--- a/src/HOL/Tools/Sledgehammer/sledgehammer_mepo.ML Sun Jun 01 14:00:58 2014 +0200
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_mepo.ML Mon Jun 02 11:59:49 2014 +0200
@@ -35,9 +35,8 @@
val trace : bool Config.T
val pseudo_abs_name : string
val default_relevance_fudge : relevance_fudge
- val mepo_suggested_facts :
- Proof.context -> params -> int -> relevance_fudge option -> term list -> term ->
- raw_fact list -> fact list
+ val mepo_suggested_facts : Proof.context -> params -> int -> relevance_fudge option ->
+ term list -> term -> raw_fact list -> fact list
end;
structure Sledgehammer_MePo : SLEDGEHAMMER_MEPO =
@@ -48,8 +47,8 @@
open Sledgehammer_Fact
open Sledgehammer_Prover
-val trace =
- Attrib.setup_config_bool @{binding sledgehammer_mepo_trace} (K false)
+val trace = Attrib.setup_config_bool @{binding sledgehammer_mepo_trace} (K false)
+
fun trace_msg ctxt msg = if Config.get ctxt trace then tracing (msg ()) else ()
val sledgehammer_prefix = "Sledgehammer" ^ Long_Name.separator
@@ -107,40 +106,34 @@
datatype ptype = PType of int * typ list
fun string_of_patternT (TVar _) = "_"
- | string_of_patternT (Type (s, ps)) =
- if null ps then s else s ^ string_of_patternsT ps
+ | string_of_patternT (Type (s, ps)) = if null ps then s else s ^ string_of_patternsT ps
| string_of_patternT (TFree (s, _)) = s
and string_of_patternsT ps = "(" ^ commas (map string_of_patternT ps) ^ ")"
fun string_of_ptype (PType (_, ps)) = string_of_patternsT ps
(*Is the second type an instance of the first one?*)
fun match_patternT (TVar _, _) = true
- | match_patternT (Type (s, ps), Type (t, qs)) =
- s = t andalso match_patternsT (ps, qs)
+ | match_patternT (Type (s, ps), Type (t, qs)) = s = t andalso match_patternsT (ps, qs)
| match_patternT (TFree (s, _), TFree (t, _)) = s = t
| match_patternT (_, _) = false
and match_patternsT (_, []) = true
| match_patternsT ([], _) = false
- | match_patternsT (p :: ps, q :: qs) =
- match_patternT (p, q) andalso match_patternsT (ps, qs)
+ | match_patternsT (p :: ps, q :: qs) = match_patternT (p, q) andalso match_patternsT (ps, qs)
fun match_ptype (PType (_, ps), PType (_, qs)) = match_patternsT (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))
+ 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))
(* Pairs a constant with the list of its type instantiations. *)
-fun ptype thy const x =
- (if const then these (try (Sign.const_typargs thy) x) else [])
-fun rich_ptype thy const (s, T) =
- PType (order_of_type T, ptype thy const (s, T))
+fun ptype thy const x = (if const then these (try (Sign.const_typargs thy) x) else [])
+fun rich_ptype thy const (s, T) = PType (order_of_type T, ptype thy const (s, T))
fun rich_pconst thy const (s, T) = (s, rich_ptype thy const (s, T))
-fun string_of_hyper_pconst (s, ps) =
- s ^ "{" ^ commas (map string_of_ptype ps) ^ "}"
+fun string_of_hyper_pconst (s, ps) = s ^ "{" ^ commas (map string_of_ptype ps) ^ "}"
fun patternT_eq (TVar _, TVar _) = true
| patternT_eq (Type (s, Ts), Type (t, Us)) = s = t andalso patternsT_eq (Ts, Us)
@@ -150,15 +143,14 @@
| patternsT_eq ([], _) = false
| patternsT_eq (_, []) = false
| patternsT_eq (T :: Ts, U :: Us) = patternT_eq (T, U) andalso patternsT_eq (Ts, Us)
+
fun ptype_eq (PType (m, Ts), PType (n, Us)) = m = n andalso patternsT_eq (Ts, Us)
- (* Add a pconstant to the table, but a [] entry means a standard connective,
- which we ignore. *)
+ (* Add a pconstant to the table, but a [] entry means a standard connective, which we ignore. *)
fun add_pconst_to_table (s, p) = Symtab.map_default (s, [p]) (insert ptype_eq p)
-(* Set constants tend to pull in too many irrelevant facts. We limit the damage
- by treating them more or less as if they were built-in but add their
- axiomatization at the end. *)
+(* Set constants tend to pull in too many irrelevant facts. We limit the damage by treating them
+ more or less as if they were built-in but add their axiomatization at the end. *)
val set_consts = [@{const_name Collect}, @{const_name Set.member}]
val set_thms = @{thms Collect_mem_eq mem_Collect_eq Collect_cong}
@@ -176,11 +168,9 @@
| (Free x, ts) => do_const false x ts
| (Abs (_, T, t'), ts) =>
((null ts andalso not ext_arg)
- (* Since lambdas on the right-hand side of equalities are usually
- extensionalized later by "abs_extensionalize_term", we don't
- penalize them here. *)
- ? add_pconst_to_table (pseudo_abs_name,
- PType (order_of_type T + 1, [])))
+ (* Since lambdas on the right-hand side of equalities are usually extensionalized later by
+ "abs_extensionalize_term", we don't penalize them here. *)
+ ? add_pconst_to_table (pseudo_abs_name, PType (order_of_type T + 1, [])))
#> fold (do_term false) (t' :: ts)
| (_, ts) => fold (do_term false) ts)
and do_term_or_formula ext_arg T =
@@ -202,8 +192,7 @@
| @{const HOL.implies} $ t1 $ t2 => do_formula t1 #> do_formula t2
| Const (@{const_name HOL.eq}, Type (_, [T, _])) $ t1 $ t2 =>
do_term_or_formula false T t1 #> do_term_or_formula true T t2
- | Const (@{const_name If}, Type (_, [_, Type (_, [T, _])]))
- $ t1 $ t2 $ t3 =>
+ | Const (@{const_name If}, Type (_, [_, Type (_, [T, _])])) $ t1 $ t2 $ t3 =>
do_formula t1 #> fold (do_term_or_formula false T) [t2, t3]
| Const (@{const_name Ex1}, _) $ Abs (_, _, t') => do_formula t'
| Const (@{const_name Ball}, _) $ t1 $ Abs (_, _, t') =>
@@ -213,18 +202,19 @@
| (t0 as Const (_, @{typ bool})) $ t1 =>
do_term false t0 #> do_formula t1 (* theory constant *)
| _ => do_term false t)
- in do_formula end
+ in
+ do_formula
+ end
fun pconsts_in_fact thy t =
- Symtab.fold (fn (s, pss) => fold (cons o pair s) pss)
- (Symtab.empty |> add_pconsts_in_term thy t) []
+ Symtab.fold (fn (s, pss) => fold (cons o pair s) pss) (Symtab.empty |> add_pconsts_in_term thy t)
+ []
(* Inserts a dummy "constant" referring to the theory name, so that relevance
takes the given theory into account. *)
-fun theory_constify ({theory_const_rel_weight, theory_const_irrel_weight, ...}
- : relevance_fudge) thy_name t =
- if exists (curry (op <) 0.0) [theory_const_rel_weight,
- theory_const_irrel_weight] then
+fun theory_constify ({theory_const_rel_weight, theory_const_irrel_weight, ...} : relevance_fudge)
+ thy_name t =
+ if exists (curry (op <) 0.0) [theory_const_rel_weight, theory_const_irrel_weight] then
Const (thy_name ^ theory_const_suffix, @{typ bool}) $ t
else
t
@@ -253,6 +243,7 @@
| (Type _, TFree _) => LESS
| (TFree (s, _), TFree (t, _)) => fast_string_ord (s, t)
| (TFree _, _) => GREATER)
+
fun ptype_ord (PType (m, ps), PType (n, qs)) =
(case dict_ord patternT_ord (ps, qs) of
EQUAL => int_ord (m, n)
@@ -281,12 +272,10 @@
(*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
+ 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. *)
+(* 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
@@ -297,8 +286,8 @@
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 ({worse_irrel_freq, higher_order_irrel_weight, ...}
- : relevance_fudge) order freq =
+fun irrel_weight_for ({worse_irrel_freq, higher_order_irrel_weight, ...} : relevance_fudge) 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)
@@ -309,9 +298,8 @@
if String.isSubstring "." s then 1.0 else local_const_multiplier
(* Computes a constant's weight, as determined by its frequency. *)
-fun generic_pconst_weight local_const_multiplier abs_weight theory_const_weight
- chained_const_weight weight_for f const_tab chained_const_tab
- (c as (s, PType (m, _))) =
+fun generic_pconst_weight local_const_multiplier abs_weight theory_const_weight chained_const_weight
+ weight_for f const_tab chained_const_tab (c as (s, PType (m, _))) =
if s = pseudo_abs_name then
abs_weight
else if String.isSuffix theory_const_suffix s then
@@ -319,30 +307,22 @@
else
multiplier_of_const_name local_const_multiplier s
* weight_for m (pconst_freq (match_ptype o f) const_tab c)
- |> (if chained_const_weight < 1.0 andalso
- pconst_hyper_mem I chained_const_tab c then
+ |> (if chained_const_weight < 1.0 andalso pconst_hyper_mem I chained_const_tab c then
curry (op *) chained_const_weight
else
I)
-fun rel_pconst_weight ({local_const_multiplier, abs_rel_weight,
- theory_const_rel_weight, ...} : relevance_fudge)
- const_tab =
- generic_pconst_weight local_const_multiplier abs_rel_weight
- theory_const_rel_weight 0.0 rel_weight_for I const_tab
- Symtab.empty
+fun rel_pconst_weight ({local_const_multiplier, abs_rel_weight, theory_const_rel_weight,
+ ...} : relevance_fudge) const_tab =
+ generic_pconst_weight local_const_multiplier abs_rel_weight theory_const_rel_weight 0.0
+ rel_weight_for I const_tab Symtab.empty
fun irrel_pconst_weight (fudge as {local_const_multiplier, abs_irrel_weight,
- theory_const_irrel_weight,
- chained_const_irrel_weight, ...})
- const_tab chained_const_tab =
- generic_pconst_weight local_const_multiplier abs_irrel_weight
- theory_const_irrel_weight chained_const_irrel_weight
- (irrel_weight_for fudge) swap const_tab
- chained_const_tab
+ theory_const_irrel_weight, chained_const_irrel_weight, ...}) const_tab chained_const_tab =
+ generic_pconst_weight local_const_multiplier abs_irrel_weight theory_const_irrel_weight
+ chained_const_irrel_weight (irrel_weight_for fudge) swap const_tab chained_const_tab
-fun stature_bonus ({intro_bonus, ...} : relevance_fudge) (_, Intro) =
- intro_bonus
+fun stature_bonus ({intro_bonus, ...} : relevance_fudge) (_, Intro) = intro_bonus
| stature_bonus {elim_bonus, ...} (_, Elim) = elim_bonus
| stature_bonus {simp_bonus, ...} (_, Simp) = simp_bonus
| stature_bonus {local_bonus, ...} (Local, _) = local_bonus
@@ -364,45 +344,42 @@
else
let
val irrel = irrel |> filter_out (pconst_mem swap rel)
- val rel_weight =
- 0.0 |> fold (curry (op +) o rel_pconst_weight fudge const_tab) rel
+ val rel_weight = 0.0 |> fold (curry (op +) o rel_pconst_weight fudge const_tab) rel
val irrel_weight =
~ (stature_bonus fudge stature)
- |> fold (curry (op +)
- o irrel_pconst_weight fudge const_tab chained_const_tab)
- irrel
+ |> fold (curry (op +) o irrel_pconst_weight fudge const_tab chained_const_tab) irrel
val res = rel_weight / (rel_weight + irrel_weight)
- in if Real.isFinite res then res else 0.0 end)
+ in
+ if Real.isFinite res then res else 0.0
+ end)
fun take_most_relevant ctxt max_facts remaining_max
- ({max_imperfect, max_imperfect_exp, ...} : relevance_fudge)
- (candidates : ((raw_fact * (string * ptype) list) * real) list) =
+ ({max_imperfect, max_imperfect_exp, ...} : relevance_fudge)
+ (candidates : ((raw_fact * (string * ptype) list) * real) list) =
let
val max_imperfect =
Real.ceil (Math.pow (max_imperfect,
- Math.pow (Real.fromInt remaining_max
- / Real.fromInt max_facts, max_imperfect_exp)))
- val (perfect, imperfect) =
- candidates |> sort (Real.compare o swap o pairself snd)
- |> take_prefix (fn (_, w) => w > 0.99999)
+ Math.pow (Real.fromInt remaining_max / Real.fromInt max_facts, 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 ctxt (fn () =>
- "Actually passed (" ^ string_of_int (length accepts) ^ " of " ^
- string_of_int (length candidates) ^ "): " ^
- (accepts |> map (fn ((((name, _), _), _), weight) =>
- name () ^ " [" ^ Real.toString weight ^ "]")
- |> commas));
+ "Actually passed (" ^ string_of_int (length accepts) ^ " of " ^
+ string_of_int (length candidates) ^ "): " ^
+ (accepts
+ |> map (fn ((((name, _), _), _), weight) => name () ^ " [" ^ Real.toString weight ^ "]")
+ |> commas));
(accepts, more_rejects @ rejects)
end
fun if_empty_replace_with_scope thy facts sc tab =
if Symtab.is_empty tab then
Symtab.empty
- |> fold (add_pconsts_in_term thy)
- (map_filter (fn ((_, (sc', _)), th) =>
- if sc' = sc then SOME (prop_of th) else NONE) facts)
+ |> fold (add_pconsts_in_term thy) (map_filter (fn ((_, (sc', _)), th) =>
+ if sc' = sc then SOME (prop_of th) else NONE) facts)
else
tab
@@ -420,7 +397,9 @@
NONE => SOME (Symtab.update (s, length args) tab)
| SOME n => if n = length args then SOME tab else NONE))
| _ => SOME tab)
- in aux (prop_of th) [] end
+ in
+ aux (prop_of th) []
+ end
(* FIXME: This is currently only useful for polymorphic type encodings. *)
fun could_benefit_from_ext facts =
@@ -442,8 +421,7 @@
val const_tab = fold (count_fact_consts thy fudge) facts Symtab.empty
val add_pconsts = add_pconsts_in_term thy
val chained_ts =
- facts |> map_filter (fn ((_, (Chained, _)), th) => SOME (prop_of th)
- | _ => NONE)
+ facts |> map_filter (try (fn ((_, (Chained, _)), th) => prop_of th))
val chained_const_tab = Symtab.empty |> fold add_pconsts chained_ts
val goal_const_tab =
Symtab.empty
@@ -451,17 +429,16 @@
|> add_pconsts concl_t
|> (fn tab => if Symtab.is_empty tab then chained_const_tab else tab)
|> fold (if_empty_replace_with_scope thy facts) [Chained, Assum, Local]
+
fun iter j remaining_max thres rel_const_tab hopeless hopeful =
let
val hopeless =
- hopeless |> j = really_hopeless_get_kicked_out_iter
- ? filter_out (fn (_, w) => w < 0.001)
+ hopeless |> j = really_hopeless_get_kicked_out_iter ? filter_out (fn (_, w) => w < 0.001)
fun relevant [] _ [] =
(* Nothing has been added this iteration. *)
if j = 0 andalso thres >= ridiculous_threshold then
(* First iteration? Try again. *)
- iter 0 max_facts (thres / threshold_divisor) rel_const_tab
- hopeless hopeful
+ iter 0 max_facts (thres / threshold_divisor) rel_const_tab hopeless hopeful
else
[]
| relevant candidates rejects [] =
@@ -471,40 +448,34 @@
val sps = maps (snd o fst) accepts
val rel_const_tab' =
rel_const_tab |> fold add_pconst_to_table sps
- fun is_dirty (s, _) =
- Symtab.lookup rel_const_tab' s <> Symtab.lookup rel_const_tab s
+
+ fun is_dirty (s, _) = Symtab.lookup rel_const_tab' s <> Symtab.lookup rel_const_tab s
+
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)))
+ 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 thres =
- 1.0 - (1.0 - thres)
- * Math.pow (decay, Real.fromInt (length accepts))
+ val thres = 1.0 - (1.0 - thres) * Math.pow (decay, Real.fromInt (length accepts))
val remaining_max = remaining_max - length accepts
in
trace_msg ctxt (fn () => "New or updated constants: " ^
- commas (rel_const_tab'
- |> Symtab.dest
- |> subtract (eq_prod (op =) (eq_list ptype_eq))
- (rel_const_tab |> Symtab.dest)
- |> map string_of_hyper_pconst));
+ commas (rel_const_tab'
+ |> Symtab.dest
+ |> subtract (eq_prod (op =) (eq_list ptype_eq)) (Symtab.dest rel_const_tab)
+ |> map string_of_hyper_pconst));
map (fst o fst) accepts @
(if remaining_max = 0 then
[]
else
- iter (j + 1) remaining_max thres rel_const_tab'
- hopeless_rejects hopeful_rejects)
+ iter (j + 1) remaining_max thres rel_const_tab' hopeless_rejects hopeful_rejects)
end
| relevant candidates rejects
- (((ax as (((_, stature), _), fact_consts)), cached_weight)
- :: hopeful) =
+ (((ax as (((_, stature), _), fact_consts)), cached_weight) :: hopeful) =
let
val weight =
(case cached_weight of
@@ -539,31 +510,34 @@
| insert_into_facts accepts ths =
let
val add = facts |> filter (member Thm.eq_thm_prop ths o snd)
- val (bef, after) =
- accepts |> filter_out (member Thm.eq_thm_prop ths o snd)
- |> take (max_facts - length add)
- |> chop special_fact_index
- in bef @ add @ after end
+ val (bef, after) = accepts
+ |> filter_out (member Thm.eq_thm_prop ths o snd)
+ |> take (max_facts - length add)
+ |> chop special_fact_index
+ in
+ bef @ add @ after
+ end
fun insert_special_facts accepts =
(* FIXME: get rid of "ext" here once it is treated as a helper *)
- [] |> could_benefit_from_ext accepts ? cons @{thm ext}
- |> add_set_const_thms accepts
- |> insert_into_facts accepts
+ []
+ |> could_benefit_from_ext accepts ? cons @{thm ext}
+ |> add_set_const_thms accepts
+ |> insert_into_facts accepts
in
- facts |> map_filter (pair_consts_fact thy fudge)
- |> iter 0 max_facts thres0 goal_const_tab []
- |> insert_special_facts
- |> tap (fn accepts => trace_msg ctxt (fn () =>
- "Total relevant: " ^ string_of_int (length accepts)))
+ facts
+ |> map_filter (pair_consts_fact thy fudge)
+ |> iter 0 max_facts thres0 goal_const_tab []
+ |> insert_special_facts
+ |> tap (fn accepts => trace_msg ctxt (fn () =>
+ "Total relevant: " ^ string_of_int (length accepts)))
end
fun mepo_suggested_facts ctxt ({fact_thresholds = (thres0, thres1), ...} : params) max_facts fudge
- hyp_ts concl_t facts =
+ hyp_ts concl_t facts =
let
val thy = Proof_Context.theory_of ctxt
val fudge = fudge |> the_default default_relevance_fudge
- val decay = Math.pow ((1.0 - thres1) / (1.0 - thres0),
- 1.0 / Real.fromInt (max_facts + 1))
+ val decay = Math.pow ((1.0 - thres1) / (1.0 - thres0), 1.0 / Real.fromInt (max_facts + 1))
in
trace_msg ctxt (fn () => "Considering " ^ string_of_int (length facts) ^ " facts");
(if thres1 < 0.0 then