diff options
Diffstat (limited to 'doc/sphinx/addendum')
| -rw-r--r-- | doc/sphinx/addendum/micromega.rst | 12 | ||||
| -rw-r--r-- | doc/sphinx/addendum/universe-polymorphism.rst | 61 |
2 files changed, 62 insertions, 11 deletions
diff --git a/doc/sphinx/addendum/micromega.rst b/doc/sphinx/addendum/micromega.rst index 238106b2e7..4a691bde3a 100644 --- a/doc/sphinx/addendum/micromega.rst +++ b/doc/sphinx/addendum/micromega.rst @@ -35,6 +35,18 @@ tactics for solving arithmetic goals over :math:`\mathbb{Q}`, use the Simplex method for solving linear goals. If it is not set, the decision procedures are using Fourier elimination. +.. flag:: Lia Cache + + This option (set by default) instructs :tacn:`lia` to cache its results in the file `.lia.cache` + +.. flag:: Nia Cache + + This option (set by default) instructs :tacn:`nia` to cache its results in the file `.nia.cache` + +.. flag:: Nra Cache + + This option (set by default) instructs :tacn:`nra` to cache its results in the file `.nra.cache` + The tactics solve propositional formulas parameterized by atomic arithmetic expressions interpreted over a domain :math:`D \in \{\mathbb{Z},\mathbb{Q},\mathbb{R}\}`. diff --git a/doc/sphinx/addendum/universe-polymorphism.rst b/doc/sphinx/addendum/universe-polymorphism.rst index 7e698bfb66..905068e316 100644 --- a/doc/sphinx/addendum/universe-polymorphism.rst +++ b/doc/sphinx/addendum/universe-polymorphism.rst @@ -147,14 +147,7 @@ Many other commands support the ``Polymorphic`` flag, including: - :cmd:`Section` will locally set the polymorphism flag inside the section. - ``Variables``, ``Context``, ``Universe`` and ``Constraint`` in a section support - polymorphism. This means that the universe variables (and associated - constraints) are discharged polymorphically over definitions that use - them. In other words, two definitions in the section sharing a common - variable will both get parameterized by the universes produced by the - variable declaration. This is in contrast to a “mononorphic” variable - which introduces global universes and constraints, making the two - definitions depend on the *same* global universes associated to the - variable. + polymorphism. See :ref:`universe-polymorphism-in-sections` for more details. - :cmd:`Hint Resolve` and :cmd:`Hint Rewrite` will use the auto/rewrite hint polymorphically, not at a single instance. @@ -375,9 +368,7 @@ to universes and explicitly instantiate polymorphic definitions. as well. Global universe names live in a separate namespace. The command supports the ``Polymorphic`` flag only in sections, meaning the universe quantification will be discharged on each section definition - independently. One cannot mix polymorphic and monomorphic - declarations in the same section. - + independently. .. cmd:: Constraint @universe_constraint Polymorphic Constraint @universe_constraint @@ -510,3 +501,51 @@ underscore or by omitting the annotation to a polymorphic definition. Lemma baz : Type@{outer}. Proof. exact Type@{inner}. Qed. About baz. + +.. _universe-polymorphism-in-sections: + +Universe polymorphism and sections +---------------------------------- + +:cmd:`Variables`, :cmd:`Context`, :cmd:`Universe` and +:cmd:`Constraint` in a section support polymorphism. This means that +the universe variables and their associated constraints are discharged +polymorphically over definitions that use them. In other words, two +definitions in the section sharing a common variable will both get +parameterized by the universes produced by the variable declaration. +This is in contrast to a “mononorphic” variable which introduces +global universes and constraints, making the two definitions depend on +the *same* global universes associated to the variable. + +It is possible to mix universe polymorphism and monomorphism in +sections, except in the following ways: + +- no monomorphic constraint may refer to a polymorphic universe: + + .. coqtop:: all reset + + Section Foo. + + Polymorphic Universe i. + Fail Constraint i = i. + + This includes constraints implictly declared by commands such as + :cmd:`Variable`, which may as a such need to be used with universe + polymorphism activated (locally by attribute or globally by option): + + .. coqtop:: all + + Fail Variable A : (Type@{i} : Type). + Polymorphic Variable A : (Type@{i} : Type). + + (in the above example the anonymous :g:`Type` constrains polymorphic + universe :g:`i` to be strictly smaller.) + +- no monomorphic constant or inductive may be declared if polymorphic + universes or universe constraints are present. + +These restrictions are required in order to produce a sensible result +when closing the section (the requirement on constants and inductives +is stricter than the one on constraints, because constants and +inductives are abstracted by *all* the section's polymorphic universes +and constraints). |