# HG changeset patch # User wenzelm # Date 1315434203 -7200 # Node ID 7798deb6f8fa9e01365edb893c30e1f0ca33b81f # Parent fe33d66551860470552a44950262f7b48007cccc# Parent df3626d1066ee623a642183d58c32490c5c0bdf4 merged diff -r df3626d1066e -r 7798deb6f8fa CONTRIBUTORS --- a/CONTRIBUTORS Thu Sep 08 00:20:09 2011 +0200 +++ b/CONTRIBUTORS Thu Sep 08 00:23:23 2011 +0200 @@ -6,6 +6,12 @@ Contributions to Isabelle2011-1 ------------------------------- +* September 2011: Peter Gammie + Theory HOL/Libary/Saturated: numbers with saturated arithmetic. + +* August 2011: Florian Haftmann, Johannes Hölzl and Lars Noschinski, TUM + Refined theory on complete lattices. + Contributions to Isabelle2011 ----------------------------- diff -r df3626d1066e -r 7798deb6f8fa NEWS --- a/NEWS Thu Sep 08 00:20:09 2011 +0200 +++ b/NEWS Thu Sep 08 00:23:23 2011 +0200 @@ -91,6 +91,9 @@ *** HOL *** +* Theory Library/Saturated provides type of numbers with saturated +arithmetic. + * Classes bot and top require underlying partial order rather than preorder: uniqueness of bot and top is guaranteed. INCOMPATIBILITY. diff -r df3626d1066e -r 7798deb6f8fa doc-src/Sledgehammer/sledgehammer.tex --- a/doc-src/Sledgehammer/sledgehammer.tex Thu Sep 08 00:20:09 2011 +0200 +++ b/doc-src/Sledgehammer/sledgehammer.tex Thu Sep 08 00:23:23 2011 +0200 @@ -942,19 +942,29 @@ \textit{raw\_mono\_guards}, \textit{raw\_mono\_tags}, \textit{mono\_guards}, \textit{mono\_tags}, and \textit{mono\_simple} are fully typed and sound. For each of these, Sledgehammer also provides a lighter, -virtually sound variant identified by a question mark (`{?}')\ that detects and -erases monotonic types, notably infinite types. (For \textit{mono\_simple}, the -types are not actually erased but rather replaced by a shared uniform type of -individuals.) As argument to the \textit{metis} proof method, the question mark -is replaced by a \hbox{``\textit{\_query}''} suffix. If the \emph{sound} option -is enabled, these encodings are fully sound. +virtually sound variant identified by a question mark (`\hbox{?}')\ that detects +and erases monotonic types, notably infinite types. (For \textit{mono\_simple}, +the types are not actually erased but rather replaced by a shared uniform type +of individuals.) As argument to the \textit{metis} proof method, the question +mark is replaced by a \hbox{``\textit{\_query}''} suffix. If the \emph{sound} +option is enabled, these encodings are fully sound. \item[$\bullet$] \textbf{% \textit{poly\_guards}??, \textit{poly\_tags}??, \textit{raw\_mono\_guards}??, \\ \textit{raw\_mono\_tags}??, \textit{mono\_guards}??, \textit{mono\_tags}?? \\ (quasi-sound):} \\ -Even lighter versions of the `{?}' encodings. +Even lighter versions of the `\hbox{?}' encodings. As argument to the +\textit{metis} proof method, the `\hbox{??}' suffix is replaced by +\hbox{``\textit{\_query\_query}''}. + +\item[$\bullet$] +\textbf{% +\textit{poly\_guards}@?, \textit{poly\_tags}@?, \textit{raw\_mono\_guards}@?, \\ +\textit{raw\_mono\_tags}@? (quasi-sound):} \\ +Alternative versions of the `\hbox{??}' encodings. As argument to the +\textit{metis} proof method, the `\hbox{@?}' suffix is replaced by +\hbox{``\textit{\_at\_query}''}. \item[$\bullet$] \textbf{% @@ -965,9 +975,9 @@ \textit{raw\_mono\_guards}, \textit{raw\_mono\_tags}, \textit{mono\_guards}, \textit{mono\_tags}, \textit{mono\_simple}, and \textit{mono\_simple\_higher} also admit a mildly unsound (but very efficient) variant identified by an -exclamation mark (`{!}') that detects and erases erases all types except those -that are clearly finite (e.g., \textit{bool}). (For \textit{mono\_simple} and -\textit{mono\_simple\_higher}, the types are not actually erased but rather +exclamation mark (`\hbox{!}') that detects and erases erases all types except +those that are clearly finite (e.g., \textit{bool}). (For \textit{mono\_simple} +and \textit{mono\_simple\_higher}, the types are not actually erased but rather replaced by a shared uniform type of individuals.) As argument to the \textit{metis} proof method, the exclamation mark is replaced by the suffix \hbox{``\textit{\_bang}''}. @@ -977,7 +987,17 @@ \textit{poly\_guards}!!, \textit{poly\_tags}!!, \textit{raw\_mono\_guards}!!, \\ \textit{raw\_mono\_tags}!!, \textit{mono\_guards}!!, \textit{mono\_tags}!! \\ (mildly unsound):} \\ -Even lighter versions of the `{!}' encodings. +Even lighter versions of the `\hbox{!}' encodings. As argument to the +\textit{metis} proof method, the `\hbox{!!}' suffix is replaced by +\hbox{``\textit{\_bang\_bang}''}. + +\item[$\bullet$] +\textbf{% +\textit{poly\_guards}@!, \textit{poly\_tags}@!, \textit{raw\_mono\_guards}@!, \\ +\textit{raw\_mono\_tags}@! (mildly unsound):} \\ +Alternative versions of the `\hbox{!!}' encodings. As argument to the +\textit{metis} proof method, the `\hbox{@!}' suffix is replaced by +\hbox{``\textit{\_at\_bang}''}. \item[$\bullet$] \textbf{\textit{smart}:} The actual encoding used depends on the ATP and should be the most efficient virtually sound encoding for that ATP. diff -r df3626d1066e -r 7798deb6f8fa src/HOL/IsaMakefile --- a/src/HOL/IsaMakefile Thu Sep 08 00:20:09 2011 +0200 +++ b/src/HOL/IsaMakefile Thu Sep 08 00:23:23 2011 +0200 @@ -463,10 +463,10 @@ Library/Quotient_Option.thy Library/Quotient_Product.thy \ Library/Quotient_Sum.thy Library/Quotient_Syntax.thy \ Library/Quotient_Type.thy Library/RBT.thy Library/RBT_Impl.thy \ - Library/RBT_Mapping.thy Library/README.html Library/Set_Algebras.thy \ - Library/State_Monad.thy Library/Ramsey.thy Library/Reflection.thy \ - Library/Sublist_Order.thy Library/Sum_of_Squares.thy \ - Library/Sum_of_Squares/sos_wrapper.ML \ + Library/RBT_Mapping.thy Library/README.html Library/Saturated.thy \ + Library/Set_Algebras.thy Library/State_Monad.thy Library/Ramsey.thy \ + Library/Reflection.thy Library/Sublist_Order.thy \ + Library/Sum_of_Squares.thy Library/Sum_of_Squares/sos_wrapper.ML \ Library/Sum_of_Squares/sum_of_squares.ML \ Library/Transitive_Closure_Table.thy Library/Univ_Poly.thy \ Library/Wfrec.thy Library/While_Combinator.thy Library/Zorn.thy \ diff -r df3626d1066e -r 7798deb6f8fa src/HOL/Library/Library.thy --- a/src/HOL/Library/Library.thy Thu Sep 08 00:20:09 2011 +0200 +++ b/src/HOL/Library/Library.thy Thu Sep 08 00:23:23 2011 +0200 @@ -55,6 +55,7 @@ Ramsey Reflection RBT_Mapping + Saturated Set_Algebras State_Monad Sum_of_Squares diff -r df3626d1066e -r 7798deb6f8fa src/HOL/Library/Saturated.thy --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Library/Saturated.thy Thu Sep 08 00:23:23 2011 +0200 @@ -0,0 +1,242 @@ +(* Author: Brian Huffman *) +(* Author: Peter Gammie *) +(* Author: Florian Haftmann *) + +header {* Saturated arithmetic *} + +theory Saturated +imports Main "~~/src/HOL/Library/Numeral_Type" "~~/src/HOL/Word/Type_Length" +begin + +subsection {* The type of saturated naturals *} + +typedef (open) ('a::len) sat = "{.. len_of TYPE('a)}" + morphisms nat_of Abs_sat + by auto + +lemma sat_eqI: + "nat_of m = nat_of n \ m = n" + by (simp add: nat_of_inject) + +lemma sat_eq_iff: + "m = n \ nat_of m = nat_of n" + by (simp add: nat_of_inject) + +lemma Abs_sa_nat_of [code abstype]: + "Abs_sat (nat_of n) = n" + by (fact nat_of_inverse) + +definition Sat :: "nat \ 'a::len sat" where + "Sat n = Abs_sat (min (len_of TYPE('a)) n)" + +lemma nat_of_Sat [simp]: + "nat_of (Sat n :: ('a::len) sat) = min (len_of TYPE('a)) n" + unfolding Sat_def by (rule Abs_sat_inverse) simp + +lemma nat_of_le_len_of [simp]: + "nat_of (n :: ('a::len) sat) \ len_of TYPE('a)" + using nat_of [where x = n] by simp + +lemma min_len_of_nat_of [simp]: + "min (len_of TYPE('a)) (nat_of (n::('a::len) sat)) = nat_of n" + by (rule min_max.inf_absorb2 [OF nat_of_le_len_of]) + +lemma min_nat_of_len_of [simp]: + "min (nat_of (n::('a::len) sat)) (len_of TYPE('a)) = nat_of n" + by (subst min_max.inf.commute) simp + +lemma Sat_nat_of [simp]: + "Sat (nat_of n) = n" + by (simp add: Sat_def nat_of_inverse) + +instantiation sat :: (len) linorder +begin + +definition + less_eq_sat_def: "x \ y \ nat_of x \ nat_of y" + +definition + less_sat_def: "x < y \ nat_of x < nat_of y" + +instance +by default (auto simp add: less_eq_sat_def less_sat_def not_le sat_eq_iff min_max.le_infI1 nat_mult_commute) + +end + +instantiation sat :: (len) "{minus, comm_semiring_0, comm_semiring_1}" +begin + +definition + "0 = Sat 0" + +definition + "1 = Sat 1" + +lemma nat_of_zero_sat [simp, code abstract]: + "nat_of 0 = 0" + by (simp add: zero_sat_def) + +lemma nat_of_one_sat [simp, code abstract]: + "nat_of 1 = min 1 (len_of TYPE('a))" + by (simp add: one_sat_def) + +definition + "x + y = Sat (nat_of x + nat_of y)" + +lemma nat_of_plus_sat [simp, code abstract]: + "nat_of (x + y) = min (nat_of x + nat_of y) (len_of TYPE('a))" + by (simp add: plus_sat_def) + +definition + "x - y = Sat (nat_of x - nat_of y)" + +lemma nat_of_minus_sat [simp, code abstract]: + "nat_of (x - y) = nat_of x - nat_of y" +proof - + from nat_of_le_len_of [of x] have "nat_of x - nat_of y \ len_of TYPE('a)" by arith + then show ?thesis by (simp add: minus_sat_def) +qed + +definition + "x * y = Sat (nat_of x * nat_of y)" + +lemma nat_of_times_sat [simp, code abstract]: + "nat_of (x * y) = min (nat_of x * nat_of y) (len_of TYPE('a))" + by (simp add: times_sat_def) + +instance proof + fix a b c :: "('a::len) sat" + show "a * b * c = a * (b * c)" + proof(cases "a = 0") + case True thus ?thesis by (simp add: sat_eq_iff) + next + case False show ?thesis + proof(cases "c = 0") + case True thus ?thesis by (simp add: sat_eq_iff) + next + case False with `a \ 0` show ?thesis + by (simp add: sat_eq_iff nat_mult_min_left nat_mult_min_right mult_assoc min_max.inf_assoc min_max.inf_absorb2) + qed + qed +next + fix a :: "('a::len) sat" + show "1 * a = a" + apply (simp add: sat_eq_iff) + apply (metis One_nat_def len_gt_0 less_Suc0 less_zeroE linorder_not_less min_max.le_iff_inf min_nat_of_len_of nat_mult_1_right nat_mult_commute) + done +next + fix a b c :: "('a::len) sat" + show "(a + b) * c = a * c + b * c" + proof(cases "c = 0") + case True thus ?thesis by (simp add: sat_eq_iff) + next + case False thus ?thesis + by (simp add: sat_eq_iff nat_mult_min_left add_mult_distrib nat_add_min_left nat_add_min_right min_max.inf_assoc min_max.inf_absorb2) + qed +qed (simp_all add: sat_eq_iff mult.commute) + +end + +instantiation sat :: (len) ordered_comm_semiring +begin + +instance +by default (auto simp add: less_eq_sat_def less_sat_def not_le sat_eq_iff min_max.le_infI1 nat_mult_commute) + +end + +instantiation sat :: (len) number +begin + +definition + number_of_sat_def [code del]: "number_of = Sat \ nat" + +instance .. + +end + +lemma [code abstract]: + "nat_of (number_of n :: ('a::len) sat) = min (nat n) (len_of TYPE('a))" + unfolding number_of_sat_def by simp + +instance sat :: (len) finite +proof + show "finite (UNIV::'a sat set)" + unfolding type_definition.univ [OF type_definition_sat] + using finite by simp +qed + +instantiation sat :: (len) equal +begin + +definition + "HOL.equal A B \ nat_of A = nat_of B" + +instance proof +qed (simp add: equal_sat_def nat_of_inject) + +end + +instantiation sat :: (len) "{bounded_lattice, distrib_lattice}" +begin + +definition + "(inf :: 'a sat \ 'a sat \ 'a sat) = min" + +definition + "(sup :: 'a sat \ 'a sat \ 'a sat) = max" + +definition + "bot = (0 :: 'a sat)" + +definition + "top = Sat (len_of TYPE('a))" + +instance proof +qed (simp_all add: inf_sat_def sup_sat_def bot_sat_def top_sat_def min_max.sup_inf_distrib1, + simp_all add: less_eq_sat_def) + +end + +instantiation sat :: (len) complete_lattice +begin + +definition + "Inf (A :: 'a sat set) = fold min top A" + +definition + "Sup (A :: 'a sat set) = fold max bot A" + +instance proof + fix x :: "'a sat" + fix A :: "'a sat set" + note finite + moreover assume "x \ A" + ultimately have "fold min top A \ min x top" by (rule min_max.fold_inf_le_inf) + then show "Inf A \ x" by (simp add: Inf_sat_def) +next + fix z :: "'a sat" + fix A :: "'a sat set" + note finite + moreover assume z: "\x. x \ A \ z \ x" + ultimately have "min z top \ fold min top A" by (blast intro: min_max.inf_le_fold_inf) + then show "z \ Inf A" by (simp add: Inf_sat_def min_def) +next + fix x :: "'a sat" + fix A :: "'a sat set" + note finite + moreover assume "x \ A" + ultimately have "max x bot \ fold max bot A" by (rule min_max.sup_le_fold_sup) + then show "x \ Sup A" by (simp add: Sup_sat_def) +next + fix z :: "'a sat" + fix A :: "'a sat set" + note finite + moreover assume z: "\x. x \ A \ x \ z" + ultimately have "fold max bot A \ max z bot" by (blast intro: min_max.fold_sup_le_sup) + then show "Sup A \ z" by (simp add: Sup_sat_def max_def bot_unique) +qed + +end + +end diff -r df3626d1066e -r 7798deb6f8fa src/HOL/Metis_Examples/Type_Encodings.thy --- a/src/HOL/Metis_Examples/Type_Encodings.thy Thu Sep 08 00:20:09 2011 +0200 +++ b/src/HOL/Metis_Examples/Type_Encodings.thy Thu Sep 08 00:23:23 2011 +0200 @@ -27,24 +27,32 @@ "poly_guards", "poly_guards?", "poly_guards??", + "poly_guards@?", "poly_guards!", "poly_guards!!", + "poly_guards@!", "poly_tags", "poly_tags?", "poly_tags??", + "poly_tags@?", "poly_tags!", "poly_tags!!", + "poly_tags@!", "poly_args", "raw_mono_guards", "raw_mono_guards?", "raw_mono_guards??", + "raw_mono_guards@?", "raw_mono_guards!", "raw_mono_guards!!", + "raw_mono_guards@!", "raw_mono_tags", "raw_mono_tags?", "raw_mono_tags??", + "raw_mono_tags@?", "raw_mono_tags!", "raw_mono_tags!!", + "raw_mono_tags@!", "raw_mono_args", "mono_guards", "mono_guards?", diff -r df3626d1066e -r 7798deb6f8fa src/HOL/Nat.thy --- a/src/HOL/Nat.thy Thu Sep 08 00:20:09 2011 +0200 +++ b/src/HOL/Nat.thy Thu Sep 08 00:23:23 2011 +0200 @@ -657,46 +657,6 @@ by (cases m) simp_all -subsubsection {* @{term min} and @{term max} *} - -lemma mono_Suc: "mono Suc" -by (rule monoI) simp - -lemma min_0L [simp]: "min 0 n = (0::nat)" -by (rule min_leastL) simp - -lemma min_0R [simp]: "min n 0 = (0::nat)" -by (rule min_leastR) simp - -lemma min_Suc_Suc [simp]: "min (Suc m) (Suc n) = Suc (min m n)" -by (simp add: mono_Suc min_of_mono) - -lemma min_Suc1: - "min (Suc n) m = (case m of 0 => 0 | Suc m' => Suc(min n m'))" -by (simp split: nat.split) - -lemma min_Suc2: - "min m (Suc n) = (case m of 0 => 0 | Suc m' => Suc(min m' n))" -by (simp split: nat.split) - -lemma max_0L [simp]: "max 0 n = (n::nat)" -by (rule max_leastL) simp - -lemma max_0R [simp]: "max n 0 = (n::nat)" -by (rule max_leastR) simp - -lemma max_Suc_Suc [simp]: "max (Suc m) (Suc n) = Suc(max m n)" -by (simp add: mono_Suc max_of_mono) - -lemma max_Suc1: - "max (Suc n) m = (case m of 0 => Suc n | Suc m' => Suc(max n m'))" -by (simp split: nat.split) - -lemma max_Suc2: - "max m (Suc n) = (case m of 0 => Suc n | Suc m' => Suc(max m' n))" -by (simp split: nat.split) - - subsubsection {* Monotonicity of Addition *} lemma Suc_pred [simp]: "n>0 ==> Suc (n - Suc 0) = n" @@ -753,11 +713,85 @@ fix a::nat and b::nat show "a ~= 0 \ b ~= 0 \ a * b ~= 0" by auto qed -lemma nat_mult_1: "(1::nat) * n = n" -by simp + +subsubsection {* @{term min} and @{term max} *} + +lemma mono_Suc: "mono Suc" +by (rule monoI) simp + +lemma min_0L [simp]: "min 0 n = (0::nat)" +by (rule min_leastL) simp + +lemma min_0R [simp]: "min n 0 = (0::nat)" +by (rule min_leastR) simp + +lemma min_Suc_Suc [simp]: "min (Suc m) (Suc n) = Suc (min m n)" +by (simp add: mono_Suc min_of_mono) + +lemma min_Suc1: + "min (Suc n) m = (case m of 0 => 0 | Suc m' => Suc(min n m'))" +by (simp split: nat.split) + +lemma min_Suc2: + "min m (Suc n) = (case m of 0 => 0 | Suc m' => Suc(min m' n))" +by (simp split: nat.split) + +lemma max_0L [simp]: "max 0 n = (n::nat)" +by (rule max_leastL) simp + +lemma max_0R [simp]: "max n 0 = (n::nat)" +by (rule max_leastR) simp + +lemma max_Suc_Suc [simp]: "max (Suc m) (Suc n) = Suc(max m n)" +by (simp add: mono_Suc max_of_mono) + +lemma max_Suc1: + "max (Suc n) m = (case m of 0 => Suc n | Suc m' => Suc(max n m'))" +by (simp split: nat.split) + +lemma max_Suc2: + "max m (Suc n) = (case m of 0 => Suc n | Suc m' => Suc(max m' n))" +by (simp split: nat.split) -lemma nat_mult_1_right: "n * (1::nat) = n" -by simp +lemma nat_add_min_left: + fixes m n q :: nat + shows "min m n + q = min (m + q) (n + q)" + by (simp add: min_def) + +lemma nat_add_min_right: + fixes m n q :: nat + shows "m + min n q = min (m + n) (m + q)" + by (simp add: min_def) + +lemma nat_mult_min_left: + fixes m n q :: nat + shows "min m n * q = min (m * q) (n * q)" + by (simp add: min_def not_le) (auto dest: mult_right_le_imp_le mult_right_less_imp_less le_less_trans) + +lemma nat_mult_min_right: + fixes m n q :: nat + shows "m * min n q = min (m * n) (m * q)" + by (simp add: min_def not_le) (auto dest: mult_left_le_imp_le mult_left_less_imp_less le_less_trans) + +lemma nat_add_max_left: + fixes m n q :: nat + shows "max m n + q = max (m + q) (n + q)" + by (simp add: max_def) + +lemma nat_add_max_right: + fixes m n q :: nat + shows "m + max n q = max (m + n) (m + q)" + by (simp add: max_def) + +lemma nat_mult_max_left: + fixes m n q :: nat + shows "max m n * q = max (m * q) (n * q)" + by (simp add: max_def not_le) (auto dest: mult_right_le_imp_le mult_right_less_imp_less le_less_trans) + +lemma nat_mult_max_right: + fixes m n q :: nat + shows "m * max n q = max (m * n) (m * q)" + by (simp add: max_def not_le) (auto dest: mult_left_le_imp_le mult_left_less_imp_less le_less_trans) subsubsection {* Additional theorems about @{term "op \"} *} @@ -1700,6 +1734,15 @@ by (auto elim!: dvdE) (auto simp add: gr0_conv_Suc) +subsection {* aliasses *} + +lemma nat_mult_1: "(1::nat) * n = n" + by simp + +lemma nat_mult_1_right: "n * (1::nat) = n" + by simp + + subsection {* size of a datatype value *} class size = diff -r df3626d1066e -r 7798deb6f8fa src/HOL/Tools/ATP/atp_translate.ML --- a/src/HOL/Tools/ATP/atp_translate.ML Thu Sep 08 00:20:09 2011 +0200 +++ b/src/HOL/Tools/ATP/atp_translate.ML Thu Sep 08 00:23:23 2011 +0200 @@ -20,11 +20,11 @@ datatype polymorphism = Polymorphic | Raw_Monomorphic | Mangled_Monomorphic datatype soundness = Sound_Modulo_Infiniteness | Sound - datatype heaviness = Heavy | Ann_Light | Arg_Light + datatype granularity = All_Vars | Positively_Naked_Vars | Ghost_Type_Arg_Vars datatype type_level = All_Types | - Noninf_Nonmono_Types of soundness * heaviness | - Fin_Nonmono_Types of heaviness | + Noninf_Nonmono_Types of soundness * granularity | + Fin_Nonmono_Types of granularity | Const_Arg_Types | No_Types type type_enc @@ -530,11 +530,11 @@ datatype order = First_Order | Higher_Order datatype polymorphism = Polymorphic | Raw_Monomorphic | Mangled_Monomorphic datatype soundness = Sound_Modulo_Infiniteness | Sound -datatype heaviness = Heavy | Ann_Light | Arg_Light +datatype granularity = All_Vars | Positively_Naked_Vars | Ghost_Type_Arg_Vars datatype type_level = All_Types | - Noninf_Nonmono_Types of soundness * heaviness | - Fin_Nonmono_Types of heaviness | + Noninf_Nonmono_Types of soundness * granularity | + Fin_Nonmono_Types of granularity | Const_Arg_Types | No_Types @@ -554,9 +554,9 @@ | level_of_type_enc (Guards (_, level)) = level | level_of_type_enc (Tags (_, level)) = level -fun heaviness_of_level (Noninf_Nonmono_Types (_, heaviness)) = heaviness - | heaviness_of_level (Fin_Nonmono_Types heaviness) = heaviness - | heaviness_of_level _ = Heavy +fun granularity_of_type_level (Noninf_Nonmono_Types (_, grain)) = grain + | granularity_of_type_level (Fin_Nonmono_Types grain) = grain + | granularity_of_type_level _ = All_Vars fun is_type_level_quasi_sound All_Types = true | is_type_level_quasi_sound (Noninf_Nonmono_Types _) = true @@ -584,13 +584,17 @@ case try_unsuffixes suffixes s of SOME s => (case try_unsuffixes suffixes s of - SOME s => (constr Ann_Light, s) + SOME s => (constr Positively_Naked_Vars, s) | NONE => case try_unsuffixes ats s of - SOME s => (constr Arg_Light, s) - | NONE => (constr Heavy, s)) + SOME s => (constr Ghost_Type_Arg_Vars, s) + | NONE => (constr All_Vars, s)) | NONE => fallback s +fun is_incompatible_type_level poly level = + poly = Mangled_Monomorphic andalso + granularity_of_type_level level = Ghost_Type_Arg_Vars + fun type_enc_from_string soundness s = (case try (unprefix "poly_") s of SOME s => (SOME Polymorphic, s) @@ -611,7 +615,7 @@ (Polymorphic, All_Types) => Simple_Types (First_Order, Polymorphic, All_Types) | (Mangled_Monomorphic, _) => - if heaviness_of_level level = Heavy then + if granularity_of_type_level level = All_Vars then Simple_Types (First_Order, Mangled_Monomorphic, level) else raise Same.SAME @@ -622,14 +626,17 @@ Simple_Types (Higher_Order, Polymorphic, All_Types) | (_, Noninf_Nonmono_Types _) => raise Same.SAME | (Mangled_Monomorphic, _) => - if heaviness_of_level level = Heavy then + if granularity_of_type_level level = All_Vars then Simple_Types (Higher_Order, Mangled_Monomorphic, level) else raise Same.SAME | _ => raise Same.SAME) - | ("guards", (SOME poly, _)) => Guards (poly, level) - | ("tags", (SOME Polymorphic, _)) => Tags (Polymorphic, level) - | ("tags", (SOME poly, _)) => Tags (poly, level) + | ("guards", (SOME poly, _)) => + if is_incompatible_type_level poly level then raise Same.SAME + else Guards (poly, level) + | ("tags", (SOME poly, _)) => + if is_incompatible_type_level poly level then raise Same.SAME + else Tags (poly, level) | ("args", (SOME poly, All_Types (* naja *))) => Guards (poly, Const_Arg_Types) | ("erased", (NONE, All_Types (* naja *))) => @@ -700,10 +707,6 @@ Mangled_Type_Args | No_Type_Args -fun should_drop_arg_type_args (Simple_Types _) = false - | should_drop_arg_type_args type_enc = - level_of_type_enc type_enc = All_Types - fun type_arg_policy type_enc s = let val mangled = (polymorphism_of_type_enc type_enc = Mangled_Monomorphic) in if s = type_tag_name then @@ -718,7 +721,9 @@ else if mangled then Mangled_Type_Args else - Explicit_Type_Args (should_drop_arg_type_args type_enc) + Explicit_Type_Args + (level = All_Types orelse + granularity_of_type_level level = Ghost_Type_Arg_Vars) end end @@ -1089,28 +1094,31 @@ t else let - fun aux Ts t = + fun trans Ts t = case t of - @{const Not} $ t1 => @{const Not} $ aux Ts t1 + @{const Not} $ t1 => @{const Not} $ trans Ts t1 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') => - t0 $ Abs (s, T, aux (T :: Ts) t') + t0 $ Abs (s, T, trans (T :: Ts) t') | (t0 as Const (@{const_name All}, _)) $ t1 => - aux Ts (t0 $ eta_expand Ts t1 1) + trans Ts (t0 $ eta_expand Ts t1 1) | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') => - t0 $ Abs (s, T, aux (T :: Ts) t') + t0 $ Abs (s, T, trans (T :: Ts) t') | (t0 as Const (@{const_name Ex}, _)) $ t1 => - aux Ts (t0 $ eta_expand Ts t1 1) - | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2 - | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2 - | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2 + trans Ts (t0 $ eta_expand Ts t1 1) + | (t0 as @{const HOL.conj}) $ t1 $ t2 => + t0 $ trans Ts t1 $ trans Ts t2 + | (t0 as @{const HOL.disj}) $ t1 $ t2 => + t0 $ trans Ts t1 $ trans Ts t2 + | (t0 as @{const HOL.implies}) $ t1 $ t2 => + t0 $ trans Ts t1 $ trans Ts t2 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _]))) $ t1 $ t2 => - t0 $ aux Ts t1 $ aux Ts t2 + t0 $ trans Ts t1 $ trans Ts t2 | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then t else t |> Envir.eta_contract |> do_lambdas ctxt Ts val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single - in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end + in t |> trans [] |> singleton (Variable.export_terms ctxt' ctxt) end end fun do_cheaply_conceal_lambdas Ts (t1 $ t2) = @@ -1148,12 +1156,12 @@ same in Sledgehammer to prevent the discovery of unreplayable proofs. *) fun freeze_term t = let - fun aux (t $ u) = aux t $ aux u - | aux (Abs (s, T, t)) = Abs (s, T, aux t) - | aux (Var ((s, i), T)) = + fun freeze (t $ u) = freeze t $ freeze u + | freeze (Abs (s, T, t)) = Abs (s, T, freeze t) + | freeze (Var ((s, i), T)) = Free (atp_weak_prefix ^ s ^ "_" ^ string_of_int i, T) - | aux t = t - in t |> exists_subterm is_Var t ? aux end + | freeze t = t + in t |> exists_subterm is_Var t ? freeze end fun presimp_prop ctxt presimp_consts t = let @@ -1198,6 +1206,30 @@ (** Finite and infinite type inference **) +fun tvar_footprint thy s ary = + (case strip_prefix_and_unascii const_prefix s of + SOME s => + s |> invert_const |> robust_const_type thy |> chop_fun ary |> fst + |> map (fn T => Term.add_tvarsT T [] |> map fst) + | NONE => []) + handle TYPE _ => [] + +fun ghost_type_args thy s ary = + let + val footprint = tvar_footprint thy s ary + fun ghosts _ [] = [] + | ghosts seen ((i, tvars) :: args) = + ghosts (union (op =) seen tvars) args + |> exists (not o member (op =) seen) tvars ? cons i + in + if forall null footprint then + [] + else + 0 upto length footprint - 1 ~~ footprint + |> sort (rev_order o list_ord Term_Ord.indexname_ord o pairself snd) + |> ghosts [] + end + type monotonicity_info = {maybe_finite_Ts : typ list, surely_finite_Ts : typ list, @@ -1221,23 +1253,25 @@ fun should_encode_type _ (_ : monotonicity_info) All_Types _ = true | should_encode_type ctxt {maybe_finite_Ts, surely_infinite_Ts, maybe_nonmono_Ts, ...} - (Noninf_Nonmono_Types (soundness, _)) T = - exists (type_intersect ctxt T) maybe_nonmono_Ts andalso - not (exists (type_instance ctxt T) surely_infinite_Ts orelse - (not (member (type_aconv ctxt) maybe_finite_Ts T) andalso - is_type_kind_of_surely_infinite ctxt soundness surely_infinite_Ts T)) + (Noninf_Nonmono_Types (soundness, grain)) T = + grain = Ghost_Type_Arg_Vars orelse + (exists (type_intersect ctxt T) maybe_nonmono_Ts andalso + not (exists (type_instance ctxt T) surely_infinite_Ts orelse + (not (member (type_aconv ctxt) maybe_finite_Ts T) andalso + is_type_kind_of_surely_infinite ctxt soundness surely_infinite_Ts + T))) | should_encode_type ctxt {surely_finite_Ts, maybe_infinite_Ts, maybe_nonmono_Ts, ...} - (Fin_Nonmono_Types _) T = - exists (type_intersect ctxt T) maybe_nonmono_Ts andalso - (exists (type_generalization ctxt T) surely_finite_Ts orelse - (not (member (type_aconv ctxt) maybe_infinite_Ts T) andalso - is_type_surely_finite ctxt T)) + (Fin_Nonmono_Types grain) T = + grain = Ghost_Type_Arg_Vars orelse + (exists (type_intersect ctxt T) maybe_nonmono_Ts andalso + (exists (type_generalization ctxt T) surely_finite_Ts orelse + (not (member (type_aconv ctxt) maybe_infinite_Ts T) andalso + is_type_surely_finite ctxt T))) | should_encode_type _ _ _ _ = false fun should_guard_type ctxt mono (Guards (_, level)) should_guard_var T = - (heaviness_of_level level = Heavy orelse should_guard_var ()) andalso - should_encode_type ctxt mono level T + should_guard_var () andalso should_encode_type ctxt mono level T | should_guard_type _ _ _ _ _ = false fun is_maybe_universal_var (IConst ((s, _), _, _)) = @@ -1249,15 +1283,21 @@ datatype tag_site = Top_Level of bool option | Eq_Arg of bool option | + Arg of string * int | Elsewhere fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false | should_tag_with_type ctxt mono (Tags (_, level)) site u T = - (if heaviness_of_level level = Heavy then - should_encode_type ctxt mono level T - else case (site, is_maybe_universal_var u) of - (Eq_Arg _, true) => should_encode_type ctxt mono level T - | _ => false) + (case granularity_of_type_level level of + All_Vars => should_encode_type ctxt mono level T + | grain => + case (site, is_maybe_universal_var u) of + (Eq_Arg _, true) => should_encode_type ctxt mono level T + | (Arg (s, j), true) => + grain = Ghost_Type_Arg_Vars andalso + member (op =) + (ghost_type_args (Proof_Context.theory_of ctxt) s (j + 1)) j + | _ => false) | should_tag_with_type _ _ _ _ _ _ = false fun fused_type ctxt mono level = @@ -1646,13 +1686,36 @@ accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, []))) | is_var_positively_naked_in_term _ _ _ _ = true -fun should_guard_var_in_formula pos phi (SOME true) name = - formula_fold pos (is_var_positively_naked_in_term name) phi false - | should_guard_var_in_formula _ _ _ _ = true +fun is_var_ghost_type_arg_in_term thy name pos tm accum = + is_var_positively_naked_in_term name pos tm accum orelse + let + val var = ATerm (name, []) + fun is_nasty_in_term (ATerm (_, [])) = false + | is_nasty_in_term (ATerm ((s, _), tms)) = + (member (op =) tms var andalso + let val ary = length tms in + case ghost_type_args thy s ary of + [] => false + | ghosts => + exists (fn (j, tm) => tm = var andalso member (op =) ghosts j) + (0 upto length tms - 1 ~~ tms) + end) orelse + exists is_nasty_in_term tms + | is_nasty_in_term _ = true + in is_nasty_in_term tm end + +fun should_guard_var_in_formula thy level pos phi (SOME true) name = + (case granularity_of_type_level level of + All_Vars => true + | Positively_Naked_Vars => + formula_fold pos (is_var_positively_naked_in_term name) phi false + | Ghost_Type_Arg_Vars => + formula_fold pos (is_var_ghost_type_arg_in_term thy name) phi false) + | should_guard_var_in_formula _ _ _ _ _ _ = true fun should_generate_tag_bound_decl _ _ _ (SOME true) _ = false | should_generate_tag_bound_decl ctxt mono (Tags (_, level)) _ T = - heaviness_of_level level <> Heavy andalso + granularity_of_type_level level <> All_Vars andalso should_encode_type ctxt mono level T | should_generate_tag_bound_decl _ _ _ _ _ = false @@ -1667,27 +1730,29 @@ | _ => raise Fail "unexpected lambda-abstraction") and ho_term_from_iterm ctxt format mono type_enc = let - fun aux site u = + fun term site u = let val (head, args) = strip_iterm_comb u val pos = case site of Top_Level pos => pos | Eq_Arg pos => pos - | Elsewhere => NONE + | _ => NONE val t = case head of IConst (name as (s, _), _, T_args) => let - val arg_site = if is_tptp_equal s then Eq_Arg pos else Elsewhere + fun arg_site j = + if is_tptp_equal s then Eq_Arg pos else Arg (s, j) in - mk_aterm format type_enc name T_args (map (aux arg_site) args) + mk_aterm format type_enc name T_args + (map2 (term o arg_site) (0 upto length args - 1) args) end | IVar (name, _) => - mk_aterm format type_enc name [] (map (aux Elsewhere) args) + mk_aterm format type_enc name [] (map (term Elsewhere) args) | IAbs ((name, T), tm) => AAbs ((name, ho_type_from_typ format type_enc true 0 T), - aux Elsewhere tm) + term Elsewhere tm) | IApp _ => raise Fail "impossible \"IApp\"" val T = ityp_of u in @@ -1696,18 +1761,20 @@ else I) end - in aux end + in term end and formula_from_iformula ctxt format mono type_enc should_guard_var = let + val thy = Proof_Context.theory_of ctxt + val level = level_of_type_enc type_enc val do_term = ho_term_from_iterm ctxt format mono type_enc o Top_Level val do_bound_type = case type_enc of - Simple_Types (_, _, level) => fused_type ctxt mono level 0 + Simple_Types _ => fused_type ctxt mono level 0 #> ho_type_from_typ format type_enc false 0 #> SOME | _ => K NONE fun do_out_of_bound_type pos phi universal (name, T) = if should_guard_type ctxt mono type_enc - (fn () => should_guard_var pos phi universal name) T then + (fn () => should_guard_var thy level pos phi universal name) T then IVar (name, T) |> type_guard_iterm format type_enc T |> do_term pos |> AAtom |> SOME @@ -1958,9 +2025,12 @@ fun add_fact_monotonic_types ctxt mono type_enc = add_iformula_monotonic_types ctxt mono type_enc |> fact_lift fun monotonic_types_for_facts ctxt mono type_enc facts = - [] |> (polymorphism_of_type_enc type_enc = Polymorphic andalso - is_type_level_monotonicity_based (level_of_type_enc type_enc)) - ? fold (add_fact_monotonic_types ctxt mono type_enc) facts + let val level = level_of_type_enc type_enc in + [] |> (polymorphism_of_type_enc type_enc = Polymorphic andalso + is_type_level_monotonicity_based level andalso + granularity_of_type_level level <> Ghost_Type_Arg_Vars) + ? fold (add_fact_monotonic_types ctxt mono type_enc) facts + end fun formula_line_for_guards_mono_type ctxt format mono type_enc T = Formula (guards_sym_formula_prefix ^ @@ -1970,7 +2040,7 @@ |> type_guard_iterm format type_enc T |> AAtom |> formula_from_iformula ctxt format mono type_enc - (K (K (K (K true)))) (SOME true) + (K (K (K (K (K (K true)))))) (SOME true) |> bound_tvars type_enc (atyps_of T) |> close_formula_universally type_enc, isabelle_info introN, NONE) @@ -2023,21 +2093,28 @@ fun formula_line_for_guards_sym_decl ctxt format conj_sym_kind mono type_enc n s j (s', T_args, T, _, ary, in_conj) = let + val thy = Proof_Context.theory_of ctxt val (kind, maybe_negate) = if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot) else (Axiom, I) val (arg_Ts, res_T) = chop_fun ary T - val num_args = length arg_Ts - val bound_names = - 1 upto num_args |> map (`I o make_bound_var o string_of_int) + val bound_names = 1 upto ary |> map (`I o make_bound_var o string_of_int) val bounds = bound_names ~~ arg_Ts |> map (fn (name, T) => IConst (name, T, [])) - val sym_needs_arg_types = exists (curry (op =) dummyT) T_args - fun should_keep_arg_type T = - sym_needs_arg_types andalso - should_guard_type ctxt mono type_enc (K true) T val bound_Ts = - arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE) + if exists (curry (op =) dummyT) T_args then + case level_of_type_enc type_enc of + All_Types => map SOME arg_Ts + | level => + if granularity_of_type_level level = Ghost_Type_Arg_Vars then + let val ghosts = ghost_type_args thy s ary in + map2 (fn j => if member (op =) ghosts j then SOME else K NONE) + (0 upto ary - 1) arg_Ts + end + else + replicate ary NONE + else + replicate ary NONE in Formula (guards_sym_formula_prefix ^ s ^ (if n > 1 then "_" ^ string_of_int j else ""), kind, @@ -2046,16 +2123,19 @@ |> type_guard_iterm format type_enc res_T |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts) |> formula_from_iformula ctxt format mono type_enc - (K (K (K (K true)))) (SOME true) + (K (K (K (K (K (K true)))))) (SOME true) |> n > 1 ? bound_tvars type_enc (atyps_of T) |> close_formula_universally type_enc |> maybe_negate, isabelle_info introN, NONE) end -fun formula_lines_for_nonuniform_tags_sym_decl ctxt format conj_sym_kind mono - type_enc n s (j, (s', T_args, T, pred_sym, ary, in_conj)) = +fun formula_lines_for_tags_sym_decl ctxt format conj_sym_kind mono type_enc n s + (j, (s', T_args, T, pred_sym, ary, in_conj)) = let + val thy = Proof_Context.theory_of ctxt + val level = level_of_type_enc type_enc + val grain = granularity_of_type_level level val ident_base = tags_sym_formula_prefix ^ s ^ (if n > 1 then "_" ^ string_of_int j else "") @@ -2063,19 +2143,28 @@ if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot) else (Axiom, I) val (arg_Ts, res_T) = chop_fun ary T - val bound_names = - 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int) + val bound_names = 1 upto ary |> map (`I o make_bound_var o string_of_int) val bounds = bound_names |> map (fn name => ATerm (name, [])) val cst = mk_aterm format type_enc (s, s') T_args val eq = maybe_negate oo eq_formula type_enc (atyps_of T) pred_sym - val should_encode = - should_encode_type ctxt mono (level_of_type_enc type_enc) + val should_encode = should_encode_type ctxt mono level val tag_with = tag_with_type ctxt format mono type_enc NONE val add_formula_for_res = if should_encode res_T then - cons (Formula (ident_base ^ "_res", kind, - eq (tag_with res_T (cst bounds)) (cst bounds), - isabelle_info simpN, NONE)) + let + val tagged_bounds = + if grain = Ghost_Type_Arg_Vars then + let val ghosts = ghost_type_args thy s ary in + map2 (fn (j, arg_T) => member (op =) ghosts j ? tag_with arg_T) + (0 upto ary - 1 ~~ arg_Ts) bounds + end + else + bounds + in + cons (Formula (ident_base ^ "_res", kind, + eq (tag_with res_T (cst bounds)) (cst tagged_bounds), + isabelle_info simpN, NONE)) + end else I fun add_formula_for_arg k = @@ -2093,7 +2182,8 @@ end in [] |> not pred_sym ? add_formula_for_res - |> Config.get ctxt type_tag_arguments + |> (Config.get ctxt type_tag_arguments andalso + grain = Positively_Naked_Vars) ? fold add_formula_for_arg (ary - 1 downto 0) end @@ -2127,13 +2217,13 @@ type_enc n s) end | Tags (_, level) => - if heaviness_of_level level = Heavy then + if granularity_of_type_level level = All_Vars then [] else let val n = length decls in (0 upto n - 1 ~~ decls) - |> maps (formula_lines_for_nonuniform_tags_sym_decl ctxt format - conj_sym_kind mono type_enc n s) + |> maps (formula_lines_for_tags_sym_decl ctxt format conj_sym_kind mono + type_enc n s) end fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind mono type_enc @@ -2168,13 +2258,22 @@ val conjsN = "Conjectures" val free_typesN = "Type variables" -val explicit_apply = NONE (* for experiments *) +val explicit_apply_threshold = 50 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_enc exporter lambda_trans readable_names preproc hyp_ts concl_t facts = let val thy = Proof_Context.theory_of ctxt val type_enc = type_enc |> adjust_type_enc format + (* Forcing explicit applications is expensive for polymorphic encodings, + because it takes only one existential variable ranging over "'a => 'b" to + ruin everything. Hence we do it only if there are few facts. *) + val explicit_apply = + if polymorphism_of_type_enc type_enc <> Polymorphic orelse + length facts <= explicit_apply_threshold then + NONE + else + SOME false val lambda_trans = if lambda_trans = smartN then if is_type_enc_higher_order type_enc then lambdasN else combinatorsN