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NEWS

author | wenzelm |

Tue, 14 Mar 2006 22:06:43 +0100 | |

changeset 19272 | 5f376320109a |

parent 19263 | a86d09815dac |

child 19277 | f7602e74d948 |

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

updated;

Isabelle NEWS -- history user-relevant changes ============================================== New in this Isabelle release ---------------------------- *** General *** * Theory syntax: the header format ``theory A = B + C:'' has been discontinued in favour of ``theory A imports B C begin''. Use isatool fixheaders to convert existing theory files. INCOMPATIBILITY. * Theory syntax: the old non-Isar theory file format has been discontinued altogether. Note that ML proof scripts may still be used with Isar theories; migration is usually quite simple with the ML function use_legacy_bindings. INCOMPATIBILITY. * Legacy goal package: reduced interface to the bare minimum required to keep existing proof scripts running. Most other user-level functions are now part of the OldGoals structure, which is *not* open by default (consider isatool expandshort before open OldGoals). Removed top_sg, prin, printyp, pprint_term/typ altogether, because these tend to cause confusion about the actual goal (!) context being used here, which is not necessarily the same as the_context(). * Command 'find_theorems': support "*" wildcard in "name:" criterion. *** Document preparation *** * Added antiquotations @{ML_type text} and @{ML_struct text} which check the given source text as ML type/structure, printing verbatim. *** Pure *** * Command 'no_translations' removes translation rules from theory syntax. * Isar: improper proof element 'guess' is like 'obtain', but derives the obtained context from the course of reasoning! For example: assume "EX x y. A x & B y" -- "any previous fact" then guess x and y by clarify This technique is potentially adventurous, depending on the facts and proof tools being involved here. * Isar: known facts from the proof context may be specified as literal propositions, using ASCII back-quote syntax. This works wherever named facts used to be allowed so far, in proof commands, proof methods, attributes etc. Literal facts are retrieved from the context according to unification of type and term parameters. For example, provided that "A" and "A ==> B" and "!!x. P x ==> Q x" are known theorems in the current context, then these are valid literal facts: `A` and `A ==> B` and `!!x. P x ==> Q x" as well as `P a ==> Q a` etc. There is also a proof method "fact" which does the same composition for explicit goal states, e.g. the following proof texts coincide with certain special cases of literal facts: have "A" by fact == note `A` have "A ==> B" by fact == note `A ==> B` have "!!x. P x ==> Q x" by fact == note `!!x. P x ==> Q x` have "P a ==> Q a" by fact == note `P a ==> Q a` * Isar: 'def' now admits simultaneous definitions, e.g.: def x == "t" and y == "u" * Isar: added command 'unfolding', which is structurally similar to 'using', but affects both the goal state and facts by unfolding given rewrite rules. Thus many occurrences of the 'unfold' method or 'unfolded' attribute may be replaced by first-class proof text. * Isar: methods 'unfold' / 'fold', attributes 'unfolded' / 'folded', and command 'unfolding' now all support object-level equalities (potentially conditional). The underlying notion of rewrite rule is analogous to the 'rule_format' attribute, but *not* that of the Simplifier (which is usually more generous). * Isar: the goal restriction operator [N] (default N = 1) evaluates a method expression within a sandbox consisting of the first N sub-goals, which need to exist. For example, ``simp_all [3]'' simplifies the first three sub-goals, while (rule foo, simp_all)[] simplifies all new goals that emerge from applying rule foo to the originally first one. * Isar: the conclusion of a long theorem statement is now either 'shows' (a simultaneous conjunction, as before), or 'obtains' (essentially a disjunction of cases with local parameters and assumptions). The latter allows to express general elimination rules adequately; in this notation common elimination rules look like this: lemma exE: -- "EX x. P x ==> (!!x. P x ==> thesis) ==> thesis" assumes "EX x. P x" obtains x where "P x" lemma conjE: -- "A & B ==> (A ==> B ==> thesis) ==> thesis" assumes "A & B" obtains A and B lemma disjE: -- "A | B ==> (A ==> thesis) ==> (B ==> thesis) ==> thesis" assumes "A | B" obtains A | B The subsequent classical rules even refer to the formal "thesis" explicitly: lemma classical: -- "(~ thesis ==> thesis) ==> thesis" obtains "~ thesis" lemma Peirce's_Law: -- "((thesis ==> something) ==> thesis) ==> thesis" obtains "thesis ==> something" The actual proof of an 'obtains' statement is analogous to that of the Isar proof element 'obtain', only that there may be several cases. Optional case names may be specified in parentheses; these will be available both in the present proof and as annotations in the resulting rule, for later use with the 'cases' method (cf. attribute case_names). * Isar: 'print_statement' prints theorems from the current theory or proof context in long statement form, according to the syntax of a top-level lemma. * Isar: 'obtain' takes an optional case name for the local context introduction rule (default "that"). * Isar/locales: new derived specification elements 'definition', 'abbreviation', 'axiomatization', which support type-inference, admit object-level specifications (equality, equivalence). See also the isar-ref manual. Examples: definition "f x y = x + y + 1" "g x = f x x" thm f_def g_def axiomatization eq (infix "===" 50) where eq_refl: "x === x" and eq_subst: "x === y ==> P x ==> P y" abbreviation (output) neq (infix "=!=" 50) "(x =!= y) <-> ~ (x === y)" These specifications may be also used in a locale context. Then the constants being introduced depend on certain fixed parameters, and the constant name is qualified by the locale base name. An internal abbreviation takes care for convenient input and output, making the parameters implicit and using the original short name. See also HOL/ex/Abstract_NAT.thy for an example of deriving polymorphic entities from a monomorphic theory. Presently, abbreviations are only available 'in' a target locale, but not inherited by general import expressions. Also note that 'abbreviation' may be used as a type-safe replacement for 'syntax' + 'translations' in common applications. * Provers/induct: improved internal context management to support local fixes and defines on-the-fly. Thus explicit meta-level connectives !! and ==> are rarely required anymore in inductive goals (using object-logic connectives for this purpose has been long obsolete anyway). The subsequent proof patterns illustrate advanced techniques of natural induction; general datatypes and inductive sets work analogously (see also src/HOL/Lambda for realistic examples). (1) This is how to ``strengthen'' an inductive goal wrt. certain parameters: lemma fixes n :: nat and x :: 'a assumes a: "A n x" shows "P n x" using a -- {* make induct insert fact a *} proof (induct n fixing: x) -- {* generalize goal to "!!x. A n x ==> P n x" *} case 0 show ?case sorry next case (Suc n) note `!!x. A n x ==> P n x` -- {* induction hypothesis, according to induction rule *} note `A (Suc n) x` -- {* induction premise, stemming from fact a *} show ?case sorry qed (2) This is how to perform induction over ``expressions of a certain form'', using a locally defined inductive parameter n == "a x" together with strengthening (the latter is usually required to get sufficiently flexible induction hypotheses): lemma fixes a :: "'a => nat" assumes a: "A (a x)" shows "P (a x)" using a proof (induct n == "a x" fixing: x) ... See also HOL/Isar_examples/Puzzle.thy for an application of the this particular technique. (3) This is how to perform existential reasoning ('obtains' or 'obtain') by induction, while avoiding explicit object-logic encodings: lemma fixes n :: nat obtains x :: 'a where "P n x" and "Q n x" proof (induct n fixing: thesis) case 0 obtain x where "P 0 x" and "Q 0 x" sorry then show thesis by (rule 0) next case (Suc n) obtain x where "P n x" and "Q n x" by (rule Suc.hyps) obtain x where "P (Suc n) x" and "Q (Suc n) x" sorry then show thesis by (rule Suc.prems) qed Here the 'fixing: thesis' specification essentially modifies the scope of the formal thesis parameter, in order to the get the whole existence statement through the induction as expected. * Provers/induct: mutual induction rules are now specified as a list of rule sharing the same induction cases. HOL packages usually provide foo_bar.inducts for mutually defined items foo and bar (e.g. inductive sets or datatypes). INCOMPATIBILITY, users need to specify mutual induction rules differently, i.e. like this: (induct rule: foo_bar.inducts) (induct set: foo bar) (induct type: foo bar) The ML function ProjectRule.projections turns old-style rules into the new format. * Provers/induct: improved handling of simultaneous goals. Instead of introducing object-level conjunction, the statement is now split into several conclusions, while the corresponding symbolic cases are nested accordingly. INCOMPATIBILITY, proofs need to be structured explicitly. For example: lemma fixes n :: nat shows "P n" and "Q n" proof (induct n) case 0 case 1 show "P 0" sorry next case 0 case 2 show "Q 0" sorry next case (Suc n) case 1 note `P n` and `Q n` show "P (Suc n)" sorry next case (Suc n) case 2 note `P n` and `Q n` show "Q (Suc n)" sorry qed The split into subcases may be deferred as follows -- this is particularly relevant for goal statements with local premises. lemma fixes n :: nat shows "A n ==> P n" and "B n ==> Q n" proof (induct n) case 0 { case 1 note `A 0` show "P 0" sorry next case 2 note `B 0` show "Q 0" sorry } next case (Suc n) note `A n ==> P n` and `B n ==> Q n` { case 1 note `A (Suc n)` show "P (Suc n)" sorry next case 2 note `B (Suc n)` show "Q (Suc n)" sorry } qed If simultaneous goals are to be used with mutual rules, the statement needs to be structured carefully as a two-level conjunction, using lists of propositions separated by 'and': lemma shows "a : A ==> P1 a" "a : A ==> P2 a" and "b : B ==> Q1 b" "b : B ==> Q2 b" "b : B ==> Q3 b" proof (induct set: A B) * Provers/induct: support coinduction as well. See src/HOL/Library/Coinductive_List.thy for various examples. * Simplifier: by default the simplifier trace only shows top level rewrites now. That is, trace_simp_depth_limit is set to 1 by default. Thus there is less danger of being flooded by the trace. The trace indicates where parts have been suppressed. * Provers/classical: removed obsolete classical version of elim_format attribute; classical elim/dest rules are now treated uniformly when manipulating the claset. * Provers/classical: stricter checks to ensure that supplied intro, dest and elim rules are well-formed; dest and elim rules must have at least one premise. * Provers/classical: attributes dest/elim/intro take an optional weight argument for the rule (just as the Pure versions). Weights are ignored by automated tools, but determine the search order of single rule steps. * Syntax: input syntax now supports dummy variable binding "%_. b", where the body does not mention the bound variable. Note that dummy patterns implicitly depend on their context of bounds, which makes "{_. _}" match any set comprehension as expected. Potential INCOMPATIBILITY -- parse translations need to cope with syntactic constant "_idtdummy" in the binding position. * Syntax: removed obsolete syntactic constant "_K" and its associated parse translation. INCOMPATIBILITY -- use dummy abstraction instead, for example "A -> B" => "Pi A (%_. B)". *** HOL *** * Alternative iff syntax "A <-> B" for equality on bool (with priority 25 like -->); output depends on the "iff" print_mode, the default is "A = B" (with priority 50). * Renamed some (legacy-named) constants in HOL.thy: op + ~> HOL.plus op - ~> HOL.minus uminus ~> HOL.uminus op * ~> HOL.times Adaptions may be required in the following cases: a) User-defined constants using any of the names "plus", "minus", or "times" The standard syntax translations for "+", "-" and "*" may go wrong. INCOMPATIBILITY: use more specific names. b) Variables named "plus", "minus", or "times" INCOMPATIBILITY: use more specific names. c) Commutative equations theorems (e. g. "a + b = b + a") Since the changing of names also changes the order of terms, commutative rewrites perhaps will be applied when not applied before or the other way round. Experience shows that thiis is rarely the case (only two adaptions in the whole Isabelle distribution). INCOMPATIBILITY: rewrite proof; sometimes already an exchange of a distributive law may suffice. d) ML code directly refering to constant names This in general only affects hand-written proof tactics, simprocs and so on. INCOMPATIBILITY: grep your sourcecode and replace names. * "LEAST x:A. P" expands to "LEAST x. x:A & P" (input only). * In the context of the assumption "~(s = t)" the Simplifier rewrites "t = s" to False (by simproc "neq_simproc"). For backward compatibility this can be disabled by ML "reset use_neq_simproc". * "m dvd n" where m and n are numbers is evaluated to True/False by simp. * Theorem Cons_eq_map_conv no longer has attribute `simp'. * Prefer ex1I over ex_ex1I in single-step reasoning, e.g. by the 'rule' method. * Tactics 'sat' and 'satx' reimplemented, several improvements: goals no longer need to be stated as "<prems> ==> False", equivalences (i.e. "=" on type bool) are handled, variable names of the form "lit_<n>" are no longer reserved, significant speedup. * inductive and datatype: provide projections of mutual rules, bundled as foo_bar.inducts; * Library: added theory Coinductive_List of potentially infinite lists as greatest fixed-point. * Library: added theory AssocList which implements (finite) maps as association lists. *** ML *** * Pure/library: val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd The semantics of "burrow" is: "take a function with *simulatanously* transforms a list of value, and apply it *simulatanously* to a list of list of values of the appropriate type". Confer this with "map" which would *not* apply its argument function simulatanously but in sequence. "fold_burrow" has an additional context. Both actually avoid the usage of "unflat" since they hide away "unflat" from the user. * Pure/library: functions map2 and fold2 with curried syntax for simultanous mapping and folding: val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c * Pure/library: indexed lists - some functions in the Isabelle library treating lists over 'a as finite mappings from [0...n] to 'a have been given more convenient names and signatures reminiscent of similar functions for alists, tables, etc: val nth: 'a list -> int -> 'a val nth_update: int * 'a -> 'a list -> 'a list val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b Note that fold_index starts counting at index 0, not 1 like foldln used to. * Pure/General/name_mangler.ML provides a functor for generic name mangling (bijective mapping from any expression values to strings). * Pure/General/rat.ML implements rational numbers. * Pure/General/table.ML: the join operations now works via exceptions DUP/SAME instead of type option. This is simpler in simple cases, and admits slightly more efficient complex applications. * Pure: datatype Context.generic joins theory/Proof.context and provides some facilities for code that works in either kind of context, notably GenericDataFun for uniform theory and proof data. * Pure: 'advanced' translation functions (parse_translation etc.) now use Context.generic instead of just theory. * Pure: simplified internal attribute type, which is now always Context.generic * thm -> Context.generic * thm. Global (theory) vs. local (Proof.context) attributes have been discontinued, while minimizing code duplication. Thm.rule_attribute and Thm.declaration_attribute build canonical attributes; see also structure Context for further operations on Context.generic, notably GenericDataFun. INCOMPATIBILITY, need to adapt attribute type declarations and definitions. * Pure/Isar: Args/Attrib parsers operate on Context.generic -- global/local versions on theory vs. Proof.context have been discontinued; Attrib.syntax and Method.syntax have been adapted accordingly. INCOMPATIBILITY, need to adapt parser expressions for attributes, methods, etc. * Pure: several functions of signature "... -> theory -> theory * ..." have been reoriented to "... -> theory -> ... * theory" in order to allow natural usage in combination with the ||>, ||>>, |-> and fold_map combinators. * Pure: primitive rule lift_rule now takes goal cterm instead of an actual goal state (thm). Use Thm.lift_rule (Thm.cprem_of st i) to achieve the old behaviour. * Pure: the "Goal" constant is now called "prop", supporting a slightly more general idea of ``protecting'' meta-level rule statements. * Pure: structure Goal provides simple interfaces for init/conclude/finish and tactical prove operations (replacing former Tactic.prove). Note that OldGoals.prove_goalw_cterm has long been obsolete, it is ill-behaved in a local proof context (e.g. with local fixes/assumes or in a locale context). * Isar: simplified treatment of user-level errors, using exception ERROR of string uniformly. Function error now merely raises ERROR, without any side effect on output channels. The Isar toplevel takes care of proper display of ERROR exceptions. ML code may use plain handle/can/try; cat_error may be used to concatenate errors like this: ... handle ERROR msg => cat_error msg "..." Toplevel ML code (run directly or through the Isar toplevel) may be embedded into the Isar toplevel with exception display/debug like this: Isar.toplevel (fn () => ...) INCOMPATIBILITY, removed special transform_error facilities, removed obsolete variants of user-level exceptions (ERROR_MESSAGE, Context.PROOF, ProofContext.CONTEXT, Proof.STATE, ProofHistory.FAIL) -- use plain ERROR instead. * Isar: theory setup now has type (theory -> theory), instead of a list. INCOMPATIBILITY, may use #> to compose setup functions. * Isar: installed ML toplevel pretty printer for type Proof.context, subject to ProofContext.debug/verbose flags. * Isar: Toplevel.theory_to_proof admits transactions that modify the theory before entering a proof state. Transactions now always see a quasi-functional intermediate checkpoint, both in interactive and batch mode. * Simplifier: the simpset of a running simplification process now contains a proof context (cf. Simplifier.the_context), which is the very context that the initial simpset has been retrieved from (by simpset_of/local_simpset_of). Consequently, all plug-in components (solver, looper etc.) may depend on arbitrary proof data. * Simplifier.inherit_context inherits the proof context (plus the local bounds) of the current simplification process; any simproc etc. that calls the Simplifier recursively should do this! Removed former Simplifier.inherit_bounds, which is already included here -- INCOMPATIBILITY. Tools based on low-level rewriting may even have to specify an explicit context using Simplifier.context/theory_context. * Simplifier/Classical Reasoner: more abstract interfaces change_simpset/claset for modifying the simpset/claset reference of a theory; raw versions simpset/claset_ref etc. have been discontinued -- INCOMPATIBILITY. * Provers: more generic wrt. syntax of object-logics, avoid hardwired "Trueprop" etc. New in Isabelle2005 (October 2005) ---------------------------------- *** General *** * Theory headers: the new header syntax for Isar theories is theory <name> imports <theory1> ... <theoryN> uses <file1> ... <fileM> begin where the 'uses' part is optional. The previous syntax theory <name> = <theory1> + ... + <theoryN>: will disappear in the next release. Use isatool fixheaders to convert existing theory files. Note that there is no change in ancient non-Isar theories now, but these will disappear soon. * Theory loader: parent theories can now also be referred to via relative and absolute paths. * Command 'find_theorems' searches for a list of criteria instead of a list of constants. Known criteria are: intro, elim, dest, name:string, simp:term, and any term. Criteria can be preceded by '-' to select theorems that do not match. Intro, elim, dest select theorems that match the current goal, name:s selects theorems whose fully qualified name contain s, and simp:term selects all simplification rules whose lhs match term. Any other term is interpreted as pattern and selects all theorems matching the pattern. Available in ProofGeneral under 'ProofGeneral -> Find Theorems' or C-c C-f. Example: C-c C-f (100) "(_::nat) + _ + _" intro -name: "HOL." prints the last 100 theorems matching the pattern "(_::nat) + _ + _", matching the current goal as introduction rule and not having "HOL." in their name (i.e. not being defined in theory HOL). * Command 'thms_containing' has been discontinued in favour of 'find_theorems'; INCOMPATIBILITY. * Communication with Proof General is now 8bit clean, which means that Unicode text in UTF-8 encoding may be used within theory texts (both formal and informal parts). Cf. option -U of the Isabelle Proof General interface. Here are some simple examples (cf. src/HOL/ex): http://isabelle.in.tum.de/library/HOL/ex/Hebrew.html http://isabelle.in.tum.de/library/HOL/ex/Chinese.html * Improved efficiency of the Simplifier and, to a lesser degree, the Classical Reasoner. Typical big applications run around 2 times faster. *** Document preparation *** * Commands 'display_drafts' and 'print_drafts' perform simple output of raw sources. Only those symbols that do not require additional LaTeX packages (depending on comments in isabellesym.sty) are displayed properly, everything else is left verbatim. isatool display and isatool print are used as front ends (these are subject to the DVI/PDF_VIEWER and PRINT_COMMAND settings, respectively). * Command tags control specific markup of certain regions of text, notably folding and hiding. Predefined tags include "theory" (for theory begin and end), "proof" for proof commands, and "ML" for commands involving ML code; the additional tags "visible" and "invisible" are unused by default. Users may give explicit tag specifications in the text, e.g. ''by %invisible (auto)''. The interpretation of tags is determined by the LaTeX job during document preparation: see option -V of isatool usedir, or options -n and -t of isatool document, or even the LaTeX macros \isakeeptag, \isafoldtag, \isadroptag. Several document versions may be produced at the same time via isatool usedir (the generated index.html will link all of them). Typical specifications include ''-V document=theory,proof,ML'' to present theory/proof/ML parts faithfully, ''-V outline=/proof,/ML'' to fold proof and ML commands, and ''-V mutilated=-theory,-proof,-ML'' to omit these parts without any formal replacement text. The Isabelle site default settings produce ''document'' and ''outline'' versions as specified above. * Several new antiquotations: @{term_type term} prints a term with its type annotated; @{typeof term} prints the type of a term; @{const const} is the same as @{term const}, but checks that the argument is a known logical constant; @{term_style style term} and @{thm_style style thm} print a term or theorem applying a "style" to it @{ML text} Predefined styles are 'lhs' and 'rhs' printing the lhs/rhs of definitions, equations, inequations etc., 'concl' printing only the conclusion of a meta-logical statement theorem, and 'prem1' .. 'prem19' to print the specified premise. TermStyle.add_style provides an ML interface for introducing further styles. See also the "LaTeX Sugar" document practical applications. The ML antiquotation prints type-checked ML expressions verbatim. * Markup commands 'chapter', 'section', 'subsection', 'subsubsection', and 'text' support optional locale specification '(in loc)', which specifies the default context for interpreting antiquotations. For example: 'text (in lattice) {* @{thm inf_assoc}*}'. * Option 'locale=NAME' of antiquotations specifies an alternative context interpreting the subsequent argument. For example: @{thm [locale=lattice] inf_assoc}. * Proper output of proof terms (@{prf ...} and @{full_prf ...}) within a proof context. * Proper output of antiquotations for theory commands involving a proof context (such as 'locale' or 'theorem (in loc) ...'). * Delimiters of outer tokens (string etc.) now produce separate LaTeX macros (\isachardoublequoteopen, isachardoublequoteclose etc.). * isatool usedir: new option -C (default true) controls whether option -D should include a copy of the original document directory; -C false prevents unwanted effects such as copying of administrative CVS data. *** 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. * 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. * New command 'no_syntax' removes grammar declarations (and translations) resulting from the given syntax specification, which is interpreted in the same manner as for the 'syntax' command. * '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. * Improved 'oracle' command provides a type-safe interface to turn an ML expression of type theory -> T -> term into a primitive rule of type theory -> T -> thm (i.e. the functionality of Thm.invoke_oracle is already included here); see also FOL/ex/IffExample.thy; INCOMPATIBILITY. * axclass: name space prefix for class "c" is now "c_class" (was "c" before); "cI" is no longer bound, use "c.intro" instead. INCOMPATIBILITY. This change avoids clashes of fact bindings for axclasses vs. locales. * Improved internal renaming of symbolic identifiers -- attach primes instead of base 26 numbers. * New flag show_question_marks controls printing of leading question marks in schematic variable names. * In schematic variable names, *any* symbol following \<^isub> or \<^isup> is now treated as part of the base name. For example, the following works without printing of awkward ".0" indexes: lemma "x\<^isub>1 = x\<^isub>2 ==> x\<^isub>2 = x\<^isub>1" by simp * Inner syntax includes (*(*nested*) comments*). * Pretty printer now supports unbreakable blocks, specified in mixfix annotations as "(00...)". * 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/Cube.thy). * 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. * Attributes 'induct' and 'cases': type or set names may now be locally fixed variables as well. * Simplifier: can now control the depth to which conditional rewriting is traced via the PG menu Isabelle -> Settings -> Trace Simp Depth Limit. * Simplifier: simplification procedures may now take the current simpset into account (cf. Simplifier.simproc(_i) / mk_simproc interface), which is very useful for calling the Simplifier recursively. Minor INCOMPATIBILITY: the 'prems' argument of simprocs is gone -- use prems_of_ss on the simpset instead. Moreover, the low-level mk_simproc no longer applies Logic.varify internally, to allow for use in a context of fixed variables. * thin_tac now works even if the assumption being deleted contains !! or ==>. More generally, erule now works even if the major premise of the elimination rule contains !! or ==>. * Method 'rules' has been renamed to 'iprover'. INCOMPATIBILITY. * Reorganized bootstrapping of the Pure theories; CPure is now derived from Pure, which contains all common declarations already. Both theories are defined via plain Isabelle/Isar .thy files. INCOMPATIBILITY: elements of CPure (such as the CPure.intro / CPure.elim / CPure.dest attributes) now appear in the Pure name space; use isatool fixcpure to adapt your theory and ML sources. * New syntax 'name(i-j, i-, i, ...)' for referring to specific selections of theorems in named facts via index ranges. * 'print_theorems': in theory mode, really print the difference wrt. the last state (works for interactive theory development only), in proof mode print all local facts (cf. 'print_facts'); * 'hide': option '(open)' hides only base names. * More efficient treatment of intermediate checkpoints in interactive theory development. * Code generator is now invoked via code_module (incremental code generation) and code_library (modular code generation, ML structures for each theory). INCOMPATIBILITY: new keywords 'file' and 'contains' must be quoted when used as identifiers. * New 'value' command for reading, evaluating and printing terms using the code generator. INCOMPATIBILITY: command keyword 'value' must be quoted when used as identifier. *** Locales *** * New commands for the interpretation of locale expressions in theories (1), locales (2) and proof contexts (3). These generate proof obligations from the expression specification. After the obligations have been discharged, theorems of the expression are added to the theory, target locale or proof context. The synopsis of the commands is a follows: (1) interpretation expr inst (2) interpretation target < expr (3) interpret expr inst Interpretation in theories and proof contexts require a parameter instantiation of terms from the current context. This is applied to specifications and theorems of the interpreted expression. Interpretation in locales only permits parameter renaming through the locale expression. Interpretation is smart in that interpretations that are active already do not occur in proof obligations, neither are instantiated theorems stored in duplicate. Use 'print_interps' to inspect active interpretations of a particular locale. For details, see the Isar Reference manual. Examples can be found in HOL/Finite_Set.thy and HOL/Algebra/UnivPoly.thy. INCOMPATIBILITY: former 'instantiate' has been withdrawn, use 'interpret' instead. * New context element 'constrains' for adding type constraints to parameters. * Context expressions: renaming of parameters with syntax redeclaration. * Locale declaration: 'includes' disallowed. * Proper static binding of attribute syntax -- i.e. types / terms / facts mentioned as arguments are always those of the locale definition context, independently of the context of later invocations. Moreover, locale operations (renaming and type / term instantiation) are applied to attribute arguments as expected. INCOMPATIBILITY of the ML interface: always pass Attrib.src instead of actual attributes; rare situations may require Attrib.attribute to embed those attributes into Attrib.src that lack concrete syntax. Attribute implementations need to cooperate properly with the static binding mechanism. Basic parsers Args.XXX_typ/term/prop and Attrib.XXX_thm etc. already do the right thing without further intervention. Only unusual applications -- such as "where" or "of" (cf. src/Pure/Isar/attrib.ML), which process arguments depending both on the context and the facts involved -- may have to assign parsed values to argument tokens explicitly. * Changed parameter management in theorem generation for long goal statements with 'includes'. INCOMPATIBILITY: produces a different theorem statement in rare situations. * Locale inspection command 'print_locale' omits notes elements. Use 'print_locale!' to have them included in the output. *** Provers *** * Provers/hypsubst.ML: improved version of the subst method, for single-step rewriting: it now works in bound variable contexts. New is 'subst (asm)', for rewriting an assumption. INCOMPATIBILITY: may rewrite a different subterm than the original subst method, which is still available as 'simplesubst'. * Provers/quasi.ML: new transitivity reasoners for transitivity only and quasi orders. * Provers/trancl.ML: new transitivity reasoner for transitive and reflexive-transitive closure of relations. * Provers/blast.ML: new reference depth_limit to make blast's depth limit (previously hard-coded with a value of 20) user-definable. * Provers/simplifier.ML has been moved to Pure, where Simplifier.setup is peformed already. Object-logics merely need to finish their initial simpset configuration as before. INCOMPATIBILITY. *** 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. INCOMPATIBILITY, * "x > y" abbreviates "y < x" and "x >= y" abbreviates "y <= x". Similarly for all quantifiers: "ALL x > y" etc. The x-symbol for >= is \<ge>. New transitivity rules have been added to HOL/Orderings.thy to support corresponding Isar calculations. * "{x:A. P}" abbreviates "{x. x:A & P}", and similarly for "\<in>" instead of ":". * theory SetInterval: changed the syntax for open intervals: Old New {..n(} {..<n} {)n..} {n<..} {m..n(} {m..<n} {)m..n} {m<..n} {)m..n(} {m<..<n} The old syntax is still supported but will disappear in the next release. For conversion use the following Emacs search and replace patterns (these are not perfect but work quite well): {)\([^\.]*\)\.\. -> {\1<\.\.} \.\.\([^(}]*\)(} -> \.\.<\1} * Theory Commutative_Ring (in Library): method comm_ring for proving equalities in commutative rings; method 'algebra' provides a generic interface. * Theory Finite_Set: changed the syntax for 'setsum', summation over finite sets: "setsum (%x. e) A", which used to be "\<Sum>x:A. e", is now either "SUM x:A. e" or "\<Sum>x \<in> A. e". The bound variable can be a tuple pattern. Some new syntax forms are available: "\<Sum>x | P. e" for "setsum (%x. e) {x. P}" "\<Sum>x = a..b. e" for "setsum (%x. e) {a..b}" "\<Sum>x = a..<b. e" for "setsum (%x. e) {a..<b}" "\<Sum>x < k. e" for "setsum (%x. e) {..<k}" The latter form "\<Sum>x < k. e" used to be based on a separate function "Summation", which has been discontinued. * theory Finite_Set: in structured induction proofs, the insert case is now 'case (insert x F)' instead of the old counterintuitive 'case (insert F x)'. * The 'refute' command has been extended to support a much larger fragment of HOL, including axiomatic type classes, constdefs and typedefs, inductive datatypes and recursion. * New tactics 'sat' and 'satx' to prove propositional tautologies. Requires zChaff with proof generation to be installed. See HOL/ex/SAT_Examples.thy for examples. * Datatype induction via method 'induct' now preserves the name of the induction variable. For example, when proving P(xs::'a list) by induction on xs, the induction step is now P(xs) ==> P(a#xs) rather than P(list) ==> P(a#list) as previously. Potential INCOMPATIBILITY in unstructured proof scripts. * Reworked implementation 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. Flag record_quick_and_dirty_sensitive can be enabled to skip the proofs triggered by a record definition or a simproc (if quick_and_dirty is enabled). Definitions of large records can take quite long. New simproc record_upd_simproc for simplification of multiple record updates enabled by default. Moreover, trivial updates are also removed: r(|x := x r|) = r. INCOMPATIBILITY: old proofs break occasionally, since simplification is more powerful by default. * typedef: proper support for polymorphic sets, which contain extra type-variables in the term. * Simplifier: automatically reasons about transitivity chains involving "trancl" (r^+) and "rtrancl" (r^*) by setting up tactics provided by Provers/trancl.ML as additional solvers. INCOMPATIBILITY: old proofs break occasionally as simplification may now solve more goals than previously. * Simplifier: converts x <= y into x = y if assumption y <= x is present. Works for all partial orders (class "order"), in particular numbers and sets. For linear orders (e.g. numbers) it treats ~ x < y just like y <= x. * Simplifier: new simproc for "let x = a in f x". If a is a free or bound variable or a constant then the let is unfolded. Otherwise first a is simplified to b, and then f b is simplified to g. If possible we abstract b from g arriving at "let x = b in h x", otherwise we unfold the let and arrive at g. The simproc can be enabled/disabled by the reference use_let_simproc. Potential INCOMPATIBILITY since simplification is more powerful by default. * Classical reasoning: the meson method now accepts theorems as arguments. * Prover support: pre-release of the Isabelle-ATP linkup, which runs background jobs to provide advice on the provability of subgoals. * Theory OrderedGroup and Ring_and_Field: various additions and improvements to faciliate calculations involving equalities and inequalities. The following theorems have been eliminated or modified (INCOMPATIBILITY): abs_eq now named abs_of_nonneg abs_of_ge_0 now named abs_of_nonneg abs_minus_eq now named abs_of_nonpos imp_abs_id now named abs_of_nonneg imp_abs_neg_id now named abs_of_nonpos mult_pos now named mult_pos_pos mult_pos_le now named mult_nonneg_nonneg mult_pos_neg_le now named mult_nonneg_nonpos mult_pos_neg2_le now named mult_nonneg_nonpos2 mult_neg now named mult_neg_neg mult_neg_le now named mult_nonpos_nonpos * Theory Parity: added rules for simplifying exponents. * Theory List: The following theorems have been eliminated or modified (INCOMPATIBILITY): list_all_Nil now named list_all.simps(1) list_all_Cons now named list_all.simps(2) list_all_conv now named list_all_iff set_mem_eq now named mem_iff * Theories SetsAndFunctions and BigO (see HOL/Library) support asymptotic "big O" calculations. See the notes in BigO.thy. *** HOL-Complex *** * Theory RealDef: better support for embedding natural numbers and integers in the reals. The following theorems have been eliminated or modified (INCOMPATIBILITY): exp_ge_add_one_self now requires no hypotheses real_of_int_add reversed direction of equality (use [symmetric]) real_of_int_minus reversed direction of equality (use [symmetric]) real_of_int_diff reversed direction of equality (use [symmetric]) real_of_int_mult reversed direction of equality (use [symmetric]) * Theory RComplete: expanded support for floor and ceiling functions. * Theory Ln is new, with properties of the natural logarithm * Hyperreal: There is a new type constructor "star" for making nonstandard types. The old type names are now type synonyms: hypreal = real star hypnat = nat star hcomplex = complex star * Hyperreal: Many groups of similarly-defined constants have been replaced by polymorphic versions (INCOMPATIBILITY): star_of <-- hypreal_of_real, hypnat_of_nat, hcomplex_of_complex starset <-- starsetNat, starsetC *s* <-- *sNat*, *sc* starset_n <-- starsetNat_n, starsetC_n *sn* <-- *sNatn*, *scn* InternalSets <-- InternalNatSets, InternalCSets starfun <-- starfun{Nat,Nat2,C,RC,CR} *f* <-- *fNat*, *fNat2*, *fc*, *fRc*, *fcR* starfun_n <-- starfun{Nat,Nat2,C,RC,CR}_n *fn* <-- *fNatn*, *fNat2n*, *fcn*, *fRcn*, *fcRn* InternalFuns <-- InternalNatFuns, InternalNatFuns2, Internal{C,RC,CR}Funs * Hyperreal: Many type-specific theorems have been removed in favor of theorems specific to various axiomatic type classes (INCOMPATIBILITY): add_commute <-- {hypreal,hypnat,hcomplex}_add_commute add_assoc <-- {hypreal,hypnat,hcomplex}_add_assocs OrderedGroup.add_0 <-- {hypreal,hypnat,hcomplex}_add_zero_left OrderedGroup.add_0_right <-- {hypreal,hcomplex}_add_zero_right right_minus <-- hypreal_add_minus left_minus <-- {hypreal,hcomplex}_add_minus_left mult_commute <-- {hypreal,hypnat,hcomplex}_mult_commute mult_assoc <-- {hypreal,hypnat,hcomplex}_mult_assoc mult_1_left <-- {hypreal,hypnat}_mult_1, hcomplex_mult_one_left mult_1_right <-- hcomplex_mult_one_right mult_zero_left <-- hcomplex_mult_zero_left left_distrib <-- {hypreal,hypnat,hcomplex}_add_mult_distrib right_distrib <-- hypnat_add_mult_distrib2 zero_neq_one <-- {hypreal,hypnat,hcomplex}_zero_not_eq_one right_inverse <-- hypreal_mult_inverse left_inverse <-- hypreal_mult_inverse_left, hcomplex_mult_inv_left order_refl <-- {hypreal,hypnat}_le_refl order_trans <-- {hypreal,hypnat}_le_trans order_antisym <-- {hypreal,hypnat}_le_anti_sym order_less_le <-- {hypreal,hypnat}_less_le linorder_linear <-- {hypreal,hypnat}_le_linear add_left_mono <-- {hypreal,hypnat}_add_left_mono mult_strict_left_mono <-- {hypreal,hypnat}_mult_less_mono2 add_nonneg_nonneg <-- hypreal_le_add_order * Hyperreal: Separate theorems having to do with type-specific versions of constants have been merged into theorems that apply to the new polymorphic constants (INCOMPATIBILITY): STAR_UNIV_set <-- {STAR_real,NatStar_real,STARC_complex}_set STAR_empty_set <-- {STAR,NatStar,STARC}_empty_set STAR_Un <-- {STAR,NatStar,STARC}_Un STAR_Int <-- {STAR,NatStar,STARC}_Int STAR_Compl <-- {STAR,NatStar,STARC}_Compl STAR_subset <-- {STAR,NatStar,STARC}_subset STAR_mem <-- {STAR,NatStar,STARC}_mem STAR_mem_Compl <-- {STAR,STARC}_mem_Compl STAR_diff <-- {STAR,STARC}_diff STAR_star_of_image_subset <-- {STAR_hypreal_of_real, NatStar_hypreal_of_real, STARC_hcomplex_of_complex}_image_subset starset_n_Un <-- starset{Nat,C}_n_Un starset_n_Int <-- starset{Nat,C}_n_Int starset_n_Compl <-- starset{Nat,C}_n_Compl starset_n_diff <-- starset{Nat,C}_n_diff InternalSets_Un <-- Internal{Nat,C}Sets_Un InternalSets_Int <-- Internal{Nat,C}Sets_Int InternalSets_Compl <-- Internal{Nat,C}Sets_Compl InternalSets_diff <-- Internal{Nat,C}Sets_diff InternalSets_UNIV_diff <-- Internal{Nat,C}Sets_UNIV_diff InternalSets_starset_n <-- Internal{Nat,C}Sets_starset{Nat,C}_n starset_starset_n_eq <-- starset{Nat,C}_starset{Nat,C}_n_eq starset_n_starset <-- starset{Nat,C}_n_starset{Nat,C} starfun_n_starfun <-- starfun{Nat,Nat2,C,RC,CR}_n_starfun{Nat,Nat2,C,RC,CR} starfun <-- starfun{Nat,Nat2,C,RC,CR} starfun_mult <-- starfun{Nat,Nat2,C,RC,CR}_mult starfun_add <-- starfun{Nat,Nat2,C,RC,CR}_add starfun_minus <-- starfun{Nat,Nat2,C,RC,CR}_minus starfun_diff <-- starfun{C,RC,CR}_diff starfun_o <-- starfun{NatNat2,Nat2,_stafunNat,C,C_starfunRC,_starfunCR}_o starfun_o2 <-- starfun{NatNat2,_stafunNat,C,C_starfunRC,_starfunCR}_o2 starfun_const_fun <-- starfun{Nat,Nat2,C,RC,CR}_const_fun starfun_inverse <-- starfun{Nat,C,RC,CR}_inverse starfun_eq <-- starfun{Nat,Nat2,C,RC,CR}_eq starfun_eq_iff <-- starfun{C,RC,CR}_eq_iff starfun_Id <-- starfunC_Id starfun_approx <-- starfun{Nat,CR}_approx starfun_capprox <-- starfun{C,RC}_capprox starfun_abs <-- starfunNat_rabs starfun_lambda_cancel <-- starfun{C,CR,RC}_lambda_cancel starfun_lambda_cancel2 <-- starfun{C,CR,RC}_lambda_cancel2 starfun_mult_HFinite_approx <-- starfunCR_mult_HFinite_capprox starfun_mult_CFinite_capprox <-- starfun{C,RC}_mult_CFinite_capprox starfun_add_capprox <-- starfun{C,RC}_add_capprox starfun_add_approx <-- starfunCR_add_approx starfun_inverse_inverse <-- starfunC_inverse_inverse starfun_divide <-- starfun{C,CR,RC}_divide starfun_n <-- starfun{Nat,C}_n starfun_n_mult <-- starfun{Nat,C}_n_mult starfun_n_add <-- starfun{Nat,C}_n_add starfun_n_add_minus <-- starfunNat_n_add_minus starfun_n_const_fun <-- starfun{Nat,C}_n_const_fun starfun_n_minus <-- starfun{Nat,C}_n_minus starfun_n_eq <-- starfun{Nat,C}_n_eq star_n_add <-- {hypreal,hypnat,hcomplex}_add star_n_minus <-- {hypreal,hcomplex}_minus star_n_diff <-- {hypreal,hcomplex}_diff star_n_mult <-- {hypreal,hcomplex}_mult star_n_inverse <-- {hypreal,hcomplex}_inverse star_n_le <-- {hypreal,hypnat}_le star_n_less <-- {hypreal,hypnat}_less star_n_zero_num <-- {hypreal,hypnat,hcomplex}_zero_num star_n_one_num <-- {hypreal,hypnat,hcomplex}_one_num star_n_abs <-- hypreal_hrabs star_n_divide <-- hcomplex_divide star_of_add <-- {hypreal_of_real,hypnat_of_nat,hcomplex_of_complex}_add star_of_minus <-- {hypreal_of_real,hcomplex_of_complex}_minus star_of_diff <-- hypreal_of_real_diff star_of_mult <-- {hypreal_of_real,hypnat_of_nat,hcomplex_of_complex}_mult star_of_one <-- {hypreal_of_real,hcomplex_of_complex}_one star_of_zero <-- {hypreal_of_real,hypnat_of_nat,hcomplex_of_complex}_zero star_of_le <-- {hypreal_of_real,hypnat_of_nat}_le_iff star_of_less <-- {hypreal_of_real,hypnat_of_nat}_less_iff star_of_eq <-- {hypreal_of_real,hypnat_of_nat,hcomplex_of_complex}_eq_iff star_of_inverse <-- {hypreal_of_real,hcomplex_of_complex}_inverse star_of_divide <-- {hypreal_of_real,hcomplex_of_complex}_divide star_of_of_nat <-- {hypreal_of_real,hcomplex_of_complex}_of_nat star_of_of_int <-- {hypreal_of_real,hcomplex_of_complex}_of_int star_of_number_of <-- {hypreal,hcomplex}_number_of star_of_number_less <-- number_of_less_hypreal_of_real_iff star_of_number_le <-- number_of_le_hypreal_of_real_iff star_of_eq_number <-- hypreal_of_real_eq_number_of_iff star_of_less_number <-- hypreal_of_real_less_number_of_iff star_of_le_number <-- hypreal_of_real_le_number_of_iff star_of_power <-- hypreal_of_real_power star_of_eq_0 <-- hcomplex_of_complex_zero_iff * Hyperreal: new method "transfer" that implements the transfer principle of nonstandard analysis. With a subgoal that mentions nonstandard types like "'a star", the command "apply transfer" replaces it with an equivalent one that mentions only standard types. To be successful, all free variables must have standard types; non- standard variables must have explicit universal quantifiers. * Hyperreal: A theory of Taylor series. *** HOLCF *** * Discontinued special version of 'constdefs' (which used to support continuous functions) in favor of the general Pure one with full type-inference. * New simplification procedure for solving continuity conditions; it is much faster on terms with many nested lambda abstractions (cubic instead of exponential time). * New syntax for domain package: selector names are now optional. Parentheses should be omitted unless argument is lazy, for example: domain 'a stream = cons "'a" (lazy "'a stream") * New command 'fixrec' for defining recursive functions with pattern matching; defining multiple functions with mutual recursion is also supported. Patterns may include the constants cpair, spair, up, sinl, sinr, or any data constructor defined by the domain package. The given equations are proven as rewrite rules. See HOLCF/ex/Fixrec_ex.thy for syntax and examples. * New commands 'cpodef' and 'pcpodef' for defining predicate subtypes of cpo and pcpo types. Syntax is exactly like the 'typedef' command, but the proof obligation additionally includes an admissibility requirement. The packages generate instances of class cpo or pcpo, with continuity and strictness theorems for Rep and Abs. * HOLCF: Many theorems have been renamed according to a more standard naming scheme (INCOMPATIBILITY): foo_inject: "foo$x = foo$y ==> x = y" foo_eq: "(foo$x = foo$y) = (x = y)" foo_less: "(foo$x << foo$y) = (x << y)" foo_strict: "foo$UU = UU" foo_defined: "... ==> foo$x ~= UU" foo_defined_iff: "(foo$x = UU) = (x = UU)" *** ZF *** * ZF/ex: theories Group and Ring provide examples in abstract algebra, including the First Isomorphism Theorem (on quotienting by the kernel of a homomorphism). * ZF/Simplifier: install second copy of type solver that actually makes use of TC rules declared to Isar proof contexts (or locales); the old version is still required for ML proof scripts. *** Cube *** * Converted to Isar theory format; use locales instead of axiomatic theories. *** ML *** * Pure/library.ML no longer defines its own option datatype, but uses that of the SML basis, which has constructors NONE and SOME instead of None and Some, as well as exception Option.Option instead of OPTION. The functions the, if_none, is_some, is_none have been adapted accordingly, while Option.map replaces apsome. * Pure/library.ML: the exception LIST has been given up in favour of the standard exceptions Empty and Subscript, as well as Library.UnequalLengths. Function like Library.hd and Library.tl are superceded by the standard hd and tl functions etc. A number of basic list functions are no longer exported to the ML toplevel, as they are variants of predefined functions. The following suggests how one can translate existing code: rev_append xs ys = List.revAppend (xs, ys) nth_elem (i, xs) = List.nth (xs, i) last_elem xs = List.last xs flat xss = List.concat xss seq fs = List.app fs partition P xs = List.partition P xs mapfilter f xs = List.mapPartial f xs * Pure/library.ML: several combinators for linear functional transformations, notably reverse application and composition: x |> f f #> g (x, y) |-> f f #-> g * Pure/library.ML: introduced/changed precedence of infix operators: infix 1 |> |-> ||> ||>> |>> |>>> #> #->; infix 2 ?; infix 3 o oo ooo oooo; infix 4 ~~ upto downto; Maybe INCOMPATIBILITY when any of those is used in conjunction with other infix operators. * Pure/library.ML: natural list combinators fold, fold_rev, and fold_map support linear functional transformations and nesting. For example: fold f [x1, ..., xN] y = y |> f x1 |> ... |> f xN (fold o fold) f [xs1, ..., xsN] y = y |> fold f xs1 |> ... |> fold f xsN fold f [x1, ..., xN] = f x1 #> ... #> f xN (fold o fold) f [xs1, ..., xsN] = fold f xs1 #> ... #> fold f xsN * Pure/library.ML: the following selectors on type 'a option are available: the: 'a option -> 'a (*partial*) these: 'a option -> 'a where 'a = 'b list the_default: 'a -> 'a option -> 'a the_list: 'a option -> 'a list * Pure/General: structure AList (cf. Pure/General/alist.ML) provides basic operations for association lists, following natural argument order; moreover the explicit equality predicate passed here avoids potentially expensive polymorphic runtime equality checks. The old functions may be expressed as follows: assoc = uncurry (AList.lookup (op =)) assocs = these oo AList.lookup (op =) overwrite = uncurry (AList.update (op =)) o swap * Pure/General: structure AList (cf. Pure/General/alist.ML) provides val make: ('a -> 'b) -> 'a list -> ('a * 'b) list val find: ('a * 'b -> bool) -> ('c * 'b) list -> 'a -> 'c list replacing make_keylist and keyfilter (occassionally used) Naive rewrites: make_keylist = AList.make keyfilter = AList.find (op =) * eq_fst and eq_snd now take explicit equality parameter, thus avoiding eqtypes. Naive rewrites: eq_fst = eq_fst (op =) eq_snd = eq_snd (op =) * Removed deprecated apl and apr (rarely used). Naive rewrites: apl (n, op) =>>= curry op n apr (op, m) =>>= fn n => op (n, m) * Pure/General: structure OrdList (cf. Pure/General/ord_list.ML) provides a reasonably efficient light-weight implementation of sets as lists. * Pure/General: generic tables (cf. Pure/General/table.ML) provide a few new operations; existing lookup and update are now curried to follow natural argument order (for use with fold etc.); INCOMPATIBILITY, use (uncurry Symtab.lookup) etc. as last resort. * Pure/General: output via the Isabelle channels of writeln/warning/error etc. is now passed through Output.output, with a hook for arbitrary transformations depending on the print_mode (cf. Output.add_mode -- the first active mode that provides a output function wins). Already formatted output may be embedded into further text via Output.raw; the result of Pretty.string_of/str_of and derived functions (string_of_term/cterm/thm etc.) is already marked raw to accommodate easy composition of diagnostic messages etc. Programmers rarely need to care about Output.output or Output.raw at all, with some notable exceptions: Output.output is required when bypassing the standard channels (writeln etc.), or in token translations to produce properly formatted results; Output.raw is required when capturing already output material that will eventually be presented to the user a second time. For the default print mode, both Output.output and Output.raw have no effect. * Pure/General: Output.time_accumulator NAME creates an operator ('a -> 'b) -> 'a -> 'b to measure runtime and count invocations; the cumulative results are displayed at the end of a batch session. * Pure/General: File.sysify_path and File.quote_sysify path have been replaced by File.platform_path and File.shell_path (with appropriate hooks). This provides a clean interface for unusual systems where the internal and external process view of file names are different. * Pure: more efficient orders for basic syntactic entities: added fast_string_ord, fast_indexname_ord, fast_term_ord; changed sort_ord and typ_ord to use fast_string_ord and fast_indexname_ord (term_ord is NOT affected); structures Symtab, Vartab, Typtab, Termtab use the fast orders now -- potential INCOMPATIBILITY for code that depends on a particular order for Symtab.keys, Symtab.dest, etc. (consider using Library.sort_strings on result). * Pure/term.ML: combinators fold_atyps, fold_aterms, fold_term_types, fold_types traverse types/terms from left to right, observing natural argument order. Supercedes previous foldl_XXX versions, add_frees, add_vars etc. have been adapted as well: INCOMPATIBILITY. * Pure: name spaces have been refined, with significant changes of the internal interfaces -- INCOMPATIBILITY. Renamed cond_extern(_table) to extern(_table). The plain name entry path is superceded by a general 'naming' context, which also includes the 'policy' to produce a fully qualified name and external accesses of a fully qualified name; NameSpace.extend is superceded by context dependent Sign.declare_name. Several theory and proof context operations modify the naming context. Especially note Theory.restore_naming and ProofContext.restore_naming to get back to a sane state; note that Theory.add_path is no longer sufficient to recover from Theory.absolute_path in particular. * Pure: new flags short_names (default false) and unique_names (default true) for controlling output of qualified names. If short_names is set, names are printed unqualified. If unique_names is reset, the name prefix is reduced to the minimum required to achieve the original result when interning again, even if there is an overlap with earlier declarations. * Pure/TheoryDataFun: change of the argument structure; 'prep_ext' is now 'extend', and 'merge' gets an additional Pretty.pp argument (useful for printing error messages). INCOMPATIBILITY. * Pure: major reorganization of the theory context. Type Sign.sg and Theory.theory are now identified, referring to the universal Context.theory (see Pure/context.ML). Actual signature and theory content is managed as theory data. The old code and interfaces were spread over many files and structures; the new arrangement introduces considerable INCOMPATIBILITY to gain more clarity: Context -- theory management operations (name, identity, inclusion, parents, ancestors, merge, etc.), plus generic theory data; Sign -- logical signature and syntax operations (declaring consts, types, etc.), plus certify/read for common entities; Theory -- logical theory operations (stating axioms, definitions, oracles), plus a copy of logical signature operations (consts, types, etc.); also a few basic management operations (Theory.copy, Theory.merge, etc.) The most basic sign_of operations (Theory.sign_of, Thm.sign_of_thm etc.) as well as the sign field in Thm.rep_thm etc. have been retained for convenience -- they merely return the theory. * Pure: type Type.tsig is superceded by theory in most interfaces. * Pure: the Isar proof context type is already defined early in Pure as Context.proof (note that ProofContext.context and Proof.context are aliases, where the latter is the preferred name). This enables other Isabelle components to refer to that type even before Isar is present. * Pure/sign/theory: discontinued named name spaces (i.e. classK, typeK, constK, axiomK, oracleK), but provide explicit operations for any of these kinds. For example, Sign.intern typeK is now Sign.intern_type, Theory.hide_space Sign.typeK is now Theory.hide_types. Also note that former Theory.hide_classes/types/consts are now Theory.hide_classes_i/types_i/consts_i, while the non '_i' versions internalize their arguments! INCOMPATIBILITY. * Pure: get_thm interface (of PureThy and ProofContext) expects datatype thmref (with constructors Name and NameSelection) instead of plain string -- INCOMPATIBILITY; * Pure: cases produced by proof methods specify options, where NONE means to remove case bindings -- INCOMPATIBILITY in (RAW_)METHOD_CASES. * Pure: the following operations retrieve axioms or theorems from a theory node or theory hierarchy, respectively: Theory.axioms_of: theory -> (string * term) list Theory.all_axioms_of: theory -> (string * term) list PureThy.thms_of: theory -> (string * thm) list PureThy.all_thms_of: theory -> (string * thm) list * Pure: print_tac now outputs the goal through the trace channel. * Isar toplevel: improved diagnostics, mostly for Poly/ML only. Reference Toplevel.debug (default false) controls detailed printing and tracing of low-level exceptions; Toplevel.profiling (default 0) controls execution profiling -- set to 1 for time and 2 for space (both increase the runtime). * Isar session: The initial use of ROOT.ML is now always timed, i.e. the log will show the actual process times, in contrast to the elapsed wall-clock time that the outer shell wrapper produces. * Simplifier: improved handling of bound variables (nameless representation, avoid allocating new strings). Simprocs that invoke the Simplifier recursively should use Simplifier.inherit_bounds to avoid local name clashes. Failure to do so produces warnings "Simplifier: renamed bound variable ..."; set Simplifier.debug_bounds for further details. * ML functions legacy_bindings and use_legacy_bindings produce ML fact bindings for all theorems stored within a given theory; this may help in porting non-Isar theories to Isar ones, while keeping ML proof scripts for the time being. * ML operator HTML.with_charset specifies the charset begin used for generated HTML files. For example: HTML.with_charset "utf-8" use_thy "Hebrew"; HTML.with_charset "utf-8" use_thy "Chinese"; *** System *** * Allow symlinks to all proper Isabelle executables (Isabelle, isabelle, isatool etc.). * ISABELLE_DOC_FORMAT setting specifies preferred document format (for isatool doc, isatool mkdir, display_drafts etc.). * isatool usedir: option -f allows specification of the ML file to be used by Isabelle; default is ROOT.ML. * New isatool version outputs the version identifier of the Isabelle distribution being used. * HOL: new isatool dimacs2hol converts files in DIMACS CNF format (containing Boolean satisfiability problems) into Isabelle/HOL theories. 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 latex output syntax of UN and INT has been changed from "\Union x \in A. B" to "\Union_{x \in A} B" i.e. the index formulae has become a subscript. Similarly for "\Union x. B", and for \Inter instead of \Union. * 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. * HOL/List: Ordering "lexico" is renamed "lenlex" and the standard lexicographic dictonary ordering has been added as "lexord". * 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 (Gdel'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 Kammller, 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 Kammller); * 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; $Id$