# HG changeset patch # User blanchet # Date 1283291183 -7200 # Node ID e34c1b09bb5e48d3c8b537d1452311940c76cb6e # Parent 162bbbea4e4d690c63539372e6751d518e560d9d shorten a few file names diff -r 162bbbea4e4d -r e34c1b09bb5e src/HOL/IsaMakefile --- 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 \ diff -r 162bbbea4e4d -r e34c1b09bb5e src/HOL/Tools/Sledgehammer/sledgehammer_fact_filter.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; diff -r 162bbbea4e4d -r e34c1b09bb5e src/HOL/Tools/Sledgehammer/sledgehammer_fact_minimize.ML --- 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; diff -r 162bbbea4e4d -r e34c1b09bb5e src/HOL/Tools/Sledgehammer/sledgehammer_filter.ML --- /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; diff -r 162bbbea4e4d -r e34c1b09bb5e src/HOL/Tools/Sledgehammer/sledgehammer_minimize.ML --- /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; diff -r 162bbbea4e4d -r e34c1b09bb5e src/HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML --- 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)\(, , \). - The 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 --| $$ "," - -- parse_formula pool -- parse_tstp_extra_arguments --| $$ ")" --| $$ "." - >> (fn (((num, role), phi), deps) => - case role of - "definition" => - (case phi of - AConn (AIff, [phi1 as AAtom _, phi2]) => - Definition (num, phi1, phi2) - | AAtom (ATerm ("c_equal", _)) => - Inference (num, phi, deps) (* Vampire's equality proxy axiom *) - | _ => raise Fail "malformed definition") - | _ => Inference (num, phi, deps)) - -(**** PARSING OF VAMPIRE OUTPUT ****) - -(* Syntax: . *) -fun parse_vampire_line pool = - scan_integer --| $$ "." -- 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: [0:] - || -> . *) -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; diff -r 162bbbea4e4d -r e34c1b09bb5e src/HOL/Tools/Sledgehammer/sledgehammer_reconstruct.ML --- /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)\(, , \). + The 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 --| $$ "," + -- parse_formula pool -- parse_tstp_extra_arguments --| $$ ")" --| $$ "." + >> (fn (((num, role), phi), deps) => + case role of + "definition" => + (case phi of + AConn (AIff, [phi1 as AAtom _, phi2]) => + Definition (num, phi1, phi2) + | AAtom (ATerm ("c_equal", _)) => + Inference (num, phi, deps) (* Vampire's equality proxy axiom *) + | _ => raise Fail "malformed definition") + | _ => Inference (num, phi, deps)) + +(**** PARSING OF VAMPIRE OUTPUT ****) + +(* Syntax: . *) +fun parse_vampire_line pool = + scan_integer --| $$ "." -- 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: [0:] + || -> . *) +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;