": " ^ (names |> map fst
+ |> sort_distinct string_ord |> space_implode " ")
+ else
+ "")
+ end
+
+fun test_theorems ({debug, verbose, overlord, atps, full_types, isar_proof,
+ isar_shrink_factor, ...} : params)
+ (prover : prover) explicit_apply timeout subgoal state
+ axioms =
+ let
+ val _ =
+ priority ("Testing " ^ n_theorems (map fst axioms) ^ "...")
+ val params =
+ {blocking = true, debug = debug, verbose = verbose, overlord = overlord,
+ atps = atps, full_types = full_types, explicit_apply = explicit_apply,
+ relevance_thresholds = (1.01, 1.01), max_relevant = NONE,
+ theory_relevant = NONE, isar_proof = isar_proof,
+ isar_shrink_factor = isar_shrink_factor, timeout = timeout, expect = ""}
+ val axioms = maps (fn (n, ths) => map (pair n) ths) axioms
+ val {context = ctxt, facts, goal} = Proof.goal state
+ val problem =
+ {subgoal = subgoal, goal = (ctxt, (facts, goal)),
+ relevance_override = {add = [], del = [], only = false},
+ axioms = SOME axioms}
+ val result as {outcome, used_thm_names, ...} = prover params (K "") problem
+ in
+ priority (case outcome of
+ NONE =>
+ if length used_thm_names = length axioms then
+ "Found proof."
+ else
+ "Found proof with " ^ n_theorems used_thm_names ^ "."
+ | SOME failure => string_for_failure failure);
+ result
+ end
+
+(* minimalization of thms *)
+
+fun filter_used_facts used = filter (member (op =) used o fst)
+
+fun sublinear_minimize _ [] p = p
+ | sublinear_minimize test (x :: xs) (seen, result) =
+ case test (xs @ seen) of
+ result as {outcome = NONE, proof, used_thm_names, ...} : prover_result =>
+ sublinear_minimize test (filter_used_facts used_thm_names xs)
+ (filter_used_facts used_thm_names seen, result)
+ | _ => sublinear_minimize test xs (x :: seen, result)
+
+(* Give the ATP some slack. The ATP gets further slack because the Sledgehammer
+ preprocessing time is included in the estimate below but isn't part of the
+ timeout. *)
+val fudge_msecs = 1000
+
+fun minimize_theorems {atps = [], ...} _ _ _ _ = error "No ATP is set."
+ | minimize_theorems (params as {debug, atps = atp :: _, full_types,
+ isar_proof, isar_shrink_factor, timeout, ...})
+ i n state axioms =
+ let
+ val thy = Proof.theory_of state
+ val prover = get_prover_fun thy atp
+ val msecs = Time.toMilliseconds timeout
+ val _ = priority ("Sledgehammer minimize: ATP " ^ quote atp ^ ".")
+ val {context = ctxt, goal, ...} = Proof.goal state
+ val (_, hyp_ts, concl_t) = strip_subgoal goal i
+ val explicit_apply =
+ not (forall (Meson.is_fol_term thy)
+ (concl_t :: hyp_ts @ maps (map prop_of o snd) axioms))
+ fun do_test timeout =
+ test_theorems params prover explicit_apply timeout i state
+ val timer = Timer.startRealTimer ()
+ in
+ (case do_test timeout axioms of
+ result as {outcome = NONE, pool, used_thm_names,
+ conjecture_shape, ...} =>
+ let
+ val time = Timer.checkRealTimer timer
+ val new_timeout =
+ Int.min (msecs, Time.toMilliseconds time + fudge_msecs)
+ |> Time.fromMilliseconds
+ val (min_thms, {proof, axiom_names, ...}) =
+ sublinear_minimize (do_test new_timeout)
+ (filter_used_facts used_thm_names axioms) ([], result)
+ val n = length min_thms
+ val _ = priority (cat_lines
+ ["Minimized: " ^ string_of_int n ^ " theorem" ^ plural_s n] ^
+ (case length (filter (curry (op =) Chained o snd o fst) min_thms) of
+ 0 => ""
+ | n => " (including " ^ Int.toString n ^ " chained)") ^ ".")
+ in
+ (SOME min_thms,
+ proof_text isar_proof
+ (pool, debug, isar_shrink_factor, ctxt, conjecture_shape)
+ (full_types, K "", proof, axiom_names, goal, i) |> fst)
+ end
+ | {outcome = SOME TimedOut, ...} =>
+ (NONE, "Timeout: You can increase the time limit using the \"timeout\" \
+ \option (e.g., \"timeout = " ^
+ string_of_int (10 + msecs div 1000) ^ " s\").")
+ | {outcome = SOME UnknownError, ...} =>
+ (* Failure sometimes mean timeout, unfortunately. *)
+ (NONE, "Failure: No proof was found with the current time limit. You \
+ \can increase the time limit using the \"timeout\" \
+ \option (e.g., \"timeout = " ^
+ string_of_int (10 + msecs div 1000) ^ " s\").")
+ | {message, ...} => (NONE, "ATP error: " ^ message))
+ handle ERROR msg => (NONE, "Error: " ^ msg)
+ end
+
+fun run_minimize params i refs state =
+ let
+ val ctxt = Proof.context_of state
+ val reserved = reserved_isar_keyword_table ()
+ val chained_ths = #facts (Proof.goal state)
+ val axioms =
+ maps (map (apsnd single)
+ o name_thm_pairs_from_ref ctxt reserved chained_ths) refs
+ in
+ case subgoal_count state of
+ 0 => priority "No subgoal!"
+ | n =>
+ (kill_atps (); priority (#2 (minimize_theorems params i n state axioms)))
+ end
+
+end;
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML Tue Aug 31 23:43:23 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,1038 +0,0 @@
-(* Title: HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML
- Author: Lawrence C. Paulson, Cambridge University Computer Laboratory
- Author: Claire Quigley, Cambridge University Computer Laboratory
- Author: Jasmin Blanchette, TU Muenchen
-
-Transfer of proofs from external provers.
-*)
-
-signature SLEDGEHAMMER_PROOF_RECONSTRUCT =
-sig
- type locality = Sledgehammer_Fact_Filter.locality
- type minimize_command = string list -> string
- type metis_params =
- bool * minimize_command * string * (string * locality) list vector * thm
- * int
- type isar_params =
- string Symtab.table * bool * int * Proof.context * int list list
- type text_result = string * (string * locality) list
-
- val metis_proof_text : metis_params -> text_result
- val isar_proof_text : isar_params -> metis_params -> text_result
- val proof_text : bool -> isar_params -> metis_params -> text_result
-end;
-
-structure Sledgehammer_Proof_Reconstruct : SLEDGEHAMMER_PROOF_RECONSTRUCT =
-struct
-
-open ATP_Problem
-open Metis_Clauses
-open Sledgehammer_Util
-open Sledgehammer_Fact_Filter
-open Sledgehammer_Translate
-
-type minimize_command = string list -> string
-type metis_params =
- bool * minimize_command * string * (string * locality) list vector * thm * int
-type isar_params =
- string Symtab.table * bool * int * Proof.context * int list list
-type text_result = string * (string * locality) list
-
-(* Simple simplifications to ensure that sort annotations don't leave a trail of
- spurious "True"s. *)
-fun s_not @{const False} = @{const True}
- | s_not @{const True} = @{const False}
- | s_not (@{const Not} $ t) = t
- | s_not t = @{const Not} $ t
-fun s_conj (@{const True}, t2) = t2
- | s_conj (t1, @{const True}) = t1
- | s_conj p = HOLogic.mk_conj p
-fun s_disj (@{const False}, t2) = t2
- | s_disj (t1, @{const False}) = t1
- | s_disj p = HOLogic.mk_disj p
-fun s_imp (@{const True}, t2) = t2
- | s_imp (t1, @{const False}) = s_not t1
- | s_imp p = HOLogic.mk_imp p
-fun s_iff (@{const True}, t2) = t2
- | s_iff (t1, @{const True}) = t1
- | s_iff (t1, t2) = HOLogic.eq_const HOLogic.boolT $ t1 $ t2
-
-fun mk_anot (AConn (ANot, [phi])) = phi
- | mk_anot phi = AConn (ANot, [phi])
-fun mk_aconn c (phi1, phi2) = AConn (c, [phi1, phi2])
-
-fun index_in_shape x = find_index (exists (curry (op =) x))
-fun is_axiom_number axiom_names num =
- num > 0 andalso num <= Vector.length axiom_names andalso
- not (null (Vector.sub (axiom_names, num - 1)))
-fun is_conjecture_number conjecture_shape num =
- index_in_shape num conjecture_shape >= 0
-
-fun negate_term (Const (@{const_name All}, T) $ Abs (s, T', t')) =
- Const (@{const_name Ex}, T) $ Abs (s, T', negate_term t')
- | negate_term (Const (@{const_name Ex}, T) $ Abs (s, T', t')) =
- Const (@{const_name All}, T) $ Abs (s, T', negate_term t')
- | negate_term (@{const HOL.implies} $ t1 $ t2) =
- @{const HOL.conj} $ t1 $ negate_term t2
- | negate_term (@{const HOL.conj} $ t1 $ t2) =
- @{const HOL.disj} $ negate_term t1 $ negate_term t2
- | negate_term (@{const HOL.disj} $ t1 $ t2) =
- @{const HOL.conj} $ negate_term t1 $ negate_term t2
- | negate_term (@{const Not} $ t) = t
- | negate_term t = @{const Not} $ t
-
-datatype ('a, 'b, 'c, 'd, 'e) raw_step =
- Definition of 'a * 'b * 'c |
- Inference of 'a * 'd * 'e list
-
-fun raw_step_number (Definition (num, _, _)) = num
- | raw_step_number (Inference (num, _, _)) = num
-
-(**** PARSING OF TSTP FORMAT ****)
-
-(*Strings enclosed in single quotes, e.g. filenames*)
-val scan_quoted = $$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'" >> implode;
-
-val scan_dollar_name =
- Scan.repeat ($$ "$") -- Symbol.scan_id >> (fn (ss, s) => implode ss ^ s)
-
-fun repair_name _ "$true" = "c_True"
- | repair_name _ "$false" = "c_False"
- | repair_name _ "$$e" = "c_equal" (* seen in Vampire proofs *)
- | repair_name _ "equal" = "c_equal" (* needed by SPASS? *)
- | repair_name pool s =
- case Symtab.lookup pool s of
- SOME s' => s'
- | NONE =>
- if String.isPrefix "sQ" s andalso String.isSuffix "_eqProxy" s then
- "c_equal" (* seen in Vampire proofs *)
- else
- s
-(* Generalized first-order terms, which include file names, numbers, etc. *)
-val parse_potential_integer =
- (scan_dollar_name || scan_quoted) >> K NONE
- || scan_integer >> SOME
-fun parse_annotation x =
- ((parse_potential_integer ::: Scan.repeat ($$ " " |-- parse_potential_integer)
- >> map_filter I) -- Scan.optional parse_annotation []
- >> uncurry (union (op =))
- || $$ "(" |-- parse_annotations --| $$ ")"
- || $$ "[" |-- parse_annotations --| $$ "]") x
-and parse_annotations x =
- (Scan.optional (parse_annotation
- ::: Scan.repeat ($$ "," |-- parse_annotation)) []
- >> (fn numss => fold (union (op =)) numss [])) x
-
-(* Vampire proof lines sometimes contain needless information such as "(0:3)",
- which can be hard to disambiguate from function application in an LL(1)
- parser. As a workaround, we extend the TPTP term syntax with such detritus
- and ignore it. *)
-fun parse_vampire_detritus x =
- (scan_integer |-- $$ ":" --| scan_integer >> K []) x
-
-fun parse_term pool x =
- ((scan_dollar_name >> repair_name pool)
- -- Scan.optional ($$ "(" |-- (parse_vampire_detritus || parse_terms pool)
- --| $$ ")") []
- --| Scan.optional ($$ "(" |-- parse_vampire_detritus --| $$ ")") []
- >> ATerm) x
-and parse_terms pool x =
- (parse_term pool ::: Scan.repeat ($$ "," |-- parse_term pool)) x
-
-fun parse_atom pool =
- parse_term pool -- Scan.option (Scan.option ($$ "!") --| $$ "="
- -- parse_term pool)
- >> (fn (u1, NONE) => AAtom u1
- | (u1, SOME (NONE, u2)) => AAtom (ATerm ("c_equal", [u1, u2]))
- | (u1, SOME (SOME _, u2)) =>
- mk_anot (AAtom (ATerm ("c_equal", [u1, u2]))))
-
-fun fo_term_head (ATerm (s, _)) = s
-
-(* TPTP formulas are fully parenthesized, so we don't need to worry about
- operator precedence. *)
-fun parse_formula pool x =
- (($$ "(" |-- parse_formula pool --| $$ ")"
- || ($$ "!" >> K AForall || $$ "?" >> K AExists)
- --| $$ "[" -- parse_terms pool --| $$ "]" --| $$ ":"
- -- parse_formula pool
- >> (fn ((q, ts), phi) => AQuant (q, map fo_term_head ts, phi))
- || $$ "~" |-- parse_formula pool >> mk_anot
- || parse_atom pool)
- -- Scan.option ((Scan.this_string "=>" >> K AImplies
- || Scan.this_string "<=>" >> K AIff
- || Scan.this_string "<~>" >> K ANotIff
- || Scan.this_string "<=" >> K AIf
- || $$ "|" >> K AOr || $$ "&" >> K AAnd)
- -- parse_formula pool)
- >> (fn (phi1, NONE) => phi1
- | (phi1, SOME (c, phi2)) => mk_aconn c (phi1, phi2))) x
-
-val parse_tstp_extra_arguments =
- Scan.optional ($$ "," |-- parse_annotation
- --| Scan.option ($$ "," |-- parse_annotations)) []
-
-(* Syntax: (fof|cnf)\(<num>, <formula_role>, <formula> <extra_arguments>\).
- The <num> could be an identifier, but we assume integers. *)
- fun parse_tstp_line pool =
- ((Scan.this_string "fof" || Scan.this_string "cnf") -- $$ "(")
- |-- scan_integer --| $$ "," -- Symbol.scan_id --| $$ ","
- -- parse_formula pool -- parse_tstp_extra_arguments --| $$ ")" --| $$ "."
- >> (fn (((num, role), phi), deps) =>
- case role of
- "definition" =>
- (case phi of
- AConn (AIff, [phi1 as AAtom _, phi2]) =>
- Definition (num, phi1, phi2)
- | AAtom (ATerm ("c_equal", _)) =>
- Inference (num, phi, deps) (* Vampire's equality proxy axiom *)
- | _ => raise Fail "malformed definition")
- | _ => Inference (num, phi, deps))
-
-(**** PARSING OF VAMPIRE OUTPUT ****)
-
-(* Syntax: <num>. <formula> <annotation> *)
-fun parse_vampire_line pool =
- scan_integer --| $$ "." -- parse_formula pool -- parse_annotation
- >> (fn ((num, phi), deps) => Inference (num, phi, deps))
-
-(**** PARSING OF SPASS OUTPUT ****)
-
-(* SPASS returns clause references of the form "x.y". We ignore "y", whose role
- is not clear anyway. *)
-val parse_dot_name = scan_integer --| $$ "." --| scan_integer
-
-val parse_spass_annotations =
- Scan.optional ($$ ":" |-- Scan.repeat (parse_dot_name
- --| Scan.option ($$ ","))) []
-
-(* It is not clear why some literals are followed by sequences of stars and/or
- pluses. We ignore them. *)
-fun parse_decorated_atom pool =
- parse_atom pool --| Scan.repeat ($$ "*" || $$ "+" || $$ " ")
-
-fun mk_horn ([], []) = AAtom (ATerm ("c_False", []))
- | mk_horn ([], pos_lits) = foldr1 (mk_aconn AOr) pos_lits
- | mk_horn (neg_lits, []) = mk_anot (foldr1 (mk_aconn AAnd) neg_lits)
- | mk_horn (neg_lits, pos_lits) =
- mk_aconn AImplies (foldr1 (mk_aconn AAnd) neg_lits,
- foldr1 (mk_aconn AOr) pos_lits)
-
-fun parse_horn_clause pool =
- Scan.repeat (parse_decorated_atom pool) --| $$ "|" --| $$ "|"
- -- Scan.repeat (parse_decorated_atom pool) --| $$ "-" --| $$ ">"
- -- Scan.repeat (parse_decorated_atom pool)
- >> (mk_horn o apfst (op @))
-
-(* Syntax: <num>[0:<inference><annotations>]
- <atoms> || <atoms> -> <atoms>. *)
-fun parse_spass_line pool =
- scan_integer --| $$ "[" --| $$ "0" --| $$ ":" --| Symbol.scan_id
- -- parse_spass_annotations --| $$ "]" -- parse_horn_clause pool --| $$ "."
- >> (fn ((num, deps), u) => Inference (num, u, deps))
-
-fun parse_line pool =
- parse_tstp_line pool || parse_vampire_line pool || parse_spass_line pool
-fun parse_lines pool = Scan.repeat1 (parse_line pool)
-fun parse_proof pool =
- fst o Scan.finite Symbol.stopper
- (Scan.error (!! (fn _ => raise Fail "unrecognized ATP output")
- (parse_lines pool)))
- o explode o strip_spaces_except_between_ident_chars
-
-(**** INTERPRETATION OF TSTP SYNTAX TREES ****)
-
-exception FO_TERM of string fo_term list
-exception FORMULA of (string, string fo_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 type_from_fo_term tfrees (u as ATerm (a, us)) =
- let val Ts = map (type_from_fo_term tfrees) us in
- case strip_prefix_and_unascii type_const_prefix a of
- SOME b => Type (invert_const b, Ts)
- | NONE =>
- if not (null us) then
- raise FO_TERM [u] (* only "tconst"s have type arguments *)
- else case strip_prefix_and_unascii tfree_prefix a of
- SOME b =>
- let val s = "'" ^ b in
- TFree (s, AList.lookup (op =) tfrees s |> the_default HOLogic.typeS)
- end
- | NONE =>
- case strip_prefix_and_unascii tvar_prefix a of
- SOME b => TVar (("'" ^ b, 0), HOLogic.typeS)
- | NONE =>
- (* Variable from the ATP, say "X1" *)
- Type_Infer.param 0 (a, HOLogic.typeS)
- end
-
-(* Type class literal applied to a type. Returns triple of polarity, class,
- type. *)
-fun type_constraint_from_term pos tfrees (u as ATerm (a, us)) =
- case (strip_prefix_and_unascii class_prefix a,
- map (type_from_fo_term tfrees) us) of
- (SOME b, [T]) => (pos, b, T)
- | _ => raise FO_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_atp_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
-
-(* First-order translation. No types are known for variables. "HOLogic.typeT"
- should allow them to be inferred. *)
-fun raw_term_from_pred thy full_types tfrees =
- let
- fun aux opt_T extra_us u =
- case u of
- ATerm ("hBOOL", [u1]) => aux (SOME @{typ bool}) [] u1
- | ATerm ("hAPP", [u1, u2]) => aux opt_T (u2 :: extra_us) u1
- | ATerm (a, us) =>
- if a = type_wrapper_name then
- case us of
- [typ_u, term_u] =>
- aux (SOME (type_from_fo_term tfrees typ_u)) extra_us term_u
- | _ => raise FO_TERM us
- else case strip_prefix_and_unascii const_prefix a of
- SOME "equal" =>
- list_comb (Const (@{const_name HOL.eq}, HOLogic.typeT),
- map (aux NONE []) us)
- | SOME b =>
- let
- val c = invert_const b
- val num_type_args = num_type_args thy c
- val (type_us, term_us) =
- chop (if full_types then 0 else num_type_args) us
- (* Extra args from "hAPP" come after any arguments given directly to
- the constant. *)
- val term_ts = map (aux NONE []) term_us
- val extra_ts = map (aux NONE []) extra_us
- val t =
- Const (c, if full_types then
- case opt_T of
- SOME T => map fastype_of term_ts ---> T
- | NONE =>
- if num_type_args = 0 then
- Sign.const_instance thy (c, [])
- else
- raise Fail ("no type information for " ^ quote c)
- else
- Sign.const_instance thy (c,
- map (type_from_fo_term tfrees) type_us))
- in list_comb (t, term_ts @ extra_ts) end
- | NONE => (* a free or schematic variable *)
- let
- val ts = map (aux NONE []) (us @ extra_us)
- val T = map fastype_of ts ---> HOLogic.typeT
- val t =
- case strip_prefix_and_unascii fixed_var_prefix a of
- SOME b => Free (b, T)
- | NONE =>
- case strip_prefix_and_unascii schematic_var_prefix a of
- SOME b => Var ((b, 0), T)
- | NONE =>
- if is_tptp_variable a then
- Var ((repair_atp_variable_name Char.toLower a, 0), T)
- else
- (* Skolem constants? *)
- Var ((repair_atp_variable_name Char.toUpper a, 0), T)
- in list_comb (t, ts) end
- in aux (SOME HOLogic.boolT) [] end
-
-fun term_from_pred thy full_types tfrees pos (u as ATerm (s, _)) =
- if String.isPrefix class_prefix s then
- add_type_constraint (type_constraint_from_term pos tfrees u)
- #> pair @{const True}
- else
- pair (raw_term_from_pred thy full_types tfrees u)
-
-val combinator_table =
- [(@{const_name COMBI}, @{thm COMBI_def_raw}),
- (@{const_name COMBK}, @{thm COMBK_def_raw}),
- (@{const_name COMBB}, @{thm COMBB_def_raw}),
- (@{const_name COMBC}, @{thm COMBC_def_raw}),
- (@{const_name COMBS}, @{thm COMBS_def_raw})]
-
-fun uncombine_term (t1 $ t2) = betapply (pairself uncombine_term (t1, t2))
- | uncombine_term (Abs (s, T, t')) = Abs (s, T, uncombine_term t')
- | uncombine_term (t as Const (x as (s, _))) =
- (case AList.lookup (op =) combinator_table s of
- SOME thm => thm |> prop_of |> specialize_type @{theory} x |> Logic.dest_equals |> snd
- | NONE => t)
- | uncombine_term t = t
-
-(* Update schematic type variables with detected sort constraints. It's not
- totally clear when 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_free quant_s free_s body_t =
- case Term.add_frees body_t [] |> filter (curry (op =) free_s o fst) of
- [] => body_t
- | frees as (_, free_T) :: _ =>
- Abs (free_s, free_T, fold (curry abstract_over) (map Free frees) body_t)
-
-(* Interpret an ATP formula as a HOL term, extracting sort constraints as they
- appear in the formula. *)
-fun prop_from_formula thy full_types tfrees phi =
- let
- fun do_formula pos phi =
- case phi of
- AQuant (_, [], phi) => do_formula pos phi
- | AQuant (q, x :: xs, phi') =>
- do_formula pos (AQuant (q, xs, phi'))
- #>> quantify_over_free (case q of
- AForall => @{const_name All}
- | AExists => @{const_name Ex})
- (repair_atp_variable_name Char.toLower x)
- | 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
- | AIf => s_imp o swap
- | AIff => s_iff
- | ANotIff => s_not o s_iff)
- | AAtom tm => term_from_pred thy full_types tfrees pos tm
- | _ => raise FORMULA [phi]
- in repair_tvar_sorts (do_formula true phi Vartab.empty) end
-
-fun check_formula ctxt =
- Type_Infer.constrain HOLogic.boolT
- #> Syntax.check_term (ProofContext.set_mode ProofContext.mode_schematic ctxt)
-
-
-(**** 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 full_types tfrees (Definition (num, phi1, phi2)) ctxt =
- let
- val thy = ProofContext.theory_of ctxt
- val t1 = prop_from_formula thy full_types tfrees phi1
- val vars = snd (strip_comb t1)
- val frees = map unvarify_term vars
- val unvarify_args = subst_atomic (vars ~~ frees)
- val t2 = prop_from_formula thy full_types tfrees phi2
- val (t1, t2) =
- HOLogic.eq_const HOLogic.typeT $ t1 $ t2
- |> unvarify_args |> uncombine_term |> check_formula ctxt
- |> HOLogic.dest_eq
- in
- (Definition (num, t1, t2),
- fold Variable.declare_term (maps OldTerm.term_frees [t1, t2]) ctxt)
- end
- | decode_line full_types tfrees (Inference (num, u, deps)) ctxt =
- let
- val thy = ProofContext.theory_of ctxt
- val t = u |> prop_from_formula thy full_types tfrees
- |> uncombine_term |> check_formula ctxt
- in
- (Inference (num, t, deps),
- fold Variable.declare_term (OldTerm.term_frees t) ctxt)
- end
-fun decode_lines ctxt full_types tfrees lines =
- fst (fold_map (decode_line full_types tfrees) 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) HOLogic.true_const
-
-fun replace_one_dep (old, new) dep = if dep = old then new else [dep]
-fun replace_deps_in_line _ (line as Definition _) = line
- | replace_deps_in_line p (Inference (num, t, deps)) =
- Inference (num, t, fold (union (op =) o replace_one_dep p) deps [])
-
-(* Discard axioms; 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 conjecture_shape axiom_names (Inference (num, t, [])) lines =
- (* No dependencies: axiom, conjecture, or (for Vampire) internal axioms or
- definitions. *)
- if is_axiom_number axiom_names num then
- (* Axioms are not proof lines. *)
- if is_only_type_information t then
- map (replace_deps_in_line (num, [])) 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 (num', _, _) :: post) =>
- pre @ map (replace_deps_in_line (num', [num])) post
- else if is_conjecture_number conjecture_shape num then
- Inference (num, negate_term t, []) :: lines
- else
- map (replace_deps_in_line (num, [])) lines
- | add_line _ _ (Inference (num, t, deps)) lines =
- (* Type information will be deleted later; skip repetition test. *)
- if is_only_type_information t then
- Inference (num, t, 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 (num, t, deps) :: lines
- | (pre, Inference (num', t', _) :: post) =>
- Inference (num, t', deps) ::
- pre @ map (replace_deps_in_line (num', [num])) post
-
-(* Recursively delete empty lines (type information) from the proof. *)
-fun add_nontrivial_line (Inference (num, t, [])) lines =
- if is_only_type_information t then delete_dep num lines
- else Inference (num, t, []) :: lines
- | add_nontrivial_line line lines = line :: lines
-and delete_dep num lines =
- fold_rev add_nontrivial_line (map (replace_deps_in_line (num, [])) 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
-
-(* Vampire is keen on producing these. *)
-fun is_trivial_formula (@{const Not} $ (Const (@{const_name HOL.eq}, _)
- $ t1 $ t2)) = (t1 aconv t2)
- | is_trivial_formula _ = false
-
-fun add_desired_line _ _ _ _ (line as Definition (num, _, _)) (j, lines) =
- (j, line :: map (replace_deps_in_line (num, [])) lines)
- | add_desired_line isar_shrink_factor conjecture_shape axiom_names frees
- (Inference (num, t, deps)) (j, lines) =
- (j + 1,
- if is_axiom_number axiom_names num orelse
- is_conjecture_number conjecture_shape num orelse
- (not (is_only_type_information t) andalso
- null (Term.add_tvars t []) andalso
- not (exists_subterm (is_bad_free frees) t) andalso
- not (is_trivial_formula t) andalso
- (null lines orelse (* last line must be kept *)
- (length deps >= 2 andalso j mod isar_shrink_factor = 0))) then
- Inference (num, t, deps) :: lines (* keep line *)
- else
- map (replace_deps_in_line (num, deps)) lines) (* drop line *)
-
-(** EXTRACTING LEMMAS **)
-
-(* Like "split_line", but ignores "\n" that follow a comma (as in SNARK's
- output). *)
-val split_proof_lines =
- let
- fun aux [] [] = []
- | aux line [] = [implode (rev line)]
- | aux line ("," :: "\n" :: rest) = aux ("," :: line) rest
- | aux line ("\n" :: rest) = aux line [] @ aux [] rest
- | aux line (s :: rest) = aux (s :: line) rest
- in aux [] o explode end
-
-(* A list consisting of the first number in each line is returned. For TSTP,
- interesting lines have the form "fof(108, axiom, ...)", where the number
- (108) is extracted. For SPASS, lines have the form "108[0:Inp] ...", where
- the first number (108) is extracted. For Vampire, we look for
- "108. ... [input]". *)
-fun used_facts_in_atp_proof axiom_names atp_proof =
- let
- fun axiom_names_at_index num =
- let val j = Int.fromString num |> the_default ~1 in
- if is_axiom_number axiom_names j then Vector.sub (axiom_names, j - 1)
- else []
- end
- val tokens_of =
- String.tokens (fn c => not (Char.isAlphaNum c) andalso c <> #"_")
- fun do_line (tag :: num :: "axiom" :: (rest as _ :: _)) =
- if tag = "cnf" orelse tag = "fof" then
- (case strip_prefix_and_unascii axiom_prefix (List.last rest) of
- SOME name =>
- if member (op =) rest "file" then
- ([(name, name |> find_first_in_list_vector axiom_names |> the)]
- handle Option.Option =>
- error ("No such fact: " ^ quote name ^ "."))
- else
- axiom_names_at_index num
- | NONE => axiom_names_at_index num)
- else
- []
- | do_line (num :: "0" :: "Inp" :: _) = axiom_names_at_index num
- | do_line (num :: rest) =
- (case List.last rest of "input" => axiom_names_at_index num | _ => [])
- | do_line _ = []
- in atp_proof |> split_proof_lines |> maps (do_line o tokens_of) end
-
-val indent_size = 2
-val no_label = ("", ~1)
-
-val raw_prefix = "X"
-val assum_prefix = "A"
-val fact_prefix = "F"
-
-fun string_for_label (s, num) = s ^ string_of_int num
-
-fun metis_using [] = ""
- | metis_using ls =
- "using " ^ space_implode " " (map string_for_label ls) ^ " "
-fun metis_apply _ 1 = "by "
- | metis_apply 1 _ = "apply "
- | metis_apply i _ = "prefer " ^ string_of_int i ^ " apply "
-fun metis_name full_types = if full_types then "metisFT" else "metis"
-fun metis_call full_types [] = metis_name full_types
- | metis_call full_types ss =
- "(" ^ metis_name full_types ^ " " ^ space_implode " " ss ^ ")"
-fun metis_command full_types i n (ls, ss) =
- metis_using ls ^ metis_apply i n ^ metis_call full_types ss
-fun metis_line full_types i n ss =
- "Try this command: " ^
- Markup.markup Markup.sendback (metis_command full_types i n ([], ss)) ^ "."
-fun minimize_line _ [] = ""
- | minimize_line minimize_command ss =
- case minimize_command ss of
- "" => ""
- | command =>
- "\nTo minimize the number of lemmas, try this: " ^
- Markup.markup Markup.sendback command ^ "."
-
-fun used_facts axiom_names =
- used_facts_in_atp_proof axiom_names
- #> List.partition (curry (op =) Chained o snd)
- #> pairself (sort_distinct (string_ord o pairself fst))
-
-fun metis_proof_text (full_types, minimize_command, atp_proof, axiom_names,
- goal, i) =
- let
- val (chained_lemmas, other_lemmas) = used_facts axiom_names atp_proof
- val n = Logic.count_prems (prop_of goal)
- in
- (metis_line full_types i n (map fst other_lemmas) ^
- minimize_line minimize_command (map fst (other_lemmas @ chained_lemmas)),
- other_lemmas @ chained_lemmas)
- end
-
-(** Isar proof construction and manipulation **)
-
-fun merge_fact_sets (ls1, ss1) (ls2, ss2) =
- (union (op =) ls1 ls2, union (op =) ss1 ss2)
-
-type label = string * int
-type facts = label list * string list
-
-datatype qualifier = Show | Then | Moreover | Ultimately
-
-datatype step =
- Fix of (string * typ) list |
- Let of term * term |
- Assume of label * term |
- Have of qualifier list * label * term * byline
-and byline =
- ByMetis of facts |
- CaseSplit of step list list * facts
-
-fun smart_case_split [] facts = ByMetis facts
- | smart_case_split proofs facts = CaseSplit (proofs, facts)
-
-fun add_fact_from_dep axiom_names num =
- if is_axiom_number axiom_names num then
- apsnd (union (op =) (map fst (Vector.sub (axiom_names, num - 1))))
- else
- apfst (insert (op =) (raw_prefix, num))
-
-fun forall_of v t = HOLogic.all_const (fastype_of v) $ lambda v t
-fun forall_vars t = fold_rev forall_of (map Var (Term.add_vars t [])) t
-
-fun step_for_line _ _ (Definition (_, t1, t2)) = Let (t1, t2)
- | step_for_line _ _ (Inference (num, t, [])) = Assume ((raw_prefix, num), t)
- | step_for_line axiom_names j (Inference (num, t, deps)) =
- Have (if j = 1 then [Show] else [], (raw_prefix, num),
- forall_vars t,
- ByMetis (fold (add_fact_from_dep axiom_names) deps ([], [])))
-
-fun proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
- atp_proof conjecture_shape axiom_names params frees =
- let
- val lines =
- atp_proof ^ "$" (* the $ sign acts as a sentinel (FIXME: needed?) *)
- |> parse_proof pool
- |> sort (int_ord o pairself raw_step_number)
- |> decode_lines ctxt full_types tfrees
- |> rpair [] |-> fold_rev (add_line conjecture_shape axiom_names)
- |> rpair [] |-> fold_rev add_nontrivial_line
- |> rpair (0, []) |-> fold_rev (add_desired_line isar_shrink_factor
- conjecture_shape axiom_names frees)
- |> snd
- in
- (if null params then [] else [Fix params]) @
- map2 (step_for_line axiom_names) (length lines downto 1) lines
- end
-
-(* When redirecting proofs, we keep information about the labels seen so far in
- the "backpatches" data structure. The first component indicates which facts
- should be associated with forthcoming proof steps. The second component is a
- pair ("assum_ls", "drop_ls"), where "assum_ls" are the labels that should
- become assumptions and "drop_ls" are the labels that should be dropped in a
- case split. *)
-type backpatches = (label * facts) list * (label list * label list)
-
-fun used_labels_of_step (Have (_, _, _, by)) =
- (case by of
- ByMetis (ls, _) => ls
- | CaseSplit (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 new_labels_of_step (Fix _) = []
- | new_labels_of_step (Let _) = []
- | new_labels_of_step (Assume (l, _)) = [l]
- | new_labels_of_step (Have (_, l, _, _)) = [l]
-val new_labels_of = maps new_labels_of_step
-
-val join_proofs =
- let
- fun aux _ [] = NONE
- | aux proof_tail (proofs as (proof1 :: _)) =
- if exists null proofs then
- NONE
- else if forall (curry (op =) (hd proof1) o hd) (tl proofs) then
- aux (hd proof1 :: proof_tail) (map tl proofs)
- else case hd proof1 of
- Have ([], l, t, _) => (* FIXME: should we really ignore the "by"? *)
- if forall (fn Have ([], l', t', _) :: _ => (l, t) = (l', t')
- | _ => false) (tl proofs) andalso
- not (exists (member (op =) (maps new_labels_of proofs))
- (used_labels_of proof_tail)) then
- SOME (l, t, map rev proofs, proof_tail)
- else
- NONE
- | _ => NONE
- in aux [] o map rev end
-
-fun case_split_qualifiers proofs =
- case length proofs of
- 0 => []
- | 1 => [Then]
- | _ => [Ultimately]
-
-fun redirect_proof conjecture_shape hyp_ts concl_t proof =
- let
- (* The first pass outputs those steps that are independent of the negated
- conjecture. The second pass flips the proof by contradiction to obtain a
- direct proof, introducing case splits when an inference depends on
- several facts that depend on the negated conjecture. *)
- fun find_hyp num =
- nth hyp_ts (index_in_shape num conjecture_shape)
- handle Subscript =>
- raise Fail ("Cannot find hypothesis " ^ Int.toString num)
- val concl_ls = map (pair raw_prefix) (List.last conjecture_shape)
- val canonicalize_labels =
- map (fn l => if member (op =) concl_ls l then hd concl_ls else l)
- #> distinct (op =)
- fun first_pass ([], contra) = ([], contra)
- | first_pass ((step as Fix _) :: proof, contra) =
- first_pass (proof, contra) |>> cons step
- | first_pass ((step as Let _) :: proof, contra) =
- first_pass (proof, contra) |>> cons step
- | first_pass ((step as Assume (l as (_, num), _)) :: proof, contra) =
- if member (op =) concl_ls l then
- first_pass (proof, contra ||> l = hd concl_ls ? cons step)
- else
- first_pass (proof, contra) |>> cons (Assume (l, find_hyp num))
- | first_pass (Have (qs, l, t, ByMetis (ls, ss)) :: proof, contra) =
- let
- val ls = canonicalize_labels ls
- val step = Have (qs, l, t, ByMetis (ls, ss))
- in
- if exists (member (op =) (fst contra)) ls then
- first_pass (proof, contra |>> cons l ||> cons step)
- else
- first_pass (proof, contra) |>> cons step
- end
- | first_pass _ = raise Fail "malformed proof"
- val (proof_top, (contra_ls, contra_proof)) =
- first_pass (proof, (concl_ls, []))
- val backpatch_label = the_default ([], []) oo AList.lookup (op =) o fst
- fun backpatch_labels patches ls =
- fold merge_fact_sets (map (backpatch_label patches) ls) ([], [])
- fun second_pass end_qs ([], assums, patches) =
- ([Have (end_qs, no_label, concl_t,
- ByMetis (backpatch_labels patches (map snd assums)))], patches)
- | second_pass end_qs (Assume (l, t) :: proof, assums, patches) =
- second_pass end_qs (proof, (t, l) :: assums, patches)
- | second_pass end_qs (Have (qs, l, t, ByMetis (ls, ss)) :: proof, assums,
- patches) =
- if member (op =) (snd (snd patches)) l andalso
- not (member (op =) (fst (snd patches)) l) andalso
- not (AList.defined (op =) (fst patches) l) then
- second_pass end_qs (proof, assums, patches ||> apsnd (append ls))
- else
- (case List.partition (member (op =) contra_ls) ls of
- ([contra_l], co_ls) =>
- if member (op =) qs Show then
- second_pass end_qs (proof, assums,
- patches |>> cons (contra_l, (co_ls, ss)))
- else
- second_pass end_qs
- (proof, assums,
- patches |>> cons (contra_l, (l :: co_ls, ss)))
- |>> cons (if member (op =) (fst (snd patches)) l then
- Assume (l, negate_term t)
- else
- Have (qs, l, negate_term t,
- ByMetis (backpatch_label patches l)))
- | (contra_ls as _ :: _, co_ls) =>
- let
- val proofs =
- map_filter
- (fn l =>
- if member (op =) concl_ls l then
- NONE
- else
- let
- val drop_ls = filter (curry (op <>) l) contra_ls
- in
- second_pass []
- (proof, assums,
- patches ||> apfst (insert (op =) l)
- ||> apsnd (union (op =) drop_ls))
- |> fst |> SOME
- end) contra_ls
- val (assumes, facts) =
- if member (op =) (fst (snd patches)) l then
- ([Assume (l, negate_term t)], (l :: co_ls, ss))
- else
- ([], (co_ls, ss))
- in
- (case join_proofs proofs of
- SOME (l, t, proofs, proof_tail) =>
- Have (case_split_qualifiers proofs @
- (if null proof_tail then end_qs else []), l, t,
- smart_case_split proofs facts) :: proof_tail
- | NONE =>
- [Have (case_split_qualifiers proofs @ end_qs, no_label,
- concl_t, smart_case_split proofs facts)],
- patches)
- |>> append assumes
- end
- | _ => raise Fail "malformed proof")
- | second_pass _ _ = raise Fail "malformed proof"
- val proof_bottom =
- second_pass [Show] (contra_proof, [], ([], ([], []))) |> fst
- in proof_top @ proof_bottom end
-
-(* FIXME: Still needed? Probably not. *)
-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 (Have (qs, l, t, by)) (proof, subst, assums) =
- (Have (qs, l, t,
- case by of
- ByMetis facts => ByMetis (relabel_facts subst facts)
- | CaseSplit (proofs, facts) =>
- CaseSplit (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
-
-val then_chain_proof =
- let
- fun aux _ [] = []
- | aux _ ((step as Assume (l, _)) :: proof) = step :: aux l proof
- | aux l' (Have (qs, l, t, by) :: proof) =
- (case by of
- ByMetis (ls, ss) =>
- Have (if member (op =) ls l' then
- (Then :: qs, l, t,
- ByMetis (filter_out (curry (op =) l') ls, ss))
- else
- (qs, l, t, ByMetis (ls, ss)))
- | CaseSplit (proofs, facts) =>
- Have (qs, l, t, CaseSplit (map (aux no_label) proofs, facts))) ::
- aux l proof
- | aux _ (step :: proof) = step :: aux no_label proof
- in aux no_label end
-
-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 (Have (qs, l, t, by)) =
- Have (qs, do_label l, t,
- case by of
- CaseSplit (proofs, facts) =>
- CaseSplit (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) (Have (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 fact_prefix, next_fact)
- in (l', (l, l') :: subst, next_fact + 1) end
- val relabel_facts =
- apfst (map (fn l =>
- case AList.lookup (op =) subst l of
- SOME l' => l'
- | NONE => raise Fail ("unknown label " ^
- quote (string_for_label l))))
- val by =
- case by of
- ByMetis facts => ByMetis (relabel_facts facts)
- | CaseSplit (proofs, facts) =>
- CaseSplit (map (aux subst (depth + 1) (1, 1)) proofs,
- relabel_facts facts)
- in
- Have (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 ctxt full_types i n =
- let
- fun fix_print_mode f x =
- setmp_CRITICAL show_no_free_types true
- (setmp_CRITICAL show_types true
- (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)
- fun do_facts (ls, ss) =
- metis_command full_types 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 (Have (qs, l, t, ByMetis facts)) =
- do_indent ind ^ do_have qs ^ " " ^
- do_label l ^ do_term t ^ " " ^ do_facts facts ^ "\n"
- | do_step ind (Have (qs, l, t, CaseSplit (proofs, facts))) =
- space_implode (do_indent ind ^ "moreover\n")
- (map (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 [Have (_, _, _, ByMetis _)] = ""
- | 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 (pool, debug, isar_shrink_factor, ctxt, conjecture_shape)
- (other_params as (full_types, _, atp_proof, axiom_names,
- goal, i)) =
- let
- val (params, hyp_ts, concl_t) = strip_subgoal goal i
- val frees = fold Term.add_frees (concl_t :: hyp_ts) []
- val tfrees = fold Term.add_tfrees (concl_t :: hyp_ts) []
- val n = Logic.count_prems (prop_of goal)
- val (one_line_proof, lemma_names) = metis_proof_text other_params
- fun isar_proof_for () =
- case proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
- atp_proof conjecture_shape axiom_names params
- frees
- |> redirect_proof conjecture_shape hyp_ts concl_t
- |> kill_duplicate_assumptions_in_proof
- |> then_chain_proof
- |> kill_useless_labels_in_proof
- |> relabel_proof
- |> string_for_proof ctxt full_types i n of
- "" => "\nNo structured proof available."
- | proof => "\n\nStructured proof:\n" ^ Markup.markup Markup.sendback proof
- val isar_proof =
- if debug then
- isar_proof_for ()
- else
- try isar_proof_for ()
- |> the_default "\nWarning: The Isar proof construction failed."
- in (one_line_proof ^ isar_proof, lemma_names) end
-
-fun proof_text isar_proof isar_params other_params =
- (if isar_proof then isar_proof_text isar_params else metis_proof_text)
- other_params
-
-end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_reconstruct.ML Tue Aug 31 23:46:23 2010 +0200
@@ -0,0 +1,1038 @@
+(* Title: HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML
+ Author: Lawrence C. Paulson, Cambridge University Computer Laboratory
+ Author: Claire Quigley, Cambridge University Computer Laboratory
+ Author: Jasmin Blanchette, TU Muenchen
+
+Transfer of proofs from external provers.
+*)
+
+signature SLEDGEHAMMER_PROOF_RECONSTRUCT =
+sig
+ type locality = Sledgehammer_Fact_Filter.locality
+ type minimize_command = string list -> string
+ type metis_params =
+ bool * minimize_command * string * (string * locality) list vector * thm
+ * int
+ type isar_params =
+ string Symtab.table * bool * int * Proof.context * int list list
+ type text_result = string * (string * locality) list
+
+ val metis_proof_text : metis_params -> text_result
+ val isar_proof_text : isar_params -> metis_params -> text_result
+ val proof_text : bool -> isar_params -> metis_params -> text_result
+end;
+
+structure Sledgehammer_Proof_Reconstruct : SLEDGEHAMMER_PROOF_RECONSTRUCT =
+struct
+
+open ATP_Problem
+open Metis_Clauses
+open Sledgehammer_Util
+open Sledgehammer_Fact_Filter
+open Sledgehammer_Translate
+
+type minimize_command = string list -> string
+type metis_params =
+ bool * minimize_command * string * (string * locality) list vector * thm * int
+type isar_params =
+ string Symtab.table * bool * int * Proof.context * int list list
+type text_result = string * (string * locality) list
+
+(* Simple simplifications to ensure that sort annotations don't leave a trail of
+ spurious "True"s. *)
+fun s_not @{const False} = @{const True}
+ | s_not @{const True} = @{const False}
+ | s_not (@{const Not} $ t) = t
+ | s_not t = @{const Not} $ t
+fun s_conj (@{const True}, t2) = t2
+ | s_conj (t1, @{const True}) = t1
+ | s_conj p = HOLogic.mk_conj p
+fun s_disj (@{const False}, t2) = t2
+ | s_disj (t1, @{const False}) = t1
+ | s_disj p = HOLogic.mk_disj p
+fun s_imp (@{const True}, t2) = t2
+ | s_imp (t1, @{const False}) = s_not t1
+ | s_imp p = HOLogic.mk_imp p
+fun s_iff (@{const True}, t2) = t2
+ | s_iff (t1, @{const True}) = t1
+ | s_iff (t1, t2) = HOLogic.eq_const HOLogic.boolT $ t1 $ t2
+
+fun mk_anot (AConn (ANot, [phi])) = phi
+ | mk_anot phi = AConn (ANot, [phi])
+fun mk_aconn c (phi1, phi2) = AConn (c, [phi1, phi2])
+
+fun index_in_shape x = find_index (exists (curry (op =) x))
+fun is_axiom_number axiom_names num =
+ num > 0 andalso num <= Vector.length axiom_names andalso
+ not (null (Vector.sub (axiom_names, num - 1)))
+fun is_conjecture_number conjecture_shape num =
+ index_in_shape num conjecture_shape >= 0
+
+fun negate_term (Const (@{const_name All}, T) $ Abs (s, T', t')) =
+ Const (@{const_name Ex}, T) $ Abs (s, T', negate_term t')
+ | negate_term (Const (@{const_name Ex}, T) $ Abs (s, T', t')) =
+ Const (@{const_name All}, T) $ Abs (s, T', negate_term t')
+ | negate_term (@{const HOL.implies} $ t1 $ t2) =
+ @{const HOL.conj} $ t1 $ negate_term t2
+ | negate_term (@{const HOL.conj} $ t1 $ t2) =
+ @{const HOL.disj} $ negate_term t1 $ negate_term t2
+ | negate_term (@{const HOL.disj} $ t1 $ t2) =
+ @{const HOL.conj} $ negate_term t1 $ negate_term t2
+ | negate_term (@{const Not} $ t) = t
+ | negate_term t = @{const Not} $ t
+
+datatype ('a, 'b, 'c, 'd, 'e) raw_step =
+ Definition of 'a * 'b * 'c |
+ Inference of 'a * 'd * 'e list
+
+fun raw_step_number (Definition (num, _, _)) = num
+ | raw_step_number (Inference (num, _, _)) = num
+
+(**** PARSING OF TSTP FORMAT ****)
+
+(*Strings enclosed in single quotes, e.g. filenames*)
+val scan_quoted = $$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'" >> implode;
+
+val scan_dollar_name =
+ Scan.repeat ($$ "$") -- Symbol.scan_id >> (fn (ss, s) => implode ss ^ s)
+
+fun repair_name _ "$true" = "c_True"
+ | repair_name _ "$false" = "c_False"
+ | repair_name _ "$$e" = "c_equal" (* seen in Vampire proofs *)
+ | repair_name _ "equal" = "c_equal" (* needed by SPASS? *)
+ | repair_name pool s =
+ case Symtab.lookup pool s of
+ SOME s' => s'
+ | NONE =>
+ if String.isPrefix "sQ" s andalso String.isSuffix "_eqProxy" s then
+ "c_equal" (* seen in Vampire proofs *)
+ else
+ s
+(* Generalized first-order terms, which include file names, numbers, etc. *)
+val parse_potential_integer =
+ (scan_dollar_name || scan_quoted) >> K NONE
+ || scan_integer >> SOME
+fun parse_annotation x =
+ ((parse_potential_integer ::: Scan.repeat ($$ " " |-- parse_potential_integer)
+ >> map_filter I) -- Scan.optional parse_annotation []
+ >> uncurry (union (op =))
+ || $$ "(" |-- parse_annotations --| $$ ")"
+ || $$ "[" |-- parse_annotations --| $$ "]") x
+and parse_annotations x =
+ (Scan.optional (parse_annotation
+ ::: Scan.repeat ($$ "," |-- parse_annotation)) []
+ >> (fn numss => fold (union (op =)) numss [])) x
+
+(* Vampire proof lines sometimes contain needless information such as "(0:3)",
+ which can be hard to disambiguate from function application in an LL(1)
+ parser. As a workaround, we extend the TPTP term syntax with such detritus
+ and ignore it. *)
+fun parse_vampire_detritus x =
+ (scan_integer |-- $$ ":" --| scan_integer >> K []) x
+
+fun parse_term pool x =
+ ((scan_dollar_name >> repair_name pool)
+ -- Scan.optional ($$ "(" |-- (parse_vampire_detritus || parse_terms pool)
+ --| $$ ")") []
+ --| Scan.optional ($$ "(" |-- parse_vampire_detritus --| $$ ")") []
+ >> ATerm) x
+and parse_terms pool x =
+ (parse_term pool ::: Scan.repeat ($$ "," |-- parse_term pool)) x
+
+fun parse_atom pool =
+ parse_term pool -- Scan.option (Scan.option ($$ "!") --| $$ "="
+ -- parse_term pool)
+ >> (fn (u1, NONE) => AAtom u1
+ | (u1, SOME (NONE, u2)) => AAtom (ATerm ("c_equal", [u1, u2]))
+ | (u1, SOME (SOME _, u2)) =>
+ mk_anot (AAtom (ATerm ("c_equal", [u1, u2]))))
+
+fun fo_term_head (ATerm (s, _)) = s
+
+(* TPTP formulas are fully parenthesized, so we don't need to worry about
+ operator precedence. *)
+fun parse_formula pool x =
+ (($$ "(" |-- parse_formula pool --| $$ ")"
+ || ($$ "!" >> K AForall || $$ "?" >> K AExists)
+ --| $$ "[" -- parse_terms pool --| $$ "]" --| $$ ":"
+ -- parse_formula pool
+ >> (fn ((q, ts), phi) => AQuant (q, map fo_term_head ts, phi))
+ || $$ "~" |-- parse_formula pool >> mk_anot
+ || parse_atom pool)
+ -- Scan.option ((Scan.this_string "=>" >> K AImplies
+ || Scan.this_string "<=>" >> K AIff
+ || Scan.this_string "<~>" >> K ANotIff
+ || Scan.this_string "<=" >> K AIf
+ || $$ "|" >> K AOr || $$ "&" >> K AAnd)
+ -- parse_formula pool)
+ >> (fn (phi1, NONE) => phi1
+ | (phi1, SOME (c, phi2)) => mk_aconn c (phi1, phi2))) x
+
+val parse_tstp_extra_arguments =
+ Scan.optional ($$ "," |-- parse_annotation
+ --| Scan.option ($$ "," |-- parse_annotations)) []
+
+(* Syntax: (fof|cnf)\(<num>, <formula_role>, <formula> <extra_arguments>\).
+ The <num> could be an identifier, but we assume integers. *)
+ fun parse_tstp_line pool =
+ ((Scan.this_string "fof" || Scan.this_string "cnf") -- $$ "(")
+ |-- scan_integer --| $$ "," -- Symbol.scan_id --| $$ ","
+ -- parse_formula pool -- parse_tstp_extra_arguments --| $$ ")" --| $$ "."
+ >> (fn (((num, role), phi), deps) =>
+ case role of
+ "definition" =>
+ (case phi of
+ AConn (AIff, [phi1 as AAtom _, phi2]) =>
+ Definition (num, phi1, phi2)
+ | AAtom (ATerm ("c_equal", _)) =>
+ Inference (num, phi, deps) (* Vampire's equality proxy axiom *)
+ | _ => raise Fail "malformed definition")
+ | _ => Inference (num, phi, deps))
+
+(**** PARSING OF VAMPIRE OUTPUT ****)
+
+(* Syntax: <num>. <formula> <annotation> *)
+fun parse_vampire_line pool =
+ scan_integer --| $$ "." -- parse_formula pool -- parse_annotation
+ >> (fn ((num, phi), deps) => Inference (num, phi, deps))
+
+(**** PARSING OF SPASS OUTPUT ****)
+
+(* SPASS returns clause references of the form "x.y". We ignore "y", whose role
+ is not clear anyway. *)
+val parse_dot_name = scan_integer --| $$ "." --| scan_integer
+
+val parse_spass_annotations =
+ Scan.optional ($$ ":" |-- Scan.repeat (parse_dot_name
+ --| Scan.option ($$ ","))) []
+
+(* It is not clear why some literals are followed by sequences of stars and/or
+ pluses. We ignore them. *)
+fun parse_decorated_atom pool =
+ parse_atom pool --| Scan.repeat ($$ "*" || $$ "+" || $$ " ")
+
+fun mk_horn ([], []) = AAtom (ATerm ("c_False", []))
+ | mk_horn ([], pos_lits) = foldr1 (mk_aconn AOr) pos_lits
+ | mk_horn (neg_lits, []) = mk_anot (foldr1 (mk_aconn AAnd) neg_lits)
+ | mk_horn (neg_lits, pos_lits) =
+ mk_aconn AImplies (foldr1 (mk_aconn AAnd) neg_lits,
+ foldr1 (mk_aconn AOr) pos_lits)
+
+fun parse_horn_clause pool =
+ Scan.repeat (parse_decorated_atom pool) --| $$ "|" --| $$ "|"
+ -- Scan.repeat (parse_decorated_atom pool) --| $$ "-" --| $$ ">"
+ -- Scan.repeat (parse_decorated_atom pool)
+ >> (mk_horn o apfst (op @))
+
+(* Syntax: <num>[0:<inference><annotations>]
+ <atoms> || <atoms> -> <atoms>. *)
+fun parse_spass_line pool =
+ scan_integer --| $$ "[" --| $$ "0" --| $$ ":" --| Symbol.scan_id
+ -- parse_spass_annotations --| $$ "]" -- parse_horn_clause pool --| $$ "."
+ >> (fn ((num, deps), u) => Inference (num, u, deps))
+
+fun parse_line pool =
+ parse_tstp_line pool || parse_vampire_line pool || parse_spass_line pool
+fun parse_lines pool = Scan.repeat1 (parse_line pool)
+fun parse_proof pool =
+ fst o Scan.finite Symbol.stopper
+ (Scan.error (!! (fn _ => raise Fail "unrecognized ATP output")
+ (parse_lines pool)))
+ o explode o strip_spaces_except_between_ident_chars
+
+(**** INTERPRETATION OF TSTP SYNTAX TREES ****)
+
+exception FO_TERM of string fo_term list
+exception FORMULA of (string, string fo_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 type_from_fo_term tfrees (u as ATerm (a, us)) =
+ let val Ts = map (type_from_fo_term tfrees) us in
+ case strip_prefix_and_unascii type_const_prefix a of
+ SOME b => Type (invert_const b, Ts)
+ | NONE =>
+ if not (null us) then
+ raise FO_TERM [u] (* only "tconst"s have type arguments *)
+ else case strip_prefix_and_unascii tfree_prefix a of
+ SOME b =>
+ let val s = "'" ^ b in
+ TFree (s, AList.lookup (op =) tfrees s |> the_default HOLogic.typeS)
+ end
+ | NONE =>
+ case strip_prefix_and_unascii tvar_prefix a of
+ SOME b => TVar (("'" ^ b, 0), HOLogic.typeS)
+ | NONE =>
+ (* Variable from the ATP, say "X1" *)
+ Type_Infer.param 0 (a, HOLogic.typeS)
+ end
+
+(* Type class literal applied to a type. Returns triple of polarity, class,
+ type. *)
+fun type_constraint_from_term pos tfrees (u as ATerm (a, us)) =
+ case (strip_prefix_and_unascii class_prefix a,
+ map (type_from_fo_term tfrees) us) of
+ (SOME b, [T]) => (pos, b, T)
+ | _ => raise FO_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_atp_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
+
+(* First-order translation. No types are known for variables. "HOLogic.typeT"
+ should allow them to be inferred. *)
+fun raw_term_from_pred thy full_types tfrees =
+ let
+ fun aux opt_T extra_us u =
+ case u of
+ ATerm ("hBOOL", [u1]) => aux (SOME @{typ bool}) [] u1
+ | ATerm ("hAPP", [u1, u2]) => aux opt_T (u2 :: extra_us) u1
+ | ATerm (a, us) =>
+ if a = type_wrapper_name then
+ case us of
+ [typ_u, term_u] =>
+ aux (SOME (type_from_fo_term tfrees typ_u)) extra_us term_u
+ | _ => raise FO_TERM us
+ else case strip_prefix_and_unascii const_prefix a of
+ SOME "equal" =>
+ list_comb (Const (@{const_name HOL.eq}, HOLogic.typeT),
+ map (aux NONE []) us)
+ | SOME b =>
+ let
+ val c = invert_const b
+ val num_type_args = num_type_args thy c
+ val (type_us, term_us) =
+ chop (if full_types then 0 else num_type_args) us
+ (* Extra args from "hAPP" come after any arguments given directly to
+ the constant. *)
+ val term_ts = map (aux NONE []) term_us
+ val extra_ts = map (aux NONE []) extra_us
+ val t =
+ Const (c, if full_types then
+ case opt_T of
+ SOME T => map fastype_of term_ts ---> T
+ | NONE =>
+ if num_type_args = 0 then
+ Sign.const_instance thy (c, [])
+ else
+ raise Fail ("no type information for " ^ quote c)
+ else
+ Sign.const_instance thy (c,
+ map (type_from_fo_term tfrees) type_us))
+ in list_comb (t, term_ts @ extra_ts) end
+ | NONE => (* a free or schematic variable *)
+ let
+ val ts = map (aux NONE []) (us @ extra_us)
+ val T = map fastype_of ts ---> HOLogic.typeT
+ val t =
+ case strip_prefix_and_unascii fixed_var_prefix a of
+ SOME b => Free (b, T)
+ | NONE =>
+ case strip_prefix_and_unascii schematic_var_prefix a of
+ SOME b => Var ((b, 0), T)
+ | NONE =>
+ if is_tptp_variable a then
+ Var ((repair_atp_variable_name Char.toLower a, 0), T)
+ else
+ (* Skolem constants? *)
+ Var ((repair_atp_variable_name Char.toUpper a, 0), T)
+ in list_comb (t, ts) end
+ in aux (SOME HOLogic.boolT) [] end
+
+fun term_from_pred thy full_types tfrees pos (u as ATerm (s, _)) =
+ if String.isPrefix class_prefix s then
+ add_type_constraint (type_constraint_from_term pos tfrees u)
+ #> pair @{const True}
+ else
+ pair (raw_term_from_pred thy full_types tfrees u)
+
+val combinator_table =
+ [(@{const_name COMBI}, @{thm COMBI_def_raw}),
+ (@{const_name COMBK}, @{thm COMBK_def_raw}),
+ (@{const_name COMBB}, @{thm COMBB_def_raw}),
+ (@{const_name COMBC}, @{thm COMBC_def_raw}),
+ (@{const_name COMBS}, @{thm COMBS_def_raw})]
+
+fun uncombine_term (t1 $ t2) = betapply (pairself uncombine_term (t1, t2))
+ | uncombine_term (Abs (s, T, t')) = Abs (s, T, uncombine_term t')
+ | uncombine_term (t as Const (x as (s, _))) =
+ (case AList.lookup (op =) combinator_table s of
+ SOME thm => thm |> prop_of |> specialize_type @{theory} x |> Logic.dest_equals |> snd
+ | NONE => t)
+ | uncombine_term t = t
+
+(* Update schematic type variables with detected sort constraints. It's not
+ totally clear when 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_free quant_s free_s body_t =
+ case Term.add_frees body_t [] |> filter (curry (op =) free_s o fst) of
+ [] => body_t
+ | frees as (_, free_T) :: _ =>
+ Abs (free_s, free_T, fold (curry abstract_over) (map Free frees) body_t)
+
+(* Interpret an ATP formula as a HOL term, extracting sort constraints as they
+ appear in the formula. *)
+fun prop_from_formula thy full_types tfrees phi =
+ let
+ fun do_formula pos phi =
+ case phi of
+ AQuant (_, [], phi) => do_formula pos phi
+ | AQuant (q, x :: xs, phi') =>
+ do_formula pos (AQuant (q, xs, phi'))
+ #>> quantify_over_free (case q of
+ AForall => @{const_name All}
+ | AExists => @{const_name Ex})
+ (repair_atp_variable_name Char.toLower x)
+ | 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
+ | AIf => s_imp o swap
+ | AIff => s_iff
+ | ANotIff => s_not o s_iff)
+ | AAtom tm => term_from_pred thy full_types tfrees pos tm
+ | _ => raise FORMULA [phi]
+ in repair_tvar_sorts (do_formula true phi Vartab.empty) end
+
+fun check_formula ctxt =
+ Type_Infer.constrain HOLogic.boolT
+ #> Syntax.check_term (ProofContext.set_mode ProofContext.mode_schematic ctxt)
+
+
+(**** 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 full_types tfrees (Definition (num, phi1, phi2)) ctxt =
+ let
+ val thy = ProofContext.theory_of ctxt
+ val t1 = prop_from_formula thy full_types tfrees phi1
+ val vars = snd (strip_comb t1)
+ val frees = map unvarify_term vars
+ val unvarify_args = subst_atomic (vars ~~ frees)
+ val t2 = prop_from_formula thy full_types tfrees phi2
+ val (t1, t2) =
+ HOLogic.eq_const HOLogic.typeT $ t1 $ t2
+ |> unvarify_args |> uncombine_term |> check_formula ctxt
+ |> HOLogic.dest_eq
+ in
+ (Definition (num, t1, t2),
+ fold Variable.declare_term (maps OldTerm.term_frees [t1, t2]) ctxt)
+ end
+ | decode_line full_types tfrees (Inference (num, u, deps)) ctxt =
+ let
+ val thy = ProofContext.theory_of ctxt
+ val t = u |> prop_from_formula thy full_types tfrees
+ |> uncombine_term |> check_formula ctxt
+ in
+ (Inference (num, t, deps),
+ fold Variable.declare_term (OldTerm.term_frees t) ctxt)
+ end
+fun decode_lines ctxt full_types tfrees lines =
+ fst (fold_map (decode_line full_types tfrees) 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) HOLogic.true_const
+
+fun replace_one_dep (old, new) dep = if dep = old then new else [dep]
+fun replace_deps_in_line _ (line as Definition _) = line
+ | replace_deps_in_line p (Inference (num, t, deps)) =
+ Inference (num, t, fold (union (op =) o replace_one_dep p) deps [])
+
+(* Discard axioms; 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 conjecture_shape axiom_names (Inference (num, t, [])) lines =
+ (* No dependencies: axiom, conjecture, or (for Vampire) internal axioms or
+ definitions. *)
+ if is_axiom_number axiom_names num then
+ (* Axioms are not proof lines. *)
+ if is_only_type_information t then
+ map (replace_deps_in_line (num, [])) 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 (num', _, _) :: post) =>
+ pre @ map (replace_deps_in_line (num', [num])) post
+ else if is_conjecture_number conjecture_shape num then
+ Inference (num, negate_term t, []) :: lines
+ else
+ map (replace_deps_in_line (num, [])) lines
+ | add_line _ _ (Inference (num, t, deps)) lines =
+ (* Type information will be deleted later; skip repetition test. *)
+ if is_only_type_information t then
+ Inference (num, t, 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 (num, t, deps) :: lines
+ | (pre, Inference (num', t', _) :: post) =>
+ Inference (num, t', deps) ::
+ pre @ map (replace_deps_in_line (num', [num])) post
+
+(* Recursively delete empty lines (type information) from the proof. *)
+fun add_nontrivial_line (Inference (num, t, [])) lines =
+ if is_only_type_information t then delete_dep num lines
+ else Inference (num, t, []) :: lines
+ | add_nontrivial_line line lines = line :: lines
+and delete_dep num lines =
+ fold_rev add_nontrivial_line (map (replace_deps_in_line (num, [])) 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
+
+(* Vampire is keen on producing these. *)
+fun is_trivial_formula (@{const Not} $ (Const (@{const_name HOL.eq}, _)
+ $ t1 $ t2)) = (t1 aconv t2)
+ | is_trivial_formula _ = false
+
+fun add_desired_line _ _ _ _ (line as Definition (num, _, _)) (j, lines) =
+ (j, line :: map (replace_deps_in_line (num, [])) lines)
+ | add_desired_line isar_shrink_factor conjecture_shape axiom_names frees
+ (Inference (num, t, deps)) (j, lines) =
+ (j + 1,
+ if is_axiom_number axiom_names num orelse
+ is_conjecture_number conjecture_shape num orelse
+ (not (is_only_type_information t) andalso
+ null (Term.add_tvars t []) andalso
+ not (exists_subterm (is_bad_free frees) t) andalso
+ not (is_trivial_formula t) andalso
+ (null lines orelse (* last line must be kept *)
+ (length deps >= 2 andalso j mod isar_shrink_factor = 0))) then
+ Inference (num, t, deps) :: lines (* keep line *)
+ else
+ map (replace_deps_in_line (num, deps)) lines) (* drop line *)
+
+(** EXTRACTING LEMMAS **)
+
+(* Like "split_line", but ignores "\n" that follow a comma (as in SNARK's
+ output). *)
+val split_proof_lines =
+ let
+ fun aux [] [] = []
+ | aux line [] = [implode (rev line)]
+ | aux line ("," :: "\n" :: rest) = aux ("," :: line) rest
+ | aux line ("\n" :: rest) = aux line [] @ aux [] rest
+ | aux line (s :: rest) = aux (s :: line) rest
+ in aux [] o explode end
+
+(* A list consisting of the first number in each line is returned. For TSTP,
+ interesting lines have the form "fof(108, axiom, ...)", where the number
+ (108) is extracted. For SPASS, lines have the form "108[0:Inp] ...", where
+ the first number (108) is extracted. For Vampire, we look for
+ "108. ... [input]". *)
+fun used_facts_in_atp_proof axiom_names atp_proof =
+ let
+ fun axiom_names_at_index num =
+ let val j = Int.fromString num |> the_default ~1 in
+ if is_axiom_number axiom_names j then Vector.sub (axiom_names, j - 1)
+ else []
+ end
+ val tokens_of =
+ String.tokens (fn c => not (Char.isAlphaNum c) andalso c <> #"_")
+ fun do_line (tag :: num :: "axiom" :: (rest as _ :: _)) =
+ if tag = "cnf" orelse tag = "fof" then
+ (case strip_prefix_and_unascii axiom_prefix (List.last rest) of
+ SOME name =>
+ if member (op =) rest "file" then
+ ([(name, name |> find_first_in_list_vector axiom_names |> the)]
+ handle Option.Option =>
+ error ("No such fact: " ^ quote name ^ "."))
+ else
+ axiom_names_at_index num
+ | NONE => axiom_names_at_index num)
+ else
+ []
+ | do_line (num :: "0" :: "Inp" :: _) = axiom_names_at_index num
+ | do_line (num :: rest) =
+ (case List.last rest of "input" => axiom_names_at_index num | _ => [])
+ | do_line _ = []
+ in atp_proof |> split_proof_lines |> maps (do_line o tokens_of) end
+
+val indent_size = 2
+val no_label = ("", ~1)
+
+val raw_prefix = "X"
+val assum_prefix = "A"
+val fact_prefix = "F"
+
+fun string_for_label (s, num) = s ^ string_of_int num
+
+fun metis_using [] = ""
+ | metis_using ls =
+ "using " ^ space_implode " " (map string_for_label ls) ^ " "
+fun metis_apply _ 1 = "by "
+ | metis_apply 1 _ = "apply "
+ | metis_apply i _ = "prefer " ^ string_of_int i ^ " apply "
+fun metis_name full_types = if full_types then "metisFT" else "metis"
+fun metis_call full_types [] = metis_name full_types
+ | metis_call full_types ss =
+ "(" ^ metis_name full_types ^ " " ^ space_implode " " ss ^ ")"
+fun metis_command full_types i n (ls, ss) =
+ metis_using ls ^ metis_apply i n ^ metis_call full_types ss
+fun metis_line full_types i n ss =
+ "Try this command: " ^
+ Markup.markup Markup.sendback (metis_command full_types i n ([], ss)) ^ "."
+fun minimize_line _ [] = ""
+ | minimize_line minimize_command ss =
+ case minimize_command ss of
+ "" => ""
+ | command =>
+ "\nTo minimize the number of lemmas, try this: " ^
+ Markup.markup Markup.sendback command ^ "."
+
+fun used_facts axiom_names =
+ used_facts_in_atp_proof axiom_names
+ #> List.partition (curry (op =) Chained o snd)
+ #> pairself (sort_distinct (string_ord o pairself fst))
+
+fun metis_proof_text (full_types, minimize_command, atp_proof, axiom_names,
+ goal, i) =
+ let
+ val (chained_lemmas, other_lemmas) = used_facts axiom_names atp_proof
+ val n = Logic.count_prems (prop_of goal)
+ in
+ (metis_line full_types i n (map fst other_lemmas) ^
+ minimize_line minimize_command (map fst (other_lemmas @ chained_lemmas)),
+ other_lemmas @ chained_lemmas)
+ end
+
+(** Isar proof construction and manipulation **)
+
+fun merge_fact_sets (ls1, ss1) (ls2, ss2) =
+ (union (op =) ls1 ls2, union (op =) ss1 ss2)
+
+type label = string * int
+type facts = label list * string list
+
+datatype qualifier = Show | Then | Moreover | Ultimately
+
+datatype step =
+ Fix of (string * typ) list |
+ Let of term * term |
+ Assume of label * term |
+ Have of qualifier list * label * term * byline
+and byline =
+ ByMetis of facts |
+ CaseSplit of step list list * facts
+
+fun smart_case_split [] facts = ByMetis facts
+ | smart_case_split proofs facts = CaseSplit (proofs, facts)
+
+fun add_fact_from_dep axiom_names num =
+ if is_axiom_number axiom_names num then
+ apsnd (union (op =) (map fst (Vector.sub (axiom_names, num - 1))))
+ else
+ apfst (insert (op =) (raw_prefix, num))
+
+fun forall_of v t = HOLogic.all_const (fastype_of v) $ lambda v t
+fun forall_vars t = fold_rev forall_of (map Var (Term.add_vars t [])) t
+
+fun step_for_line _ _ (Definition (_, t1, t2)) = Let (t1, t2)
+ | step_for_line _ _ (Inference (num, t, [])) = Assume ((raw_prefix, num), t)
+ | step_for_line axiom_names j (Inference (num, t, deps)) =
+ Have (if j = 1 then [Show] else [], (raw_prefix, num),
+ forall_vars t,
+ ByMetis (fold (add_fact_from_dep axiom_names) deps ([], [])))
+
+fun proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
+ atp_proof conjecture_shape axiom_names params frees =
+ let
+ val lines =
+ atp_proof ^ "$" (* the $ sign acts as a sentinel (FIXME: needed?) *)
+ |> parse_proof pool
+ |> sort (int_ord o pairself raw_step_number)
+ |> decode_lines ctxt full_types tfrees
+ |> rpair [] |-> fold_rev (add_line conjecture_shape axiom_names)
+ |> rpair [] |-> fold_rev add_nontrivial_line
+ |> rpair (0, []) |-> fold_rev (add_desired_line isar_shrink_factor
+ conjecture_shape axiom_names frees)
+ |> snd
+ in
+ (if null params then [] else [Fix params]) @
+ map2 (step_for_line axiom_names) (length lines downto 1) lines
+ end
+
+(* When redirecting proofs, we keep information about the labels seen so far in
+ the "backpatches" data structure. The first component indicates which facts
+ should be associated with forthcoming proof steps. The second component is a
+ pair ("assum_ls", "drop_ls"), where "assum_ls" are the labels that should
+ become assumptions and "drop_ls" are the labels that should be dropped in a
+ case split. *)
+type backpatches = (label * facts) list * (label list * label list)
+
+fun used_labels_of_step (Have (_, _, _, by)) =
+ (case by of
+ ByMetis (ls, _) => ls
+ | CaseSplit (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 new_labels_of_step (Fix _) = []
+ | new_labels_of_step (Let _) = []
+ | new_labels_of_step (Assume (l, _)) = [l]
+ | new_labels_of_step (Have (_, l, _, _)) = [l]
+val new_labels_of = maps new_labels_of_step
+
+val join_proofs =
+ let
+ fun aux _ [] = NONE
+ | aux proof_tail (proofs as (proof1 :: _)) =
+ if exists null proofs then
+ NONE
+ else if forall (curry (op =) (hd proof1) o hd) (tl proofs) then
+ aux (hd proof1 :: proof_tail) (map tl proofs)
+ else case hd proof1 of
+ Have ([], l, t, _) => (* FIXME: should we really ignore the "by"? *)
+ if forall (fn Have ([], l', t', _) :: _ => (l, t) = (l', t')
+ | _ => false) (tl proofs) andalso
+ not (exists (member (op =) (maps new_labels_of proofs))
+ (used_labels_of proof_tail)) then
+ SOME (l, t, map rev proofs, proof_tail)
+ else
+ NONE
+ | _ => NONE
+ in aux [] o map rev end
+
+fun case_split_qualifiers proofs =
+ case length proofs of
+ 0 => []
+ | 1 => [Then]
+ | _ => [Ultimately]
+
+fun redirect_proof conjecture_shape hyp_ts concl_t proof =
+ let
+ (* The first pass outputs those steps that are independent of the negated
+ conjecture. The second pass flips the proof by contradiction to obtain a
+ direct proof, introducing case splits when an inference depends on
+ several facts that depend on the negated conjecture. *)
+ fun find_hyp num =
+ nth hyp_ts (index_in_shape num conjecture_shape)
+ handle Subscript =>
+ raise Fail ("Cannot find hypothesis " ^ Int.toString num)
+ val concl_ls = map (pair raw_prefix) (List.last conjecture_shape)
+ val canonicalize_labels =
+ map (fn l => if member (op =) concl_ls l then hd concl_ls else l)
+ #> distinct (op =)
+ fun first_pass ([], contra) = ([], contra)
+ | first_pass ((step as Fix _) :: proof, contra) =
+ first_pass (proof, contra) |>> cons step
+ | first_pass ((step as Let _) :: proof, contra) =
+ first_pass (proof, contra) |>> cons step
+ | first_pass ((step as Assume (l as (_, num), _)) :: proof, contra) =
+ if member (op =) concl_ls l then
+ first_pass (proof, contra ||> l = hd concl_ls ? cons step)
+ else
+ first_pass (proof, contra) |>> cons (Assume (l, find_hyp num))
+ | first_pass (Have (qs, l, t, ByMetis (ls, ss)) :: proof, contra) =
+ let
+ val ls = canonicalize_labels ls
+ val step = Have (qs, l, t, ByMetis (ls, ss))
+ in
+ if exists (member (op =) (fst contra)) ls then
+ first_pass (proof, contra |>> cons l ||> cons step)
+ else
+ first_pass (proof, contra) |>> cons step
+ end
+ | first_pass _ = raise Fail "malformed proof"
+ val (proof_top, (contra_ls, contra_proof)) =
+ first_pass (proof, (concl_ls, []))
+ val backpatch_label = the_default ([], []) oo AList.lookup (op =) o fst
+ fun backpatch_labels patches ls =
+ fold merge_fact_sets (map (backpatch_label patches) ls) ([], [])
+ fun second_pass end_qs ([], assums, patches) =
+ ([Have (end_qs, no_label, concl_t,
+ ByMetis (backpatch_labels patches (map snd assums)))], patches)
+ | second_pass end_qs (Assume (l, t) :: proof, assums, patches) =
+ second_pass end_qs (proof, (t, l) :: assums, patches)
+ | second_pass end_qs (Have (qs, l, t, ByMetis (ls, ss)) :: proof, assums,
+ patches) =
+ if member (op =) (snd (snd patches)) l andalso
+ not (member (op =) (fst (snd patches)) l) andalso
+ not (AList.defined (op =) (fst patches) l) then
+ second_pass end_qs (proof, assums, patches ||> apsnd (append ls))
+ else
+ (case List.partition (member (op =) contra_ls) ls of
+ ([contra_l], co_ls) =>
+ if member (op =) qs Show then
+ second_pass end_qs (proof, assums,
+ patches |>> cons (contra_l, (co_ls, ss)))
+ else
+ second_pass end_qs
+ (proof, assums,
+ patches |>> cons (contra_l, (l :: co_ls, ss)))
+ |>> cons (if member (op =) (fst (snd patches)) l then
+ Assume (l, negate_term t)
+ else
+ Have (qs, l, negate_term t,
+ ByMetis (backpatch_label patches l)))
+ | (contra_ls as _ :: _, co_ls) =>
+ let
+ val proofs =
+ map_filter
+ (fn l =>
+ if member (op =) concl_ls l then
+ NONE
+ else
+ let
+ val drop_ls = filter (curry (op <>) l) contra_ls
+ in
+ second_pass []
+ (proof, assums,
+ patches ||> apfst (insert (op =) l)
+ ||> apsnd (union (op =) drop_ls))
+ |> fst |> SOME
+ end) contra_ls
+ val (assumes, facts) =
+ if member (op =) (fst (snd patches)) l then
+ ([Assume (l, negate_term t)], (l :: co_ls, ss))
+ else
+ ([], (co_ls, ss))
+ in
+ (case join_proofs proofs of
+ SOME (l, t, proofs, proof_tail) =>
+ Have (case_split_qualifiers proofs @
+ (if null proof_tail then end_qs else []), l, t,
+ smart_case_split proofs facts) :: proof_tail
+ | NONE =>
+ [Have (case_split_qualifiers proofs @ end_qs, no_label,
+ concl_t, smart_case_split proofs facts)],
+ patches)
+ |>> append assumes
+ end
+ | _ => raise Fail "malformed proof")
+ | second_pass _ _ = raise Fail "malformed proof"
+ val proof_bottom =
+ second_pass [Show] (contra_proof, [], ([], ([], []))) |> fst
+ in proof_top @ proof_bottom end
+
+(* FIXME: Still needed? Probably not. *)
+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 (Have (qs, l, t, by)) (proof, subst, assums) =
+ (Have (qs, l, t,
+ case by of
+ ByMetis facts => ByMetis (relabel_facts subst facts)
+ | CaseSplit (proofs, facts) =>
+ CaseSplit (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
+
+val then_chain_proof =
+ let
+ fun aux _ [] = []
+ | aux _ ((step as Assume (l, _)) :: proof) = step :: aux l proof
+ | aux l' (Have (qs, l, t, by) :: proof) =
+ (case by of
+ ByMetis (ls, ss) =>
+ Have (if member (op =) ls l' then
+ (Then :: qs, l, t,
+ ByMetis (filter_out (curry (op =) l') ls, ss))
+ else
+ (qs, l, t, ByMetis (ls, ss)))
+ | CaseSplit (proofs, facts) =>
+ Have (qs, l, t, CaseSplit (map (aux no_label) proofs, facts))) ::
+ aux l proof
+ | aux _ (step :: proof) = step :: aux no_label proof
+ in aux no_label end
+
+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 (Have (qs, l, t, by)) =
+ Have (qs, do_label l, t,
+ case by of
+ CaseSplit (proofs, facts) =>
+ CaseSplit (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) (Have (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 fact_prefix, next_fact)
+ in (l', (l, l') :: subst, next_fact + 1) end
+ val relabel_facts =
+ apfst (map (fn l =>
+ case AList.lookup (op =) subst l of
+ SOME l' => l'
+ | NONE => raise Fail ("unknown label " ^
+ quote (string_for_label l))))
+ val by =
+ case by of
+ ByMetis facts => ByMetis (relabel_facts facts)
+ | CaseSplit (proofs, facts) =>
+ CaseSplit (map (aux subst (depth + 1) (1, 1)) proofs,
+ relabel_facts facts)
+ in
+ Have (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 ctxt full_types i n =
+ let
+ fun fix_print_mode f x =
+ setmp_CRITICAL show_no_free_types true
+ (setmp_CRITICAL show_types true
+ (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)
+ fun do_facts (ls, ss) =
+ metis_command full_types 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 (Have (qs, l, t, ByMetis facts)) =
+ do_indent ind ^ do_have qs ^ " " ^
+ do_label l ^ do_term t ^ " " ^ do_facts facts ^ "\n"
+ | do_step ind (Have (qs, l, t, CaseSplit (proofs, facts))) =
+ space_implode (do_indent ind ^ "moreover\n")
+ (map (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 [Have (_, _, _, ByMetis _)] = ""
+ | 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 (pool, debug, isar_shrink_factor, ctxt, conjecture_shape)
+ (other_params as (full_types, _, atp_proof, axiom_names,
+ goal, i)) =
+ let
+ val (params, hyp_ts, concl_t) = strip_subgoal goal i
+ val frees = fold Term.add_frees (concl_t :: hyp_ts) []
+ val tfrees = fold Term.add_tfrees (concl_t :: hyp_ts) []
+ val n = Logic.count_prems (prop_of goal)
+ val (one_line_proof, lemma_names) = metis_proof_text other_params
+ fun isar_proof_for () =
+ case proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
+ atp_proof conjecture_shape axiom_names params
+ frees
+ |> redirect_proof conjecture_shape hyp_ts concl_t
+ |> kill_duplicate_assumptions_in_proof
+ |> then_chain_proof
+ |> kill_useless_labels_in_proof
+ |> relabel_proof
+ |> string_for_proof ctxt full_types i n of
+ "" => "\nNo structured proof available."
+ | proof => "\n\nStructured proof:\n" ^ Markup.markup Markup.sendback proof
+ val isar_proof =
+ if debug then
+ isar_proof_for ()
+ else
+ try isar_proof_for ()
+ |> the_default "\nWarning: The Isar proof construction failed."
+ in (one_line_proof ^ isar_proof, lemma_names) end
+
+fun proof_text isar_proof isar_params other_params =
+ (if isar_proof then isar_proof_text isar_params else metis_proof_text)
+ other_params
+
+end;