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Diffstat (limited to 'doc/sphinx/language')
| -rw-r--r-- | doc/sphinx/language/cic.rst | 26 |
1 files changed, 22 insertions, 4 deletions
diff --git a/doc/sphinx/language/cic.rst b/doc/sphinx/language/cic.rst index 3d3a1b11b1..ac0f0f8ea6 100644 --- a/doc/sphinx/language/cic.rst +++ b/doc/sphinx/language/cic.rst @@ -605,7 +605,7 @@ Subtyping rules At the moment, we did not take into account one rule between universes which says that any term in a universe of index i is also a term in -the universe of index i+1 (this is the *cumulativity* rule of|Cic|). +the universe of index i+1 (this is the *cumulativity* rule of |Cic|). This property extends the equivalence relation of convertibility into a *subtyping* relation inductively defined by: @@ -640,7 +640,7 @@ a *subtyping* relation inductively defined by: respectively then .. math:: - E[Γ] ⊢ t~w_1 … w_m ≤_{βδιζη} t~w_1' … w_m' + E[Γ] ⊢ t~w_1 … w_m ≤_{βδιζη} t'~w_1' … w_m' (notice that :math:`t` and :math:`t'` are both fully applied, i.e., they have a sort as a type) if @@ -1025,8 +1025,26 @@ the Type hierarchy. Template polymorphism +++++++++++++++++++++ -Inductive types declared in :math:`\Type` are polymorphic over their arguments -in :math:`\Type`. If :math:`A` is an arity of some sort and :math:`s` is a sort, we write :math:`A_{/s}` +Inductive types can be made polymorphic over their arguments +in :math:`\Type`. + +.. opt:: Auto Template Polymorphism + + This option, enabled by default, makes every inductive type declared + at level :math:`Type` (without annotations or hiding it behind a + definition) template polymorphic. + + This can be prevented using the ``notemplate`` attribute. + + An inductive type can be forced to be template polymorphic using the + ``template`` attribute. + + Template polymorphism and universe polymorphism (see Chapter + :ref:`polymorphicuniverses`) are incompatible, so if the later is + enabled it will prevail over automatic template polymorphism and + cause an error when using the ``template`` attribute. + +If :math:`A` is an arity of some sort and :math:`s` is a sort, we write :math:`A_{/s}` for the arity obtained from :math:`A` by replacing its sort with :math:`s`. Especially, if :math:`A` is well-typed in some global environment and local context, then :math:`A_{/s}` is typable by typability of all products in the |