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.
- Support for optional "where" notation clauses for record fields.
- (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].
- New syntax to do implicit generalization in binders and inside terms.
- New tentative syntax for introduction of record objects without mentioning
the constructor {| field := body; ... |}, turning missing fields into holes
(compatible with refine and Program).
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).
- New command "Create HintDb name [discriminated]" to explicitely declare
a new hint database and optionaly turn on a discrimination net
implementation to index all the lemmas in the database.
- New commands "Hint Transparent" and "Hint Opaque" to set the unfolding
status of definitions used by auto. This information is taken into account
by the discrimination net and the unification algorithm.
- "Hint Extern" now takes an optional pattern and applies the given tactic
all the time if no pattern is given.
- 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).
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, now working inside record
declarations.
- 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 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".
- (?X ?Y) patterns now match any application instead of only unary
applications (possible source of incompatibility).
- 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.
- The C-zar (formerly know as declarative) proof language is now properly
documented.
Tactics
- New tactics "apply -> term", "apply <- term", "apply -> term in
ident", "apply <- term in ident" for applying equivalences (iff).
- "apply" and "rewrite" now take open terms (terms with undefined existentials)
as input.
- 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 ? 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.
- 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 can use [Typeclasses Opaque/Transparent [cst]] to indicate
that [cst] should not be unfolded during unification for morphism
resolution, by default all constants are transparent.
- 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 now 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".
coqdoc
- 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.
- A "--interpolate" option permits to use typesetting information from the
typechecked part of the file to typeset identifiers appearing in Coq escapings
inside the documentation.
- Better handling of utf8 ("--utf8" option) and respect of spaces in the source.
- Support for hyperlinking and indexing developments in the TeX output.
- New option "color" of the coqdoc style file to render identifiers using colors.
- Additional macros in the TeX ouput allowing to customize indentation and size of
empty lines. New environment "coqdoccode" for Coq code.
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.
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