Kananaskis 11

Kananaskis-11

(Released: 3 March 2017)

We are pleased to announce the Kananaskis-11 release of HOL 4.

New features:

• We have ported HOL Light’s PAT_CONV and PATH_CONV “conversionals”, providing nice machinery for applying conversions to specific sub-terms.

• The tactic PAT_ABBREV_TAC (also available in the Q module) can now use patterns that are more polymorphic than the sub-term in the goal that is ultimately matched. (Github issue)

• We have implemented the rule for constant specification described by Rob Arthan in HOL Constant Definition Done Right.
  The new primitive gen_prim_specification in the kernel is used to implement the new rule, gen_new_specification, and is also used to re-implement new_definition and new_specification.
  We removed prim_constant_definition from the kernel, but kept prim_specification because the new derivation of new_specification uses pairs.
  (Github pull-req)

• Various commands for moving over and selecting HOL tactics in the emacs mode have been improved.
  We have also added a new command hol-find-eval-next-tactic (bound to M-h M-e by default), which selects and highlights the next tactic in the source text, and then applies it to the current goal in the *HOL* buffer.
  This shortcuts the current idiom, which requires the tactic to be highlighted manually, and then applied via M-h e.
  (The advantage of the latter is that one can select specific tactic sequences to be applied all at once.)

• Record updates can now be more polymorphic. For example, if one defined

     Datatype`rcd = <| myset : α -> bool ; size : num |>`
  

  one used to get back an update constant for the myset field:

     rcd_myset_fupd : ((α -> bool) -> (α -> bool)) -> α rcd -> α rcd
  

  Now, the same constant is

     rcd_myset_fupd : ((α -> bool) -> (β -> bool)) -> α rcd -> β rcd
  

  One might use this to define

     Define`img (f:α->β) r = r with myset updated_by IMAGE f`
  

  This definition would have previously been rejected. (Github issue)

  This change can cause incompatibilities.
  If one wants the old behaviour, it should suffice to overload the record update syntax to use a more specific type.
  For example:

     val _ = gen_remove_ovl_mapping
               (GrammarSpecials.recfupd_special ^ "myset")
               ``λf x. rcd_myset_fupd f x``
  
     val _ = Parse.add_record_fupdate(
           "myset", Term.inst[beta |-> alpha] ``rcd_myset_fupd``);
  

• PolyML “heaps” are now implemented with its SaveState technology, used hierarchically.
  This should make heaps smaller as they now only save deltas over the last used heap.

Bugs fixed:

• An embarrassing infinite loop bug in the integration of the integer decision procedures (the Omega test, Cooper’s algorithm) into the simplifier was fixed.

• Theorems can now have names that are the same as SML constructor names (e.g., Empty). (Github issue)

• Holmake will now follow INCLUDES specifications from Holmakefiles when given “phony” targets to build on the command-line. (A typical phony target is all.) As in the past, it will still act only locally if given just a clean target (clean, cleanDeps or cleanAll). To clean recursively, you must also pass the -r flag to Holmake. (Github issue)

• We fixed three problems with Datatype. Thanks to Ramana Kumar for the reports.
  First, Datatype will no longer create a recursive type if the recursive instance is qualified with a theory name other than the current one.
  In other words,

      Datatype`num = C1 num$num | C2`
  

  won’t create a recursive type (assuming this is not called in theory num).
  (Hol_datatype had the same problem.)

  Second, Datatype will handle antiquotations in its input properly (Hol_datatype already did).

  Third, Datatype (and Hol_datatype) allows the definition of identical record types in different theories.

• Attempts to define constants or types with invalid names are now caught much earlier.
  An invalid name is one that contains “non-graphical” characters (as per SML’s Char.isGraph) or parentheses.
  This means that Unicode cannot be used in the kernel’s name for a constant, but certainly doesn’t prevent Unicode being used in overloaded notation.
  Functions such as overload_on, add_rule and set_mapped_fixity can still be used to create pretty notation with as many Unicode characters included as desired.

• Loading theories under Poly/ML would fail unnecessarily if the current directory was unwritable.
  Working in such directories will likely cause problems when and if an export_theory call is made, so there is a warning emitted in this situation, but the load now succeeds.
  Thanks to Narges Khakpour for the bug report.

• The function thm_to_string was creating ugly strings full of special codes (encoding type information) rather than using the “raw” backend.

• Bare record operations (e.g., rcdtype_field, the function that accesses field of type rcdtype) would occasionally pretty-print badly. (Github issue)

New tools:

• Holyhammer: A method for automatically finding relevant theorems for Metis.
  Given a term, the procedure selects a large number of lemmas through different predictors such as KNN or Mepo.
  These lemmas are given to the external provers E-prover (1.9), Vampire (2.6) or Z3 (4.0).
  The necessary lemmas in the provers' proofs are then returned to the user.
  Modifications to the kernels to track dependencies between theorems allow predictors to learn from the induced relation improving future predictions.
  The build of the source directory src/holyhammer needs ocaml (> 3.12.1) installed as well as a recent version of g++ that supports the C++11 standard.
  The three ATPs have to be installed independently.
  At least one of them should be present, preferably E-prover (1.9).

  Thanks to Thibault Gauthier for this tool.

• A principle for making coinductive definitions, Hol_coreln.
  The input syntax is the same as for Hol_reln, that is: a conjunction of introduction rules.
  For example, if one is representing coalgebraic lists as a subset of the type :num → α option, the coinductive predicate specifying the subset would be given as

     val (lrep_ok_rules, lrep_ok_coind, lrep_ok_cases) = Hol_coreln`
       lrep_ok (λn. NONE)
           ∧
       ∀h t.
         lrep_ok t
             ⇒
         lrep_ok (λn. if n = 0 then SOME h else t(n - 1))
     `;
  

  as is now done in src/llist/llistScript.sml.

  Thanks to Andrea Condoluci for this tool.

New examples:

• A theory of balanced binary trees (examples/balanced_bst), based on Haskell code by Leijen and Palamarchuk, and mechanised by Scott Owens. The type supports operations such as insert, union, delete, filters and folds. Operations are parameterised by comparison operators for comparing keys. Balanced trees can themselves be compared.

• A formalisation of pattern matches (examples/pattern_matches).
  Pattern matching is not directly supported by higher-order logic.
  HOL4’s parser therefore compiles case-expressions (case x of ...) to decision trees based on case constants.
  For non-trivial case expressions, there is a big discrepancy between the user’s view and this internal representation.
  The pattern_matches example defines a new general-purpose representation for case expressions that mirrors the input syntax in the internal representation closely.
  Because of this close connection, the new representation is more intuitive and often much more compact.
  Complicated parsers and pretty-printers are no longer required.
  Proofs can more closely follow the user’s intentions, and code generators (like CakeML) can produce better code.
  Moreover, the new representation is strictly more general than the currently used representation.
  The new representation allows for guards, patterns with multiple occurrences of the same bound variable, unbound variables, arithmetic expressions in patterns, and more.
  The example provides the definitions as well as tools to work with the new case-expressions.
  These tools include support for evaluating and simplifying them, a highly configurable pattern compilation algorithm inside the logic, and optimisations like detecting redundant rows and eliminating them.

Incompatibilities:

• The function optionSyntax.dest_none will now unwrap the type of its result, e.g., returning :α rather than :α option when applied to NONE : α option. This brings it into line with the behaviour of listSyntax.dest_nil. See this github issue.

• The functions Q.MATCH_RENAME_TAC and Q.MATCH_ASSUM_RENAME_TAC have been adjusted to lose their second arguments (the list of variable names that are not to be bound). For example, applying Q.MATCH_RENAME_TAC `(f x = Pair c1 c2) ⇒ X` ["X"] to the goal

       ?- (f x = Pair C'' C0') ⇒ (f C'' = f C0')
  

  used to result in the renamed goal

       ?- (f x = Pair c1 c2) ⇒ (f c1 = f c2)
  

  where the X in the pattern was ignored.
  The interface now achieves the same end by simply allowing the user to write underscores in the pattern.
  Thus, the tactic would become Q.MATCH_RENAME_TAC `(f x = Pair c1 c2) ⇒ _` .
  Multiple underscores can be used to ignore multiple sub-terms.

  Of course, the qmatch_rename_tac and qmatch_assum_rename_tac names for these tactics in bossLib have changed types as well.
  The new Q.MATCH_GOALSUB_RENAME_TAC and Q.MATCH_ASMSUB_RENAME_TAC (and their lower-case versions) have similar types, without explicit lists of variable names to ignore.

• The theory state_option was removed.
  The better-developed errorStateMonad theory should be used instead.

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