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NEWS

author | paulson |

Tue, 08 Jun 2004 16:40:41 +0200 | |

changeset 14885 | 0a840138dcd7 |

parent 14878 | b884a7ba7238 |

child 14897 | 577f95db94e4 |

permissions | -rw-r--r-- |

Groups, Rings and supporting lemmas in ZF

Isabelle NEWS -- history user-relevant changes ============================================== New in this Isabelle release ---------------------------- *** General *** * Pure: considerably improved version of 'constdefs' command. Now performs automatic type-inference of declared constants; additional support for local structure declarations (cf. locales and HOL records), see also isar-ref manual. Potential INCOMPATIBILITY: need to observe strictly sequential dependencies of definitions within a single 'constdefs' section; moreover, the declared name needs to be an identifier. If all fails, consider to fall back on 'consts' and 'defs' separately. * Pure: improved indexed syntax and implicit structures. First of all, indexed syntax provides a notational device for subscripted application, using the new syntax \<^bsub>term\<^esub> for arbitrary expressions. Secondly, in a local context with structure declarations, number indexes \<^sub>n or the empty index (default number 1) refer to a certain fixed variable implicitly; option show_structs controls printing of implicit structures. Typical applications of these concepts involve record types and locales. * Pure: clear separation of logical types and nonterminals, where the latter may only occur in 'syntax' specifications or type abbreviations. Before that distinction was only partially implemented via type class "logic" vs. "{}". Potential INCOMPATIBILITY in rare cases of improper use of 'types'/'consts' instead of 'nonterminals'/'syntax'. Some very exotic syntax specifications may require further adaption (e.g. Cube/Base.thy). * Pure: removed obsolete type class "logic", use the top sort {} instead. Note that non-logical types should be declared as 'nonterminals' rather than 'types'. INCOMPATIBILITY for new object-logic specifications. * Pure/Syntax: inner syntax includes (*(*nested*) comments*). * Pure/Syntax: pretty pinter now supports unbreakable blocks, specified in mixfix annotations as "(00...)". * Pure/Syntax: 'advanced' translation functions (parse_translation etc.) may depend on the signature of the theory context being presently used for parsing/printing, see also isar-ref manual. * Pure: tuned internal renaming of symbolic identifiers -- attach primes instead of base 26 numbers. * ML: all output via channels of writeln/warning/error etc. is now passed through Output.output. This gives interface builders a chance to adapt text encodings in arbitrary manners (say as XML entities); see the hook provided by Output.add_mode. On the other hand, results of Pretty.string_of/str_of (including string_of_term, string_of_thm etc.) are still 'raw' (containing funny \<^raw...> symbols), which requires separate application of Output.output whenever strings are *not* passed on to writeln/warning/error etc. *** HOL *** * HOL/record: reimplementation of records. Improved scalability for records with many fields, avoiding performance problems for type inference. Records are no longer composed of nested field types, but of nested extension types. Therefore the record type only grows linear in the number of extensions and not in the number of fields. The top-level (users) view on records is preserved. Potential INCOMPATIBILITY only in strange cases, where the theory depends on the old record representation. The type generated for a record is called <record_name>_ext_type. * HOL: symbolic syntax of Hilbert Choice Operator is now as follows: syntax (epsilon) "_Eps" :: "[pttrn, bool] => 'a" ("(3\<some>_./ _)" [0, 10] 10) The symbol \<some> is displayed as the alternative epsilon of LaTeX and x-symbol; use option '-m epsilon' to get it actually printed. Moreover, the mathematically important symbolic identifier \<epsilon> becomes available as variable, constant etc. * Simplifier: "record_upd_simproc" for simplification of multiple record updates enabled by default. INCOMPATIBILITY: old proofs break occasionally, since simplification is more powerful by default. *** HOLCF *** * HOLCF: discontinued special version of 'constdefs' (which used to support continuous functions) in favor of the general Pure one with full type-inference. *** ZF *** * ZF/ex/{Group,Ring}: examples in abstract algebra, including the First Isomorphism Theorem (on quotienting by the kernel of a homomorphism). New in Isabelle2004 (April 2004) -------------------------------- *** General *** * Provers/order.ML: new efficient reasoner for partial and linear orders. Replaces linorder.ML. * Pure: Greek letters (except small lambda, \<lambda>), as well as Gothic (\<aa>...\<zz>\<AA>...\<ZZ>), calligraphic (\<A>...\<Z>), and Euler (\<a>...\<z>), are now considered normal letters, and can therefore be used anywhere where an ASCII letter (a...zA...Z) has until now. COMPATIBILITY: This obviously changes the parsing of some terms, especially where a symbol has been used as a binder, say '\<Pi>x. ...', which is now a type error since \<Pi>x will be parsed as an identifier. Fix it by inserting a space around former symbols. Call 'isatool fixgreek' to try to fix parsing errors in existing theory and ML files. * Pure: Macintosh and Windows line-breaks are now allowed in theory files. * Pure: single letter sub/superscripts (\<^isub> and \<^isup>) are now allowed in identifiers. Similar to Greek letters \<^isub> is now considered a normal (but invisible) letter. For multiple letter subscripts repeat \<^isub> like this: x\<^isub>1\<^isub>2. * Pure: There are now sub-/superscripts that can span more than one character. Text between \<^bsub> and \<^esub> is set in subscript in ProofGeneral and LaTeX, text between \<^bsup> and \<^esup> in superscript. The new control characters are not identifier parts. * Pure: Control-symbols of the form \<^raw:...> will literally print the content of "..." to the latex file instead of \isacntrl... . The "..." may consist of any printable characters excluding the end bracket >. * Pure: Using new Isar command "finalconsts" (or the ML functions Theory.add_finals or Theory.add_finals_i) it is now possible to declare constants "final", which prevents their being given a definition later. It is useful for constants whose behaviour is fixed axiomatically rather than definitionally, such as the meta-logic connectives. * Pure: 'instance' now handles general arities with general sorts (i.e. intersections of classes), * Presentation: generated HTML now uses a CSS style sheet to make layout (somewhat) independent of content. It is copied from lib/html/isabelle.css. It can be changed to alter the colors/layout of generated pages. *** Isar *** * Tactic emulation methods rule_tac, erule_tac, drule_tac, frule_tac, cut_tac, subgoal_tac and thin_tac: - Now understand static (Isar) contexts. As a consequence, users of Isar locales are no longer forced to write Isar proof scripts. For details see Isar Reference Manual, paragraph 4.3.2: Further tactic emulations. - INCOMPATIBILITY: names of variables to be instantiated may no longer be enclosed in quotes. Instead, precede variable name with `?'. This is consistent with the instantiation attribute "where". * Attributes "where" and "of": - Now take type variables of instantiated theorem into account when reading the instantiation string. This fixes a bug that caused instantiated theorems to have too special types in some circumstances. - "where" permits explicit instantiations of type variables. * Calculation commands "moreover" and "also" no longer interfere with current facts ("this"), admitting arbitrary combinations with "then" and derived forms. * Locales: - Goal statements involving the context element "includes" no longer generate theorems with internal delta predicates (those ending on "_axioms") in the premise. Resolve particular premise with <locale>.intro to obtain old form. - Fixed bug in type inference ("unify_frozen") that prevented mix of target specification and "includes" elements in goal statement. - Rule sets <locale>.intro and <locale>.axioms no longer declared as [intro?] and [elim?] (respectively) by default. - Experimental command for instantiation of locales in proof contexts: instantiate <label>[<attrs>]: <loc> Instantiates locale <loc> and adds all its theorems to the current context taking into account their attributes. Label and attrs are optional modifiers, like in theorem declarations. If present, names of instantiated theorems are qualified with <label>, and the attributes <attrs> are applied after any attributes these theorems might have already. If the locale has assumptions, a chained fact of the form "<loc> t1 ... tn" is expected from which instantiations of the parameters are derived. The command does not support old-style locales declared with "locale (open)". A few (very simple) examples can be found in FOL/ex/LocaleInst.thy. * HOL: Tactic emulation methods induct_tac and case_tac understand static (Isar) contexts. *** HOL *** * Proof import: new image HOL4 contains the imported library from the HOL4 system with about 2500 theorems. It is imported by replaying proof terms produced by HOL4 in Isabelle. The HOL4 image can be used like any other Isabelle image. See HOL/Import/HOL/README for more information. * Simplifier: - Much improved handling of linear and partial orders. Reasoners for linear and partial orders are set up for type classes "linorder" and "order" respectively, and are added to the default simpset as solvers. This means that the simplifier can build transitivity chains to solve goals from the assumptions. - INCOMPATIBILITY: old proofs break occasionally. Typically, applications of blast or auto after simplification become unnecessary because the goal is solved by simplification already. * Numerics: new theory Ring_and_Field contains over 250 basic numerical laws, all proved in axiomatic type classes for semirings, rings and fields. * Numerics: - Numeric types (nat, int, and in HOL-Complex rat, real, complex, etc.) are now formalized using the Ring_and_Field theory mentioned above. - INCOMPATIBILITY: simplification and arithmetic behaves somewhat differently than before, because now they are set up once in a generic manner. - INCOMPATIBILITY: many type-specific arithmetic laws have gone. Look for the general versions in Ring_and_Field (and Power if they concern exponentiation). * Type "rat" of the rational numbers is now available in HOL-Complex. * Records: - Record types are now by default printed with their type abbreviation instead of the list of all field types. This can be configured via the reference "print_record_type_abbr". - Simproc "record_upd_simproc" for simplification of multiple updates added (not enabled by default). - Simproc "record_ex_sel_eq_simproc" to simplify EX x. sel r = x resp. EX x. x = sel r to True (not enabled by default). - Tactic "record_split_simp_tac" to split and simplify records added. * 'specification' command added, allowing for definition by specification. There is also an 'ax_specification' command that introduces the new constants axiomatically. * arith(_tac) is now able to generate counterexamples for reals as well. * HOL-Algebra: new locale "ring" for non-commutative rings. * HOL-ex: InductiveInvariant_examples illustrates advanced recursive function definitions, thanks to Sava Krsti\'{c} and John Matthews. * HOL-Matrix: a first theory for matrices in HOL with an application of matrix theory to linear programming. * Unions and Intersections: The x-symbol output syntax of UN and INT has been changed from "\<Union>x \<in> A. B" to "\<Union\<^bsub>x \<in> A\<^esub> B" i.e. the index formulae has become a subscript, like in normal math. Similarly for "\<Union>x. B", and for \<Inter> instead of \<Union>. The subscript version is also accepted as input syntax. * Unions and Intersections over Intervals: There is new short syntax "UN i<=n. A" for "UN i:{0..n}. A". There is also an x-symbol version with subscripts "\<Union>\<^bsub>i <= n\<^esub>. A" like in normal math, and corresponding versions for < and for intersection. * ML: the legacy theory structures Int and List have been removed. They had conflicted with ML Basis Library structures having the same names. * 'refute' command added to search for (finite) countermodels. Only works for a fragment of HOL. The installation of an external SAT solver is highly recommended. See "HOL/Refute.thy" for details. * 'quickcheck' command: Allows to find counterexamples by evaluating formulae under an assignment of free variables to random values. In contrast to 'refute', it can deal with inductive datatypes, but cannot handle quantifiers. See "HOL/ex/Quickcheck_Examples.thy" for examples. *** HOLCF *** * Streams now come with concatenation and are part of the HOLCF image New in Isabelle2003 (May 2003) ------------------------------ *** General *** * Provers/simplifier: - Completely reimplemented method simp (ML: Asm_full_simp_tac): Assumptions are now subject to complete mutual simplification, not just from left to right. The simplifier now preserves the order of assumptions. Potential INCOMPATIBILITY: -- simp sometimes diverges where the old version did not, e.g. invoking simp on the goal [| P (f x); y = x; f x = f y |] ==> Q now gives rise to the infinite reduction sequence P(f x) --(f x = f y)--> P(f y) --(y = x)--> P(f x) --(f x = f y)--> ... Using "simp (asm_lr)" (ML: Asm_lr_simp_tac) instead often solves this kind of problem. -- Tactics combining classical reasoner and simplification (such as auto) are also affected by this change, because many of them rely on simp. They may sometimes diverge as well or yield a different numbers of subgoals. Try to use e.g. force, fastsimp, or safe instead of auto in case of problems. Sometimes subsequent calls to the classical reasoner will fail because a preceeding call to the simplifier too eagerly simplified the goal, e.g. deleted redundant premises. - The simplifier trace now shows the names of the applied rewrite rules - You can limit the number of recursive invocations of the simplifier during conditional rewriting (where the simplifie tries to solve the conditions before applying the rewrite rule): ML "simp_depth_limit := n" where n is an integer. Thus you can force termination where previously the simplifier would diverge. - Accepts free variables as head terms in congruence rules. Useful in Isar. - No longer aborts on failed congruence proof. Instead, the congruence is ignored. * Pure: New generic framework for extracting programs from constructive proofs. See HOL/Extraction.thy for an example instantiation, as well as HOL/Extraction for some case studies. * Pure: The main goal of the proof state is no longer shown by default, only the subgoals. This behaviour is controlled by a new flag. PG menu: Isabelle/Isar -> Settings -> Show Main Goal (ML: Proof.show_main_goal). * Pure: You can find all matching introduction rules for subgoal 1, i.e. all rules whose conclusion matches subgoal 1: PG menu: Isabelle/Isar -> Show me -> matching rules The rules are ordered by how closely they match the subgoal. In particular, rules that solve a subgoal outright are displayed first (or rather last, the way they are printed). (ML: ProofGeneral.print_intros()) * Pure: New flag trace_unify_fail causes unification to print diagnostic information (PG: in trace buffer) when it fails. This is useful for figuring out why single step proofs like rule, erule or assumption failed. * Pure: Locale specifications now produce predicate definitions according to the body of text (covering assumptions modulo local definitions); predicate "loc_axioms" covers newly introduced text, while "loc" is cumulative wrt. all included locale expressions; the latter view is presented only on export into the global theory context; potential INCOMPATIBILITY, use "(open)" option to fall back on the old view without predicates; * Pure: predefined locales "var" and "struct" are useful for sharing parameters (as in CASL, for example); just specify something like ``var x + var y + struct M'' as import; * Pure: improved thms_containing: proper indexing of facts instead of raw theorems; check validity of results wrt. current name space; include local facts of proof configuration (also covers active locales), cover fixed variables in index; may use "_" in term specification; an optional limit for the number of printed facts may be given (the default is 40); * Pure: disallow duplicate fact bindings within new-style theory files (batch-mode only); * Provers: improved induct method: assumptions introduced by case "foo" are split into "foo.hyps" (from the rule) and "foo.prems" (from the goal statement); "foo" still refers to all facts collectively; * Provers: the function blast.overloaded has been removed: all constants are regarded as potentially overloaded, which improves robustness in exchange for slight decrease in efficiency; * Provers/linorder: New generic prover for transitivity reasoning over linear orders. Note: this prover is not efficient! * Isar: preview of problems to finish 'show' now produce an error rather than just a warning (in interactive mode); *** HOL *** * arith(_tac) - Produces a counter example if it cannot prove a goal. Note that the counter example may be spurious if the goal is not a formula of quantifier-free linear arithmetic. In ProofGeneral the counter example appears in the trace buffer. - Knows about div k and mod k where k is a numeral of type nat or int. - Calls full Presburger arithmetic (by Amine Chaieb) if quantifier-free linear arithmetic fails. This takes account of quantifiers and divisibility. Presburger arithmetic can also be called explicitly via presburger(_tac). * simp's arithmetic capabilities have been enhanced a bit: it now takes ~= in premises into account (by performing a case split); * simp reduces "m*(n div m) + n mod m" to n, even if the two summands are distributed over a sum of terms; * New tactic "trans_tac" and method "trans" instantiate Provers/linorder.ML for axclasses "order" and "linorder" (predicates "<=", "<" and "="). * function INCOMPATIBILITIES: Pi-sets have been redefined and moved from main HOL to Library/FuncSet; constant "Fun.op o" is now called "Fun.comp"; * 'typedef' command has new option "open" to suppress the set definition; * functions Min and Max on finite sets have been introduced (theory Finite_Set); * attribute [symmetric] now works for relations as well; it turns (x,y) : R^-1 into (y,x) : R, and vice versa; * induct over a !!-quantified statement (say !!x1..xn): each "case" automatically performs "fix x1 .. xn" with exactly those names. * Map: `empty' is no longer a constant but a syntactic abbreviation for %x. None. Warning: empty_def now refers to the previously hidden definition of the empty set. * Algebra: formalization of classical algebra. Intended as base for any algebraic development in Isabelle. Currently covers group theory (up to Sylow's theorem) and ring theory (Universal Property of Univariate Polynomials). Contributions welcome; * GroupTheory: deleted, since its material has been moved to Algebra; * Complex: new directory of the complex numbers with numeric constants, nonstandard complex numbers, and some complex analysis, standard and nonstandard (Jacques Fleuriot); * HOL-Complex: new image for analysis, replacing HOL-Real and HOL-Hyperreal; * Hyperreal: introduced Gauge integration and hyperreal logarithms (Jacques Fleuriot); * Real/HahnBanach: updated and adapted to locales; * NumberTheory: added Gauss's law of quadratic reciprocity (by Avigad, Gray and Kramer); * UNITY: added the Meier-Sanders theory of progress sets; * MicroJava: bytecode verifier and lightweight bytecode verifier as abstract algorithms, instantiated to the JVM; * Bali: Java source language formalization. Type system, operational semantics, axiomatic semantics. Supported language features: classes, interfaces, objects,virtual methods, static methods, static/instance fields, arrays, access modifiers, definite assignment, exceptions. *** ZF *** * ZF/Constructible: consistency proof for AC (Gödel's constructible universe, etc.); * Main ZF: virtually all theories converted to new-style format; *** ML *** * Pure: Tactic.prove provides sane interface for internal proofs; omits the infamous "standard" operation, so this is more appropriate than prove_goalw_cterm in many situations (e.g. in simprocs); * Pure: improved error reporting of simprocs; * Provers: Simplifier.simproc(_i) provides sane interface for setting up simprocs; *** Document preparation *** * uses \par instead of \\ for line breaks in theory text. This may shift some page breaks in large documents. To get the old behaviour use \renewcommand{\isanewline}{\mbox{}\\\mbox{}} in root.tex. * minimized dependencies of isabelle.sty and isabellesym.sty on other packages * \<euro> now needs package babel/greek instead of marvosym (which broke \Rightarrow) * normal size for \<zero>...\<nine> (uses \mathbf instead of textcomp package) New in Isabelle2002 (March 2002) -------------------------------- *** Document preparation *** * greatly simplified document preparation setup, including more graceful interpretation of isatool usedir -i/-d/-D options, and more instructive isatool mkdir; users should basically be able to get started with "isatool mkdir HOL Test && isatool make"; alternatively, users may run a separate document processing stage manually like this: "isatool usedir -D output HOL Test && isatool document Test/output"; * theory dependency graph may now be incorporated into documents; isatool usedir -g true will produce session_graph.eps/.pdf for use with \includegraphics of LaTeX; * proper spacing of consecutive markup elements, especially text blocks after section headings; * support bold style (for single symbols only), input syntax is like this: "\<^bold>\<alpha>" or "\<^bold>A"; * \<bullet> is now output as bold \cdot by default, which looks much better in printed text; * added default LaTeX bindings for \<tturnstile> and \<TTurnstile>; note that these symbols are currently unavailable in Proof General / X-Symbol; new symbols \<zero>, \<one>, ..., \<nine>, and \<euro>; * isatool latex no longer depends on changed TEXINPUTS, instead isatool document copies the Isabelle style files to the target location; *** Isar *** * Pure/Provers: improved proof by cases and induction; - 'case' command admits impromptu naming of parameters (such as "case (Suc n)"); - 'induct' method divinates rule instantiation from the inductive claim; no longer requires excessive ?P bindings for proper instantiation of cases; - 'induct' method properly enumerates all possibilities of set/type rules; as a consequence facts may be also passed through *type* rules without further ado; - 'induct' method now derives symbolic cases from the *rulified* rule (before it used to rulify cases stemming from the internal atomized version); this means that the context of a non-atomic statement becomes is included in the hypothesis, avoiding the slightly cumbersome show "PROP ?case" form; - 'induct' may now use elim-style induction rules without chaining facts, using ``missing'' premises from the goal state; this allows rules stemming from inductive sets to be applied in unstructured scripts, while still benefitting from proper handling of non-atomic statements; NB: major inductive premises need to be put first, all the rest of the goal is passed through the induction; - 'induct' proper support for mutual induction involving non-atomic rule statements (uses the new concept of simultaneous goals, see below); - append all possible rule selections, but only use the first success (no backtracking); - removed obsolete "(simplified)" and "(stripped)" options of methods; - undeclared rule case names default to numbers 1, 2, 3, ...; - added 'print_induct_rules' (covered by help item in recent Proof General versions); - moved induct/cases attributes to Pure, methods to Provers; - generic method setup instantiated for FOL and HOL; * Pure: support multiple simultaneous goal statements, for example "have a: A and b: B" (same for 'theorem' etc.); being a pure meta-level mechanism, this acts as if several individual goals had been stated separately; in particular common proof methods need to be repeated in order to cover all claims; note that a single elimination step is *not* sufficient to establish the two conjunctions, so this fails: assume "A & B" then have A and B .. (*".." fails*) better use "obtain" in situations as above; alternative refer to multi-step methods like 'auto', 'simp_all', 'blast+' etc.; * Pure: proper integration with ``locales''; unlike the original version by Florian Kammüller, Isar locales package high-level proof contexts rather than raw logical ones (e.g. we admit to include attributes everywhere); operations on locales include merge and rename; support for implicit arguments (``structures''); simultaneous type-inference over imports and text; see also HOL/ex/Locales.thy for some examples; * Pure: the following commands have been ``localized'', supporting a target locale specification "(in name)": 'lemma', 'theorem', 'corollary', 'lemmas', 'theorems', 'declare'; the results will be stored both within the locale and at the theory level (exported and qualified by the locale name); * Pure: theory goals may now be specified in ``long'' form, with ad-hoc contexts consisting of arbitrary locale elements. for example ``lemma foo: fixes x assumes "A x" shows "B x"'' (local syntax and definitions may be given, too); the result is a meta-level rule with the context elements being discharged in the obvious way; * Pure: new proof command 'using' allows to augment currently used facts after a goal statement ('using' is syntactically analogous to 'apply', but acts on the goal's facts only); this allows chained facts to be separated into parts given before and after a claim, as in ``from a and b have C using d and e <proof>''; * Pure: renamed "antecedent" case to "rule_context"; * Pure: new 'judgment' command records explicit information about the object-logic embedding (used by several tools internally); no longer use hard-wired "Trueprop"; * Pure: added 'corollary' command; * Pure: fixed 'token_translation' command; * Pure: removed obsolete 'exported' attribute; * Pure: dummy pattern "_" in is/let is now automatically lifted over bound variables: "ALL x. P x --> Q x" (is "ALL x. _ --> ?C x") supersedes more cumbersome ... (is "ALL x. _ x --> ?C x"); * Pure: method 'atomize' presents local goal premises as object-level statements (atomic meta-level propositions); setup controlled via rewrite rules declarations of 'atomize' attribute; example application: 'induct' method with proper rule statements in improper proof *scripts*; * Pure: emulation of instantiation tactics (rule_tac, cut_tac, etc.) now consider the syntactic context of assumptions, giving a better chance to get type-inference of the arguments right (this is especially important for locales); * Pure: "sorry" no longer requires quick_and_dirty in interactive mode; * Pure/obtain: the formal conclusion "thesis", being marked as ``internal'', may no longer be reference directly in the text; potential INCOMPATIBILITY, may need to use "?thesis" in rare situations; * Pure: generic 'sym' attribute which declares a rule both as pure 'elim?' and for the 'symmetric' operation; * Pure: marginal comments ``--'' may now occur just anywhere in the text; the fixed correlation with particular command syntax has been discontinued; * Pure: new method 'rules' is particularly well-suited for proof search in intuitionistic logic; a bit slower than 'blast' or 'fast', but often produces more compact proof terms with less detours; * Pure/Provers/classical: simplified integration with pure rule attributes and methods; the classical "intro?/elim?/dest?" declarations coincide with the pure ones; the "rule" method no longer includes classically swapped intros; "intro" and "elim" methods no longer pick rules from the context; also got rid of ML declarations AddXIs/AddXEs/AddXDs; all of this has some potential for INCOMPATIBILITY; * Provers/classical: attribute 'swapped' produces classical inversions of introduction rules; * Provers/simplifier: 'simplified' attribute may refer to explicit rules instead of full simplifier context; 'iff' attribute handles conditional rules; * HOL: 'typedef' now allows alternative names for Rep/Abs morphisms; * HOL: 'recdef' now fails on unfinished automated proofs, use "(permissive)" option to recover old behavior; * HOL: 'inductive' no longer features separate (collective) attributes for 'intros' (was found too confusing); * HOL: properly declared induction rules less_induct and wf_induct_rule; *** HOL *** * HOL: moved over to sane numeral syntax; the new policy is as follows: - 0 and 1 are polymorphic constants, which are defined on any numeric type (nat, int, real etc.); - 2, 3, 4, ... and -1, -2, -3, ... are polymorphic numerals, based binary representation internally; - type nat has special constructor Suc, and generally prefers Suc 0 over 1::nat and Suc (Suc 0) over 2::nat; This change may cause significant problems of INCOMPATIBILITY; here are some hints on converting existing sources: - due to the new "num" token, "-0" and "-1" etc. are now atomic entities, so expressions involving "-" (unary or binary minus) need to be spaced properly; - existing occurrences of "1" may need to be constraint "1::nat" or even replaced by Suc 0; similar for old "2"; - replace "#nnn" by "nnn", and "#-nnn" by "-nnn"; - remove all special provisions on numerals in proofs; * HOL: simp rules nat_number expand numerals on nat to Suc/0 representation (depends on bin_arith_simps in the default context); * HOL: symbolic syntax for x^2 (numeral 2); * HOL: the class of all HOL types is now called "type" rather than "term"; INCOMPATIBILITY, need to adapt references to this type class in axclass/classes, instance/arities, and (usually rare) occurrences in typings (of consts etc.); internally the class is called "HOL.type", ML programs should refer to HOLogic.typeS; * HOL/record package improvements: - new derived operations "fields" to build a partial record section, "extend" to promote a fixed record to a record scheme, and "truncate" for the reverse; cf. theorems "xxx.defs", which are *not* declared as simp by default; - shared operations ("more", "fields", etc.) now need to be always qualified) --- potential INCOMPATIBILITY; - removed "make_scheme" operations (use "make" with "extend") -- INCOMPATIBILITY; - removed "more" class (simply use "term") -- INCOMPATIBILITY; - provides cases/induct rules for use with corresponding Isar methods (for concrete records, record schemes, concrete more parts, and schematic more parts -- in that order); - internal definitions directly based on a light-weight abstract theory of product types over typedef rather than datatype; * HOL: generic code generator for generating executable ML code from specifications; specific support for HOL constructs such as inductive datatypes and sets, as well as recursive functions; can be invoked via 'generate_code' theory section; * HOL: canonical cases/induct rules for n-tuples (n = 3..7); * HOL: consolidated and renamed several theories. In particular: Ord.thy has been absorbed into HOL.thy String.thy has been absorbed into List.thy * HOL: concrete setsum syntax "\<Sum>i:A. b" == "setsum (%i. b) A" (beware of argument permutation!); * HOL: linorder_less_split superseded by linorder_cases; * HOL/List: "nodups" renamed to "distinct"; * HOL: added "The" definite description operator; move Hilbert's "Eps" to peripheral theory "Hilbert_Choice"; some INCOMPATIBILITIES: - Ex_def has changed, now need to use some_eq_ex * HOL: made split_all_tac safe; EXISTING PROOFS MAY FAIL OR LOOP, so in this (rare) case use: delSWrapper "split_all_tac" addSbefore ("unsafe_split_all_tac", unsafe_split_all_tac) * HOL: added safe wrapper "split_conv_tac" to claset; EXISTING PROOFS MAY FAIL; * HOL: introduced f^n = f o ... o f; warning: due to the limits of Isabelle's type classes, ^ on functions and relations has too general a domain, namely ('a * 'b) set and 'a => 'b; this means that it may be necessary to attach explicit type constraints; * HOL/Relation: the prefix name of the infix "O" has been changed from "comp" to "rel_comp"; INCOMPATIBILITY: a few theorems have been renamed accordingly (eg "compI" -> "rel_compI"). * HOL: syntax translations now work properly with numerals and records expressions; * HOL: bounded abstraction now uses syntax "%" / "\<lambda>" instead of "lam" -- INCOMPATIBILITY; * HOL: got rid of some global declarations (potential INCOMPATIBILITY for ML tools): const "()" renamed "Product_Type.Unity", type "unit" renamed "Product_Type.unit"; * HOL: renamed rtrancl_into_rtrancl2 to converse_rtrancl_into_rtrancl * HOL: removed obsolete theorem "optionE" (use "option.exhaust", or the "cases" method); * HOL/GroupTheory: group theory examples including Sylow's theorem (by Florian Kammüller); * HOL/IMP: updated and converted to new-style theory format; several parts turned into readable document, with proper Isar proof texts and some explanations (by Gerwin Klein); * HOL-Real: added Complex_Numbers (by Gertrud Bauer); * HOL-Hyperreal is now a logic image; *** HOLCF *** * Isar: consts/constdefs supports mixfix syntax for continuous operations; * Isar: domain package adapted to new-style theory format, e.g. see HOLCF/ex/Dnat.thy; * theory Lift: proper use of rep_datatype lift instead of ML hacks -- potential INCOMPATIBILITY; now use plain induct_tac instead of former lift.induct_tac, always use UU instead of Undef; * HOLCF/IMP: updated and converted to new-style theory; *** ZF *** * Isar: proper integration of logic-specific tools and packages, including theory commands '(co)inductive', '(co)datatype', 'rep_datatype', 'inductive_cases', as well as methods 'ind_cases', 'induct_tac', 'case_tac', and 'typecheck' (with attribute 'TC'); * theory Main no longer includes AC; for the Axiom of Choice, base your theory on Main_ZFC; * the integer library now covers quotients and remainders, with many laws relating division to addition, multiplication, etc.; * ZF/UNITY: Chandy and Misra's UNITY is now available in ZF, giving a typeless version of the formalism; * ZF/AC, Coind, IMP, Resid: updated and converted to new-style theory format; * ZF/Induct: new directory for examples of inductive definitions, including theory Multiset for multiset orderings; converted to new-style theory format; * ZF: many new theorems about lists, ordinals, etc.; *** General *** * Pure/kernel: meta-level proof terms (by Stefan Berghofer); reference variable proof controls level of detail: 0 = no proofs (only oracle dependencies), 1 = lemma dependencies, 2 = compact proof terms; see also ref manual for further ML interfaces; * Pure/axclass: removed obsolete ML interface goal_subclass/goal_arity; * Pure/syntax: new token syntax "num" for plain numerals (without "#" of "xnum"); potential INCOMPATIBILITY, since -0, -1 etc. are now separate tokens, so expressions involving minus need to be spaced properly; * Pure/syntax: support non-oriented infixes, using keyword "infix" rather than "infixl" or "infixr"; * Pure/syntax: concrete syntax for dummy type variables admits genuine sort constraint specifications in type inference; e.g. "x::_::foo" ensures that the type of "x" is of sort "foo" (but not necessarily a type variable); * Pure/syntax: print modes "type_brackets" and "no_type_brackets" control output of nested => (types); the default behavior is "type_brackets"; * Pure/syntax: builtin parse translation for "_constify" turns valued tokens into AST constants; * Pure/syntax: prefer later declarations of translations and print translation functions; potential INCOMPATIBILITY: need to reverse multiple declarations for same syntax element constant; * Pure/show_hyps reset by default (in accordance to existing Isar practice); * Provers/classical: renamed addaltern to addafter, addSaltern to addSafter; * Provers/clasimp: ``iff'' declarations now handle conditional rules as well; * system: tested support for MacOS X; should be able to get Isabelle + Proof General to work in a plain Terminal after installing Poly/ML (e.g. from the Isabelle distribution area) and GNU bash alone (e.g. from http://www.apple.com); full X11, XEmacs and X-Symbol support requires further installations, e.g. from http://fink.sourceforge.net/); * system: support Poly/ML 4.1.1 (able to manage larger heaps); * system: reduced base memory usage by Poly/ML (approx. 20 MB instead of 40 MB), cf. ML_OPTIONS; * system: Proof General keywords specification is now part of the Isabelle distribution (see etc/isar-keywords.el); * system: support for persistent Proof General sessions (refrain from outdating all loaded theories on startup); user may create writable logic images like this: ``isabelle -q HOL Test''; * system: smart selection of Isabelle process versus Isabelle interface, accommodates case-insensitive file systems (e.g. HFS+); may run both "isabelle" and "Isabelle" even if file names are badly damaged (executable inspects the case of the first letter of its own name); added separate "isabelle-process" and "isabelle-interface"; * system: refrain from any attempt at filtering input streams; no longer support ``8bit'' encoding of old isabelle font, instead proper iso-latin characters may now be used; the related isatools "symbolinput" and "nonascii" have disappeared as well; * system: removed old "xterm" interface (the print modes "xterm" and "xterm_color" are still available for direct use in a suitable terminal); New in Isabelle99-2 (February 2001) ----------------------------------- *** Overview of INCOMPATIBILITIES *** * HOL: please note that theories in the Library and elsewhere often use the new-style (Isar) format; to refer to their theorems in an ML script you must bind them to ML identifers by e.g. val thm_name = thm "thm_name"; * HOL: inductive package no longer splits induction rule aggressively, but only as far as specified by the introductions given; the old format may be recovered via ML function complete_split_rule or attribute 'split_rule (complete)'; * HOL: induct renamed to lfp_induct, lfp_Tarski to lfp_unfold, gfp_Tarski to gfp_unfold; * HOL: contrapos, contrapos2 renamed to contrapos_nn, contrapos_pp; * HOL: infix "dvd" now has priority 50 rather than 70 (because it is a relation); infix "^^" has been renamed "``"; infix "``" has been renamed "`"; "univalent" has been renamed "single_valued"; * HOL/Real: "rinv" and "hrinv" replaced by overloaded "inverse" operation; * HOLCF: infix "`" has been renamed "$"; the symbol syntax is \<cdot>; * Isar: 'obtain' no longer declares "that" fact as simp/intro; * Isar/HOL: method 'induct' now handles non-atomic goals; as a consequence, it is no longer monotonic wrt. the local goal context (which is now passed through the inductive cases); * Document preparation: renamed standard symbols \<ll> to \<lless> and \<gg> to \<ggreater>; *** Document preparation *** * \isabellestyle{NAME} selects version of Isabelle output (currently available: are "it" for near math-mode best-style output, "sl" for slanted text style, and "tt" for plain type-writer; if no \isabellestyle command is given, output is according to slanted type-writer); * support sub/super scripts (for single symbols only), input syntax is like this: "A\<^sup>*" or "A\<^sup>\<star>"; * some more standard symbols; see Appendix A of the system manual for the complete list of symbols defined in isabellesym.sty; * improved isabelle style files; more abstract symbol implementation (should now use \isamath{...} and \isatext{...} in custom symbol definitions); * antiquotation @{goals} and @{subgoals} for output of *dynamic* goals state; Note that presentation of goal states does not conform to actual human-readable proof documents. Please do not include goal states into document output unless you really know what you are doing! * proper indentation of antiquoted output with proportional LaTeX fonts; * no_document ML operator temporarily disables LaTeX document generation; * isatool unsymbolize tunes sources for plain ASCII communication; *** Isar *** * Pure: Isar now suffers initial goal statements to contain unbound schematic variables (this does not conform to actual readable proof documents, due to unpredictable outcome and non-compositional proof checking); users who know what they are doing may use schematic goals for Prolog-style synthesis of proven results; * Pure: assumption method (an implicit finishing) now handles actual rules as well; * Pure: improved 'obtain' --- moved to Pure, insert "that" into initial goal, declare "that" only as Pure intro (only for single steps); the "that" rule assumption may now be involved in implicit finishing, thus ".." becomes a feasible for trivial obtains; * Pure: default proof step now includes 'intro_classes'; thus trivial instance proofs may be performed by ".."; * Pure: ?thesis / ?this / "..." now work for pure meta-level statements as well; * Pure: more robust selection of calculational rules; * Pure: the builtin notion of 'finished' goal now includes the ==-refl rule (as well as the assumption rule); * Pure: 'thm_deps' command visualizes dependencies of theorems and lemmas, using the graph browser tool; * Pure: predict failure of "show" in interactive mode; * Pure: 'thms_containing' now takes actual terms as arguments; * HOL: improved method 'induct' --- now handles non-atomic goals (potential INCOMPATIBILITY); tuned error handling; * HOL: cases and induct rules now provide explicit hints about the number of facts to be consumed (0 for "type" and 1 for "set" rules); any remaining facts are inserted into the goal verbatim; * HOL: local contexts (aka cases) may now contain term bindings as well; the 'cases' and 'induct' methods new provide a ?case binding for the result to be shown in each case; * HOL: added 'recdef_tc' command; * isatool convert assists in eliminating legacy ML scripts; *** HOL *** * HOL/Library: a collection of generic theories to be used together with main HOL; the theory loader path already includes this directory by default; the following existing theories have been moved here: HOL/Induct/Multiset, HOL/Induct/Acc (as Accessible_Part), HOL/While (as While_Combinator), HOL/Lex/Prefix (as List_Prefix); * HOL/Unix: "Some aspects of Unix file-system security", a typical modelling and verification task performed in Isabelle/HOL + Isabelle/Isar + Isabelle document preparation (by Markus Wenzel). * HOL/Algebra: special summation operator SUM no longer exists, it has been replaced by setsum; infix 'assoc' now has priority 50 (like 'dvd'); axiom 'one_not_zero' has been moved from axclass 'ring' to 'domain', this makes the theory consistent with mathematical literature; * HOL basics: added overloaded operations "inverse" and "divide" (infix "/"), syntax for generic "abs" operation, generic summation operator \<Sum>; * HOL/typedef: simplified package, provide more useful rules (see also HOL/subset.thy); * HOL/datatype: induction rule for arbitrarily branching datatypes is now expressed as a proper nested rule (old-style tactic scripts may require atomize_strip_tac to cope with non-atomic premises); * HOL: renamed theory "Prod" to "Product_Type", renamed "split" rule to "split_conv" (old name still available for compatibility); * HOL: improved concrete syntax for strings (e.g. allows translation rules with string literals); * HOL-Real-Hyperreal: this extends HOL-Real with the hyperreals and Fleuriot's mechanization of analysis, including the transcendental functions for the reals; * HOL/Real, HOL/Hyperreal: improved arithmetic simplification; *** CTT *** * CTT: x-symbol support for Pi, Sigma, -->, : (membership); note that "lam" is displayed as TWO lambda-symbols * CTT: theory Main now available, containing everything (that is, Bool and Arith); *** General *** * Pure: the Simplifier has been implemented properly as a derived rule outside of the actual kernel (at last!); the overall performance penalty in practical applications is about 50%, while reliability of the Isabelle inference kernel has been greatly improved; * print modes "brackets" and "no_brackets" control output of nested => (types) and ==> (props); the default behaviour is "brackets"; * Provers: fast_tac (and friends) now handle actual object-logic rules as assumptions as well; * system: support Poly/ML 4.0; * system: isatool install handles KDE version 1 or 2; New in Isabelle99-1 (October 2000) ---------------------------------- *** Overview of INCOMPATIBILITIES *** * HOL: simplification of natural numbers is much changed; to partly recover the old behaviour (e.g. to prevent n+n rewriting to #2*n) issue the following ML commands: Delsimprocs Nat_Numeral_Simprocs.cancel_numerals; Delsimprocs [Nat_Numeral_Simprocs.combine_numerals]; * HOL: simplification no longer dives into case-expressions; this is controlled by "t.weak_case_cong" for each datatype t; * HOL: nat_less_induct renamed to less_induct; * HOL: systematic renaming of the SOME (Eps) rules, may use isatool fixsome to patch .thy and .ML sources automatically; select_equality -> some_equality select_eq_Ex -> some_eq_ex selectI2EX -> someI2_ex selectI2 -> someI2 selectI -> someI select1_equality -> some1_equality Eps_sym_eq -> some_sym_eq_trivial Eps_eq -> some_eq_trivial * HOL: exhaust_tac on datatypes superceded by new generic case_tac; * HOL: removed obsolete theorem binding expand_if (refer to split_if instead); * HOL: the recursion equations generated by 'recdef' are now called f.simps instead of f.rules; * HOL: qed_spec_mp now also handles bounded ALL as well; * HOL: 0 is now overloaded, so the type constraint ":: nat" may sometimes be needed; * HOL: the constant for "f``x" is now "image" rather than "op ``"; * HOL: the constant for "f-``x" is now "vimage" rather than "op -``"; * HOL: the disjoint sum is now "<+>" instead of "Plus"; the cartesian product is now "<*>" instead of "Times"; the lexicographic product is now "<*lex*>" instead of "**"; * HOL: theory Sexp is now in HOL/Induct examples (it used to be part of main HOL, but was unused); better use HOL's datatype package; * HOL: removed "symbols" syntax for constant "override" of theory Map; the old syntax may be recovered as follows: syntax (symbols) override :: "('a ~=> 'b) => ('a ~=> 'b) => ('a ~=> 'b)" (infixl "\\<oplus>" 100) * HOL/Real: "rabs" replaced by overloaded "abs" function; * HOL/ML: even fewer consts are declared as global (see theories Ord, Lfp, Gfp, WF); this only affects ML packages that refer to const names internally; * HOL and ZF: syntax for quotienting wrt an equivalence relation changed from A/r to A//r; * ZF: new treatment of arithmetic (nat & int) may break some old proofs; * Isar: renamed some attributes (RS -> THEN, simplify -> simplified, rulify -> rule_format, elimify -> elim_format, ...); * Isar/Provers: intro/elim/dest attributes changed; renamed intro/intro!/intro!! flags to intro!/intro/intro? (in most cases, one should have to change intro!! to intro? only); replaced "delrule" by "rule del"; * Isar/HOL: renamed "intrs" to "intros" in inductive definitions; * Provers: strengthened force_tac by using new first_best_tac; * LaTeX document preparation: several changes of isabelle.sty (see lib/texinputs); *** Document preparation *** * formal comments (text blocks etc.) in new-style theories may now contain antiquotations of thm/prop/term/typ/text to be presented according to latex print mode; concrete syntax is like this: @{term[show_types] "f(x) = a + x"}; * isatool mkdir provides easy setup of Isabelle session directories, including proper document sources; * generated LaTeX sources are now deleted after successful run (isatool document -c); may retain a copy somewhere else via -D option of isatool usedir; * isatool usedir -D now lets isatool latex -o sty update the Isabelle style files, achieving self-contained LaTeX sources and simplifying LaTeX debugging; * old-style theories now produce (crude) LaTeX output as well; * browser info session directories are now self-contained (may be put on WWW server seperately); improved graphs of nested sessions; removed graph for 'all sessions'; * several improvements in isabelle style files; \isabellestyle{it} produces fake math mode output; \isamarkupheader is now \section by default; see lib/texinputs/isabelle.sty etc.; *** Isar *** * Isar/Pure: local results and corresponding term bindings are now subject to Hindley-Milner polymorphism (similar to ML); this accommodates incremental type-inference very nicely; * Isar/Pure: new derived language element 'obtain' supports generalized existence reasoning; * Isar/Pure: new calculational elements 'moreover' and 'ultimately' support accumulation of results, without applying any rules yet; useful to collect intermediate results without explicit name references, and for use with transitivity rules with more than 2 premises; * Isar/Pure: scalable support for case-analysis type proofs: new 'case' language element refers to local contexts symbolically, as produced by certain proof methods; internally, case names are attached to theorems as "tags"; * Isar/Pure: theory command 'hide' removes declarations from class/type/const name spaces; * Isar/Pure: theory command 'defs' supports option "(overloaded)" to indicate potential overloading; * Isar/Pure: changed syntax of local blocks from {{ }} to { }; * Isar/Pure: syntax of sorts made 'inner', i.e. have to write "{a,b,c}" instead of {a,b,c}; * Isar/Pure now provides its own version of intro/elim/dest attributes; useful for building new logics, but beware of confusion with the version in Provers/classical; * Isar/Pure: the local context of (non-atomic) goals is provided via case name 'antecedent'; * Isar/Pure: removed obsolete 'transfer' attribute (transfer of thms to the current context is now done automatically); * Isar/Pure: theory command 'method_setup' provides a simple interface for definining proof methods in ML; * Isar/Provers: intro/elim/dest attributes changed; renamed intro/intro!/intro!! flags to intro!/intro/intro? (INCOMPATIBILITY, in most cases, one should have to change intro!! to intro? only); replaced "delrule" by "rule del"; * Isar/Provers: new 'hypsubst' method, plain 'subst' method and 'symmetric' attribute (the latter supercedes [RS sym]); * Isar/Provers: splitter support (via 'split' attribute and 'simp' method modifier); 'simp' method: 'only:' modifier removes loopers as well (including splits); * Isar/Provers: Simplifier and Classical methods now support all kind of modifiers used in the past, including 'cong', 'iff', etc. * Isar/Provers: added 'fastsimp' and 'clarsimp' methods (combination of Simplifier and Classical reasoner); * Isar/HOL: new proof method 'cases' and improved version of 'induct' now support named cases; major packages (inductive, datatype, primrec, recdef) support case names and properly name parameters; * Isar/HOL: new transitivity rules for substitution in inequalities -- monotonicity conditions are extracted to be proven at end of calculations; * Isar/HOL: removed 'case_split' thm binding, should use 'cases' proof method anyway; * Isar/HOL: removed old expand_if = split_if; theorems if_splits = split_if split_if_asm; datatype package provides theorems foo.splits = foo.split foo.split_asm for each datatype; * Isar/HOL: tuned inductive package, rename "intrs" to "intros" (potential INCOMPATIBILITY), emulation of mk_cases feature for proof scripts: new 'inductive_cases' command and 'ind_cases' method; (Note: use "(cases (simplified))" method in proper proof texts); * Isar/HOL: added global 'arith_split' attribute for 'arith' method; * Isar: names of theorems etc. may be natural numbers as well; * Isar: 'pr' command: optional arguments for goals_limit and ProofContext.prems_limit; no longer prints theory contexts, but only proof states; * Isar: diagnostic commands 'pr', 'thm', 'prop', 'term', 'typ' admit additional print modes to be specified; e.g. "pr(latex)" will print proof state according to the Isabelle LaTeX style; * Isar: improved support for emulating tactic scripts, including proof methods 'rule_tac' etc., 'cut_tac', 'thin_tac', 'subgoal_tac', 'rename_tac', 'rotate_tac', 'tactic', and 'case_tac' / 'induct_tac' (for HOL datatypes); * Isar: simplified (more robust) goal selection of proof methods: 1st goal, all goals, or explicit goal specifier (tactic emulation); thus 'proof method scripts' have to be in depth-first order; * Isar: tuned 'let' syntax: replaced 'as' keyword by 'and'; * Isar: removed 'help' command, which hasn't been too helpful anyway; should instead use individual commands for printing items (print_commands, print_methods etc.); * Isar: added 'nothing' --- the empty list of theorems; *** HOL *** * HOL/MicroJava: formalization of a fragment of Java, together with a corresponding virtual machine and a specification of its bytecode verifier and a lightweight bytecode verifier, including proofs of type-safety; by Gerwin Klein, Tobias Nipkow, David von Oheimb, and Cornelia Pusch (see also the homepage of project Bali at http://isabelle.in.tum.de/Bali/); * HOL/Algebra: new theory of rings and univariate polynomials, by Clemens Ballarin; * HOL/NumberTheory: fundamental Theorem of Arithmetic, Chinese Remainder Theorem, Fermat/Euler Theorem, Wilson's Theorem, by Thomas M Rasmussen; * HOL/Lattice: fundamental concepts of lattice theory and order structures, including duals, properties of bounds versus algebraic laws, lattice operations versus set-theoretic ones, the Knaster-Tarski Theorem for complete lattices etc.; may also serve as a demonstration for abstract algebraic reasoning using axiomatic type classes, and mathematics-style proof in Isabelle/Isar; by Markus Wenzel; * HOL/Prolog: a (bare-bones) implementation of Lambda-Prolog, by David von Oheimb; * HOL/IMPP: extension of IMP with local variables and mutually recursive procedures, by David von Oheimb; * HOL/Lambda: converted into new-style theory and document; * HOL/ex/Multiquote: example of multiple nested quotations and anti-quotations -- basically a generalized version of de-Bruijn representation; very useful in avoiding lifting of operations; * HOL/record: added general record equality rule to simpset; fixed select-update simplification procedure to handle extended records as well; admit "r" as field name; * HOL: 0 is now overloaded over the new sort "zero", allowing its use with other numeric types and also as the identity of groups, rings, etc.; * HOL: new axclass plus_ac0 for addition with the AC-laws and 0 as identity. Types nat and int belong to this axclass; * HOL: greatly improved simplification involving numerals of type nat, int, real: (i + #8 + j) = Suc k simplifies to #7 + (i + j) = k i*j + k + j*#3*i simplifies to #4*(i*j) + k two terms #m*u and #n*u are replaced by #(m+n)*u (where #m, #n and u can implicitly be 1; this is simproc combine_numerals) and the term/formula #m*u+x ~~ #n*u+y simplifies simplifies to #(m-n)+x ~~ y or x ~~ #(n-m)+y, where ~~ is one of = < <= or - (simproc cancel_numerals); * HOL: meson_tac is available (previously in ex/meson.ML); it is a powerful prover for predicate logic but knows nothing of clasets; see ex/mesontest.ML and ex/mesontest2.ML for example applications; * HOL: new version of "case_tac" subsumes both boolean case split and "exhaust_tac" on datatypes; INCOMPATIBILITY: exhaust_tac no longer exists, may define val exhaust_tac = case_tac for ad-hoc portability; * HOL: simplification no longer dives into case-expressions: only the selector expression is simplified, but not the remaining arms; to enable full simplification of case-expressions for datatype t, you may remove t.weak_case_cong from the simpset, either globally (Delcongs [thm"t.weak_case_cong"];) or locally (delcongs [...]). * HOL/recdef: the recursion equations generated by 'recdef' for function 'f' are now called f.simps instead of f.rules; if all termination conditions are proved automatically, these simplification rules are added to the simpset, as in primrec; rules may be named individually as well, resulting in a separate list of theorems for each equation; * HOL/While is a new theory that provides a while-combinator. It permits the definition of tail-recursive functions without the provision of a termination measure. The latter is necessary once the invariant proof rule for while is applied. * HOL: new (overloaded) notation for the set of elements below/above some element: {..u}, {..u(}, {l..}, {)l..}. See theory SetInterval. * HOL: theorems impI, allI, ballI bound as "strip"; * HOL: new tactic induct_thm_tac: thm -> string -> int -> tactic induct_tac th "x1 ... xn" expects th to have a conclusion of the form P v1 ... vn and abbreviates res_inst_tac [("v1","x1"),...,("vn","xn")] th; * HOL/Real: "rabs" replaced by overloaded "abs" function; * HOL: theory Sexp now in HOL/Induct examples (it used to be part of main HOL, but was unused); * HOL: fewer consts declared as global (e.g. have to refer to "Lfp.lfp" instead of "lfp" internally; affects ML packages only); * HOL: tuned AST representation of nested pairs, avoiding bogus output in case of overlap with user translations (e.g. judgements over tuples); (note that the underlying logical represenation is still bogus); *** ZF *** * ZF: simplification automatically cancels common terms in arithmetic expressions over nat and int; * ZF: new treatment of nat to minimize type-checking: all operators coerce their operands to a natural number using the function natify, making the algebraic laws unconditional; * ZF: as above, for int: operators coerce their operands to an integer using the function intify; * ZF: the integer library now contains many of the usual laws for the orderings, including $<=, and monotonicity laws for $+ and $*; * ZF: new example ZF/ex/NatSum to demonstrate integer arithmetic simplification; * FOL and ZF: AddIffs now available, giving theorems of the form P<->Q to the simplifier and classical reasoner simultaneously; *** General *** * Provers: blast_tac now handles actual object-logic rules as assumptions; note that auto_tac uses blast_tac internally as well; * Provers: new functions rulify/rulify_no_asm: thm -> thm for turning outer -->/All/Ball into ==>/!!; qed_spec_mp now uses rulify_no_asm; * Provers: delrules now handles destruct rules as well (no longer need explicit make_elim); * Provers: Blast_tac now warns of and ignores "weak elimination rules" e.g. [| inj ?f; ?f ?x = ?f ?y; ?x = ?y ==> ?W |] ==> ?W use instead the strong form, [| inj ?f; ~ ?W ==> ?f ?x = ?f ?y; ?x = ?y ==> ?W |] ==> ?W in HOL, FOL and ZF the function cla_make_elim will create such rules from destruct-rules; * Provers: Simplifier.easy_setup provides a fast path to basic Simplifier setup for new object-logics; * Pure: AST translation rules no longer require constant head on LHS; * Pure: improved name spaces: ambiguous output is qualified; support for hiding of names; * system: smart setup of canonical ML_HOME, ISABELLE_INTERFACE, and XSYMBOL_HOME; no longer need to do manual configuration in most situations; * system: compression of ML heaps images may now be controlled via -c option of isabelle and isatool usedir (currently only observed by Poly/ML); * system: isatool installfonts may handle X-Symbol fonts as well (very useful for remote X11); * system: provide TAGS file for Isabelle sources; * ML: infix 'OF' is a version of 'MRS' with more appropriate argument order; * ML: renamed flags Syntax.trace_norm_ast to Syntax.trace_ast; global timing flag supersedes proof_timing and Toplevel.trace; * ML: new combinators |>> and |>>> for incremental transformations with secondary results (e.g. certain theory extensions): * ML: PureThy.add_defs gets additional argument to indicate potential overloading (usually false); * ML: PureThy.add_thms/add_axioms/add_defs now return theorems as results; New in Isabelle99 (October 1999) -------------------------------- *** Overview of INCOMPATIBILITIES (see below for more details) *** * HOL: The THEN and ELSE parts of conditional expressions (if P then x else y) are no longer simplified. (This allows the simplifier to unfold recursive functional programs.) To restore the old behaviour, declare Delcongs [if_weak_cong]; * HOL: Removed the obsolete syntax "Compl A"; use -A for set complement; * HOL: the predicate "inj" is now defined by translation to "inj_on"; * HOL/datatype: mutual_induct_tac no longer exists -- use induct_tac "x_1 ... x_n" instead of mutual_induct_tac ["x_1", ..., "x_n"] * HOL/typedef: fixed type inference for representing set; type arguments now have to occur explicitly on the rhs as type constraints; * ZF: The con_defs part of an inductive definition may no longer refer to constants declared in the same theory; * HOL, ZF: the function mk_cases, generated by the inductive definition package, has lost an argument. To simplify its result, it uses the default simpset instead of a supplied list of theorems. * HOL/List: the constructors of type list are now Nil and Cons; * Simplifier: the type of the infix ML functions setSSolver addSSolver setSolver addSolver is now simpset * solver -> simpset where `solver' is a new abstract type for packaging solvers. A solver is created via mk_solver: string -> (thm list -> int -> tactic) -> solver where the string argument is only a comment. *** Proof tools *** * Provers/Arith/fast_lin_arith.ML contains a functor for creating a decision procedure for linear arithmetic. Currently it is used for types `nat', `int', and `real' in HOL (see below); it can, should and will be instantiated for other types and logics as well. * The simplifier now accepts rewrite rules with flexible heads, eg hom ?f ==> ?f(?x+?y) = ?f ?x + ?f ?y They are applied like any rule with a non-pattern lhs, i.e. by first-order matching. *** General *** * New Isabelle/Isar subsystem provides an alternative to traditional tactical theorem proving; together with the ProofGeneral/isar user interface it offers an interactive environment for developing human readable proof documents (Isar == Intelligible semi-automated reasoning); for further information see isatool doc isar-ref, src/HOL/Isar_examples and http://isabelle.in.tum.de/Isar/ * improved and simplified presentation of theories: better HTML markup (including colors), graph views in several sizes; isatool usedir now provides a proper interface for user theories (via -P option); actual document preparation based on (PDF)LaTeX is available as well (for new-style theories only); see isatool doc system for more information; * native support for Proof General, both for classic Isabelle and Isabelle/Isar; * ML function thm_deps visualizes dependencies of theorems and lemmas, using the graph browser tool; * Isabelle manuals now also available as PDF; * theory loader rewritten from scratch (may not be fully bug-compatible); old loadpath variable has been replaced by show_path, add_path, del_path, reset_path functions; new operations such as update_thy, touch_thy, remove_thy, use/update_thy_only (see also isatool doc ref); * improved isatool install: option -k creates KDE application icon, option -p DIR installs standalone binaries; * added ML_PLATFORM setting (useful for cross-platform installations); more robust handling of platform specific ML images for SML/NJ; * the settings environment is now statically scoped, i.e. it is never created again in sub-processes invoked from isabelle, isatool, or Isabelle; * path element specification '~~' refers to '$ISABELLE_HOME'; * in locales, the "assumes" and "defines" parts may be omitted if empty; * new print_mode "xsymbols" for extended symbol support (e.g. genuine long arrows); * new print_mode "HTML"; * new flag show_tags controls display of tags of theorems (which are basically just comments that may be attached by some tools); * Isamode 2.6 requires patch to accomodate change of Isabelle font mode and goal output format: diff -r Isamode-2.6/elisp/isa-load.el Isamode/elisp/isa-load.el 244c244 < (list (isa-getenv "ISABELLE") "-msymbols" logic-name) --- > (list (isa-getenv "ISABELLE") "-misabelle_font" "-msymbols" logic-name) diff -r Isabelle-2.6/elisp/isa-proofstate.el Isamode/elisp/isa-proofstate.el 181c181 < (defconst proofstate-proofstart-regexp "^Level [0-9]+$" --- > (defconst proofstate-proofstart-regexp "^Level [0-9]+" * function bind_thms stores lists of theorems (cf. bind_thm); * new shorthand tactics ftac, eatac, datac, fatac; * qed (and friends) now accept "" as result name; in that case the theorem is not stored, but proper checks and presentation of the result still apply; * theorem database now also indexes constants "Trueprop", "all", "==>", "=="; thus thms_containing, findI etc. may retrieve more rules; *** HOL *** ** HOL arithmetic ** * There are now decision procedures for linear arithmetic over nat and int: 1. arith_tac copes with arbitrary formulae involving `=', `<', `<=', `+', `-', `Suc', `min', `max' and numerical constants; other subterms are treated as atomic; subformulae not involving type `nat' or `int' are ignored; quantified subformulae are ignored unless they are positive universal or negative existential. The tactic has to be invoked by hand and can be a little bit slow. In particular, the running time is exponential in the number of occurrences of `min' and `max', and `-' on `nat'. 2. fast_arith_tac is a cut-down version of arith_tac: it only takes (negated) (in)equalities among the premises and the conclusion into account (i.e. no compound formulae) and does not know about `min' and `max', and `-' on `nat'. It is fast and is used automatically by the simplifier. NB: At the moment, these decision procedures do not cope with mixed nat/int formulae where the two parts interact, such as `m < n ==> int(m) < int(n)'. * HOL/Numeral provides a generic theory of numerals (encoded efficiently as bit strings); setup for types nat/int/real is in place; INCOMPATIBILITY: since numeral syntax is now polymorphic, rather than int, existing theories and proof scripts may require a few additional type constraints; * integer division and remainder can now be performed on constant arguments; * many properties of integer multiplication, division and remainder are now available; * An interface to the Stanford Validity Checker (SVC) is available through the tactic svc_tac. Propositional tautologies and theorems of linear arithmetic are proved automatically. SVC must be installed separately, and its results must be TAKEN ON TRUST (Isabelle does not check the proofs, but tags any invocation of the underlying oracle). For SVC see http://verify.stanford.edu/SVC * IsaMakefile: the HOL-Real target now builds an actual image; ** HOL misc ** * HOL/Real/HahnBanach: the Hahn-Banach theorem for real vector spaces (in Isabelle/Isar) -- by Gertrud Bauer; * HOL/BCV: generic model of bytecode verification, i.e. data-flow analysis for assembly languages with subtypes; * HOL/TLA (Lamport's Temporal Logic of Actions): major reorganization -- avoids syntactic ambiguities and treats state, transition, and temporal levels more uniformly; introduces INCOMPATIBILITIES due to changed syntax and (many) tactics; * HOL/inductive: Now also handles more general introduction rules such as "ALL y. (y, x) : r --> y : acc r ==> x : acc r"; monotonicity theorems are now maintained within the theory (maintained via the "mono" attribute); * HOL/datatype: Now also handles arbitrarily branching datatypes (using function types) such as datatype 'a tree = Atom 'a | Branch "nat => 'a tree" * HOL/record: record_simproc (part of the default simpset) takes care of selectors applied to updated records; record_split_tac is no longer part of the default claset; update_defs may now be removed from the simpset in many cases; COMPATIBILITY: old behavior achieved by claset_ref () := claset() addSWrapper record_split_wrapper; Delsimprocs [record_simproc] * HOL/typedef: fixed type inference for representing set; type arguments now have to occur explicitly on the rhs as type constraints; * HOL/recdef (TFL): 'congs' syntax now expects comma separated list of theorem names rather than an ML expression; * HOL/defer_recdef (TFL): like recdef but the well-founded relation can be supplied later. Program schemes can be defined, such as "While B C s = (if B s then While B C (C s) else s)" where the well-founded relation can be chosen after B and C have been given. * HOL/List: the constructors of type list are now Nil and Cons; INCOMPATIBILITY: while [] and infix # syntax is still there, of course, ML tools referring to List.list.op # etc. have to be adapted; * HOL_quantifiers flag superseded by "HOL" print mode, which is disabled by default; run isabelle with option -m HOL to get back to the original Gordon/HOL-style output; * HOL/Ord.thy: new bounded quantifier syntax (input only): ALL x<y. P, ALL x<=y. P, EX x<y. P, EX x<=y. P; * HOL basic syntax simplified (more orthogonal): all variants of All/Ex now support plain / symbolic / HOL notation; plain syntax for Eps operator is provided as well: "SOME x. P[x]"; * HOL/Sum.thy: sum_case has been moved to HOL/Datatype; * HOL/Univ.thy: infix syntax <*>, <+>, <**>, <+> eliminated and made thus available for user theories; * HOLCF/IOA/Sequents: renamed 'Cons' to 'Consq' to avoid clash with HOL/List; hardly an INCOMPATIBILITY since '>>' syntax is used all the time; * HOL: new tactic smp_tac: int -> int -> tactic, which applies spec several times and then mp; *** LK *** * the notation <<...>> is now available as a notation for sequences of formulas; * the simplifier is now installed * the axiom system has been generalized (thanks to Soren Heilmann) * the classical reasoner now has a default rule database *** ZF *** * new primrec section allows primitive recursive functions to be given directly (as in HOL) over datatypes and the natural numbers; * new tactics induct_tac and exhaust_tac for induction (or case analysis) over datatypes and the natural numbers; * the datatype declaration of type T now defines the recursor T_rec; * simplification automatically does freeness reasoning for datatype constructors; * automatic type-inference, with AddTCs command to insert new type-checking rules; * datatype introduction rules are now added as Safe Introduction rules to the claset; * the syntax "if P then x else y" is now available in addition to if(P,x,y); *** Internal programming interfaces *** * tuned simplifier trace output; new flag debug_simp; * structures Vartab / Termtab (instances of TableFun) offer efficient tables indexed by indexname_ord / term_ord (compatible with aconv); * AxClass.axclass_tac lost the theory argument; * tuned current_goals_markers semantics: begin / end goal avoids printing empty lines; * removed prs and prs_fn hook, which was broken because it did not include \n in its semantics, forcing writeln to add one uncoditionally; replaced prs_fn by writeln_fn; consider std_output: string -> unit if you really want to output text without newline; * Symbol.output subject to print mode; INCOMPATIBILITY: defaults to plain output, interface builders may have to enable 'isabelle_font' mode to get Isabelle font glyphs as before; * refined token_translation interface; INCOMPATIBILITY: output length now of type real instead of int; * theory loader actions may be traced via new ThyInfo.add_hook interface (see src/Pure/Thy/thy_info.ML); example application: keep your own database of information attached to *whole* theories -- as opposed to intra-theory data slots offered via TheoryDataFun; * proper handling of dangling sort hypotheses (at last!); Thm.strip_shyps and Drule.strip_shyps_warning take care of removing extra sort hypotheses that can be witnessed from the type signature; the force_strip_shyps flag is gone, any remaining shyps are simply left in the theorem (with a warning issued by strip_shyps_warning); New in Isabelle98-1 (October 1998) ---------------------------------- *** Overview of INCOMPATIBILITIES (see below for more details) *** * several changes of automated proof tools; * HOL: major changes to the inductive and datatype packages, including some minor incompatibilities of theory syntax; * HOL: renamed r^-1 to 'converse' from 'inverse'; 'inj_onto' is now called `inj_on'; * HOL: removed duplicate thms in Arith: less_imp_add_less should be replaced by trans_less_add1 le_imp_add_le should be replaced by trans_le_add1 * HOL: unary minus is now overloaded (new type constraints may be required); * HOL and ZF: unary minus for integers is now #- instead of #~. In ZF, expressions such as n#-1 must be changed to n#- 1, since #-1 is now taken as an integer constant. * Pure: ML function 'theory_of' renamed to 'theory'; *** Proof tools *** * Simplifier: 1. Asm_full_simp_tac is now more aggressive. 1. It will sometimes reorient premises if that increases their power to simplify. 2. It does no longer proceed strictly from left to right but may also rotate premises to achieve further simplification. For compatibility reasons there is now Asm_lr_simp_tac which is like the old Asm_full_simp_tac in that it does not rotate premises. 2. The simplifier now knows a little bit about nat-arithmetic. * Classical reasoner: wrapper mechanism for the classical reasoner now allows for selected deletion of wrappers, by introduction of names for wrapper functionals. This implies that addbefore, addSbefore, addaltern, and addSaltern now take a pair (name, tactic) as argument, and that adding two tactics with the same name overwrites the first one (emitting a warning). type wrapper = (int -> tactic) -> (int -> tactic) setWrapper, setSWrapper, compWrapper and compSWrapper are replaced by addWrapper, addSWrapper: claset * (string * wrapper) -> claset delWrapper, delSWrapper: claset * string -> claset getWrapper is renamed to appWrappers, getSWrapper to appSWrappers; * Classical reasoner: addbefore/addSbefore now have APPEND/ORELSE semantics; addbefore now affects only the unsafe part of step_tac etc.; this affects addss/auto_tac/force_tac, so EXISTING PROOFS MAY FAIL, but proofs should be fixable easily, e.g. by replacing Auto_tac by Force_tac; * Classical reasoner: setwrapper to setWrapper and compwrapper to compWrapper; added safe wrapper (and access functions for it); * HOL/split_all_tac is now much faster and fails if there is nothing to split. Some EXISTING PROOFS MAY REQUIRE ADAPTION because the order and the names of the automatically generated variables have changed. split_all_tac has moved within claset() from unsafe wrappers to safe wrappers, which means that !!-bound variables are split much more aggressively, and safe_tac and clarify_tac now split such variables. If this splitting is not appropriate, use delSWrapper "split_all_tac". Note: the same holds for record_split_tac, which does the job of split_all_tac for record fields. * HOL/Simplifier: Rewrite rules for case distinctions can now be added permanently to the default simpset using Addsplits just like Addsimps. They can be removed via Delsplits just like Delsimps. Lower-case versions are also available. * HOL/Simplifier: The rule split_if is now part of the default simpset. This means that the simplifier will eliminate all occurrences of if-then-else in the conclusion of a goal. To prevent this, you can either remove split_if completely from the default simpset by `Delsplits [split_if]' or remove it in a specific call of the simplifier using `... delsplits [split_if]'. You can also add/delete other case splitting rules to/from the default simpset: every datatype generates suitable rules `split_t_case' and `split_t_case_asm' (where t is the name of the datatype). * Classical reasoner / Simplifier combination: new force_tac (and derivatives Force_tac, force) combines rewriting and classical reasoning (and whatever other tools) similarly to auto_tac, but is aimed to solve the given subgoal completely. *** General *** * new top-level commands `Goal' and `Goalw' that improve upon `goal' and `goalw': the theory is no longer needed as an explicit argument - the current theory context is used; assumptions are no longer returned at the ML-level unless one of them starts with ==> or !!; it is recommended to convert to these new commands using isatool fixgoal (backup your sources first!); * new top-level commands 'thm' and 'thms' for retrieving theorems from the current theory context, and 'theory' to lookup stored theories; * new theory section 'locale' for declaring constants, assumptions and definitions that have local scope; * new theory section 'nonterminals' for purely syntactic types; * new theory section 'setup' for generic ML setup functions (e.g. package initialization); * the distribution now includes Isabelle icons: see lib/logo/isabelle-{small,tiny}.xpm; * isatool install - install binaries with absolute references to ISABELLE_HOME/bin; * isatool logo -- create instances of the Isabelle logo (as EPS); * print mode 'emacs' reserved for Isamode; * support multiple print (ast) translations per constant name; * theorems involving oracles are now printed with a suffixed [!]; *** HOL *** * there is now a tutorial on Isabelle/HOL (do 'isatool doc tutorial'); * HOL/inductive package reorganized and improved: now supports mutual definitions such as inductive EVEN ODD intrs null "0 : EVEN" oddI "n : EVEN ==> Suc n : ODD" evenI "n : ODD ==> Suc n : EVEN" new theorem list "elims" contains an elimination rule for each of the recursive sets; inductive definitions now handle disjunctive premises correctly (also ZF); INCOMPATIBILITIES: requires Inductive as an ancestor; component "mutual_induct" no longer exists - the induction rule is always contained in "induct"; * HOL/datatype package re-implemented and greatly improved: now supports mutually recursive datatypes such as datatype 'a aexp = IF_THEN_ELSE ('a bexp) ('a aexp) ('a aexp) | SUM ('a aexp) ('a aexp) | DIFF ('a aexp) ('a aexp) | NUM 'a and 'a bexp = LESS ('a aexp) ('a aexp) | AND ('a bexp) ('a bexp) | OR ('a bexp) ('a bexp) as well as indirectly recursive datatypes such as datatype ('a, 'b) term = Var 'a | App 'b ((('a, 'b) term) list) The new tactic mutual_induct_tac [<var_1>, ..., <var_n>] i performs induction on mutually / indirectly recursive datatypes. Primrec equations are now stored in theory and can be accessed via <function_name>.simps. INCOMPATIBILITIES: - Theories using datatypes must now have theory Datatype as an ancestor. - The specific <typename>.induct_tac no longer exists - use the generic induct_tac instead. - natE has been renamed to nat.exhaust - use exhaust_tac instead of res_inst_tac ... natE. Note that the variable names in nat.exhaust differ from the names in natE, this may cause some "fragile" proofs to fail. - The theorems split_<typename>_case and split_<typename>_case_asm have been renamed to <typename>.split and <typename>.split_asm. - Since default sorts of type variables are now handled correctly, some datatype definitions may have to be annotated with explicit sort constraints. - Primrec definitions no longer require function name and type of recursive argument. Consider using isatool fixdatatype to adapt your theories and proof scripts to the new package (backup your sources first!). * HOL/record package: considerably improved implementation; now includes concrete syntax for record types, terms, updates; theorems for surjective pairing and splitting !!-bound record variables; proof support is as follows: 1) standard conversions (selectors or updates applied to record constructor terms) are part of the standard simpset; 2) inject equations of the form ((x, y) = (x', y')) == x=x' & y=y' are made part of standard simpset and claset via addIffs; 3) a tactic for record field splitting (record_split_tac) is part of the standard claset (addSWrapper); To get a better idea about these rules you may retrieve them via something like 'thms "foo.simps"' or 'thms "foo.iffs"', where "foo" is the name of your record type. The split tactic 3) conceptually simplifies by the following rule: "(!!x. PROP ?P x) == (!!a b. PROP ?P (a, b))" Thus any record variable that is bound by meta-all will automatically blow up into some record constructor term, consequently the simplifications of 1), 2) apply. Thus force_tac, auto_tac etc. shall solve record problems automatically. * reorganized the main HOL image: HOL/Integ and String loaded by default; theory Main includes everything; * automatic simplification of integer sums and comparisons, using cancellation; * added option_map_eq_Some and not_Some_eq to the default simpset and claset; * added disj_not1 = "(~P | Q) = (P --> Q)" to the default simpset; * many new identities for unions, intersections, set difference, etc.; * expand_if, expand_split, expand_sum_case and expand_nat_case are now called split_if, split_split, split_sum_case and split_nat_case (to go with add/delsplits); * HOL/Prod introduces simplification procedure unit_eq_proc rewriting (?x::unit) = (); this is made part of the default simpset, which COULD MAKE EXISTING PROOFS FAIL under rare circumstances (consider 'Delsimprocs [unit_eq_proc];' as last resort); also note that unit_abs_eta_conv is added in order to counter the effect of unit_eq_proc on (%u::unit. f u), replacing it by f rather than by %u.f(); * HOL/Fun INCOMPATIBILITY: `inj_onto' is now called `inj_on' (which makes more sense); * HOL/Set INCOMPATIBILITY: rule `equals0D' is now a well-formed destruct rule; It and 'sym RS equals0D' are now in the default claset, giving automatic disjointness reasoning but breaking a few old proofs. * HOL/Relation INCOMPATIBILITY: renamed the relational operator r^-1 to 'converse' from 'inverse' (for compatibility with ZF and some literature); * HOL/recdef can now declare non-recursive functions, with {} supplied as the well-founded relation; * HOL/Set INCOMPATIBILITY: the complement of set A is now written -A instead of Compl A. The "Compl" syntax remains available as input syntax for this release ONLY. * HOL/Update: new theory of function updates: f(a:=b) == %x. if x=a then b else f x may also be iterated as in f(a:=b,c:=d,...); * HOL/Vimage: new theory for inverse image of a function, syntax f-``B; * HOL/List: - new function list_update written xs[i:=v] that updates the i-th list position. May also be iterated as in xs[i:=a,j:=b,...]. - new function `upt' written [i..j(] which generates the list [i,i+1,...,j-1], i.e. the upper bound is excluded. To include the upper bound write [i..j], which is a shorthand for [i..j+1(]. - new lexicographic orderings and corresponding wellfoundedness theorems. * HOL/Arith: - removed 'pred' (predecessor) function; - generalized some theorems about n-1; - many new laws about "div" and "mod"; - new laws about greatest common divisors (see theory ex/Primes); * HOL/Relation: renamed the relational operator r^-1 "converse" instead of "inverse"; * HOL/Induct/Multiset: a theory of multisets, including the wellfoundedness of the multiset ordering; * directory HOL/Real: a construction of the reals using Dedekind cuts (not included by default); * directory HOL/UNITY: Chandy and Misra's UNITY formalism; * directory HOL/Hoare: a new version of Hoare logic which permits many-sorted programs, i.e. different program variables may have different types. * calling (stac rew i) now fails if "rew" has no effect on the goal [previously, this check worked only if the rewrite rule was unconditional] Now rew can involve either definitions or equalities (either == or =). *** ZF *** * theory Main includes everything; INCOMPATIBILITY: theory ZF.thy contains only the theorems proved on ZF.ML; * ZF INCOMPATIBILITY: rule `equals0D' is now a well-formed destruct rule; It and 'sym RS equals0D' are now in the default claset, giving automatic disjointness reasoning but breaking a few old proofs. * ZF/Update: new theory of function updates with default rewrite rule f(x:=y) ` z = if(z=x, y, f`z) may also be iterated as in f(a:=b,c:=d,...); * in let x=t in u(x), neither t nor u(x) has to be an FOL term. * calling (stac rew i) now fails if "rew" has no effect on the goal [previously, this check worked only if the rewrite rule was unconditional] Now rew can involve either definitions or equalities (either == or =). * case_tac provided for compatibility with HOL (like the old excluded_middle_tac, but with subgoals swapped) *** Internal programming interfaces *** * Pure: several new basic modules made available for general use, see also src/Pure/README; * improved the theory data mechanism to support encapsulation (data kind name replaced by private Object.kind, acting as authorization key); new type-safe user interface via functor TheoryDataFun; generic print_data function becomes basically useless; * removed global_names compatibility flag -- all theory declarations are qualified by default; * module Pure/Syntax now offers quote / antiquote translation functions (useful for Hoare logic etc. with implicit dependencies); see HOL/ex/Antiquote for an example use; * Simplifier now offers conversions (asm_)(full_)rewrite: simpset -> cterm -> thm; * new tactical CHANGED_GOAL for checking that a tactic modifies a subgoal; * Display.print_goals function moved to Locale.print_goals; * standard print function for goals supports current_goals_markers variable for marking begin of proof, end of proof, start of goal; the default is ("", "", ""); setting current_goals_markers := ("<proof>", "</proof>", "<goal>") causes SGML like tagged proof state printing, for example; New in Isabelle98 (January 1998) -------------------------------- *** Overview of INCOMPATIBILITIES (see below for more details) *** * changed lexical syntax of terms / types: dots made part of long identifiers, e.g. "%x.x" no longer possible, should be "%x. x"; * simpset (and claset) reference variable replaced by functions simpset / simpset_ref; * no longer supports theory aliases (via merge) and non-trivial implicit merge of thms' signatures; * most internal names of constants changed due to qualified names; * changed Pure/Sequence interface (see Pure/seq.ML); *** General Changes *** * hierachically structured name spaces (for consts, types, axms, thms etc.); new lexical class 'longid' (e.g. Foo.bar.x) may render much of old input syntactically incorrect (e.g. "%x.x"); COMPATIBILITY: isatool fixdots ensures space after dots (e.g. "%x. x"); set long_names for fully qualified output names; NOTE: ML programs (special tactics, packages etc.) referring to internal names may have to be adapted to cope with fully qualified names; in case of severe backward campatibility problems try setting 'global_names' at compile time to have enrything declared within a flat name space; one may also fine tune name declarations in theories via the 'global' and 'local' section; * reimplemented the implicit simpset and claset using the new anytype data filed in signatures; references simpset:simpset ref etc. are replaced by functions simpset:unit->simpset and simpset_ref:unit->simpset ref; COMPATIBILITY: use isatool fixclasimp to patch your ML files accordingly; * HTML output now includes theory graph data for display with Java applet or isatool browser; data generated automatically via isatool usedir (see -i option, ISABELLE_USEDIR_OPTIONS); * defs may now be conditional; improved rewrite_goals_tac to handle conditional equations; * defs now admits additional type arguments, using TYPE('a) syntax; * theory aliases via merge (e.g. M=A+B+C) no longer supported, always creates a new theory node; implicit merge of thms' signatures is restricted to 'trivial' ones; COMPATIBILITY: one may have to use transfer:theory->thm->thm in (rare) cases; * improved handling of draft signatures / theories; draft thms (and ctyps, cterms) are automatically promoted to real ones; * slightly changed interfaces for oracles: admit many per theory, named (e.g. oracle foo = mlfun), additional name argument for invoke_oracle; * print_goals: optional output of const types (set show_consts and show_types); * improved output of warnings (###) and errors (***); * subgoal_tac displays a warning if the new subgoal has type variables; * removed old README and Makefiles; * replaced print_goals_ref hook by print_current_goals_fn and result_error_fn; * removed obsolete init_pps and init_database; * deleted the obsolete tactical STATE, which was declared by fun STATE tacfun st = tacfun st st; * cd and use now support path variables, e.g. $ISABELLE_HOME, or ~ (which abbreviates $HOME); * changed Pure/Sequence interface (see Pure/seq.ML); COMPATIBILITY: use isatool fixseq to adapt your ML programs (this works for fully qualified references to the Sequence structure only!); * use_thy no longer requires writable current directory; it always reloads .ML *and* .thy file, if either one is out of date; *** Classical Reasoner *** * Clarify_tac, clarify_tac, clarify_step_tac, Clarify_step_tac: new tactics that use classical reasoning to simplify a subgoal without splitting it into several subgoals; * Safe_tac: like safe_tac but uses the default claset; *** Simplifier *** * added simplification meta rules: (asm_)(full_)simplify: simpset -> thm -> thm; * simplifier.ML no longer part of Pure -- has to be loaded by object logics (again); * added prems argument to simplification procedures; * HOL, FOL, ZF: added infix function `addsplits': instead of `<simpset> setloop (split_tac <thms>)' you can simply write `<simpset> addsplits <thms>' *** Syntax *** * TYPE('a) syntax for type reflection terms; * no longer handles consts with name "" -- declare as 'syntax' instead; * pretty printer: changed order of mixfix annotation preference (again!); * Pure: fixed idt/idts vs. pttrn/pttrns syntactic categories; *** HOL *** * HOL: there is a new splitter `split_asm_tac' that can be used e.g. with `addloop' of the simplifier to faciliate case splitting in premises. * HOL/TLA: Stephan Merz's formalization of Lamport's Temporal Logic of Actions; * HOL/Auth: new protocol proofs including some for the Internet protocol TLS; * HOL/Map: new theory of `maps' a la VDM; * HOL/simplifier: simplification procedures nat_cancel_sums for cancelling out common nat summands from =, <, <= (in)equalities, or differences; simplification procedures nat_cancel_factor for cancelling common factor from =, <, <= (in)equalities over natural sums; nat_cancel contains both kinds of procedures, it is installed by default in Arith.thy -- this COULD MAKE EXISTING PROOFS FAIL; * HOL/simplifier: terms of the form `? x. P1(x) & ... & Pn(x) & x=t & Q1(x) & ... Qn(x)' (or t=x) are rewritten to `P1(t) & ... & Pn(t) & Q1(t) & ... Qn(t)', and those of the form `! x. P1(x) & ... & Pn(x) & x=t & Q1(x) & ... Qn(x) --> R(x)' (or t=x) are rewritten to `P1(t) & ... & Pn(t) & Q1(t) & ... Qn(t) --> R(t)', * HOL/datatype Each datatype `t' now comes with a theorem `split_t_case' of the form P(t_case f1 ... fn x) = ( (!y1 ... ym1. x = C1 y1 ... ym1 --> P(f1 y1 ... ym1)) & ... (!y1 ... ymn. x = Cn y1 ... ymn --> P(f1 y1 ... ymn)) ) and a theorem `split_t_case_asm' of the form P(t_case f1 ... fn x) = ~( (? y1 ... ym1. x = C1 y1 ... ym1 & ~P(f1 y1 ... ym1)) | ... (? y1 ... ymn. x = Cn y1 ... ymn & ~P(f1 y1 ... ymn)) ) which can be added to a simpset via `addsplits'. The existing theorems expand_list_case and expand_option_case have been renamed to split_list_case and split_option_case. * HOL/Arithmetic: - `pred n' is automatically converted to `n-1'. Users are strongly encouraged not to use `pred' any longer, because it will disappear altogether at some point. - Users are strongly encouraged to write "0 < n" rather than "n ~= 0". Theorems and proof tools have been modified towards this `standard'. * HOL/Lists: the function "set_of_list" has been renamed "set" (and its theorems too); the function "nth" now takes its arguments in the reverse order and has acquired the infix notation "!" as in "xs!n". * HOL/Set: UNIV is now a constant and is no longer translated to Compl{}; * HOL/Set: The operator (UN x.B x) now abbreviates (UN x:UNIV. B x) and its specialist theorems (like UN1_I) are gone. Similarly for (INT x.B x); * HOL/record: extensible records with schematic structural subtyping (single inheritance); EXPERIMENTAL version demonstrating the encoding, still lacks various theorems and concrete record syntax; *** HOLCF *** * removed "axioms" and "generated by" sections; * replaced "ops" section by extended "consts" section, which is capable of handling the continuous function space "->" directly; * domain package: . proves theorems immediately and stores them in the theory, . creates hierachical name space, . now uses normal mixfix annotations (instead of cinfix...), . minor changes to some names and values (for consistency), . e.g. cases -> casedist, dists_eq -> dist_eqs, [take_lemma] -> take_lemmas, . separator between mutual domain defs: changed "," to "and", . improved handling of sort constraints; now they have to appear on the left-hand side of the equations only; * fixed LAM <x,y,zs>.b syntax; * added extended adm_tac to simplifier in HOLCF -- can now discharge adm (%x. P (t x)), where P is chainfinite and t continuous; *** FOL and ZF *** * FOL: there is a new splitter `split_asm_tac' that can be used e.g. with `addloop' of the simplifier to faciliate case splitting in premises. * qed_spec_mp, qed_goal_spec_mp, qed_goalw_spec_mp are available, as in HOL, they strip ALL and --> from proved theorems; New in Isabelle94-8 (May 1997) ------------------------------ *** General Changes *** * new utilities to build / run / maintain Isabelle etc. (in parts still somewhat experimental); old Makefiles etc. still functional; * new 'Isabelle System Manual'; * INSTALL text, together with ./configure and ./build scripts; * reimplemented type inference for greater efficiency, better error messages and clean internal interface; * prlim command for dealing with lots of subgoals (an easier way of setting goals_limit); *** Syntax *** * supports alternative (named) syntax tables (parser and pretty printer); internal interface is provided by add_modesyntax(_i); * Pure, FOL, ZF, HOL, HOLCF now support symbolic input and output; to be used in conjunction with the Isabelle symbol font; uses the "symbols" syntax table; * added token_translation interface (may translate name tokens in arbitrary ways, dependent on their type (free, bound, tfree, ...) and the current print_mode); IMPORTANT: user print translation functions are responsible for marking newly introduced bounds (Syntax.mark_boundT); * token translations for modes "xterm" and "xterm_color" that display names in bold, underline etc. or colors (which requires a color version of xterm); * infixes may now be declared with names independent of their syntax; * added typed_print_translation (like print_translation, but may access type of constant); *** Classical Reasoner *** Blast_tac: a new tactic! It is often more powerful than fast_tac, but has some limitations. Blast_tac... + ignores addss, addbefore, addafter; this restriction is intrinsic + ignores elimination rules that don't have the correct format (the conclusion MUST be a formula variable) + ignores types, which can make HOL proofs fail + rules must not require higher-order unification, e.g. apply_type in ZF [message "Function Var's argument not a bound variable" relates to this] + its proof strategy is more general but can actually be slower * substitution with equality assumptions no longer permutes other assumptions; * minor changes in semantics of addafter (now called addaltern); renamed setwrapper to setWrapper and compwrapper to compWrapper; added safe wrapper (and access functions for it); * improved combination of classical reasoner and simplifier: + functions for handling clasimpsets + improvement of addss: now the simplifier is called _after_ the safe steps. + safe variant of addss called addSss: uses safe simplifications _during_ the safe steps. It is more complete as it allows multiple instantiations of unknowns (e.g. with slow_tac). *** Simplifier *** * added interface for simplification procedures (functions that produce *proven* rewrite rules on the fly, depending on current redex); * ordering on terms as parameter (used for ordered rewriting); * new functions delcongs, deleqcongs, and Delcongs. richer rep_ss; * the solver is now split into a safe and an unsafe part. This should be invisible for the normal user, except that the functions setsolver and addsolver have been renamed to setSolver and addSolver; added safe_asm_full_simp_tac; *** HOL *** * a generic induction tactic `induct_tac' which works for all datatypes and also for type `nat'; * a generic case distinction tactic `exhaust_tac' which works for all datatypes and also for type `nat'; * each datatype comes with a function `size'; * patterns in case expressions allow tuple patterns as arguments to constructors, for example `case x of [] => ... | (x,y,z)#ps => ...'; * primrec now also works with type nat; * recdef: a new declaration form, allows general recursive functions to be defined in theory files. See HOL/ex/Fib, HOL/ex/Primes, HOL/Subst/Unify. * the constant for negation has been renamed from "not" to "Not" to harmonize with FOL, ZF, LK, etc.; * HOL/ex/LFilter theory of a corecursive "filter" functional for infinite lists; * HOL/Modelcheck demonstrates invocation of model checker oracle; * HOL/ex/Ring.thy declares cring_simp, which solves equational problems in commutative rings, using axiomatic type classes for + and *; * more examples in HOL/MiniML and HOL/Auth; * more default rewrite rules for quantifiers, union/intersection; * a new constant `arbitrary == @x.False'; * HOLCF/IOA replaces old HOL/IOA; * HOLCF changes: derived all rules and arities + axiomatic type classes instead of classes + typedef instead of faking type definitions + eliminated the internal constants less_fun, less_cfun, UU_fun, UU_cfun etc. + new axclasses cpo, chfin, flat with flat < chfin < pcpo < cpo < po + eliminated the types void, one, tr + use unit lift and bool lift (with translations) instead of one and tr + eliminated blift from Lift3.thy (use Def instead of blift) all eliminated rules are derived as theorems --> no visible changes ; *** ZF *** * ZF now has Fast_tac, Simp_tac and Auto_tac. Union_iff is a now a default rewrite rule; this may affect some proofs. eq_cs is gone but can be put back as ZF_cs addSIs [equalityI]; New in Isabelle94-7 (November 96) --------------------------------- * allowing negative levels (as offsets) in prlev and choplev; * super-linear speedup for large simplifications; * FOL, ZF and HOL now use miniscoping: rewriting pushes quantifications in as far as possible (COULD MAKE EXISTING PROOFS FAIL); can suppress it using the command Delsimps (ex_simps @ all_simps); De Morgan laws are also now included, by default; * improved printing of ==> : ~: * new object-logic "Sequents" adds linear logic, while replacing LK and Modal (thanks to Sara Kalvala); * HOL/Auth: correctness proofs for authentication protocols; * HOL: new auto_tac combines rewriting and classical reasoning (many examples on HOL/Auth); * HOL: new command AddIffs for declaring theorems of the form P=Q to the rewriter and classical reasoner simultaneously; * function uresult no longer returns theorems in "standard" format; regain previous version by: val uresult = standard o uresult; New in Isabelle94-6 ------------------- * oracles -- these establish an interface between Isabelle and trusted external reasoners, which may deliver results as theorems; * proof objects (in particular record all uses of oracles); * Simp_tac, Fast_tac, etc. that refer to implicit simpset / claset; * "constdefs" section in theory files; * "primrec" section (HOL) no longer requires names; * internal type "tactic" now simply "thm -> thm Sequence.seq"; New in Isabelle94-5 ------------------- * reduced space requirements; * automatic HTML generation from theories; * theory files no longer require "..." (quotes) around most types; * new examples, including two proofs of the Church-Rosser theorem; * non-curried (1994) version of HOL is no longer distributed; New in Isabelle94-4 ------------------- * greatly reduced space requirements; * theory files (.thy) no longer require \...\ escapes at line breaks; * searchable theorem database (see the section "Retrieving theorems" on page 8 of the Reference Manual); * new examples, including Grabczewski's monumental case study of the Axiom of Choice; * The previous version of HOL renamed to Old_HOL; * The new version of HOL (previously called CHOL) uses a curried syntax for functions. Application looks like f a b instead of f(a,b); * Mutually recursive inductive definitions finally work in HOL; * In ZF, pattern-matching on tuples is now available in all abstractions and translates to the operator "split"; New in Isabelle94-3 ------------------- * new infix operator, addss, allowing the classical reasoner to perform simplification at each step of its search. Example: fast_tac (cs addss ss) * a new logic, CHOL, the same as HOL, but with a curried syntax for functions. Application looks like f a b instead of f(a,b). Also pairs look like (a,b) instead of <a,b>; * PLEASE NOTE: CHOL will eventually replace HOL! * In CHOL, pattern-matching on tuples is now available in all abstractions. It translates to the operator "split". A new theory of integers is available; * In ZF, integer numerals now denote two's-complement binary integers. Arithmetic operations can be performed by rewriting. See ZF/ex/Bin.ML; * Many new examples: I/O automata, Church-Rosser theorem, equivalents of the Axiom of Choice; New in Isabelle94-2 ------------------- * Significantly faster resolution; * the different sections in a .thy file can now be mixed and repeated freely; * Database of theorems for FOL, HOL and ZF. New commands including qed, qed_goal and bind_thm store theorems in the database. * Simple database queries: return a named theorem (get_thm) or all theorems of a given theory (thms_of), or find out what theory a theorem was proved in (theory_of_thm); * Bugs fixed in the inductive definition and datatype packages; * The classical reasoner provides deepen_tac and depth_tac, making FOL_dup_cs and HOL_dup_cs obsolete; * Syntactic ambiguities caused by the new treatment of syntax in Isabelle94-1 have been removed; * Simpler definition of function space in ZF; * new results about cardinal and ordinal arithmetic in ZF; * 'subtype' facility in HOL for introducing new types as subsets of existing types; $Id$