# HG changeset patch # User huffman # Date 1315448668 25200 # Node ID 1120cba9bce438518998ec5b3db8f211f199a653 # Parent 353ddca2e4c0facd4a6d55182d326b32407d359b# Parent 7798deb6f8fa9e01365edb893c30e1f0ca33b81f merged diff -r 353ddca2e4c0 -r 1120cba9bce4 ANNOUNCE --- a/ANNOUNCE Wed Sep 07 17:41:29 2011 -0700 +++ b/ANNOUNCE Wed Sep 07 19:24:28 2011 -0700 @@ -1,34 +1,15 @@ -Subject: Announcing Isabelle2011 +Subject: Announcing Isabelle2011-1 To: isabelle-users@cl.cam.ac.uk -Isabelle2011 is now available. - -This version significantly improves upon Isabelle2009-2, see the NEWS -file in the distribution for more details. Some notable changes are: - -* Experimental Prover IDE based on Isabelle/Scala and jEdit. - -* Coercive subtyping (configured in HOL/Complex_Main). - -* HOL code generation: Scala as another target language. - -* HOL: partial_function definitions. +Isabelle2011-1 is now available. -* HOL: various tool enhancements, including Quickcheck, Nitpick, - Sledgehammer, SMT integration. - -* HOL: various additions to theory library, including HOL-Algebra, - Imperative_HOL, Multivariate_Analysis, Probability. +This version improves upon Isabelle2011, see the NEWS file in the +distribution for more details. Some important changes are: -* HOLCF: reorganization of library and related tools. - -* HOL/SPARK: interactive proof environment for verification conditions - generated by the SPARK Ada program verifier. - -* Improved Isabelle/Isar implementation manual (covering Isabelle/ML). +* FIXME -You may get Isabelle2011 from the following mirror sites: +You may get Isabelle2011-1 from the following mirror sites: Cambridge (UK) http://www.cl.cam.ac.uk/research/hvg/Isabelle/ Munich (Germany) http://isabelle.in.tum.de/ diff -r 353ddca2e4c0 -r 1120cba9bce4 Admin/CHECKLIST --- a/Admin/CHECKLIST Wed Sep 07 17:41:29 2011 -0700 +++ b/Admin/CHECKLIST Wed Sep 07 19:24:28 2011 -0700 @@ -3,9 +3,7 @@ - test polyml-5.4.0, polyml-5.3.0, polyml-5.2.1, smlnj; -- test Proof General 4.1, 4.0, 3.7.1.1; - -- test Scala wrapper; +- test Proof General 4.1, 3.7.1.1; - check HTML header of library; diff -r 353ddca2e4c0 -r 1120cba9bce4 Admin/makebundle --- a/Admin/makebundle Wed Sep 07 17:41:29 2011 -0700 +++ b/Admin/makebundle Wed Sep 07 19:24:28 2011 -0700 @@ -75,7 +75,13 @@ ) case "$PLATFORM" in - x86-cygwin) + *-darwin) + perl -pi -e "s,lookAndFeel=.*,lookAndFeel=com.apple.laf.AquaLookAndFeel,g;" \ + "$TMP/$ISABELLE_NAME/src/Tools/jEdit/dist/properties/jEdit.props" + ;; + *-cygwin) + perl -pi -e "s,lookAndFeel=.*,lookAndFeel=com.sun.java.swing.plaf.windows.WindowsLookAndFeel,g;" \ + "$TMP/$ISABELLE_NAME/src/Tools/jEdit/dist/properties/jEdit.props" rm "$TMP/$ISABELLE_NAME/contrib/ProofGeneral" ln -s ProofGeneral-3.7.1.1 "$TMP/$ISABELLE_NAME/contrib/ProofGeneral" ;; diff -r 353ddca2e4c0 -r 1120cba9bce4 CONTRIBUTORS --- a/CONTRIBUTORS Wed Sep 07 17:41:29 2011 -0700 +++ b/CONTRIBUTORS Wed Sep 07 19:24:28 2011 -0700 @@ -3,8 +3,14 @@ who is listed as an author in one of the source files of this Isabelle distribution. -Contributions to this Isabelle version --------------------------------------- +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 353ddca2e4c0 -r 1120cba9bce4 NEWS --- a/NEWS Wed Sep 07 17:41:29 2011 -0700 +++ b/NEWS Wed Sep 07 19:24:28 2011 -0700 @@ -1,8 +1,8 @@ Isabelle NEWS -- history user-relevant changes ============================================== -New in this Isabelle version ----------------------------- +New in Isabelle2011-1 (October 2011) +------------------------------------ *** General *** @@ -34,6 +34,13 @@ See also ~~/src/Tools/jEdit/README.html for further information, including some remaining limitations. +* Theory loader: source files are exclusively located via the master +directory of each theory node (where the .thy file itself resides). +The global load path (such as src/HOL/Library) has been discontinued. +Note that the path element ~~ may be used to reference theories in the +Isabelle home folder -- for instance, "~~/src/HOL/Library/FuncSet". +INCOMPATIBILITY. + * Theory loader: source files are identified by content via SHA1 digests. Discontinued former path/modtime identification and optional ISABELLE_FILE_IDENT plugin scripts. @@ -48,13 +55,6 @@ * Discontinued old lib/scripts/polyml-platform, which has been obsolete since Isabelle2009-2. -* Theory loader: source files are exclusively located via the master -directory of each theory node (where the .thy file itself resides). -The global load path (such as src/HOL/Library) has been discontinued. -Note that the path element ~~ may be used to reference theories in the -Isabelle home folder -- for instance, "~~/src/HOL/Library/FuncSet". -INCOMPATIBILITY. - * Various optional external tools are referenced more robustly and uniformly by explicit Isabelle settings as follows: @@ -82,29 +82,38 @@ that the result needs to be unique, which means fact specifications may have to be refined after enriching a proof context. +* Attribute "case_names" has been refined: the assumptions in each case +can be named now by following the case name with [name1 name2 ...]. + * Isabelle/Isar reference manual provides more formal references in syntax diagrams. -* Attribute case_names has been refined: the assumptions in each case can -be named now by following the case name with [name1 name2 ...]. - *** HOL *** -* Classes bot and top require underlying partial order rather than preorder: -uniqueness of bot and top is guaranteed. INCOMPATIBILITY. +* 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. * Class complete_lattice: generalized a couple of lemmas from sets; -generalized theorems INF_cong and SUP_cong. New type classes for complete -boolean algebras and complete linear orders. Lemmas Inf_less_iff, -less_Sup_iff, INF_less_iff, less_SUP_iff now reside in class complete_linorder. -Changed proposition of lemmas Inf_bool_def, Sup_bool_def, Inf_fun_def, Sup_fun_def, -Inf_apply, Sup_apply. +generalized theorems INF_cong and SUP_cong. New type classes for +complete boolean algebras and complete linear orders. Lemmas +Inf_less_iff, less_Sup_iff, INF_less_iff, less_SUP_iff now reside in +class complete_linorder. + +Changed proposition of lemmas Inf_bool_def, Sup_bool_def, Inf_fun_def, +Sup_fun_def, Inf_apply, Sup_apply. + Redundant lemmas Inf_singleton, Sup_singleton, Inf_binary, Sup_binary, INF_eq, SUP_eq, INF_UNIV_range, SUP_UNIV_range, Int_eq_Inter, -INTER_eq_Inter_image, Inter_def, INT_eq, Un_eq_Union, UNION_eq_Union_image, -Union_def, UN_singleton, UN_eq have been discarded. -More consistent and less misunderstandable names: +INTER_eq_Inter_image, Inter_def, INT_eq, Un_eq_Union, +UNION_eq_Union_image, Union_def, UN_singleton, UN_eq have been +discarded. + +More consistent and comprehensive names: + INFI_def ~> INF_def SUPR_def ~> SUP_def INF_leI ~> INF_lower @@ -122,30 +131,35 @@ INCOMPATIBILITY. -* Theorem collections ball_simps and bex_simps do not contain theorems referring -to UNION any longer; these have been moved to collection UN_ball_bex_simps. -INCOMPATIBILITY. - -* Archimedean_Field.thy: - floor now is defined as parameter of a separate type class floor_ceiling. - -* Finite_Set.thy: more coherent development of fold_set locales: +* Theorem collections ball_simps and bex_simps do not contain theorems +referring to UNION any longer; these have been moved to collection +UN_ball_bex_simps. INCOMPATIBILITY. + +* Theory Archimedean_Field: floor now is defined as parameter of a +separate type class floor_ceiling. + +* Theory Finite_Set: more coherent development of fold_set locales: locale fun_left_comm ~> locale comp_fun_commute locale fun_left_comm_idem ~> locale comp_fun_idem - -Both use point-free characterisation; interpretation proofs may need adjustment. -INCOMPATIBILITY. + +Both use point-free characterization; interpretation proofs may need +adjustment. INCOMPATIBILITY. * Code generation: - - theory Library/Code_Char_ord provides native ordering of characters - in the target language. - - commands code_module and code_library are legacy, use export_code instead. - - method evaluation is legacy, use method eval instead. - - legacy evaluator "SML" is deactivated by default. To activate it, add the following - line in your theory: + + - Theory Library/Code_Char_ord provides native ordering of + characters in the target language. + + - Commands code_module and code_library are legacy, use export_code instead. + + - Method "evaluation" is legacy, use method "eval" instead. + + - Legacy evaluator "SML" is deactivated by default. May be + reactivated by the following theory command: + setup {* Value.add_evaluator ("SML", Codegen.eval_term) *} - + * Declare ext [intro] by default. Rare INCOMPATIBILITY. * Nitpick: @@ -168,51 +182,57 @@ - Removed "metisF" -- use "metis" instead. INCOMPATIBILITY. - Obsoleted "metisFT" -- use "metis (full_types)" instead. INCOMPATIBILITY. -* "try": - - Renamed "try_methods" and added "simp:", "intro:", "dest:", and "elim:" - options. INCOMPATIBILITY. - - Introduced "try" that not only runs "try_methods" but also "solve_direct", - "sledgehammer", "quickcheck", and "nitpick". +* Command 'try': + - Renamed 'try_methods' and added "simp:", "intro:", "dest:", and + "elim:" options. INCOMPATIBILITY. + - Introduced 'tryÄ that not only runs 'try_methods' but also + 'solve_direct', 'sledgehammer', 'quickcheck', and 'nitpick'. * Quickcheck: + - Added "eval" option to evaluate terms for the found counterexample - (currently only supported by the default (exhaustive) tester) + (currently only supported by the default (exhaustive) tester). + - Added post-processing of terms to obtain readable counterexamples - (currently only supported by the default (exhaustive) tester) + (currently only supported by the default (exhaustive) tester). + - New counterexample generator quickcheck[narrowing] enables - narrowing-based testing. - It requires that the Glasgow Haskell compiler is installed and - its location is known to Isabelle with the environment variable - ISABELLE_GHC. + narrowing-based testing. Requires the Glasgow Haskell compiler + with its installation location defined in the Isabelle settings + environment as ISABELLE_GHC. + - Removed quickcheck tester "SML" based on the SML code generator - from HOL-Library + (formly in HOL/Library). * Function package: discontinued option "tailrec". -INCOMPATIBILITY. Use partial_function instead. - -* HOL-Probability: +INCOMPATIBILITY. Use 'partial_function' instead. + +* Session HOL-Probability: - Caratheodory's extension lemma is now proved for ring_of_sets. - Infinite products of probability measures are now available. - - Use extended reals instead of positive extended reals. - INCOMPATIBILITY. - -* Old recdef package has been moved to Library/Old_Recdef.thy, where it -must be loaded explicitly. INCOMPATIBILITY. - -* Well-founded recursion combinator "wfrec" has been moved to -Library/Wfrec.thy. INCOMPATIBILITY. - -* Theory Library/Nat_Infinity has been renamed to Library/Extended_Nat. -The names of the following types and constants have changed: - inat (type) ~> enat + - Use extended reals instead of positive extended + reals. INCOMPATIBILITY. + +* Old 'recdef' package has been moved to theory Library/Old_Recdef, +from where it must be imported explicitly. INCOMPATIBILITY. + +* Well-founded recursion combinator "wfrec" has been moved to theory +Library/Wfrec. INCOMPATIBILITY. + +* Theory Library/Nat_Infinity has been renamed to +Library/Extended_Nat, with name changes of the following types and +constants: + + type inat ~> type enat Fin ~> enat Infty ~> infinity (overloaded) iSuc ~> eSuc the_Fin ~> the_enat + Every theorem name containing "inat", "Fin", "Infty", or "iSuc" has been renamed accordingly. -* Limits.thy: Type "'a net" has been renamed to "'a filter", in +* Theory Limits: Type "'a net" has been renamed to "'a filter", in accordance with standard mathematical terminology. INCOMPATIBILITY. * Session Multivariate_Analysis: Type "('a, 'b) cart" has been renamed @@ -283,10 +303,10 @@ real_abs_sub_norm ~> norm_triangle_ineq3 norm_cauchy_schwarz_abs ~> Cauchy_Schwarz_ineq2 -* Complex_Main: The locale interpretations for the bounded_linear and -bounded_bilinear locales have been removed, in order to reduce the -number of duplicate lemmas. Users must use the original names for -distributivity theorems, potential INCOMPATIBILITY. +* Theory Complex_Main: The locale interpretations for the +bounded_linear and bounded_bilinear locales have been removed, in +order to reduce the number of duplicate lemmas. Users must use the +original names for distributivity theorems, potential INCOMPATIBILITY. divide.add ~> add_divide_distrib divide.diff ~> diff_divide_distrib @@ -296,7 +316,7 @@ mult_right.setsum ~> setsum_right_distrib mult_left.diff ~> left_diff_distrib -* Complex_Main: Several redundant theorems have been removed or +* Theory Complex_Main: Several redundant theorems have been removed or replaced by more general versions. INCOMPATIBILITY. real_of_int_real_of_nat ~> real_of_int_of_nat_eq @@ -365,26 +385,30 @@ *** Document preparation *** -* Discontinued special treatment of hard tabulators, which are better -avoided in the first place. Implicit tab-width is 1. - -* Antiquotation @{rail} layouts railroad syntax diagrams, see also -isar-ref manual. - -* Antiquotation @{value} evaluates the given term and presents its result. - * Localized \isabellestyle switch can be used within blocks or groups like this: \isabellestyle{it} %preferred default {\isabellestylett @{text "typewriter stuff"}} -* New term style "isub" as ad-hoc conversion of variables x1, y23 into -subscripted form x\<^isub>1, y\<^isub>2\<^isub>3. +* Antiquotation @{rail} layouts railroad syntax diagrams, see also +isar-ref manual, both for description and actual application of the +same. + +* Antiquotation @{value} evaluates the given term and presents its +result. + +* Antiquotations: term style "isub" provides ad-hoc conversion of +variables x1, y23 into subscripted form x\<^isub>1, +y\<^isub>2\<^isub>3. * Predefined LaTeX macros for Isabelle symbols \ and \ (e.g. see ~~/src/HOL/Library/Monad_Syntax.thy). +* Discontinued special treatment of hard tabulators, which are better +avoided in the first place (no universally agreed standard expansion). +Implicit tab-width is now 1. + *** ML *** @@ -443,12 +467,22 @@ INCOMPATIBILITY, classical tactics and derived proof methods require proper Proof.context. + +*** System *** + * Scala layer provides JVM method invocation service for static -methods of type (String)String, see Invoke_Scala.method in ML. -For example: +methods of type (String)String, see Invoke_Scala.method in ML. For +example: Invoke_Scala.method "java.lang.System.getProperty" "java.home" +Togeter with YXML.string_of_body/parse_body and XML.Encode/Decode this +allows to pass structured values between ML and Scala. + +* The IsabelleText fonts includes some further glyphs to support the +Prover IDE. Potential INCOMPATIBILITY: users who happen to have +installed a local copy (which is normally *not* required) need to +delete or update it from ~~/lib/fonts/. New in Isabelle2011 (January 2011) diff -r 353ddca2e4c0 -r 1120cba9bce4 README --- a/README Wed Sep 07 17:41:29 2011 -0700 +++ b/README Wed Sep 07 19:24:28 2011 -0700 @@ -16,8 +16,8 @@ * The Poly/ML compiler and runtime system (version 5.2.1 or later). * The GNU bash shell (version 3.x or 2.x). * Perl (version 5.x). + * Java 1.6.x from Oracle or Apple -- for Scala and jEdit. * GNU Emacs (version 23) -- for the Proof General 4.x interface. - * Java 1.6.x from Oracle/Sun or Apple -- for Scala and jEdit. * A complete LaTeX installation -- for document preparation. Installation @@ -31,17 +31,18 @@ User interface + Isabelle/jEdit is an emerging Prover IDE based on advanced + technology of Isabelle/Scala. It provides a metaphor of continuous + proof checking of a versioned collection of theory sources, with + instantaneous feedback in real-time and rich semantic markup + associated with the formal text. + The classic Isabelle user interface is Proof General by David Aspinall and others. It is a generic Emacs interface for proof assistants, including Isabelle. Its most prominent feature is script management, providing a metaphor of stepwise proof script editing. - Isabelle/jEdit is an experimental Prover IDE based on advanced - technology of Isabelle/Scala. It provides a metaphor of continuous - proof checking of a versioned collection of theory sources, with - instantaneous feedback in real-time. - Other sources of information The Isabelle Page diff -r 353ddca2e4c0 -r 1120cba9bce4 doc-src/Sledgehammer/sledgehammer.tex --- a/doc-src/Sledgehammer/sledgehammer.tex Wed Sep 07 17:41:29 2011 -0700 +++ b/doc-src/Sledgehammer/sledgehammer.tex Wed Sep 07 19:24:28 2011 -0700 @@ -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 353ddca2e4c0 -r 1120cba9bce4 doc-src/System/Thy/Misc.thy --- a/doc-src/System/Thy/Misc.thy Wed Sep 07 17:41:29 2011 -0700 +++ b/doc-src/System/Thy/Misc.thy Wed Sep 07 19:24:28 2011 -0700 @@ -336,8 +336,8 @@ sub-chunks separated by @{text "\<^bold>Y"}. Markup chunks start with an empty sub-chunk, and a second empty sub-chunk indicates close of an element. Any other non-empty chunk consists of plain - text. For example, see @{file "~~/src/Pure/General/yxml.ML"} or - @{file "~~/src/Pure/General/yxml.scala"}. + text. For example, see @{file "~~/src/Pure/PIDE/yxml.ML"} or + @{file "~~/src/Pure/PIDE/yxml.scala"}. YXML documents may be detected quickly by checking that the first two characters are @{text "\<^bold>X\<^bold>Y"}. diff -r 353ddca2e4c0 -r 1120cba9bce4 doc-src/System/Thy/document/Misc.tex --- a/doc-src/System/Thy/document/Misc.tex Wed Sep 07 17:41:29 2011 -0700 +++ b/doc-src/System/Thy/document/Misc.tex Wed Sep 07 19:24:28 2011 -0700 @@ -376,8 +376,8 @@ sub-chunks separated by \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E626F6C643E}{}\isactrlbold Y{\isaliteral{22}{\isachardoublequote}}}. Markup chunks start with an empty sub-chunk, and a second empty sub-chunk indicates close of an element. Any other non-empty chunk consists of plain - text. For example, see \verb|~~/src/Pure/General/yxml.ML| or - \verb|~~/src/Pure/General/yxml.scala|. + text. For example, see \verb|~~/src/Pure/PIDE/yxml.ML| or + \verb|~~/src/Pure/PIDE/yxml.scala|. YXML documents may be detected quickly by checking that the first two characters are \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E626F6C643E}{}\isactrlbold X\isaliteral{5C3C5E626F6C643E}{}\isactrlbold Y{\isaliteral{22}{\isachardoublequote}}}.% diff -r 353ddca2e4c0 -r 1120cba9bce4 doc/Contents --- a/doc/Contents Wed Sep 07 17:41:29 2011 -0700 +++ b/doc/Contents Wed Sep 07 19:24:28 2011 -0700 @@ -1,4 +1,4 @@ -Learning and using Isabelle +Miscellaneous tutorials tutorial Tutorial on Isabelle/HOL main What's in Main isar-overview Tutorial on Isar diff -r 353ddca2e4c0 -r 1120cba9bce4 src/HOL/Decision_Procs/Commutative_Ring_Complete.thy --- a/src/HOL/Decision_Procs/Commutative_Ring_Complete.thy Wed Sep 07 17:41:29 2011 -0700 +++ b/src/HOL/Decision_Procs/Commutative_Ring_Complete.thy Wed Sep 07 19:24:28 2011 -0700 @@ -12,8 +12,7 @@ begin text {* Formalization of normal form *} -fun - isnorm :: "('a::{comm_ring}) pol \ bool" +fun isnorm :: "'a::comm_ring pol \ bool" where "isnorm (Pc c) \ True" | "isnorm (Pinj i (Pc c)) \ False" @@ -26,35 +25,40 @@ | "isnorm (PX P i Q) \ isnorm P \ isnorm Q" (* Some helpful lemmas *) -lemma norm_Pinj_0_False:"isnorm (Pinj 0 P) = False" -by(cases P, auto) +lemma norm_Pinj_0_False: "isnorm (Pinj 0 P) = False" + by (cases P) auto -lemma norm_PX_0_False:"isnorm (PX (Pc 0) i Q) = False" -by(cases i, auto) +lemma norm_PX_0_False: "isnorm (PX (Pc 0) i Q) = False" + by (cases i) auto -lemma norm_Pinj:"isnorm (Pinj i Q) \ isnorm Q" -by(cases i,simp add: norm_Pinj_0_False norm_PX_0_False,cases Q) auto +lemma norm_Pinj: "isnorm (Pinj i Q) \ isnorm Q" + by (cases i) (simp add: norm_Pinj_0_False norm_PX_0_False, cases Q, auto) -lemma norm_PX2:"isnorm (PX P i Q) \ isnorm Q" -by(cases i, auto, cases P, auto, case_tac pol2, auto) +lemma norm_PX2: "isnorm (PX P i Q) \ isnorm Q" + by (cases i) (auto, cases P, auto, case_tac pol2, auto) + +lemma norm_PX1: "isnorm (PX P i Q) \ isnorm P" + by (cases i) (auto, cases P, auto, case_tac pol2, auto) -lemma norm_PX1:"isnorm (PX P i Q) \ isnorm P" -by(cases i, auto, cases P, auto, case_tac pol2, auto) - -lemma mkPinj_cn:"\y~=0; isnorm Q\ \ isnorm (mkPinj y Q)" -apply(auto simp add: mkPinj_def norm_Pinj_0_False split: pol.split) -apply(case_tac nat, auto simp add: norm_Pinj_0_False) -by(case_tac pol, auto) (case_tac y, auto) +lemma mkPinj_cn: "y ~= 0 \ isnorm Q \ isnorm (mkPinj y Q)" + apply (auto simp add: mkPinj_def norm_Pinj_0_False split: pol.split) + apply (case_tac nat, auto simp add: norm_Pinj_0_False) + apply (case_tac pol, auto) + apply (case_tac y, auto) + done lemma norm_PXtrans: - assumes A:"isnorm (PX P x Q)" and "isnorm Q2" + assumes A: "isnorm (PX P x Q)" and "isnorm Q2" shows "isnorm (PX P x Q2)" -proof(cases P) - case (PX p1 y p2) with assms show ?thesis by(cases x, auto, cases p2, auto) +proof (cases P) + case (PX p1 y p2) + with assms show ?thesis by (cases x) (auto, cases p2, auto) next - case Pc with assms show ?thesis by (cases x) auto + case Pc + with assms show ?thesis by (cases x) auto next - case Pinj with assms show ?thesis by (cases x) auto + case Pinj + with assms show ?thesis by (cases x) auto qed lemma norm_PXtrans2: @@ -62,7 +66,7 @@ shows "isnorm (PX P (Suc (n+x)) Q2)" proof (cases P) case (PX p1 y p2) - with assms show ?thesis by (cases x, auto, cases p2, auto) + with assms show ?thesis by (cases x) (auto, cases p2, auto) next case Pc with assms show ?thesis by (cases x) auto @@ -83,27 +87,33 @@ with assms show ?thesis by (cases x) (auto simp add: mkPinj_cn mkPX_def) next case (PX P1 y P2) - with assms have Y0: "y>0" by (cases y) auto + with assms have Y0: "y > 0" by (cases y) auto from assms PX have "isnorm P1" "isnorm P2" by (auto simp add: norm_PX1[of P1 y P2] norm_PX2[of P1 y P2]) from assms PX Y0 show ?thesis - by (cases x, auto simp add: mkPX_def norm_PXtrans2[of P1 y _ Q _], cases P2, auto) + by (cases x) (auto simp add: mkPX_def norm_PXtrans2[of P1 y _ Q _], cases P2, auto) qed text {* add conserves normalizedness *} -lemma add_cn:"isnorm P \ isnorm Q \ isnorm (P \ Q)" -proof(induct P Q rule: add.induct) - case (2 c i P2) thus ?case by (cases P2, simp_all, cases i, simp_all) +lemma add_cn: "isnorm P \ isnorm Q \ isnorm (P \ Q)" +proof (induct P Q rule: add.induct) + case (2 c i P2) + thus ?case by (cases P2) (simp_all, cases i, simp_all) next - case (3 i P2 c) thus ?case by (cases P2, simp_all, cases i, simp_all) + case (3 i P2 c) + thus ?case by (cases P2) (simp_all, cases i, simp_all) next case (4 c P2 i Q2) - then have "isnorm P2" "isnorm Q2" by (auto simp only: norm_PX1[of P2 i Q2] norm_PX2[of P2 i Q2]) - with 4 show ?case by(cases i, simp, cases P2, auto, case_tac pol2, auto) + then have "isnorm P2" "isnorm Q2" + by (auto simp only: norm_PX1[of P2 i Q2] norm_PX2[of P2 i Q2]) + with 4 show ?case + by (cases i) (simp, cases P2, auto, case_tac pol2, auto) next case (5 P2 i Q2 c) - then have "isnorm P2" "isnorm Q2" by (auto simp only: norm_PX1[of P2 i Q2] norm_PX2[of P2 i Q2]) - with 5 show ?case by(cases i, simp, cases P2, auto, case_tac pol2, auto) + then have "isnorm P2" "isnorm Q2" + by (auto simp only: norm_PX1[of P2 i Q2] norm_PX2[of P2 i Q2]) + with 5 show ?case + by (cases i) (simp, cases P2, auto, case_tac pol2, auto) next case (6 x P2 y Q2) then have Y0: "y>0" by (cases y) (auto simp add: norm_Pinj_0_False) @@ -115,14 +125,17 @@ moreover note 6 X0 moreover - from 6 have "isnorm P2" "isnorm Q2" by (auto simp add: norm_Pinj[of _ P2] norm_Pinj[of _ Q2]) + from 6 have "isnorm P2" "isnorm Q2" + by (auto simp add: norm_Pinj[of _ P2] norm_Pinj[of _ Q2]) moreover - from 6 `x < y` y have "isnorm (Pinj d Q2)" by (cases d, simp, cases Q2, auto) + from 6 `x < y` y have "isnorm (Pinj d Q2)" + by (cases d, simp, cases Q2, auto) ultimately have ?case by (simp add: mkPinj_cn) } moreover { assume "x=y" moreover - from 6 have "isnorm P2" "isnorm Q2" by(auto simp add: norm_Pinj[of _ P2] norm_Pinj[of _ Q2]) + from 6 have "isnorm P2" "isnorm Q2" + by (auto simp add: norm_Pinj[of _ P2] norm_Pinj[of _ Q2]) moreover note 6 Y0 moreover @@ -133,30 +146,35 @@ moreover note 6 Y0 moreover - from 6 have "isnorm P2" "isnorm Q2" by (auto simp add: norm_Pinj[of _ P2] norm_Pinj[of _ Q2]) + from 6 have "isnorm P2" "isnorm Q2" + by (auto simp add: norm_Pinj[of _ P2] norm_Pinj[of _ Q2]) moreover - from 6 `x > y` x have "isnorm (Pinj d P2)" by (cases d, simp, cases P2, auto) - ultimately have ?case by (simp add: mkPinj_cn)} + from 6 `x > y` x have "isnorm (Pinj d P2)" + by (cases d) (simp, cases P2, auto) + ultimately have ?case by (simp add: mkPinj_cn) } ultimately show ?case by blast next case (7 x P2 Q2 y R) - have "x=0 \ (x = 1) \ (x > 1)" by arith + have "x = 0 \ x = 1 \ x > 1" by arith moreover { assume "x = 0" with 7 have ?case by (auto simp add: norm_Pinj_0_False) } moreover { assume "x = 1" - from 7 have "isnorm R" "isnorm P2" by (auto simp add: norm_Pinj[of _ P2] norm_PX2[of Q2 y R]) + from 7 have "isnorm R" "isnorm P2" + by (auto simp add: norm_Pinj[of _ P2] norm_PX2[of Q2 y R]) with 7 `x = 1` have "isnorm (R \ P2)" by simp - with 7 `x = 1` have ?case by (simp add: norm_PXtrans[of Q2 y _]) } + with 7 `x = 1` have ?case + by (simp add: norm_PXtrans[of Q2 y _]) } moreover { assume "x > 1" hence "EX d. x=Suc (Suc d)" by arith - then obtain d where X:"x=Suc (Suc d)" .. + then obtain d where X: "x=Suc (Suc d)" .. with 7 have NR: "isnorm R" "isnorm P2" by (auto simp add: norm_Pinj[of _ P2] norm_PX2[of Q2 y R]) with 7 X have "isnorm (Pinj (x - 1) P2)" by (cases P2) auto with 7 X NR have "isnorm (R \ Pinj (x - 1) P2)" by simp - with `isnorm (PX Q2 y R)` X have ?case by (simp add: norm_PXtrans[of Q2 y _]) } + with `isnorm (PX Q2 y R)` X have ?case + by (simp add: norm_PXtrans[of Q2 y _]) } ultimately show ?case by blast next case (8 Q2 y R x P2) @@ -183,7 +201,7 @@ with 9 have X0: "x>0" by (cases x) auto with 9 have NP1: "isnorm P1" and NP2: "isnorm P2" by (auto simp add: norm_PX1[of P1 _ P2] norm_PX2[of P1 _ P2]) - with 9 have NQ1:"isnorm Q1" and NQ2: "isnorm Q2" + with 9 have NQ1: "isnorm Q1" and NQ2: "isnorm Q2" by (auto simp add: norm_PX1[of Q1 _ Q2] norm_PX2[of Q1 _ Q2]) have "y < x \ x = y \ x < y" by arith moreover @@ -194,7 +212,7 @@ have "isnorm (PX P1 d (Pc 0))" proof (cases P1) case (PX p1 y p2) - with 9 sm1 sm2 show ?thesis by - (cases d, simp, cases p2, auto) + with 9 sm1 sm2 show ?thesis by (cases d) (simp, cases p2, auto) next case Pc with 9 sm1 sm2 show ?thesis by (cases d) auto next @@ -214,35 +232,37 @@ have "isnorm (PX Q1 d (Pc 0))" proof (cases Q1) case (PX p1 y p2) - with 9 sm1 sm2 show ?thesis by - (cases d, simp, cases p2, auto) + with 9 sm1 sm2 show ?thesis by (cases d) (simp, cases p2, auto) next case Pc with 9 sm1 sm2 show ?thesis by (cases d) auto next case Pinj with 9 sm1 sm2 show ?thesis by (cases d) auto qed ultimately have "isnorm (P2 \ Q2)" "isnorm (PX Q1 (y - x) (Pc 0) \ P1)" by auto - with X0 sm1 sm2 have ?case by (simp add: mkPX_cn)} + with X0 sm1 sm2 have ?case by (simp add: mkPX_cn) } ultimately show ?case by blast qed simp text {* mul concerves normalizedness *} -lemma mul_cn :"isnorm P \ isnorm Q \ isnorm (P \ Q)" -proof(induct P Q rule: mul.induct) +lemma mul_cn: "isnorm P \ isnorm Q \ isnorm (P \ Q)" +proof (induct P Q rule: mul.induct) case (2 c i P2) thus ?case - by (cases P2, simp_all) (cases "i",simp_all add: mkPinj_cn) + by (cases P2) (simp_all, cases i, simp_all add: mkPinj_cn) next case (3 i P2 c) thus ?case - by (cases P2, simp_all) (cases "i",simp_all add: mkPinj_cn) + by (cases P2) (simp_all, cases i, simp_all add: mkPinj_cn) next case (4 c P2 i Q2) - then have "isnorm P2" "isnorm Q2" by (auto simp only: norm_PX1[of P2 i Q2] norm_PX2[of P2 i Q2]) + then have "isnorm P2" "isnorm Q2" + by (auto simp only: norm_PX1[of P2 i Q2] norm_PX2[of P2 i Q2]) with 4 show ?case - by - (cases "c = 0", simp_all, cases "i = 0", simp_all add: mkPX_cn) + by (cases "c = 0") (simp_all, cases "i = 0", simp_all add: mkPX_cn) next case (5 P2 i Q2 c) - then have "isnorm P2" "isnorm Q2" by (auto simp only: norm_PX1[of P2 i Q2] norm_PX2[of P2 i Q2]) + then have "isnorm P2" "isnorm Q2" + by (auto simp only: norm_PX1[of P2 i Q2] norm_PX2[of P2 i Q2]) with 5 show ?case - by - (cases "c = 0", simp_all, cases "i = 0", simp_all add: mkPX_cn) + by (cases "c = 0") (simp_all, cases "i = 0", simp_all add: mkPX_cn) next case (6 x P2 y Q2) have "x < y \ x = y \ x > y" by arith @@ -256,7 +276,7 @@ moreover from 6 have "isnorm P2" "isnorm Q2" by (auto simp add: norm_Pinj[of _ P2] norm_Pinj[of _ Q2]) moreover - from 6 `x < y` y have "isnorm (Pinj d Q2)" by - (cases d, simp, cases Q2, auto) + from 6 `x < y` y have "isnorm (Pinj d Q2)" by (cases d) (simp, cases Q2, auto) ultimately have ?case by (simp add: mkPinj_cn) } moreover { assume "x = y" @@ -278,7 +298,7 @@ moreover from 6 have "isnorm P2" "isnorm Q2" by (auto simp add: norm_Pinj[of _ P2] norm_Pinj[of _ Q2]) moreover - from 6 `x > y` x have "isnorm (Pinj d P2)" by - (cases d, simp, cases P2, auto) + from 6 `x > y` x have "isnorm (Pinj d P2)" by (cases d) (simp, cases P2, auto) ultimately have ?case by (simp add: mkPinj_cn) } ultimately show ?case by blast next @@ -356,7 +376,7 @@ proof (induct P) case (Pinj i P2) then have "isnorm P2" by (simp add: norm_Pinj[of i P2]) - with Pinj show ?case by - (cases P2, auto, cases i, auto) + with Pinj show ?case by (cases P2) (auto, cases i, auto) next case (PX P1 x P2) note PX1 = this from PX have "isnorm P2" "isnorm P1" @@ -364,7 +384,7 @@ with PX show ?case proof (cases P1) case (PX p1 y p2) - with PX1 show ?thesis by - (cases x, auto, cases p2, auto) + with PX1 show ?thesis by (cases x) (auto, cases p2, auto) next case Pinj with PX1 show ?thesis by (cases x) auto @@ -372,15 +392,18 @@ qed simp text {* sub conserves normalizedness *} -lemma sub_cn:"isnorm p \ isnorm q \ isnorm (p \ q)" -by (simp add: sub_def add_cn neg_cn) +lemma sub_cn: "isnorm p \ isnorm q \ isnorm (p \ q)" + by (simp add: sub_def add_cn neg_cn) text {* sqr conserves normalizizedness *} -lemma sqr_cn:"isnorm P \ isnorm (sqr P)" +lemma sqr_cn: "isnorm P \ isnorm (sqr P)" proof (induct P) + case Pc + then show ?case by simp +next case (Pinj i Q) then show ?case - by - (cases Q, auto simp add: mkPX_cn mkPinj_cn, cases i, auto simp add: mkPX_cn mkPinj_cn) + by (cases Q) (auto simp add: mkPX_cn mkPinj_cn, cases i, auto simp add: mkPX_cn mkPinj_cn) next case (PX P1 x P2) then have "x + x ~= 0" "isnorm P2" "isnorm P1" @@ -389,20 +412,23 @@ and "isnorm (mkPX (sqr P1) (x + x) (sqr P2))" by (auto simp add: add_cn mkPX_cn mkPinj_cn mul_cn) then show ?case by (auto simp add: add_cn mkPX_cn mkPinj_cn mul_cn) -qed simp +qed text {* pow conserves normalizedness *} -lemma pow_cn:"isnorm P \ isnorm (pow n P)" -proof (induct n arbitrary: P rule: nat_less_induct) - case (1 k) +lemma pow_cn: "isnorm P \ isnorm (pow n P)" +proof (induct n arbitrary: P rule: less_induct) + case (less k) show ?case proof (cases "k = 0") + case True + then show ?thesis by simp + next case False then have K2: "k div 2 < k" by (cases k) auto - from 1 have "isnorm (sqr P)" by (simp add: sqr_cn) - with 1 False K2 show ?thesis - by - (simp add: allE[of _ "(k div 2)" _] allE[of _ "(sqr P)" _], cases k, auto simp add: mul_cn) - qed simp + from less have "isnorm (sqr P)" by (simp add: sqr_cn) + with less False K2 show ?thesis + by (simp add: allE[of _ "(k div 2)" _] allE[of _ "(sqr P)" _], cases k, auto simp add: mul_cn) + qed qed end diff -r 353ddca2e4c0 -r 1120cba9bce4 src/HOL/Decision_Procs/Ferrack.thy --- a/src/HOL/Decision_Procs/Ferrack.thy Wed Sep 07 17:41:29 2011 -0700 +++ b/src/HOL/Decision_Procs/Ferrack.thy Wed Sep 07 19:24:28 2011 -0700 @@ -676,13 +676,13 @@ {assume nz: "n = 0" hence ?thesis by (simp add: Let_def simp_num_pair_def)} moreover { assume nnz: "n \ 0" - {assume "\ ?g > 1" hence ?thesis by (simp add: Let_def simp_num_pair_def simpnum_ci) } + {assume "\ ?g > 1" hence ?thesis by (simp add: Let_def simp_num_pair_def) } moreover {assume g1:"?g>1" hence g0: "?g > 0" by simp from g1 nnz have gp0: "?g' \ 0" by simp hence g'p: "?g' > 0" using gcd_ge_0_int[where x="n" and y="numgcd ?t'"] by arith hence "?g'= 1 \ ?g' > 1" by arith - moreover {assume "?g'=1" hence ?thesis by (simp add: Let_def simp_num_pair_def simpnum_ci)} + moreover {assume "?g'=1" hence ?thesis by (simp add: Let_def simp_num_pair_def)} moreover {assume g'1:"?g'>1" from dvdnumcoeff_aux2[OF g1] have th1:"dvdnumcoeff ?t' ?g" .. let ?tt = "reducecoeffh ?t' ?g'" @@ -800,32 +800,34 @@ proof(induct p rule: simpfm.induct) case (6 a) hence nb: "numbound0 a" by simp hence "numbound0 (simpnum a)" by (simp only: simpnum_numbound0[OF nb]) - thus ?case by (cases "simpnum a", auto simp add: Let_def) + thus ?case by (cases "simpnum a") (auto simp add: Let_def) next case (7 a) hence nb: "numbound0 a" by simp hence "numbound0 (simpnum a)" by (simp only: simpnum_numbound0[OF nb]) - thus ?case by (cases "simpnum a", auto simp add: Let_def) + thus ?case by (cases "simpnum a") (auto simp add: Let_def) next case (8 a) hence nb: "numbound0 a" by simp hence "numbound0 (simpnum a)" by (simp only: simpnum_numbound0[OF nb]) - thus ?case by (cases "simpnum a", auto simp add: Let_def) + thus ?case by (cases "simpnum a") (auto simp add: Let_def) next case (9 a) hence nb: "numbound0 a" by simp hence "numbound0 (simpnum a)" by (simp only: simpnum_numbound0[OF nb]) - thus ?case by (cases "simpnum a", auto simp add: Let_def) + thus ?case by (cases "simpnum a") (auto simp add: Let_def) next case (10 a) hence nb: "numbound0 a" by simp hence "numbound0 (simpnum a)" by (simp only: simpnum_numbound0[OF nb]) - thus ?case by (cases "simpnum a", auto simp add: Let_def) + thus ?case by (cases "simpnum a") (auto simp add: Let_def) next case (11 a) hence nb: "numbound0 a" by simp hence "numbound0 (simpnum a)" by (simp only: simpnum_numbound0[OF nb]) - thus ?case by (cases "simpnum a", auto simp add: Let_def) + thus ?case by (cases "simpnum a") (auto simp add: Let_def) qed(auto simp add: disj_def imp_def iff_def conj_def not_bn) lemma simpfm_qf: "qfree p \ qfree (simpfm p)" -by (induct p rule: simpfm.induct, auto simp add: disj_qf imp_qf iff_qf conj_qf not_qf Let_def) - (case_tac "simpnum a",auto)+ + apply (induct p rule: simpfm.induct) + apply (auto simp add: Let_def) + apply (case_tac "simpnum a", auto)+ + done consts prep :: "fm \ fm" recdef prep "measure fmsize" @@ -854,7 +856,7 @@ "prep p = p" (hints simp add: fmsize_pos) lemma prep: "\ bs. Ifm bs (prep p) = Ifm bs p" -by (induct p rule: prep.induct, auto) + by (induct p rule: prep.induct) auto (* Generic quantifier elimination *) function (sequential) qelim :: "fm \ (fm \ fm) \ fm" where @@ -1037,7 +1039,7 @@ assumes qfp: "qfree p" shows "(Ifm bs (rlfm p) = Ifm bs p) \ isrlfm (rlfm p)" using qfp -by (induct p rule: rlfm.induct, auto simp add: lt le gt ge eq neq conj disj conj_lin disj_lin) +by (induct p rule: rlfm.induct) (auto simp add: lt le gt ge eq neq conj disj conj_lin disj_lin) (* Operations needed for Ferrante and Rackoff *) lemma rminusinf_inf: @@ -1045,9 +1047,11 @@ shows "\ z. \ x < z. Ifm (x#bs) (minusinf p) = Ifm (x#bs) p" (is "\ z. \ x. ?P z x p") using lp proof (induct p rule: minusinf.induct) - case (1 p q) thus ?case by (auto,rule_tac x= "min z za" in exI) auto + case (1 p q) + thus ?case apply auto apply (rule_tac x= "min z za" in exI) apply auto done next - case (2 p q) thus ?case by (auto,rule_tac x= "min z za" in exI) auto + case (2 p q) + thus ?case apply auto apply (rule_tac x= "min z za" in exI) apply auto done next case (3 c e) from 3 have nb: "numbound0 e" by simp diff -r 353ddca2e4c0 -r 1120cba9bce4 src/HOL/HOLCF/Representable.thy --- a/src/HOL/HOLCF/Representable.thy Wed Sep 07 17:41:29 2011 -0700 +++ b/src/HOL/HOLCF/Representable.thy Wed Sep 07 19:24:28 2011 -0700 @@ -5,7 +5,7 @@ header {* Representable domains *} theory Representable -imports Algebraic Map_Functions Countable +imports Algebraic Map_Functions "~~/src/HOL/Library/Countable" begin default_sort cpo diff -r 353ddca2e4c0 -r 1120cba9bce4 src/HOL/IsaMakefile --- a/src/HOL/IsaMakefile Wed Sep 07 17:41:29 2011 -0700 +++ b/src/HOL/IsaMakefile Wed Sep 07 19:24:28 2011 -0700 @@ -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 353ddca2e4c0 -r 1120cba9bce4 src/HOL/Library/Abstract_Rat.thy --- a/src/HOL/Library/Abstract_Rat.thy Wed Sep 07 17:41:29 2011 -0700 +++ b/src/HOL/Library/Abstract_Rat.thy Wed Sep 07 19:24:28 2011 -0700 @@ -10,64 +10,57 @@ type_synonym Num = "int \ int" -abbreviation - Num0_syn :: Num ("0\<^sub>N") -where "0\<^sub>N \ (0, 0)" +abbreviation Num0_syn :: Num ("0\<^sub>N") + where "0\<^sub>N \ (0, 0)" -abbreviation - Numi_syn :: "int \ Num" ("_\<^sub>N") -where "i\<^sub>N \ (i, 1)" +abbreviation Numi_syn :: "int \ Num" ("_\<^sub>N") + where "i\<^sub>N \ (i, 1)" -definition - isnormNum :: "Num \ bool" -where +definition isnormNum :: "Num \ bool" where "isnormNum = (\(a,b). (if a = 0 then b = 0 else b > 0 \ gcd a b = 1))" -definition - normNum :: "Num \ Num" -where - "normNum = (\(a,b). (if a=0 \ b = 0 then (0,0) else - (let g = gcd a b - in if b > 0 then (a div g, b div g) else (- (a div g), - (b div g)))))" +definition normNum :: "Num \ Num" where + "normNum = (\(a,b). + (if a=0 \ b = 0 then (0,0) else + (let g = gcd a b + in if b > 0 then (a div g, b div g) else (- (a div g), - (b div g)))))" -declare gcd_dvd1_int[presburger] -declare gcd_dvd2_int[presburger] +declare gcd_dvd1_int[presburger] gcd_dvd2_int[presburger] + lemma normNum_isnormNum [simp]: "isnormNum (normNum x)" proof - - have " \ a b. x = (a,b)" by auto - then obtain a b where x[simp]: "x = (a,b)" by blast - {assume "a=0 \ b = 0" hence ?thesis by (simp add: normNum_def isnormNum_def)} + obtain a b where x: "x = (a, b)" by (cases x) + { assume "a=0 \ b = 0" hence ?thesis by (simp add: x normNum_def isnormNum_def) } moreover - {assume anz: "a \ 0" and bnz: "b \ 0" + { assume anz: "a \ 0" and bnz: "b \ 0" let ?g = "gcd a b" let ?a' = "a div ?g" let ?b' = "b div ?g" let ?g' = "gcd ?a' ?b'" - from anz bnz have "?g \ 0" by simp with gcd_ge_0_int[of a b] + from anz bnz have "?g \ 0" by simp with gcd_ge_0_int[of a b] have gpos: "?g > 0" by arith - have gdvd: "?g dvd a" "?g dvd b" by arith+ - from zdvd_mult_div_cancel[OF gdvd(1)] zdvd_mult_div_cancel[OF gdvd(2)] - anz bnz - have nz':"?a' \ 0" "?b' \ 0" - by - (rule notI, simp)+ - from anz bnz have stupid: "a \ 0 \ b \ 0" by arith + have gdvd: "?g dvd a" "?g dvd b" by arith+ + from zdvd_mult_div_cancel[OF gdvd(1)] zdvd_mult_div_cancel[OF gdvd(2)] anz bnz + have nz': "?a' \ 0" "?b' \ 0" by - (rule notI, simp)+ + from anz bnz have stupid: "a \ 0 \ b \ 0" by arith from div_gcd_coprime_int[OF stupid] have gp1: "?g' = 1" . from bnz have "b < 0 \ b > 0" by arith moreover - {assume b: "b > 0" - from b have "?b' \ 0" - by (presburger add: pos_imp_zdiv_nonneg_iff[OF gpos]) - with nz' have b': "?b' > 0" by arith - from b b' anz bnz nz' gp1 have ?thesis - by (simp add: isnormNum_def normNum_def Let_def split_def fst_conv snd_conv)} - moreover {assume b: "b < 0" - {assume b': "?b' \ 0" + { assume b: "b > 0" + from b have "?b' \ 0" + by (presburger add: pos_imp_zdiv_nonneg_iff[OF gpos]) + with nz' have b': "?b' > 0" by arith + from b b' anz bnz nz' gp1 have ?thesis + by (simp add: x isnormNum_def normNum_def Let_def split_def) } + moreover { + assume b: "b < 0" + { assume b': "?b' \ 0" from gpos have th: "?g \ 0" by arith from mult_nonneg_nonneg[OF th b'] zdvd_mult_div_cancel[OF gdvd(2)] have False using b by arith } - hence b': "?b' < 0" by (presburger add: linorder_not_le[symmetric]) - from anz bnz nz' b b' gp1 have ?thesis - by (simp add: isnormNum_def normNum_def Let_def split_def)} + hence b': "?b' < 0" by (presburger add: linorder_not_le[symmetric]) + from anz bnz nz' b b' gp1 have ?thesis + by (simp add: x isnormNum_def normNum_def Let_def split_def) } ultimately have ?thesis by blast } ultimately show ?thesis by blast @@ -75,63 +68,55 @@ text {* Arithmetic over Num *} -definition - Nadd :: "Num \ Num \ Num" (infixl "+\<^sub>N" 60) -where - "Nadd = (\(a,b) (a',b'). if a = 0 \ b = 0 then normNum(a',b') - else if a'=0 \ b' = 0 then normNum(a,b) +definition Nadd :: "Num \ Num \ Num" (infixl "+\<^sub>N" 60) where + "Nadd = (\(a,b) (a',b'). if a = 0 \ b = 0 then normNum(a',b') + else if a'=0 \ b' = 0 then normNum(a,b) else normNum(a*b' + b*a', b*b'))" -definition - Nmul :: "Num \ Num \ Num" (infixl "*\<^sub>N" 60) -where - "Nmul = (\(a,b) (a',b'). let g = gcd (a*a') (b*b') +definition Nmul :: "Num \ Num \ Num" (infixl "*\<^sub>N" 60) where + "Nmul = (\(a,b) (a',b'). let g = gcd (a*a') (b*b') in (a*a' div g, b*b' div g))" -definition - Nneg :: "Num \ Num" ("~\<^sub>N") -where - "Nneg \ (\(a,b). (-a,b))" +definition Nneg :: "Num \ Num" ("~\<^sub>N") + where "Nneg \ (\(a,b). (-a,b))" -definition - Nsub :: "Num \ Num \ Num" (infixl "-\<^sub>N" 60) -where - "Nsub = (\a b. a +\<^sub>N ~\<^sub>N b)" +definition Nsub :: "Num \ Num \ Num" (infixl "-\<^sub>N" 60) + where "Nsub = (\a b. a +\<^sub>N ~\<^sub>N b)" -definition - Ninv :: "Num \ Num" -where - "Ninv \ \(a,b). if a < 0 then (-b, \a\) else (b,a)" +definition Ninv :: "Num \ Num" + where "Ninv = (\(a,b). if a < 0 then (-b, \a\) else (b,a))" -definition - Ndiv :: "Num \ Num \ Num" (infixl "\
\<^sub>N" 60) -where - "Ndiv \ \a b. a *\<^sub>N Ninv b" +definition Ndiv :: "Num \ Num \ Num" (infixl "\
\<^sub>N" 60) + where "Ndiv = (\a b. a *\<^sub>N Ninv b)" lemma Nneg_normN[simp]: "isnormNum x \ isnormNum (~\<^sub>N x)" - by(simp add: isnormNum_def Nneg_def split_def) + by (simp add: isnormNum_def Nneg_def split_def) + lemma Nadd_normN[simp]: "isnormNum (x +\<^sub>N y)" by (simp add: Nadd_def split_def) + lemma Nsub_normN[simp]: "\ isnormNum y\ \ isnormNum (x -\<^sub>N y)" by (simp add: Nsub_def split_def) -lemma Nmul_normN[simp]: assumes xn:"isnormNum x" and yn: "isnormNum y" + +lemma Nmul_normN[simp]: + assumes xn: "isnormNum x" and yn: "isnormNum y" shows "isnormNum (x *\<^sub>N y)" -proof- - have "\a b. x = (a,b)" and "\ a' b'. y = (a',b')" by auto - then obtain a b a' b' where ab: "x = (a,b)" and ab': "y = (a',b')" by blast - {assume "a = 0" - hence ?thesis using xn ab ab' - by (simp add: isnormNum_def Let_def Nmul_def split_def)} +proof - + obtain a b where x: "x = (a, b)" by (cases x) + obtain a' b' where y: "y = (a', b')" by (cases y) + { assume "a = 0" + hence ?thesis using xn x y + by (simp add: isnormNum_def Let_def Nmul_def split_def) } moreover - {assume "a' = 0" - hence ?thesis using yn ab ab' - by (simp add: isnormNum_def Let_def Nmul_def split_def)} + { assume "a' = 0" + hence ?thesis using yn x y + by (simp add: isnormNum_def Let_def Nmul_def split_def) } moreover - {assume a: "a \0" and a': "a'\0" - hence bp: "b > 0" "b' > 0" using xn yn ab ab' by (simp_all add: isnormNum_def) - from mult_pos_pos[OF bp] have "x *\<^sub>N y = normNum (a*a', b*b')" - using ab ab' a a' bp by (simp add: Nmul_def Let_def split_def normNum_def) - hence ?thesis by simp} + { assume a: "a \0" and a': "a'\0" + hence bp: "b > 0" "b' > 0" using xn yn x y by (simp_all add: isnormNum_def) + from mult_pos_pos[OF bp] have "x *\<^sub>N y = normNum (a * a', b * b')" + using x y a a' bp by (simp add: Nmul_def Let_def split_def normNum_def) + hence ?thesis by simp } ultimately show ?thesis by blast qed @@ -139,89 +124,77 @@ by (simp add: Ninv_def isnormNum_def split_def) (cases "fst x = 0", auto simp add: gcd_commute_int) -lemma isnormNum_int[simp]: +lemma isnormNum_int[simp]: "isnormNum 0\<^sub>N" "isnormNum ((1::int)\<^sub>N)" "i \ 0 \ isnormNum (i\<^sub>N)" by (simp_all add: isnormNum_def) text {* Relations over Num *} -definition - Nlt0:: "Num \ bool" ("0>\<^sub>N") -where - "Nlt0 = (\(a,b). a < 0)" +definition Nlt0:: "Num \ bool" ("0>\<^sub>N") + where "Nlt0 = (\(a,b). a < 0)" -definition - Nle0:: "Num \ bool" ("0\\<^sub>N") -where - "Nle0 = (\(a,b). a \ 0)" +definition Nle0:: "Num \ bool" ("0\\<^sub>N") + where "Nle0 = (\(a,b). a \ 0)" -definition - Ngt0:: "Num \ bool" ("0<\<^sub>N") -where - "Ngt0 = (\(a,b). a > 0)" +definition Ngt0:: "Num \ bool" ("0<\<^sub>N") + where "Ngt0 = (\(a,b). a > 0)" -definition - Nge0:: "Num \ bool" ("0\\<^sub>N") -where - "Nge0 = (\(a,b). a \ 0)" +definition Nge0:: "Num \ bool" ("0\\<^sub>N") + where "Nge0 = (\(a,b). a \ 0)" -definition - Nlt :: "Num \ Num \ bool" (infix "<\<^sub>N" 55) -where - "Nlt = (\a b. 0>\<^sub>N (a -\<^sub>N b))" +definition Nlt :: "Num \ Num \ bool" (infix "<\<^sub>N" 55) + where "Nlt = (\a b. 0>\<^sub>N (a -\<^sub>N b))" -definition - Nle :: "Num \ Num \ bool" (infix "\\<^sub>N" 55) -where - "Nle = (\a b. 0\\<^sub>N (a -\<^sub>N b))" +definition Nle :: "Num \ Num \ bool" (infix "\\<^sub>N" 55) + where "Nle = (\a b. 0\\<^sub>N (a -\<^sub>N b))" -definition - "INum = (\(a,b). of_int a / of_int b)" +definition "INum = (\(a,b). of_int a / of_int b)" lemma INum_int [simp]: "INum (i\<^sub>N) = ((of_int i) ::'a::field)" "INum 0\<^sub>N = (0::'a::field)" by (simp_all add: INum_def) -lemma isnormNum_unique[simp]: - assumes na: "isnormNum x" and nb: "isnormNum y" +lemma isnormNum_unique[simp]: + assumes na: "isnormNum x" and nb: "isnormNum y" shows "((INum x ::'a::{field_char_0, field_inverse_zero}) = INum y) = (x = y)" (is "?lhs = ?rhs") proof - have "\ a b a' b'. x = (a,b) \ y = (a',b')" by auto - then obtain a b a' b' where xy[simp]: "x = (a,b)" "y=(a',b')" by blast - assume H: ?lhs - {assume "a = 0 \ b = 0 \ a' = 0 \ b' = 0" + obtain a b where x: "x = (a, b)" by (cases x) + obtain a' b' where y: "y = (a', b')" by (cases y) + assume H: ?lhs + { assume "a = 0 \ b = 0 \ a' = 0 \ b' = 0" hence ?rhs using na nb H - by (simp add: INum_def split_def isnormNum_def split: split_if_asm)} + by (simp add: x y INum_def split_def isnormNum_def split: split_if_asm) } moreover { assume az: "a \ 0" and bz: "b \ 0" and a'z: "a'\0" and b'z: "b'\0" - from az bz a'z b'z na nb have pos: "b > 0" "b' > 0" by (simp_all add: isnormNum_def) - from H bz b'z have eq:"a * b' = a'*b" - by (simp add: INum_def eq_divide_eq divide_eq_eq of_int_mult[symmetric] del: of_int_mult) - from az a'z na nb have gcd1: "gcd a b = 1" "gcd b a = 1" "gcd a' b' = 1" "gcd b' a' = 1" - by (simp_all add: isnormNum_def add: gcd_commute_int) - from eq have raw_dvd: "a dvd a'*b" "b dvd b'*a" "a' dvd a*b'" "b' dvd b*a'" - apply - + from az bz a'z b'z na nb have pos: "b > 0" "b' > 0" by (simp_all add: x y isnormNum_def) + from H bz b'z have eq: "a * b' = a'*b" + by (simp add: x y INum_def eq_divide_eq divide_eq_eq of_int_mult[symmetric] del: of_int_mult) + from az a'z na nb have gcd1: "gcd a b = 1" "gcd b a = 1" "gcd a' b' = 1" "gcd b' a' = 1" + by (simp_all add: x y isnormNum_def add: gcd_commute_int) + from eq have raw_dvd: "a dvd a' * b" "b dvd b' * a" "a' dvd a * b'" "b' dvd b * a'" + apply - apply algebra apply algebra apply simp apply algebra done from zdvd_antisym_abs[OF coprime_dvd_mult_int[OF gcd1(2) raw_dvd(2)] - coprime_dvd_mult_int[OF gcd1(4) raw_dvd(4)]] + coprime_dvd_mult_int[OF gcd1(4) raw_dvd(4)]] have eq1: "b = b'" using pos by arith with eq have "a = a'" using pos by simp - with eq1 have ?rhs by simp} + with eq1 have ?rhs by (simp add: x y) } ultimately show ?rhs by blast next assume ?rhs thus ?lhs by simp qed -lemma isnormNum0[simp]: "isnormNum x \ (INum x = (0::'a::{field_char_0, field_inverse_zero})) = (x = 0\<^sub>N)" +lemma isnormNum0[simp]: + "isnormNum x \ (INum x = (0::'a::{field_char_0, field_inverse_zero})) = (x = 0\<^sub>N)" unfolding INum_int(2)[symmetric] - by (rule isnormNum_unique, simp_all) + by (rule isnormNum_unique) simp_all -lemma of_int_div_aux: "d ~= 0 ==> ((of_int x)::'a::field_char_0) / (of_int d) = +lemma of_int_div_aux: "d ~= 0 ==> ((of_int x)::'a::field_char_0) / (of_int d) = of_int (x div d) + (of_int (x mod d)) / ((of_int d)::'a)" proof - assume "d ~= 0" @@ -231,7 +204,7 @@ by auto then have eq: "of_int x = ?t" by (simp only: of_int_mult[symmetric] of_int_add [symmetric]) - then have "of_int x / of_int d = ?t / of_int d" + then have "of_int x / of_int d = ?t / of_int d" using cong[OF refl[of ?f] eq] by simp then show ?thesis by (simp add: add_divide_distrib algebra_simps `d ~= 0`) qed @@ -241,25 +214,26 @@ apply (frule of_int_div_aux [of d n, where ?'a = 'a]) apply simp apply (simp add: dvd_eq_mod_eq_0) -done + done lemma normNum[simp]: "INum (normNum x) = (INum x :: 'a::{field_char_0, field_inverse_zero})" -proof- - have "\ a b. x = (a,b)" by auto - then obtain a b where x[simp]: "x = (a,b)" by blast - {assume "a=0 \ b = 0" hence ?thesis - by (simp add: INum_def normNum_def split_def Let_def)} - moreover - {assume a: "a\0" and b: "b\0" +proof - + obtain a b where x: "x = (a, b)" by (cases x) + { assume "a = 0 \ b = 0" + hence ?thesis by (simp add: x INum_def normNum_def split_def Let_def) } + moreover + { assume a: "a \ 0" and b: "b \ 0" let ?g = "gcd a b" from a b have g: "?g \ 0"by simp from of_int_div[OF g, where ?'a = 'a] - have ?thesis by (auto simp add: INum_def normNum_def split_def Let_def)} + have ?thesis by (auto simp add: x INum_def normNum_def split_def Let_def) } ultimately show ?thesis by blast qed -lemma INum_normNum_iff: "(INum x ::'a::{field_char_0, field_inverse_zero}) = INum y \ normNum x = normNum y" (is "?lhs = ?rhs") +lemma INum_normNum_iff: + "(INum x ::'a::{field_char_0, field_inverse_zero}) = INum y \ normNum x = normNum y" + (is "?lhs = ?rhs") proof - have "normNum x = normNum y \ (INum (normNum x) :: 'a) = INum (normNum y)" by (simp del: normNum) @@ -268,139 +242,157 @@ qed lemma Nadd[simp]: "INum (x +\<^sub>N y) = INum x + (INum y :: 'a :: {field_char_0, field_inverse_zero})" -proof- -let ?z = "0:: 'a" - have " \ a b. x = (a,b)" " \ a' b'. y = (a',b')" by auto - then obtain a b a' b' where x[simp]: "x = (a,b)" - and y[simp]: "y = (a',b')" by blast - {assume "a=0 \ a'= 0 \ b =0 \ b' = 0" hence ?thesis - apply (cases "a=0",simp_all add: Nadd_def) - apply (cases "b= 0",simp_all add: INum_def) - apply (cases "a'= 0",simp_all) - apply (cases "b'= 0",simp_all) +proof - + let ?z = "0:: 'a" + obtain a b where x: "x = (a, b)" by (cases x) + obtain a' b' where y: "y = (a', b')" by (cases y) + { assume "a=0 \ a'= 0 \ b =0 \ b' = 0" + hence ?thesis + apply (cases "a=0", simp_all add: x y Nadd_def) + apply (cases "b= 0", simp_all add: INum_def) + apply (cases "a'= 0", simp_all) + apply (cases "b'= 0", simp_all) done } - moreover - {assume aa':"a \ 0" "a'\ 0" and bb': "b \ 0" "b' \ 0" - {assume z: "a * b' + b * a' = 0" + moreover + { assume aa': "a \ 0" "a'\ 0" and bb': "b \ 0" "b' \ 0" + { assume z: "a * b' + b * a' = 0" hence "of_int (a*b' + b*a') / (of_int b* of_int b') = ?z" by simp - hence "of_int b' * of_int a / (of_int b * of_int b') + of_int b * of_int a' / (of_int b * of_int b') = ?z" by (simp add:add_divide_distrib) - hence th: "of_int a / of_int b + of_int a' / of_int b' = ?z" using bb' aa' by simp - from z aa' bb' have ?thesis - by (simp add: th Nadd_def normNum_def INum_def split_def)} - moreover {assume z: "a * b' + b * a' \ 0" + hence "of_int b' * of_int a / (of_int b * of_int b') + + of_int b * of_int a' / (of_int b * of_int b') = ?z" + by (simp add:add_divide_distrib) + hence th: "of_int a / of_int b + of_int a' / of_int b' = ?z" using bb' aa' + by simp + from z aa' bb' have ?thesis + by (simp add: x y th Nadd_def normNum_def INum_def split_def) } + moreover { + assume z: "a * b' + b * a' \ 0" let ?g = "gcd (a * b' + b * a') (b*b')" have gz: "?g \ 0" using z by simp have ?thesis using aa' bb' z gz - of_int_div[where ?'a = 'a, OF gz gcd_dvd1_int[where x="a * b' + b * a'" and y="b*b'"]] of_int_div[where ?'a = 'a, - OF gz gcd_dvd2_int[where x="a * b' + b * a'" and y="b*b'"]] - by (simp add: Nadd_def INum_def normNum_def Let_def add_divide_distrib)} - ultimately have ?thesis using aa' bb' - by (simp add: Nadd_def INum_def normNum_def Let_def) } + of_int_div[where ?'a = 'a, OF gz gcd_dvd1_int[where x="a * b' + b * a'" and y="b*b'"]] + of_int_div[where ?'a = 'a, OF gz gcd_dvd2_int[where x="a * b' + b * a'" and y="b*b'"]] + by (simp add: x y Nadd_def INum_def normNum_def Let_def add_divide_distrib) } + ultimately have ?thesis using aa' bb' + by (simp add: x y Nadd_def INum_def normNum_def Let_def) } ultimately show ?thesis by blast qed -lemma Nmul[simp]: "INum (x *\<^sub>N y) = INum x * (INum y:: 'a :: {field_char_0, field_inverse_zero}) " -proof- +lemma Nmul[simp]: "INum (x *\<^sub>N y) = INum x * (INum y:: 'a :: {field_char_0, field_inverse_zero})" +proof - let ?z = "0::'a" - have " \ a b. x = (a,b)" " \ a' b'. y = (a',b')" by auto - then obtain a b a' b' where x: "x = (a,b)" and y: "y = (a',b')" by blast - {assume "a=0 \ a'= 0 \ b = 0 \ b' = 0" hence ?thesis - apply (cases "a=0",simp_all add: x y Nmul_def INum_def Let_def) - apply (cases "b=0",simp_all) - apply (cases "a'=0",simp_all) + obtain a b where x: "x = (a, b)" by (cases x) + obtain a' b' where y: "y = (a', b')" by (cases y) + { assume "a=0 \ a'= 0 \ b = 0 \ b' = 0" + hence ?thesis + apply (cases "a=0", simp_all add: x y Nmul_def INum_def Let_def) + apply (cases "b=0", simp_all) + apply (cases "a'=0", simp_all) done } moreover - {assume z: "a \ 0" "a' \ 0" "b \ 0" "b' \ 0" + { assume z: "a \ 0" "a' \ 0" "b \ 0" "b' \ 0" let ?g="gcd (a*a') (b*b')" have gz: "?g \ 0" using z by simp - from z of_int_div[where ?'a = 'a, OF gz gcd_dvd1_int[where x="a*a'" and y="b*b'"]] - of_int_div[where ?'a = 'a , OF gz gcd_dvd2_int[where x="a*a'" and y="b*b'"]] - have ?thesis by (simp add: Nmul_def x y Let_def INum_def)} + from z of_int_div[where ?'a = 'a, OF gz gcd_dvd1_int[where x="a*a'" and y="b*b'"]] + of_int_div[where ?'a = 'a , OF gz gcd_dvd2_int[where x="a*a'" and y="b*b'"]] + have ?thesis by (simp add: Nmul_def x y Let_def INum_def) } ultimately show ?thesis by blast qed lemma Nneg[simp]: "INum (~\<^sub>N x) = - (INum x ::'a:: field)" by (simp add: Nneg_def split_def INum_def) -lemma Nsub[simp]: shows "INum (x -\<^sub>N y) = INum x - (INum y:: 'a :: {field_char_0, field_inverse_zero})" -by (simp add: Nsub_def split_def) +lemma Nsub[simp]: "INum (x -\<^sub>N y) = INum x - (INum y:: 'a :: {field_char_0, field_inverse_zero})" + by (simp add: Nsub_def split_def) lemma Ninv[simp]: "INum (Ninv x) = (1::'a :: field_inverse_zero) / (INum x)" by (simp add: Ninv_def INum_def split_def) -lemma Ndiv[simp]: "INum (x \
\<^sub>N y) = INum x / (INum y ::'a :: {field_char_0, field_inverse_zero})" by (simp add: Ndiv_def) +lemma Ndiv[simp]: "INum (x \
\<^sub>N y) = INum x / (INum y ::'a :: {field_char_0, field_inverse_zero})" + by (simp add: Ndiv_def) -lemma Nlt0_iff[simp]: assumes nx: "isnormNum x" - shows "((INum x :: 'a :: {field_char_0, linordered_field_inverse_zero})< 0) = 0>\<^sub>N x " -proof- - have " \ a b. x = (a,b)" by simp - then obtain a b where x[simp]:"x = (a,b)" by blast - {assume "a = 0" hence ?thesis by (simp add: Nlt0_def INum_def) } +lemma Nlt0_iff[simp]: + assumes nx: "isnormNum x" + shows "((INum x :: 'a :: {field_char_0, linordered_field_inverse_zero})< 0) = 0>\<^sub>N x" +proof - + obtain a b where x: "x = (a, b)" by (cases x) + { assume "a = 0" hence ?thesis by (simp add: x Nlt0_def INum_def) } moreover - {assume a: "a\0" hence b: "(of_int b::'a) > 0" using nx by (simp add: isnormNum_def) + { assume a: "a \ 0" hence b: "(of_int b::'a) > 0" + using nx by (simp add: x isnormNum_def) from pos_divide_less_eq[OF b, where b="of_int a" and a="0::'a"] - have ?thesis by (simp add: Nlt0_def INum_def)} + have ?thesis by (simp add: x Nlt0_def INum_def) } ultimately show ?thesis by blast qed -lemma Nle0_iff[simp]:assumes nx: "isnormNum x" +lemma Nle0_iff[simp]: + assumes nx: "isnormNum x" shows "((INum x :: 'a :: {field_char_0, linordered_field_inverse_zero}) \ 0) = 0\\<^sub>N x" -proof- - have " \ a b. x = (a,b)" by simp - then obtain a b where x[simp]:"x = (a,b)" by blast - {assume "a = 0" hence ?thesis by (simp add: Nle0_def INum_def) } +proof - + obtain a b where x: "x = (a, b)" by (cases x) + { assume "a = 0" hence ?thesis by (simp add: x Nle0_def INum_def) } moreover - {assume a: "a\0" hence b: "(of_int b :: 'a) > 0" using nx by (simp add: isnormNum_def) + { assume a: "a \ 0" hence b: "(of_int b :: 'a) > 0" + using nx by (simp add: x isnormNum_def) from pos_divide_le_eq[OF b, where b="of_int a" and a="0::'a"] - have ?thesis by (simp add: Nle0_def INum_def)} + have ?thesis by (simp add: x Nle0_def INum_def) } ultimately show ?thesis by blast qed -lemma Ngt0_iff[simp]:assumes nx: "isnormNum x" shows "((INum x :: 'a :: {field_char_0, linordered_field_inverse_zero})> 0) = 0<\<^sub>N x" -proof- - have " \ a b. x = (a,b)" by simp - then obtain a b where x[simp]:"x = (a,b)" by blast - {assume "a = 0" hence ?thesis by (simp add: Ngt0_def INum_def) } +lemma Ngt0_iff[simp]: + assumes nx: "isnormNum x" + shows "((INum x :: 'a :: {field_char_0, linordered_field_inverse_zero})> 0) = 0<\<^sub>N x" +proof - + obtain a b where x: "x = (a, b)" by (cases x) + { assume "a = 0" hence ?thesis by (simp add: x Ngt0_def INum_def) } moreover - {assume a: "a\0" hence b: "(of_int b::'a) > 0" using nx by (simp add: isnormNum_def) + { assume a: "a \ 0" hence b: "(of_int b::'a) > 0" using nx + by (simp add: x isnormNum_def) from pos_less_divide_eq[OF b, where b="of_int a" and a="0::'a"] - have ?thesis by (simp add: Ngt0_def INum_def)} - ultimately show ?thesis by blast -qed -lemma Nge0_iff[simp]:assumes nx: "isnormNum x" - shows "((INum x :: 'a :: {field_char_0, linordered_field_inverse_zero}) \ 0) = 0\\<^sub>N x" -proof- - have " \ a b. x = (a,b)" by simp - then obtain a b where x[simp]:"x = (a,b)" by blast - {assume "a = 0" hence ?thesis by (simp add: Nge0_def INum_def) } - moreover - {assume a: "a\0" hence b: "(of_int b::'a) > 0" using nx by (simp add: isnormNum_def) - from pos_le_divide_eq[OF b, where b="of_int a" and a="0::'a"] - have ?thesis by (simp add: Nge0_def INum_def)} + have ?thesis by (simp add: x Ngt0_def INum_def) } ultimately show ?thesis by blast qed -lemma Nlt_iff[simp]: assumes nx: "isnormNum x" and ny: "isnormNum y" +lemma Nge0_iff[simp]: + assumes nx: "isnormNum x" + shows "((INum x :: 'a :: {field_char_0, linordered_field_inverse_zero}) \ 0) = 0\\<^sub>N x" +proof - + obtain a b where x: "x = (a, b)" by (cases x) + { assume "a = 0" hence ?thesis by (simp add: x Nge0_def INum_def) } + moreover + { assume "a \ 0" hence b: "(of_int b::'a) > 0" using nx + by (simp add: x isnormNum_def) + from pos_le_divide_eq[OF b, where b="of_int a" and a="0::'a"] + have ?thesis by (simp add: x Nge0_def INum_def) } + ultimately show ?thesis by blast +qed + +lemma Nlt_iff[simp]: + assumes nx: "isnormNum x" and ny: "isnormNum y" shows "((INum x :: 'a :: {field_char_0, linordered_field_inverse_zero}) < INum y) = (x <\<^sub>N y)" -proof- +proof - let ?z = "0::'a" - have "((INum x ::'a) < INum y) = (INum (x -\<^sub>N y) < ?z)" using nx ny by simp - also have "\ = (0>\<^sub>N (x -\<^sub>N y))" using Nlt0_iff[OF Nsub_normN[OF ny]] by simp + have "((INum x ::'a) < INum y) = (INum (x -\<^sub>N y) < ?z)" + using nx ny by simp + also have "\ = (0>\<^sub>N (x -\<^sub>N y))" + using Nlt0_iff[OF Nsub_normN[OF ny]] by simp finally show ?thesis by (simp add: Nlt_def) qed -lemma Nle_iff[simp]: assumes nx: "isnormNum x" and ny: "isnormNum y" +lemma Nle_iff[simp]: + assumes nx: "isnormNum x" and ny: "isnormNum y" shows "((INum x :: 'a :: {field_char_0, linordered_field_inverse_zero})\ INum y) = (x \\<^sub>N y)" -proof- - have "((INum x ::'a) \ INum y) = (INum (x -\<^sub>N y) \ (0::'a))" using nx ny by simp - also have "\ = (0\\<^sub>N (x -\<^sub>N y))" using Nle0_iff[OF Nsub_normN[OF ny]] by simp +proof - + have "((INum x ::'a) \ INum y) = (INum (x -\<^sub>N y) \ (0::'a))" + using nx ny by simp + also have "\ = (0\\<^sub>N (x -\<^sub>N y))" + using Nle0_iff[OF Nsub_normN[OF ny]] by simp finally show ?thesis by (simp add: Nle_def) qed lemma Nadd_commute: assumes "SORT_CONSTRAINT('a::{field_char_0, field_inverse_zero})" shows "x +\<^sub>N y = y +\<^sub>N x" -proof- +proof - have n: "isnormNum (x +\<^sub>N y)" "isnormNum (y +\<^sub>N x)" by simp_all have "(INum (x +\<^sub>N y)::'a) = INum (y +\<^sub>N x)" by simp with isnormNum_unique[OF n] show ?thesis by simp @@ -409,7 +401,7 @@ lemma [simp]: assumes "SORT_CONSTRAINT('a::{field_char_0, field_inverse_zero})" shows "(0, b) +\<^sub>N y = normNum y" - and "(a, 0) +\<^sub>N y = normNum y" + and "(a, 0) +\<^sub>N y = normNum y" and "x +\<^sub>N (0, b) = normNum x" and "x +\<^sub>N (a, 0) = normNum x" apply (simp add: Nadd_def split_def) @@ -420,14 +412,13 @@ lemma normNum_nilpotent_aux[simp]: assumes "SORT_CONSTRAINT('a::{field_char_0, field_inverse_zero})" - assumes nx: "isnormNum x" + assumes nx: "isnormNum x" shows "normNum x = x" -proof- +proof - let ?a = "normNum x" have n: "isnormNum ?a" by simp - have th:"INum ?a = (INum x ::'a)" by simp - with isnormNum_unique[OF n nx] - show ?thesis by simp + have th: "INum ?a = (INum x ::'a)" by simp + with isnormNum_unique[OF n nx] show ?thesis by simp qed lemma normNum_nilpotent[simp]: @@ -445,7 +436,7 @@ lemma Nadd_normNum1[simp]: assumes "SORT_CONSTRAINT('a::{field_char_0, field_inverse_zero})" shows "normNum x +\<^sub>N y = x +\<^sub>N y" -proof- +proof - have n: "isnormNum (normNum x +\<^sub>N y)" "isnormNum (x +\<^sub>N y)" by simp_all have "INum (normNum x +\<^sub>N y) = INum x + (INum y :: 'a)" by simp also have "\ = INum (x +\<^sub>N y)" by simp @@ -455,7 +446,7 @@ lemma Nadd_normNum2[simp]: assumes "SORT_CONSTRAINT('a::{field_char_0, field_inverse_zero})" shows "x +\<^sub>N normNum y = x +\<^sub>N y" -proof- +proof - have n: "isnormNum (x +\<^sub>N normNum y)" "isnormNum (x +\<^sub>N y)" by simp_all have "INum (x +\<^sub>N normNum y) = INum x + (INum y :: 'a)" by simp also have "\ = INum (x +\<^sub>N y)" by simp @@ -465,7 +456,7 @@ lemma Nadd_assoc: assumes "SORT_CONSTRAINT('a::{field_char_0, field_inverse_zero})" shows "x +\<^sub>N y +\<^sub>N z = x +\<^sub>N (y +\<^sub>N z)" -proof- +proof - have n: "isnormNum (x +\<^sub>N y +\<^sub>N z)" "isnormNum (x +\<^sub>N (y +\<^sub>N z))" by simp_all have "INum (x +\<^sub>N y +\<^sub>N z) = (INum (x +\<^sub>N (y +\<^sub>N z)) :: 'a)" by simp with isnormNum_unique[OF n] show ?thesis by simp @@ -476,10 +467,10 @@ lemma Nmul_assoc: assumes "SORT_CONSTRAINT('a::{field_char_0, field_inverse_zero})" - assumes nx: "isnormNum x" and ny:"isnormNum y" and nz:"isnormNum z" + assumes nx: "isnormNum x" and ny: "isnormNum y" and nz: "isnormNum z" shows "x *\<^sub>N y *\<^sub>N z = x *\<^sub>N (y *\<^sub>N z)" -proof- - from nx ny nz have n: "isnormNum (x *\<^sub>N y *\<^sub>N z)" "isnormNum (x *\<^sub>N (y *\<^sub>N z))" +proof - + from nx ny nz have n: "isnormNum (x *\<^sub>N y *\<^sub>N z)" "isnormNum (x *\<^sub>N (y *\<^sub>N z))" by simp_all have "INum (x +\<^sub>N y +\<^sub>N z) = (INum (x +\<^sub>N (y +\<^sub>N z)) :: 'a)" by simp with isnormNum_unique[OF n] show ?thesis by simp @@ -487,14 +478,15 @@ lemma Nsub0: assumes "SORT_CONSTRAINT('a::{field_char_0, field_inverse_zero})" - assumes x: "isnormNum x" and y:"isnormNum y" shows "(x -\<^sub>N y = 0\<^sub>N) = (x = y)" -proof- - { fix h :: 'a - from isnormNum_unique[where 'a = 'a, OF Nsub_normN[OF y], where y="0\<^sub>N"] - have "(x -\<^sub>N y = 0\<^sub>N) = (INum (x -\<^sub>N y) = (INum 0\<^sub>N :: 'a)) " by simp - also have "\ = (INum x = (INum y :: 'a))" by simp - also have "\ = (x = y)" using x y by simp - finally show ?thesis . } + assumes x: "isnormNum x" and y: "isnormNum y" + shows "x -\<^sub>N y = 0\<^sub>N \ x = y" +proof - + fix h :: 'a + from isnormNum_unique[where 'a = 'a, OF Nsub_normN[OF y], where y="0\<^sub>N"] + have "(x -\<^sub>N y = 0\<^sub>N) = (INum (x -\<^sub>N y) = (INum 0\<^sub>N :: 'a)) " by simp + also have "\ = (INum x = (INum y :: 'a))" by simp + also have "\ = (x = y)" using x y by simp + finally show ?thesis . qed lemma Nmul0[simp]: "c *\<^sub>N 0\<^sub>N = 0\<^sub>N" " 0\<^sub>N *\<^sub>N c = 0\<^sub>N" @@ -502,24 +494,26 @@ lemma Nmul_eq0[simp]: assumes "SORT_CONSTRAINT('a::{field_char_0, field_inverse_zero})" - assumes nx:"isnormNum x" and ny: "isnormNum y" - shows "(x*\<^sub>N y = 0\<^sub>N) = (x = 0\<^sub>N \ y = 0\<^sub>N)" -proof- - { fix h :: 'a - have " \ a b a' b'. x = (a,b) \ y= (a',b')" by auto - then obtain a b a' b' where xy[simp]: "x = (a,b)" "y = (a',b')" by blast - have n0: "isnormNum 0\<^sub>N" by simp - show ?thesis using nx ny - apply (simp only: isnormNum_unique[where ?'a = 'a, OF Nmul_normN[OF nx ny] n0, symmetric] Nmul[where ?'a = 'a]) - by (simp add: INum_def split_def isnormNum_def split: split_if_asm) - } + assumes nx: "isnormNum x" and ny: "isnormNum y" + shows "x*\<^sub>N y = 0\<^sub>N \ x = 0\<^sub>N \ y = 0\<^sub>N" +proof - + fix h :: 'a + obtain a b where x: "x = (a, b)" by (cases x) + obtain a' b' where y: "y = (a', b')" by (cases y) + have n0: "isnormNum 0\<^sub>N" by simp + show ?thesis using nx ny + apply (simp only: isnormNum_unique[where ?'a = 'a, OF Nmul_normN[OF nx ny] n0, symmetric] + Nmul[where ?'a = 'a]) + apply (simp add: x y INum_def split_def isnormNum_def split: split_if_asm) + done qed + lemma Nneg_Nneg[simp]: "~\<^sub>N (~\<^sub>N c) = c" by (simp add: Nneg_def split_def) -lemma Nmul1[simp]: - "isnormNum c \ 1\<^sub>N *\<^sub>N c = c" - "isnormNum c \ c *\<^sub>N (1\<^sub>N) = c" +lemma Nmul1[simp]: + "isnormNum c \ 1\<^sub>N *\<^sub>N c = c" + "isnormNum c \ c *\<^sub>N (1\<^sub>N) = c" apply (simp_all add: Nmul_def Let_def split_def isnormNum_def) apply (cases "fst c = 0", simp_all, cases c, simp_all)+ done diff -r 353ddca2e4c0 -r 1120cba9bce4 src/HOL/Library/Library.thy --- a/src/HOL/Library/Library.thy Wed Sep 07 17:41:29 2011 -0700 +++ b/src/HOL/Library/Library.thy Wed Sep 07 19:24:28 2011 -0700 @@ -55,6 +55,7 @@ Ramsey Reflection RBT_Mapping + Saturated Set_Algebras State_Monad Sum_of_Squares diff -r 353ddca2e4c0 -r 1120cba9bce4 src/HOL/Library/Saturated.thy --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Library/Saturated.thy Wed Sep 07 19:24:28 2011 -0700 @@ -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 353ddca2e4c0 -r 1120cba9bce4 src/HOL/Metis_Examples/Type_Encodings.thy --- a/src/HOL/Metis_Examples/Type_Encodings.thy Wed Sep 07 17:41:29 2011 -0700 +++ b/src/HOL/Metis_Examples/Type_Encodings.thy Wed Sep 07 19:24:28 2011 -0700 @@ -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 353ddca2e4c0 -r 1120cba9bce4 src/HOL/Nat.thy --- a/src/HOL/Nat.thy Wed Sep 07 17:41:29 2011 -0700 +++ b/src/HOL/Nat.thy Wed Sep 07 19:24:28 2011 -0700 @@ -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 353ddca2e4c0 -r 1120cba9bce4 src/HOL/Tools/ATP/atp_translate.ML --- a/src/HOL/Tools/ATP/atp_translate.ML Wed Sep 07 17:41:29 2011 -0700 +++ b/src/HOL/Tools/ATP/atp_translate.ML Wed Sep 07 19:24:28 2011 -0700 @@ -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 diff -r 353ddca2e4c0 -r 1120cba9bce4 src/Pure/PIDE/document.ML --- a/src/Pure/PIDE/document.ML Wed Sep 07 17:41:29 2011 -0700 +++ b/src/Pure/PIDE/document.ML Wed Sep 07 19:24:28 2011 -0700 @@ -331,7 +331,6 @@ let val is_init = Toplevel.is_init tr; val is_proof = Keyword.is_proof (Toplevel.name_of tr); - val do_print = not is_init andalso (Toplevel.print_of tr orelse is_proof); val _ = Multithreading.interrupted (); val _ = Toplevel.status tr Markup.forked; @@ -343,13 +342,18 @@ in (case result of NONE => - (if null errs then Exn.interrupt () else (); - Toplevel.status tr Markup.failed; - (st, no_print)) + let + val _ = if null errs then Exn.interrupt () else (); + val _ = Toplevel.status tr Markup.failed; + in (st, no_print) end | SOME st' => - (Toplevel.status tr Markup.finished; - proof_status tr st'; - (st', if do_print then print_state tr st' else no_print))) + let + val _ = Toplevel.status tr Markup.finished; + val _ = proof_status tr st'; + val do_print = + not is_init andalso + (Toplevel.print_of tr orelse (is_proof andalso Toplevel.is_proof st')); + in (st', if do_print then print_state tr st' else no_print) end) end; end; diff -r 353ddca2e4c0 -r 1120cba9bce4 src/Pure/PIDE/xml.ML --- a/src/Pure/PIDE/xml.ML Wed Sep 07 17:41:29 2011 -0700 +++ b/src/Pure/PIDE/xml.ML Wed Sep 07 19:24:28 2011 -0700 @@ -47,6 +47,7 @@ val parse_element: string list -> tree * string list val parse_document: string list -> tree * string list val parse: string -> tree + val cache: unit -> tree -> tree exception XML_ATOM of string exception XML_BODY of body structure Encode: XML_DATA_OPS @@ -228,6 +229,48 @@ end; +(** cache for substructural sharing **) + +fun tree_ord tu = + if pointer_eq tu then EQUAL + else + (case tu of + (Text _, Elem _) => LESS + | (Elem _, Text _) => GREATER + | (Text s, Text s') => fast_string_ord (s, s') + | (Elem e, Elem e') => + prod_ord + (prod_ord fast_string_ord (list_ord (prod_ord fast_string_ord fast_string_ord))) + (list_ord tree_ord) (e, e')); + +structure Treetab = Table(type key = tree val ord = tree_ord); + +fun cache () = + let + val strings = Unsynchronized.ref (Symtab.empty: unit Symtab.table); + val trees = Unsynchronized.ref (Treetab.empty: unit Treetab.table); + + fun string s = + if size s <= 1 then s + else + (case Symtab.lookup_key (! strings) s of + SOME (s', ()) => s' + | NONE => (Unsynchronized.change strings (Symtab.update (s, ())); s)); + + fun tree t = + (case Treetab.lookup_key (! trees) t of + SOME (t', ()) => t' + | NONE => + let + val t' = + (case t of + Elem ((a, ps), b) => Elem ((string a, map (pairself string) ps), map tree b) + | Text s => Text (string s)); + val _ = Unsynchronized.change trees (Treetab.update (t', ())); + in t' end); + in tree end; + + (** XML as data representation language **) diff -r 353ddca2e4c0 -r 1120cba9bce4 src/Pure/PIDE/xml.scala --- a/src/Pure/PIDE/xml.scala Wed Sep 07 17:41:29 2011 -0700 +++ b/src/Pure/PIDE/xml.scala Wed Sep 07 19:24:28 2011 -0700 @@ -84,7 +84,8 @@ def content(body: Body): Iterator[String] = content_stream(body).iterator - /* pipe-lined cache for partial sharing */ + + /** cache for partial sharing (weak table) **/ class Cache(initial_size: Int = 131071, max_string: Int = 100) { diff -r 353ddca2e4c0 -r 1120cba9bce4 src/Pure/Syntax/syntax.ML --- a/src/Pure/Syntax/syntax.ML Wed Sep 07 17:41:29 2011 -0700 +++ b/src/Pure/Syntax/syntax.ML Wed Sep 07 19:24:28 2011 -0700 @@ -99,6 +99,7 @@ val string_of_sort_global: theory -> sort -> string type syntax val eq_syntax: syntax * syntax -> bool + val join_syntax: syntax -> unit val lookup_const: syntax -> string -> string option val is_keyword: syntax -> string -> bool val tokenize: syntax -> bool -> Symbol_Pos.T list -> Lexicon.token list @@ -508,6 +509,8 @@ fun eq_syntax (Syntax (_, s1), Syntax (_, s2)) = s1 = s2; +fun join_syntax (Syntax ({gram, ...}, _)) = ignore (Future.join gram); + fun lookup_const (Syntax ({consts, ...}, _)) = Symtab.lookup consts; fun is_keyword (Syntax ({lexicon, ...}, _)) = Scan.is_literal lexicon o Symbol.explode; fun tokenize (Syntax ({lexicon, ...}, _)) = Lexicon.tokenize lexicon; diff -r 353ddca2e4c0 -r 1120cba9bce4 src/Pure/System/session.scala --- a/src/Pure/System/session.scala Wed Sep 07 17:41:29 2011 -0700 +++ b/src/Pure/System/session.scala Wed Sep 07 19:24:28 2011 -0700 @@ -22,7 +22,7 @@ //{{{ case object Global_Settings - case object Perspective + case object Caret_Focus case object Assignment case class Commands_Changed(nodes: Set[Document.Node.Name], commands: Set[Command]) @@ -52,7 +52,7 @@ /* pervasive event buses */ val global_settings = new Event_Bus[Session.Global_Settings.type] - val perspective = new Event_Bus[Session.Perspective.type] + val caret_focus = new Event_Bus[Session.Caret_Focus.type] val assignments = new Event_Bus[Session.Assignment.type] val commands_changed = new Event_Bus[Session.Commands_Changed] val phase_changed = new Event_Bus[Session.Phase] diff -r 353ddca2e4c0 -r 1120cba9bce4 src/Pure/theory.ML --- a/src/Pure/theory.ML Wed Sep 07 17:41:29 2011 -0700 +++ b/src/Pure/theory.ML Wed Sep 07 19:24:28 2011 -0700 @@ -147,6 +147,7 @@ |> Sign.local_path |> Sign.map_naming (Name_Space.set_theory_name name) |> apply_wrappers wrappers + |> tap (Syntax.join_syntax o Sign.syn_of) end; fun end_theory thy = diff -r 353ddca2e4c0 -r 1120cba9bce4 src/Tools/jEdit/README.html --- a/src/Tools/jEdit/README.html Wed Sep 07 17:41:29 2011 -0700 +++ b/src/Tools/jEdit/README.html Wed Sep 07 19:24:28 2011 -0700 @@ -144,6 +144,11 @@ Workaround: Force re-parsing of files using such commands via reload menu of jEdit. +
  • No way to delete document nodes from the overall collection of + theories.
    + Workaround: Restart whole Isabelle/jEdit session in + worst-case situation.
    • +
  • No support for non-local markup, e.g. commands reporting on previous commands (proof end on proof head), or markup produced by loading external files.
    • diff -r 353ddca2e4c0 -r 1120cba9bce4 src/Tools/jEdit/src/document_view.scala --- a/src/Tools/jEdit/src/document_view.scala Wed Sep 07 17:41:29 2011 -0700 +++ b/src/Tools/jEdit/src/document_view.scala Wed Sep 07 19:24:28 2011 -0700 @@ -362,7 +362,7 @@ private val caret_listener = new CaretListener { private val delay = Swing_Thread.delay_last(session.input_delay) { - session.perspective.event(Session.Perspective) + session.caret_focus.event(Session.Caret_Focus) } override def caretUpdate(e: CaretEvent) { delay() } } diff -r 353ddca2e4c0 -r 1120cba9bce4 src/Tools/jEdit/src/output_dockable.scala --- a/src/Tools/jEdit/src/output_dockable.scala Wed Sep 07 17:41:29 2011 -0700 +++ b/src/Tools/jEdit/src/output_dockable.scala Wed Sep 07 19:24:28 2011 -0700 @@ -106,7 +106,7 @@ react { case Session.Global_Settings => handle_resize() case changed: Session.Commands_Changed => handle_update(Some(changed.commands)) - case Session.Perspective => if (follow_caret && handle_perspective()) handle_update() + case Session.Caret_Focus => if (follow_caret && handle_perspective()) handle_update() case bad => System.err.println("Output_Dockable: ignoring bad message " + bad) } } @@ -116,14 +116,14 @@ { Isabelle.session.global_settings += main_actor Isabelle.session.commands_changed += main_actor - Isabelle.session.perspective += main_actor + Isabelle.session.caret_focus += main_actor } override def exit() { Isabelle.session.global_settings -= main_actor Isabelle.session.commands_changed -= main_actor - Isabelle.session.perspective -= main_actor + Isabelle.session.caret_focus -= main_actor }