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Changes from V8.3 to V8.4
=========================
New proof engine
Changes from V8.2 to V8.3
=========================
Rewriting tactics
- Tactic "rewrite" now supports rewriting on ad hoc equalities such as eq_true.
- "Hint Rewrite" now checks that the lemma looks like an equation.
- New tactic "etransitivity".
- Support for heterogeneous equality (JMeq) in "injection" and "discriminate".
- Tactic "subst" now supports heterogeneous equality and equality
proofs that are dependent (use "simple subst" for preserving compatibility).
- Added support for Leibniz-rewriting of dependent hypotheses.
- Renamed "Morphism" into "Proper" and "respect" into "proper_prf"
(possible source of incompatibility).
- New tactic variants "rewrite* by" and "autorewrite*" that rewrite
respectively the first and all matches whose side-conditions are
solved.
- "Require Import Setoid" does not export all of "Morphisms" and
"RelationClasses" anymore (possible source of incompatibility, fixed
by importing "Morphisms" too).
- Support added for using Chung-Kil Hur's Heq library for rewriting over
heterogeneous equality (courtesy of the library's author).
- Tactic "replace" supports matching terms with holes.
Automation tactics
- Tactic "intuition" now preserves inner "iff" and "not" (exceptional
source of incompatibilities solvable by redefining "intuition" as
"unfold iff, not in *; intuition", or by using "Set Intuition Unfolding".)
- Tactic "tauto" now proves classical tautologies as soon as classical logic
(i.e. library Classical_Prop or Classical) is loaded.
- Tactic "gappa" has been removed from the Dp plugin.
- Tactic "firstorder" now supports the combination of its "using" and
"with" options.
- New "Hint Resolve ->" (or "<-") for declaring iff's as oriented
hints (wish #2104).
- An inductive type as argument of the "using" option of "auto/eauto/firstorder"
is interpreted as using the collection of its constructors.
- New decision tactic "nsatz" to prove polynomial equations
by computation of Groebner bases.
Other tactics
- Tactic "discriminate" now performs intros before trying to discriminate an
hypothesis of the goal (previously it applied intro only if the goal
had the form t1<>t2) (exceptional source of incompatibilities - former
behavior can be obtained by "Unset Discriminate Introduction").
- Tactic "quote" now supports quotation of arbitrary terms (not just the
goal).
- Tactic "idtac" now displays its "list" arguments.
- New introduction patterns "*" for introducing the next block of dependent
variables and "**" for introducing all quantified variables and hypotheses.
- Pattern Unification for existential variables activated in tactics and
new option "Unset Tactic Evars Pattern Unification" to deactivate it.
- Resolution of canonical structure is now part of the tactic's unification
algorithm.
- New tactic "decide lemma with hyp" for rewriting decidability lemmas
when one knows which side is true.
- Improved support of dependent goals over objects in dependent types for
"destruct" (rare source of incompatibility that can be avoided by unsetting
option "Dependent Propositions Elimination").
- Tactic "exists", "eexists", "destruct" and "edestruct" supports iteration
using comma-separated arguments.
- Tactic names "case" and "elim" now support clauses "as" and "in" and become
then synonymous of "destruct" and "induction" respectively.
- A new tactic name "exfalso" for the use of 'ex-falso quodlibet' principle.
This tactic is simply a shortcut for "elimtype False".
- Made quantified hypotheses get the name they would have if introduced in
the context (possible but rare source of incompatibilities).
- When applying a component of a conjunctive lemma, "apply in" (and
sequences of "apply in") now leave the side conditions of the lemmas
uniformly after the main goal (possible source of rare incompatibilities).
- In "simpl c" and "change c with d", c can be a pattern.
- Tactic "revert" now preserves let-in's making it the exact inverse of
"intro".
- New tactics "clear dependent H" and "revert dependent H" that
clears (resp. reverts) H and all the hypotheses that depend on H.
- Ltac's pattern-matching now supports matching metavariables that
depend on variables bound upwards in the pattern.
Tactic definitions
- Ltac definitions support Local option for non-export outside modules.
- Support for parsing non-empty lists with separators in tactic notations.
- New command "Locate Ltac" to get the full name of an Ltac definition.
Notations
- Record syntax "{|x=...; y=...|}" now works inside patterns too.
- Abbreviations from non-imported module now invisible at printing time.
- Abbreviations now use implicit arguments and arguments scopes for printing.
- Abbreviations to pure names now strictly behave like the name they refer to
(make redirections of qualified names easier).
- Abbreviations for applied constant now propagate the implicit arguments
and arguments scope of the underlying reference (possible source of
incompatibilities generally solvable by changing such abbreviations from
e.g. "Notation foo' := (foo x)" to "Notation foo' y := (foo x (y:=y))").
- The "where" clause now supports multiple notations per defined object.
- Recursive notations automatically expand one step on the left for better
factorization; recursion notations inner separators now ensured being tokens.
- Added "Reserved Infix" as a specific shortcut of the corresponding
"Reserved Notation".
- Open/Close Scope command supports Global option in sections.
Specification language
- New support for local binders in the syntax of Record/Structure fields.
- Fixpoint/CoFixpoint now support building part or all of bodies using tactics.
- Binders given before ":" in lemmas and in definitions built by tactics are
now automatically introduced (possible source of incompatibility that can
be resolved by invoking "Unset Automatic Introduction").
- New support for multiple implicit arguments signatures per reference.
Module system
- Include Type is now deprecated since Include now accept both modules and
module types.
- Declare ML Module supports Local option.
- The sharing between non-logical object and the management of the
name-space has been improved by the new "Delta-equivalence" on
qualified name.
- The include operator has been extended to high-order structures
- Sequences of Include can be abbreviated via new syntax "<+".
- A module (or module type) can be given several "<:" signatures.
- Interactive proofs are now permitted in module type. Functors can hence
be declared as Module Type and be used later to type themselves.
- A functor application can be prefixed by a "!" to make it ignore any
"Inline" annotation in the type of its argument(s) (for examples of
use of the new features, see libraries Structures and Numbers).
- Coercions are now active only when modules are imported (use "Set Automatic
Coercions Import" to get the behavior of the previous versions of Coq).
Extraction
- When using (Recursive) Extraction Library, the filenames are directly the
Coq ones with new appropriate extensions : we do not force anymore
uncapital first letters for Ocaml and capital ones for Haskell.
- The extraction now tries harder to avoid code transformations that can be
dangerous for the complexity. In particular many eta-expansions at the top
of functions body are now avoided, clever partial applications will likely
be preserved, let-ins are almost always kept, etc.
- In the same spirit, auto-inlining is now disabled by default, except for
induction principles, since this feature was producing more frequently
weird code than clear gain. The previous behavior can be restored via
"Set Extraction AutoInline".
- Unicode characters in identifiers are now transformed into ascii strings
that are legal in Ocaml and other languages.
- Harsh support of module extraction to Haskell and Scheme: module hierarchy
is flattened, module abbreviations and functor applications are expanded,
module types and unapplied functors are discarded.
- Less unsupported situations when extracting modules to Ocaml. In particular
module parameters might be alpha-renamed if a name clash is detected.
- Extract Inductive is now possible toward non-inductive types (e.g. nat => int)
- Extraction Implicit: this new experimental command allows to mark
some arguments of a function or constructor for removed during
extraction, even if these arguments don't fit the usual elimination
principles of extraction, for instance the length n of a vector.
- Files ExtrOcaml*.v in plugins/extraction try to provide a library of common
extraction commands: mapping of basics types toward Ocaml's counterparts,
conversions from/to int and big_int, or even complete mapping of nat,Z,N
to int or big_int, or mapping of ascii to char and string to char list
(in this case recognition of ascii constants is hard-wired in the extraction).
Program
- Streamlined definitions using well-founded recursion and measures so
that they can work on any subset of the arguments directly (uses currying).
- Try to automatically clear structural fixpoint prototypes in
obligations to avoid issues with opacity.
- Use return type clause inference in pattern-matching as in the standard
typing algorithm.
- Support [Local Obligation Tactic] and [Next Obligation with tactic].
- Use [Show Obligation Tactic] to print the current default tactic.
- [fst] and [snd] have maximal implicit arguments in Program now (possible
source of incompatibility).
Type classes
- Declaring axiomatic type class instances in Module Type should be now
done via new command "Declare Instance", while the syntax "Instance"
now always provides a concrete instance, both in and out of Module Type.
- Use [Existing Class foo] to declare foo as a class a posteriori.
[foo] can be an inductive type or a constant definition. No
projections or instances are defined.
- Various bug fixes and improvements: support for defined fields,
anonymous instances, declarations giving terms, better handling of
sections and [Context].
Vernacular commands
- New command "Timeout <n> <command>." interprets a command and a timeout
interrupts the interpretation after <n> seconds.
- New command "Compute <expr>." is a shortcut for "Eval vm_compute in <expr>".
- New command "Fail <command>." interprets a command and is successful iff
the command fails on an error (but not an anomaly). Handy for tests and
illustration of wrong commands.
- Most commands referring to constant (e.g. Print or About) now support
referring to the constant by a notation string.
- New option "Boolean Equality Schemes" to make generation of boolean
equality automatic for datatypes (together with option "Decidable
Equality Schemes", this replaces deprecated option "Equality Scheme").
- Made support for automatic generation of case analysis schemes available
to user (governed by option "Set Case Analysis Schemes").
- New command "(Global?) Generalizable [All|No] Variable(s)? ident(s)?" to
declare which identifiers are generalizable in `{} and `() binders.
- New command "Print Opaque Dependencies" to display opaque constants in
addition to all variables, parameters or axioms a theorem or
definition relies on.
- New command "Declare Reduction <id> := <conv_expr>", allowing to write
later "Eval <id> in ...". This command accepts a Local variant.
- Syntax of Implicit Type now supports more than one block of variables of
a given type.
- Command "Canonical Structure" now warns when it has no effects.
- Commands of the form "Set X" or "Unset X" now support "Local" and "Global"
prefixes.
Library
- Use "standard" Coq names for the properties of eq and identity
(e.g. refl_equal is now eq_refl). Support for compatibility is provided.
- The function Compare_dec.nat_compare is now defined directly,
instead of relying on lt_eq_lt_dec. The earlier version is still
available under the name nat_compare_alt.
- Lemmas in library Relations and Reals have been homogenized a bit.
- The implicit argument of Logic.eq is now maximally inserted, allowing
to simply write "eq" instead of "@eq _" in morphism signatures.
- Wrongly named lemmas (Zlt_gt_succ and Zlt_succ_gt) fixed (potential source
of incompatibilities)
- List library:
- Definitions of list, length and app are now in Init/Datatypes.
Support for compatibility is provided.
- Definition of Permutation is now in Sorting/Permtation.v
- Some other light revisions and extensions (possible source
of incompatibilities solvable by qualifying names accordingly).
- In ListSet, set_map has been fixed (source of incompatibilities if used).
- Sorting library:
- new mergesort of worst-case complexity O(n*ln(n)) made available in
Mergesort.v;
- former notion of permutation up to setoid from Permutation.v is
deprecated and moved to PermutSetoid.v;
- heapsort from Heap.v of worst-case complexity O(n*n) is deprecated;
- new file Sorted.v for some definitions of being sorted.
- Structure library. This new library is meant to contain generic
structures such as types with equalities or orders, either
in Module version (for now) or Type Classes (still to do):
- DecidableType.v and OrderedType.v: initial notions for FSets/FMaps,
left for compatibility but considered as deprecated.
- Equalities.v and Orders.v: evolutions of the previous files,
with fine-grain Module architecture, many variants, use of
Equivalence and other relevant Type Classes notions.
- OrdersTac.v: a generic tactic for solving chains of (in)equalities
over variables. See {Nat,N,Z,P}OrderedType.v for concrete instances.
- GenericMinMax.v: any ordered type can be equipped with min and max.
We derived here all the generic properties of these functions.
- MSets library: an important evolution of the FSets library.
"MSets" stands for Modular (Finite) Sets, by contrast with a forthcoming
library of Class (Finite) Sets contributed by S. Lescuyer which will be
integrated with the next release of Coq. The main features of MSets are:
- The use of Equivalence, Proper and other Type Classes features
easing the handling of setoid equalities.
- The interfaces are now stated in iff-style. Old specifications
are now derived properties.
- The compare functions are now pure, and return a "comparison" value.
Thanks to the CompSpec inductive type, reasoning on them remains easy.
- Sets structures requiring invariants (i.e. sorted lists) are
built first as "Raw" sets (pure objects and separate proofs) and
attached with their proofs thanks to a generic functor. "Raw" sets
have now a proper interface and can be manipulated directly.
Note: No Maps yet in MSets. The FSets library is still provided
for compatibility, but will probably be considered as deprecated in the
next release of Coq.
- Numbers library:
- The abstract layer (NatInt, Natural/Abstract, Integer/Abstract) has
been simplified and enhance thanks to new features of the module
system such as Include (see above). It has been extended to Euclidean
division (three flavors for integers: Trunc, Floor and Math).
- The arbitrary-large efficient numbers (BigN, BigZ, BigQ) has also
been reworked. They benefit from the abstract layer improvements
(especially for div and mod). Note that some specifications have
slightly changed (compare, div, mod, shift{r,l}). Ring/Field should
work better (true recognition of constants).
Tools
- Option -R now supports binding Coq root read-only.
- New coqtop/coqc option -beautify to reformat .v files (usable
e.g. to globally update notations).
- New tool beautify-archive to beautify a full archive of developments.
- New coqtop/coqc option -compat X.Y to simulate the general behavior
of previous versions of Coq (provides e.g. support for 8.2 compatibility).
Coqdoc
- List have been revamped. List depth and scope is now determined by
an "offside" whitespace rule.
- Text may be italicized by placing it in _underscores_.
- The "--index <string>" flag changes the filename of the index.
- The "--toc-depth <int>" flag limits the depth of headers which are
included in the table of contents.
- The "--lib-name <string>" flag prints "<string> Foo" instead of
"Library Foo" where library titles are called for. The
"--no-lib-name" flag eliminates the extra title.
- New option "--parse-comments" to allow parsing of regular "(* *)"
comments.
- New option "--plain-comments" to disable interpretation inside comments.
- New option "--interpolate" to try and typeset identifiers in Coq escapings
using the available globalization information.
- New option "--external url root" to refer to external libraries.
- Links to section variables and notations now supported.
Internal infrastructure
- To avoid confusion with the repository of user's contributions,
the subdirectory "contrib" has been renamed into "plugins".
On platforms supporting ocaml native dynlink, code located there
is built as loadable plugins for coqtop.
- An experimental build mechanism via ocamlbuild is provided.
From the top of the archive, run ./configure as usual, and
then ./build. Feedback about this build mechanism is most welcome.
Compiling Coq on platforms such as Windows might be simpler
this way, but this remains to be tested.
- The Makefile system has been simplified and factorized with
the ocamlbuild system. In particular "make" takes advantage
of .mllib files for building .cma/.cmxa. The .vo files to
compile are now listed in several vo.itarget files.
Changes from V8.1 to V8.2
=========================
Language
- If a fixpoint is not written with an explicit { struct ... }, then
all arguments are tried successively (from left to right) until one is
found that satisfies the structural decreasing condition.
- New experimental typeclass system giving ad-hoc polymorphism and
overloading based on dependent records and implicit arguments.
- New syntax "let 'pat := b in c" for let-binding using irrefutable patterns.
- New syntax "forall {A}, T" for specifying maximally inserted implicit
arguments in terms.
- Sort of Record/Structure, Inductive and CoInductive defaults to Type
if omitted.
- (Co)Inductive types can be defined as records
(e.g. "CoInductive stream := { hd : nat; tl : stream }.")
- New syntax "Theorem id1:t1 ... with idn:tn" for proving mutually dependent
statements.
- Support for sort-polymorphism on constants denoting inductive types.
- Several evolutions of the module system (handling of module aliases,
functorial module types, an Include feature, etc).
- Prop now a subtype of Set (predicative and impredicative forms).
- Recursive inductive types in Prop with a single constructor of which
all arguments are in Prop is now considered to be a singleton
type. It consequently supports all eliminations to Prop, Set and Type.
As a consequence, Acc_rect has now a more direct proof [possible source
of easily fixed incompatibility in case of manual definition of a recursor
in a recursive singleton inductive type].
Vernacular commands
- Added option Global to "Arguments Scope" for section surviving.
- Added option "Unset Elimination Schemes" to deactivate the automatic
generation of elimination schemes.
- Modification of the Scheme command so you can ask for the name to be
automatically computed (e.g. Scheme Induction for nat Sort Set).
- New command "Combined Scheme" to build combined mutual induction
principles from existing mutual induction principles.
- New command "Scheme Equality" to build a decidable (boolean) equality
for simple inductive datatypes and a decision property over this equality
(e.g. Scheme Equality for nat).
- Added option "Set Equality Scheme" to make automatic the declaration
of the boolean equality when possible.
- Source of universe inconsistencies now printed when option
"Set Printing Universes" is activated.
- New option "Set Printing Existential Instances" for making the display of
existential variable instances explicit.
- Support for option "[id1 ... idn]", and "-[id1 ... idn]", for the
"compute"/"cbv" reduction strategy, respectively meaning reduce only, or
everything but, the constants id1 ... idn. "lazy" alone or followed by
"[id1 ... idn]", and "-[id1 ... idn]" also supported, meaning apply
all of beta-iota-zeta-delta, possibly restricting delta.
- New command "Strategy" to control the expansion of constants during
conversion tests. It generalizes commands Opaque and Transparent by
introducing a range of levels. Lower levels are assigned to constants
that should be expanded first.
- New options Global and Local to Opaque and Transparent.
- New command "Print Assumptions" to display all variables, parameters
or axioms a theorem or definition relies on.
- "Add Rec LoadPath" now provides references to libraries using partially
qualified names (this holds also for coqtop/coqc option -R).
- SearchAbout supports negated search criteria, reference to logical objects
by their notation, and more generally search of subterms.
- "Declare ML Module" now allows to import .cmxs files when Coq is
compiled in native code with a version of OCaml that supports native
Dynlink (>= 3.11).
- Specific sort constraints on Record now taken into account.
- "Print LoadPath" supports a path argument to filter the display.
Libraries
- Several parts of the libraries are now in Type, in particular FSets,
SetoidList, ListSet, Sorting, Zmisc. This may induce a few
incompatibilities. In case of trouble while fixing existing development,
it may help to simply declare Set as an alias for Type (see file
SetIsType).
- New arithmetical library in theories/Numbers. It contains:
* an abstract modular development of natural and integer arithmetics
in Numbers/Natural/Abstract and Numbers/Integer/Abstract
* an implementation of efficient computational bounded and unbounded
integers that can be mapped to processor native arithmetics.
See Numbers/Cyclic/Int31 for 31-bit integers and Numbers/Natural/BigN
for unbounded natural numbers and Numbers/Integer/BigZ for unbounded
integers.
* some proofs that both older libraries Arith, ZArith and NArith and
newer BigN and BigZ implement the abstract modular development.
This allows in particular BigN and BigZ to already come with a
large database of basic lemmas and some generic tactics (ring),
This library has still an experimental status, as well as the
processor-acceleration mechanism, but both its abstract and its
concrete parts are already quite usable and could challenge the use
of nat, N and Z in actual developments. Moreover, an extension of
this framework to rational numbers is ongoing, and an efficient
Q structure is already provided (see Numbers/Rational/BigQ), but
this part is currently incomplete (no abstract layer and generic
lemmas).
- Many changes in FSets/FMaps. In practice, compatibility with earlier
version should be fairly good, but some adaptations may be required.
* Interfaces of unordered ("weak") and ordered sets have been factorized
thanks to new features of Coq modules (in particular Include), see
FSetInterface. Same for maps. Hints in these interfaces have been
reworked (they are now placed in a "set" database).
* To allow full subtyping between weak and ordered sets, a field
"eq_dec" has been added to OrderedType. The old version of OrderedType
is now called MiniOrderedType and functor MOT_to_OT allow to
convert to the new version. The interfaces and implementations
of sets now contain also such a "eq_dec" field.
* FSetDecide, contributed by Aaron Bohannon, contains a decision
procedure allowing to solve basic set-related goals (for instance,
is a point in a particular set ?). See FSetProperties for examples.
* Functors of properties have been improved, especially the ones about
maps, that now propose some induction principles. Some properties
of fold need less hypothesis.
* More uniformity in implementations of sets and maps: they all use
implicit arguments, and no longer export unnecessary scopes (see
bug #1347)
* Internal parts of the implementations based on AVL have evolved a
lot. The main files FSetAVL and FMapAVL are now much more
lightweight now. In particular, minor changes in some functions
has allowed to fully separate the proofs of operational
correctness from the proofs of well-balancing: well-balancing is
critical for efficiency, but not anymore for proving that these
trees implement our interfaces, hence we have moved these proofs
into appendix files FSetFullAVL and FMapFullAVL. Moreover, a few
functions like union and compare have been modified in order to be
structural yet efficient. The appendix files also contains
alternative versions of these few functions, much closer to the
initial Ocaml code and written via the Function framework.
- Library IntMap, subsumed by FSets/FMaps, has been removed from
Coq Standard Library and moved into a user contribution Cachan/IntMap
- Better computational behavior of some constants (eq_nat_dec and
le_lt_dec more efficient, Z_lt_le_dec and Positive_as_OT.compare
transparent, ...) (exceptional source of incompatibilities).
- Boolean operators moved from module Bool to module Datatypes (may need
to rename qualified references in script and force notations || and &&
to be at levels 50 and 40 respectively).
- The constructors xI and xO of type positive now have postfix notations
"~1" and "~0", allowing to write numbers in binary form easily, for instance
6 is 1~1~0 and 4*p is p~0~0 (see BinPos.v).
- Improvements to NArith (Nminus, Nmin, Nmax), and to QArith (in particular
a better power function).
- Changes in ZArith: several additional lemmas (used in theories/Numbers),
especially in Zdiv, Znumtheory, Zpower. Moreover, many results in
Zdiv have been generalized: the divisor may simply be non-null
instead of strictly positive (see lemmas with name ending by
"_full"). An alternative file ZOdiv proposes a different behavior
(the one of Ocaml) when dividing by negative numbers.
- Changes in Arith: EqNat and Wf_nat now exported from Arith, some
constructions on nat that were outside Arith are now in (e.g. iter_nat).
- In SetoidList, eqlistA now expresses that two lists have similar elements
at the same position, while the predicate previously called eqlistA
is now equivlistA (this one only states that the lists contain the same
elements, nothing more).
- Changes in Reals:
* Most statement in "sigT" (including the
completeness axiom) are now in "sig" (in case of incompatibility,
use proj1_sig instead of projT1, sig instead of sigT, etc).
* More uniform naming scheme (identifiers in French moved to English,
consistent use of 0 -- zero -- instead of O -- letter O --, etc).
* Lemma on prod_f_SO is now on prod_f_R0.
* Useless hypothesis of ln_exists1 dropped.
* New Rlogic.v states a few logical properties about R axioms.
* RIneq.v extended and made cleaner.
- Slight restructuration of the Logic library regarding choice and classical
logic. Addition of files providing intuitionistic axiomatizations of
descriptions: Epsilon.v, Description.v and IndefiniteDescription.v.
- Definition of pred and minus made compatible with the structural
decreasing criterion for use in fixpoints.
- Files Relations/Rstar.v and Relations/Newman.v moved out to the user
contribution repository (contribution CoC_History). New lemmas about
transitive closure added and some bound variables renamed (exceptional
risk of incompatibilities).
- Syntax for binders in terms (e.g. for "exists") supports anonymous names.
Notations, coercions, implicit arguments and type inference
- More automation in the inference of the return clause of dependent
pattern-matching problems.
- Experimental allowance for omission of the clauses easily detectable as
impossible in pattern-matching problems.
- Improved inference of implicit arguments.
- New options "Set Maximal Implicit Insertion", "Set Reversible Pattern
Implicit", "Set Strongly Strict Implicit" and "Set Printing Implicit
Defensive" for controlling inference and use of implicit arguments.
- New modifier in "Implicit Arguments" to force an implicit argument to
be maximally inserted.
- New modifier of "Implicit Arguments" to enrich the set of implicit arguments.
- New options Global and Local to "Implicit Arguments" for section
surviving or non export outside module.
- Level "constr" moved from 9 to 8.
- Structure/Record now printed as Record (unless option Printing All is set).
- Support for parametric notations defining constants.
- Insertion of coercions below product types refrains to unfold
constants (possible source of incompatibility).
- New support for fix/cofix in notations.
Tactic Language
- Second-order pattern-matching now working in Ltac "match" clauses
(syntax for second-order unification variable is "@?X").
- Support for matching on let bindings in match context using syntax
"H := body" or "H := body : type".
- Ltac accepts integer arguments (syntax is "ltac:nnn" for nnn an integer).
- The general sequence tactical "expr_0 ; [ expr_1 | ... | expr_n ]"
is extended so that at most one expr_i may have the form "expr .."
or just "..". Also, n can be different from the number of subgoals
generated by expr_0. In this case, the value of expr (or idtac in
case of just "..") is applied to the intermediate subgoals to make
the number of tactics equal to the number of subgoals.
- A name used as the name of the parameter of a lemma (like f in
"apply f_equal with (f:=t)") is now interpreted as a ltac variable
if such a variable exists (this is a possible source of
incompatibility and it can be fixed by renaming the variables of a
ltac function into names that do not clash with the lemmas
parameter names used in the tactic).
- New syntax "Ltac tac ::= ..." to rebind a tactic to a new expression.
- "let rec ... in ... " now supported for expressions without explicit
parameters; interpretation is lazy to the contrary of "let ... in ...";
hence, the "rec" keyword can be used to turn the argument of a
"let ... in ..." into a lazy one.
- Patterns for hypotheses types in "match goal" are now interpreted in
type_scope.
- A bound variable whose name is not used elsewhere now serves as
metavariable in "match" and it gets instantiated by an identifier
(allow e.g. to extract the name of a statement like "exists x, P x").
- New printing of Ltac call trace for better debugging.
Tactics
- New tactics "apply -> term", "apply <- term", "apply -> term in
ident", "apply <- term in ident" for applying equivalences (iff).
- Slight improvement of the hnf and simpl tactics when applied on
expressions with explicit occurrences of match or fix.
- New tactics "eapply in", "erewrite", "erewrite in".
- New tactics "ediscriminate", "einjection", "esimplify_eq".
- Tactics "discriminate", "injection", "simplify_eq" now support any
term as argument. Clause "with" is also supported.
- Unfoldable references can be given by notation's string rather than by name
in unfold.
- The "with" arguments are now typed using informations from the current goal:
allows support for coercions and more inference of implicit arguments.
- Application of "f_equal"-style lemmas works better.
- Tactics elim, case, destruct and induction now support variants eelim,
ecase, edestruct and einduction.
- Tactics destruct and induction now support the "with" option and the
"in" clause option. If the option "in" is used, an equality is added
to remember the term to which the induction or case analysis applied
(possible source of parsing incompatibilities when destruct or induction is
part of a let-in expression in Ltac; extra parentheses are then required).
- New support for "as" clause in tactics "apply in" and "eapply in".
- Some new intro patterns:
* intro pattern "?A" genererates a fresh name based on A.
Caveat about a slight loss of compatibility:
Some intro patterns don't need space between them. In particular
intros ?a?b used to be legal and equivalent to intros ? a ? b. Now it
is still legal but equivalent to intros ?a ?b.
* intro pattern "(A & ... & Y & Z)" synonym to "(A,....,(Y,Z)))))"
for right-associative constructs like /\ or exists.
- Several syntax extensions concerning "rewrite":
* "rewrite A,B,C" can be used to rewrite A, then B, then C. These rewrites
occur only on the first subgoal: in particular, side-conditions of the
"rewrite A" are not concerned by the "rewrite B,C".
* "rewrite A by tac" allows to apply tac on all side-conditions generated by
the "rewrite A".
* "rewrite A at n" allows to select occurrences to rewrite: rewrite only
happen at the n-th exact occurrence of the first successful matching of
A in the goal.
* "rewrite 3 A" or "rewrite 3!A" is equivalent to "rewrite A,A,A".
* "rewrite !A" means rewriting A as long as possible (and at least once).
* "rewrite 3?A" means rewriting A at most three times.
* "rewrite ?A" means rewriting A as long as possible (possibly never).
* many of the above extensions can be combined with each other.
- Introduction patterns better respect the structure of context in presence of
missing or extra names in nested disjunction-conjunction patterns [possible
source of rare incompatibilities].
- New syntax "rename a into b, c into d" for "rename a into b; rename c into d"
- New tactics "dependent induction/destruction H [ generalizing id_1 .. id_n ]"
to do induction-inversion on instantiated inductive families à la BasicElim.
- Tactics "apply" and "apply in" now able to reason modulo unfolding of
constants (possible source of incompatibility in situations where apply
may fail, e.g. as argument of a try or a repeat and in a ltac function);
versions that do not unfold are renamed into "simple apply" and
"simple apply in" (usable for compatibility or for automation).
- Tactics "apply" and "apply in" now able to traverse conjunctions and to
select the first matching lemma among the components of the conjunction;
tactic "apply" also able to apply lemmas of conclusion an empty type.
- Tactic "apply" now supports application of several lemmas in a row.
- Tactics "set" and "pose" can set functions using notation "(f x1..xn := c)".
- New tactic "instantiate" (without argument).
- Tactic firstorder "with" and "using" options have their meaning swapped for
consistency with auto/eauto (source of incompatibility).
- Tactic "generalize" now supports "at" options to specify occurrences
and "as" options to name the quantified hypotheses.
- New tactic "specialize H with a" or "specialize (H a)" allows to transform
in-place a universally-quantified hypothesis (H : forall x, T x) into its
instantiated form (H : T a). Nota: "specialize" was in fact there in earlier
versions of Coq, but was undocumented, and had a slightly different behavior.
- New tactic "contradict H" can be used to solve any kind of goal as long as
the user can provide afterwards a proof of the negation of the hypothesis H.
If H is already a negation, say ~T, then a proof of T is asked.
If the current goal is a negation, say ~U, then U is saved in H afterwards,
hence this new tactic "contradict" extends earlier tactic "swap", which is
now obsolete.
- Tactics f_equal is now done in ML instead of Ltac: it now works on any
equality of functions, regardless of the arity of the function.
- New options "before id", "at top", "at bottom" for tactics "move"/"intro".
- Some more debug of reflexive omega (romega), and internal clarifications.
Moreover, romega now has a variant "romega with *" that can be also used
on non-Z goals (nat, N, positive) via a call to a translation tactic named
zify (its purpose is to Z-ify your goal...). This zify may also be used
independantly of romega.
- Tactic "remember" now supports an "in" clause to remember only selected
occurrences of a term.
- Tactic "pose proof" supports name overwriting in case of specialization of an
hypothesis.
- Semi-decision tactic "jp" for first-order intuitionistic logic moved to user
contributions (subsumed by "firstorder").
Program
- Moved useful tactics in theories/Program and documented them.
- Add Program.Basics which contains standard definitions for functional
programming (id, apply, flip...)
- More robust obligation handling, dependent pattern-matching and
well-founded definitions.
- New syntax " dest term as pat in term " for destructing objects using
an irrefutable pattern while keeping equalities (use this instead of
"let" in Programs).
- Program CoFixpoint is accepted, Program Fixpoint uses the new way to infer
which argument decreases structurally.
- Program Lemma, Axiom etc... now permit to have obligations in the statement
iff they can be automatically solved by the default tactic.
- Renamed "Obligations Tactic" command to "Obligation Tactic".
- New command "Preterm [ of id ]" to see the actual term fed to Coq for
debugging purposes.
- New option "Transparent Obligations" to control the declaration of
obligations as transparent or opaque. All obligations are now transparent
by default, otherwise the system declares them opaque if possible.
- Changed the notations "left" and "right" to "in_left" and "in_right" to hide
the proofs in standard disjunctions, to avoid breaking existing scripts when
importing Program. Also, put them in program_scope.
Type Classes
- New "Class", "Instance" and "Program Instance" commands to define
classes and instances documented in the reference manual.
- New binding construct " [ Class_1 param_1 .. param_n, Class_2 ... ] "
for binding type classes, usable everywhere.
- New command " Print Classes " and " Print Instances some_class " to
print tables for typeclasses.
- New default eauto hint database "typeclass_instances" used by the default
typeclass instance search tactic.
- New theories directory "theories/Classes" for standard typeclasses
declarations. Module Classes.RelationClasses is a typeclass port of
Relation_Definitions plus a generic development of algebra on
n-ary heterogeneous predicates.
Setoid rewriting
- Complete (and still experimental) rewrite of the tactic
based on typeclasses. The old interface and semantics are
almost entirely respected, except:
- Import Setoid is now mandatory to be able to call setoid_replace
and declare morphisms.
- "-->", "++>" and "==>" are now right associative notations
declared at level 55 in scope signature_scope.
Their introduction may break existing scripts that defined
them as notations with different levels.
- One needs to use [Typeclasses unfold [cst]] if [cst] is used
as an abbreviation hiding products in types of morphisms,
e.g. if ones redefines [relation] and declares morphisms
whose type mentions [relation].
- The [setoid_rewrite]'s semantics change when rewriting with
a lemma: it can rewrite two different instantiations of the lemma
at once. Use [setoid_rewrite H at 1] for (almost) the usual semantics.
[setoid_rewrite] will also try to rewrite under binders now, and can
succeed on different terms than before. In particular, it will unify under
let-bound variables. When called through [rewrite], the semantics are
unchanged though.
- [Add Morphism term : id] has different semantics when used with
parametric morphism: it will try to find a relation on the parameters
too. The behavior has also changed with respect to default relations:
the most recently declared Setoid/Relation will be used, the documentation
explains how to customize this behavior.
- Parametric Relation and Morphism are declared differently, using the
new [Add Parametric] commands, documented in the manual.
- Setoid_Theory is now an alias to Equivalence, scripts building objects
of type Setoid_Theory need to unfold (or "red") the definitions
of Reflexive, Symmetric and Transitive in order to get the same goals
as before. Scripts which introduced variables explicitely will not break.
- The order of subgoals when doing [setoid_rewrite] with side-conditions
is always the same: first the new goal, then the conditions.
- New standard library modules Classes.Morphisms declares
standard morphisms on refl/sym/trans relations.
Classes.Morphisms_Prop declares morphisms on propositional
connectives and Classes.Morphisms_Relations on generalized predicate
connectives. Classes.Equivalence declares notations and tactics
related to equivalences and Classes.SetoidTactics defines the
setoid_replace tactics and some support for the "Add *" interface,
notably the tactic applied automatically before each "Add Morphism"
proof.
- User-defined subrelations are supported, as well as higher-order morphisms
and rewriting under binders. The tactic is also extensible entirely in Ltac.
The documentation has been updated to cover these features.
- [setoid_rewrite] and [rewrite] now support the [at] modifier to select
occurrences to rewrite, and both use the [setoid_rewrite] code, even when
rewriting with leibniz equality if occurrences are specified.
Extraction
- Improved behavior of the Caml extraction of modules: name clashes should
not happen anymore.
- The command Extract Inductive has now a syntax for infix notations. This
allows in particular to map Coq lists and pairs onto Caml ones:
Extract Inductive list => list [ "[]" "(::)" ].
Extract Inductive prod => "(*)" [ "(,)" ].
- In pattern matchings, a default pattern "| _ -> ..." is now used whenever
possible if several branches are identical. For instance, functions
corresponding to decidability of equalities are now linear instead of
quadratic.
- A new instruction Extraction Blacklist id1 .. idn allows to prevent filename
conflits with existing code, for instance when extracting module List
to Ocaml.
CoqIDE
- CoqIDE font defaults to monospace so as indentation to be meaningful.
- CoqIDE supports nested goals and any other kind of declaration in the middle
of a proof.
- Undoing non-tactic commands in CoqIDE works faster.
- New CoqIDE menu for activating display of various implicit informations.
- Added the possibility to choose the location of tabs in coqide:
(in Edit->Preferences->Misc)
- New Open and Save As dialogs in CoqIDE which filter *.v files.
Tools
- New stand-alone .vo files verifier "coqchk".
- Extended -I coqtop/coqc option to specify a logical dir: "-I dir -as coqdir".
- New coqtop/coqc option -exclude-dir to exclude subdirs for option -R.
- The binary "parser" has been renamed to "coq-parser".
- Improved coqdoc and dump of globalization information to give more
meta-information on identifiers. All categories of Coq definitions are
supported, which makes typesetting trivial in the generated documentation.
Support for hyperlinking and indexing developments in the tex output
has been implemented as well.
Miscellaneous
- Coq installation provides enough files so that Ocaml's extensions need not
the Coq sources to be compiled (this assumes O'Caml 3.10 and Camlp5).
- New commands "Set Whelp Server" and "Set Whelp Getter" to customize the
Whelp search tool.
- Syntax of "Test Printing Let ref" and "Test Printing If ref" changed into
"Test Printing Let for ref" and "Test Printing If for ref".
- An overhauled build system (new Makefiles); see dev/doc/build-system.txt.
- Add -browser option to configure script.
- Build a shared library for the C part of Coq, and use it by default on
non-(Windows or MacOS) systems. Bytecode executables are now pure. The
behaviour is configurable with -coqrunbyteflags, -coqtoolsbyteflags and
-custom configure options.
- Complexity tests can be skipped by setting the environment variable
COQTEST_SKIPCOMPLEXITY.
Changes from V8.1gamma to V8.1
==============================
Bug fixes
- Many bugs have been fixed (cf coq-bugs web page)
Tactics
- New tactics ring, ring_simplify and new tactic field now able to manage
power to a positive integer constant. Tactic ring on Z and R, and
field on R manage power (may lead to incompatibilities with V8.1gamma).
- Tactic field_simplify now applicable in hypotheses.
- New field_simplify_eq for simplifying field equations into ring equations.
- Tactics ring, ring_simplify, field, field_simplify and field_simplify_eq
all able to apply user-given equations to rewrite monoms on the fly
(see documentation).
Libraries
- New file ConstructiveEpsilon.v defining an epsilon operator and
proving the axiom of choice constructively for a countable domain
and a decidable predicate.
Changes from V8.1beta to V8.1gamma
==================================
Syntax
- changed parsing precedence of let/in and fun constructions of Ltac:
let x := t in e1; e2 is now parsed as let x := t in (e1;e2).
Language and commands
- Added sort-polymorphism for definitions in Type (but finally abandonned).
- Support for implicit arguments in the types of parameters in
(co-)fixpoints and (co-)inductive declarations.
- Improved type inference: use as much of possible general information.
before applying irreversible unification heuristics (allow e.g. to
infer the predicate in "(exist _ 0 (refl_equal 0) : {n:nat | n=0 })").
- Support for Miller-Pfenning's patterns unification in type synthesis
(e.g. can infer P such that P x y = phi(x,y)).
- Support for "where" clause in cofixpoint definitions.
- New option "Set Printing Universes" for making Type levels explicit.
Tactics
- Improved implementation of the ring and field tactics. For compatibility
reasons, the previous tactics are renamed as legacy ring and legacy field,
but should be considered as deprecated.
- New declarative mathematical proof language.
- Support for argument lists of arbitrary length in Tactic Notation.
- [rewrite ... in H] now fails if [H] is used either in an hypothesis
or in the goal.
- The semantics of [rewrite ... in *] has been slightly modified (see doc).
- Support for "as" clause in tactic injection.
- New forward-reasoning tactic "apply in".
- Ltac fresh operator now builds names from a concatenation of its arguments.
- New ltac tactic "remember" to abstract over a subterm and keep an equality
- Support for Miller-Pfenning's patterns unification in apply/rewrite/...
(may lead to few incompatibilities - generally now useless tactic calls).
Bug fixes
- Fix for notations involving basic "match" expressions.
- Numerous other bugs solved (a few fixes may lead to incompatibilities).
Changes from V8.0 to V8.1beta
=============================
Logic
- Added sort-polymorphism on inductive families
- Allowance for recursively non uniform parameters in inductive types
Syntax
- No more support for version 7 syntax and for translation to version 8 syntax.
- In fixpoints, the { struct ... } annotation is not mandatory any more when
only one of the arguments has an inductive type
- Added disjunctive patterns in match-with patterns
- Support for primitive interpretation of string literals
- Extended support for Unicode ranges
Vernacular commands
- Added "Print Ltac qualid" to print a user defined tactic.
- Added "Print Rewrite HintDb" to print the content of a DB used by
autorewrite.
- Added "Print Canonical Projections".
- Added "Example" as synonym of "Definition".
- Added "Proposition" and "Corollary" as extra synonyms of "Lemma".
- New command "Whelp" to send requests to the Helm database of proofs
formalized in the Calculus of Inductive Constructions.
- Command "functional induction" has been re-implemented from the new
"Function" command.
Ltac and tactic syntactic extensions
- New primitive "external" for communication with tool external to Coq
- New semantics for "match t with": if a clause returns a
tactic, it is now applied to the current goal. If it fails, the next
clause or next matching subterm is tried (i.e. it behaves as "match
goal with" does). The keyword "lazymatch" can be used to delay the
evaluation of tactics occurring in matching clauses.
- Hint base names can be parametric in auto and trivial.
- Occurrence values can be parametric in unfold, pattern, etc.
- Added entry constr_may_eval for tactic extensions.
- Low-priority term printer made available in ML-written tactic extensions.
- "Tactic Notation" extended to allow notations of tacticals.
Tactics
- New implementation and generalization of [setoid_]* (setoid_rewrite,
setoid_symmetry, setoid_transitivity, setoid_reflexivity and autorewite).
New syntax for declaring relations and morphisms (old syntax still working
with minor modifications, but deprecated).
- New implementation (still experimental) of the ring tactic with a built-in
notion of coefficients and a better usage of setoids.
- New conversion tactic "vm_compute": evaluates the goal (or an hypothesis)
with a call-by-value strategy, using the compiled version of terms.
- When rewriting H where H is not directly a Coq equality, search first H for
a registered setoid equality before starting to reduce in H. This is unlikely
to break any script. Should this happen nonetheless, one can insert manually
some "unfold ... in H" before rewriting.
- Fixed various bugs about (setoid) rewrite ... in ... (in particular #1101)
- "rewrite ... in" now accepts a clause as place where to rewrite instead of
juste a simple hypothesis name. For instance:
rewrite H in H1,H2 |- * means rewrite H in H1; rewrite H in H2; rewrite H
rewrite H in * |- will do try rewrite H in Hi for all hypothesis Hi <> H.
- Added "dependent rewrite term" and "dependent rewrite term in hyp".
- Added "autorewrite with ... in hyp [using ...]".
- Tactic "replace" now accepts a "by" tactic clause.
- Added "clear - id" to clear all hypotheses except the ones depending in id.
- The argument of Declare Left Step and Declare Right Step is now a term
(it used to be a reference).
- Omega now handles arbitrary precision integers.
- Several bug fixes in Reflexive Omega (romega).
- Idtac can now be left implicit in a [...|...] construct: for instance,
[ foo | | bar ] stands for [ foo | idtac | bar ].
- Fixed a "fold" bug (non critical but possible source of incompatibilities).
- Added classical_left and classical_right which transforms |- A \/ B into
~B |- A and ~A |- B respectively.
- Added command "Declare Implicit Tactic" to set up a default tactic to be
used to solve unresolved subterms of term arguments of tactics.
- Better support for coercions to Sortclass in tactics expecting type
arguments.
- Tactic "assert" now accepts "as" intro patterns and "by" tactic clauses.
- New tactic "pose proof" that generalizes "assert (id:=p)" with intro patterns.
- New introduction pattern "?" for letting Coq choose a name.
- Introduction patterns now support side hypotheses (e.g. intros [|] on
"(nat -> nat) -> nat" works).
- New introduction patterns "->" and "<-" for immediate rewriting of
introduced hypotheses.
- Introduction patterns coming after non trivial introduction patterns now
force full introduction of the first pattern (e.g. "intros [[|] p]" on
"nat->nat->nat" now behaves like "intros [[|?] p]")
- Added "eassumption".
- Added option 'using lemmas' to auto, trivial and eauto.
- Tactic "congruence" is now complete for its intended scope (ground
equalities and inequalities with constructors). Furthermore, it
tries to equates goal and hypotheses.
- New tactic "rtauto" solves pure propositional logic and gives a
reflective version of the available proof.
- Numbering of "pattern", "unfold", "simpl", ... occurrences in "match
with" made consistent with the printing of the return clause after
the term to match in the "match-with" construct (use "Set Printing All"
to see hidden occurrences).
- Generalization of induction "induction x1...xn using scheme" where
scheme is an induction principle with complex predicates (like the
ones generated by function induction).
- Some small Ltac tactics has been added to the standard library
(file Tactics.v):
* f_equal : instead of using the different f_equalX lemmas
* case_eq : a "case" without loss of information. An equality
stating the current situation is generated in every sub-cases.
* swap : for a negated goal ~B and a negated hypothesis H:~A,
swap H asks you to prove A from hypothesis B
* revert : revert H is generalize H; clear H.
Extraction
- All type parts should now disappear instead of sometimes producing _
(for instance in Map.empty).
- Haskell extraction: types of functions are now printed, better
unsafeCoerce mechanism, both for hugs and ghc.
- Scheme extraction improved, see http://www.pps.jussieu.fr/~letouzey/scheme.
- Many bug fixes.
Modules
- Added "Locate Module qualid" to get the full path of a module.