diff options
Diffstat (limited to 'doc/sphinx/addendum')
| -rw-r--r-- | doc/sphinx/addendum/program.rst | 8 | ||||
| -rw-r--r-- | doc/sphinx/addendum/type-classes.rst | 17 | ||||
| -rw-r--r-- | doc/sphinx/addendum/universe-polymorphism.rst | 110 |
3 files changed, 87 insertions, 48 deletions
diff --git a/doc/sphinx/addendum/program.rst b/doc/sphinx/addendum/program.rst index 298ea4b4ab..104f84a253 100644 --- a/doc/sphinx/addendum/program.rst +++ b/doc/sphinx/addendum/program.rst @@ -99,15 +99,15 @@ coercions. Enables the program mode, in which 1) typechecking allows subset coercions and 2) the elaboration of pattern matching of :cmd:`Fixpoint` and - :cmd:`Definition` act as if the :attr:`program` attribute had been + :cmd:`Definition` acts as if the :attr:`program` attribute has been used, generating obligations if there are unresolved holes after typechecking. -.. attr:: program +.. attr:: program{? = {| yes | no } } :name: program; Program - Allows using the Program mode on a specific - definition. An alternative syntax is to use the legacy ``Program`` + This :term:`boolean attribute` allows using or disabling the Program mode on a specific + definition. An alternative and commonly used syntax is to use the legacy ``Program`` prefix (cf. :n:`@legacy_attr`) as it is elsewhere in this chapter. .. _syntactic_control: diff --git a/doc/sphinx/addendum/type-classes.rst b/doc/sphinx/addendum/type-classes.rst index 56d90b33d8..22527dc379 100644 --- a/doc/sphinx/addendum/type-classes.rst +++ b/doc/sphinx/addendum/type-classes.rst @@ -320,10 +320,9 @@ Summary of the commands maintained. Like any command declaring a record, this command supports the - :attr:`universes(polymorphic)`, :attr:`universes(monomorphic)`, - :attr:`universes(template)`, :attr:`universes(notemplate)`, - :attr:`universes(cumulative)`, :attr:`universes(noncumulative)` and - :attr:`private(matching)` attributes. + :attr:`universes(polymorphic)`, :attr:`universes(template)`, + :attr:`universes(cumulative)`, and :attr:`private(matching)` + attributes. .. cmd:: Existing Class @qualid @@ -391,6 +390,16 @@ Summary of the commands equivalent to ``Hint Resolve ident : typeclass_instances``, except it registers instances for :cmd:`Print Instances`. + .. flag:: Instance Generalized Output + + .. deprecated:: 8.13 + + Disabled by default, this provides compatibility with Coq + version 8.12 and earlier. + + When enabled, the type of the instance is implicitly generalized + over unbound and :ref:`generalizable <implicit-generalization>` variables as though surrounded by ``\`{}``. + .. cmd:: Print Instances @reference Shows the list of instances associated with the typeclass :token:`reference`. diff --git a/doc/sphinx/addendum/universe-polymorphism.rst b/doc/sphinx/addendum/universe-polymorphism.rst index 1fb337b30a..4615a8dfca 100644 --- a/doc/sphinx/addendum/universe-polymorphism.rst +++ b/doc/sphinx/addendum/universe-polymorphism.rst @@ -122,33 +122,37 @@ in a universe strictly higher than :g:`Set`. Polymorphic, Monomorphic ------------------------- -.. attr:: universes(polymorphic) - :name: universes(polymorphic); Polymorphic +.. attr:: universes(polymorphic{? = {| yes | no } }) + :name: universes(polymorphic); Polymorphic; Monomorphic + + This :term:`boolean attribute` can be used to control whether universe + polymorphism is enabled in the definition of an inductive type. + There is also a legacy syntax using the ``Polymorphic`` prefix (see + :n:`@legacy_attr`) which, as shown in the examples, is more + commonly used. + + When ``universes(polymorphic=no)`` is used, global universe constraints + are produced, even when the :flag:`Universe Polymorphism` flag is + on. There is also a legacy syntax using the ``Monomorphic`` prefix + (see :n:`@legacy_attr`). - This attribute can be used to declare universe polymorphic - definitions and inductive types. There is also a legacy syntax - using the ``Polymorphic`` prefix (see :n:`@legacy_attr`) which, as - shown in the examples, is more commonly used. +.. attr:: universes(monomorphic) -.. flag:: Universe Polymorphism + .. deprecated:: 8.13 - This flag is off by default. When it is on, new declarations are - polymorphic unless the :attr:`universes(monomorphic)` attribute is - used. + Use :attr:`universes(polymorphic=no) <universes(polymorphic)>` + instead. -.. attr:: universes(monomorphic) - :name: universes(monomorphic); Monomorphic +.. flag:: Universe Polymorphism - This attribute can be used to declare universe monomorphic - definitions and inductive types (i.e. global universe constraints - are produced), even when the :flag:`Universe Polymorphism` flag is - on. There is also a legacy syntax using the ``Monomorphic`` prefix - (see :n:`@legacy_attr`). + This flag is off by default. When it is on, new declarations are + polymorphic unless the :attr:`universes(polymorphic=no) <universes(polymorphic)>` + attribute is used to override the default. Many other commands can be used to declare universe polymorphic or monomorphic constants depending on whether the :flag:`Universe -Polymorphism` flag is on or the :attr:`universes(polymorphic)` or -:attr:`universes(monomorphic)` attributes are used: +Polymorphism` flag is on or the :attr:`universes(polymorphic)` +attribute is used: - :cmd:`Lemma`, :cmd:`Axiom`, etc. can be used to declare universe polymorphic constants. @@ -171,19 +175,27 @@ Polymorphism` flag is on or the :attr:`universes(polymorphic)` or Cumulative, NonCumulative ------------------------- -.. attr:: universes(cumulative) - :name: universes(cumulative); Cumulative +.. attr:: universes(cumulative{? = {| yes | no } }) + :name: universes(cumulative); Cumulative; NonCumulative Polymorphic inductive types, coinductive types, variants and - records can be declared cumulative using this attribute or the - legacy ``Cumulative`` prefix (see :n:`@legacy_attr`) which, as + records can be declared cumulative using this :term:`boolean attribute` + or the legacy ``Cumulative`` prefix (see :n:`@legacy_attr`) which, as shown in the examples, is more commonly used. This means that two instances of the same inductive type (family) are convertible based on the universe variances; they do not need to be equal. - .. exn:: The cumulative and noncumulative attributes can only be used in a polymorphic context. + When the attribtue is off, the inductive type is non-cumulative + even if the :flag:`Polymorphic Inductive Cumulativity` flag is on. + There is also a legacy syntax using the ``NonCumulative`` prefix + (see :n:`@legacy_attr`). + + This means that two instances of the same inductive type (family) + are convertible only if all the universes are equal. + + .. exn:: The cumulative attribute can only be used in a polymorphic context. Using this attribute requires being in a polymorphic context, i.e. either having the :flag:`Universe Polymorphism` flag on, or @@ -192,26 +204,21 @@ Cumulative, NonCumulative .. note:: - ``#[ universes(polymorphic), universes(cumulative) ]`` can be - abbreviated into ``#[ universes(polymorphic, cumulative) ]``. + :n:`#[ universes(polymorphic{? = yes }), universes(cumulative{? = {| yes | no } }) ]` can be + abbreviated into :n:`#[ universes(polymorphic{? = yes }, cumulative{? = {| yes | no } }) ]`. -.. flag:: Polymorphic Inductive Cumulativity +.. attr:: universes(noncumulative) - When this flag is on (it is off by default), it makes all - subsequent *polymorphic* inductive definitions cumulative, unless - the :attr:`universes(noncumulative)` attribute is used. It has no - effect on *monomorphic* inductive definitions. + .. deprecated:: 8.13 -.. attr:: universes(noncumulative) - :name: universes(noncumulative); NonCumulative + Use :attr:`universes(cumulative=no) <universes(cumulative)>` instead. - Declares the inductive type as non-cumulative even if the - :flag:`Polymorphic Inductive Cumulativity` flag is on. There is - also a legacy syntax using the ``NonCumulative`` prefix (see - :n:`@legacy_attr`). +.. flag:: Polymorphic Inductive Cumulativity - This means that two instances of the same inductive type (family) - are convertible only if all the universes are equal. + When this flag is on (it is off by default), it makes all + subsequent *polymorphic* inductive definitions cumulative, unless + the :attr:`universes(cumulative=no) <universes(cumulative)>` attribute is + used to override the default. It has no effect on *monomorphic* inductive definitions. Consider the examples below. @@ -246,6 +253,7 @@ The following is an example of a record with non-trivial subtyping relation: .. coqtop:: all Polymorphic Cumulative Record packType := {pk : Type}. + About packType. :g:`packType` binds a covariant universe, i.e. @@ -254,6 +262,27 @@ The following is an example of a record with non-trivial subtyping relation: E[Γ] ⊢ \mathsf{packType}@\{i\} =_{βδιζη} \mathsf{packType}@\{j\}~\mbox{ whenever }~i ≤ j +Specifying cumulativity +~~~~~~~~~~~~~~~~~~~~~~~ + +The variance of the universe parameters for a cumulative inductive may be specified by the user. + +For the following type, universe ``a`` has its variance automatically +inferred (it is irrelevant), ``b`` is required to be irrelevant, +``c`` is covariant and ``d`` is invariant. With these annotations +``c`` and ``d`` have less general variances than would be inferred. + +.. coqtop:: all + + Polymorphic Cumulative Inductive Dummy@{a *b +c =d} : Prop := dummy. + About Dummy. + +Insufficiently restrictive variance annotations lead to errors: + +.. coqtop:: all + + Fail Polymorphic Cumulative Record bad@{*a} := {p : Type@{a}}. + An example of a proof using cumulativity ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ @@ -280,7 +309,7 @@ An example of a proof using cumulativity End down. Cumulativity Weak Constraints ------------------------------ +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. flag:: Cumulativity Weak Constraints @@ -383,6 +412,7 @@ Explicit Universes | _ | @qualid univ_decl ::= @%{ {* @ident } {? + } {? %| {*, @univ_constraint } {? + } } %} + cumul_univ_decl ::= @%{ {* {? {| = | + | * } } @ident } {? + } {? %| {*, @univ_constraint } {? + } } %} univ_constraint ::= @universe_name {| < | = | <= } @universe_name The syntax has been extended to allow users to explicitly bind names |