diff options
Diffstat (limited to 'doc/sphinx/addendum')
| -rw-r--r-- | doc/sphinx/addendum/generalized-rewriting.rst | 2 | ||||
| -rw-r--r-- | doc/sphinx/addendum/implicit-coercions.rst | 4 | ||||
| -rw-r--r-- | doc/sphinx/addendum/micromega.rst | 2 | ||||
| -rw-r--r-- | doc/sphinx/addendum/omega.rst | 35 | ||||
| -rw-r--r-- | doc/sphinx/addendum/program.rst | 6 | ||||
| -rw-r--r-- | doc/sphinx/addendum/sprop.rst | 52 | ||||
| -rw-r--r-- | doc/sphinx/addendum/type-classes.rst | 6 | ||||
| -rw-r--r-- | doc/sphinx/addendum/universe-polymorphism.rst | 15 |
8 files changed, 76 insertions, 46 deletions
diff --git a/doc/sphinx/addendum/generalized-rewriting.rst b/doc/sphinx/addendum/generalized-rewriting.rst index 315c9d4a80..759f630b85 100644 --- a/doc/sphinx/addendum/generalized-rewriting.rst +++ b/doc/sphinx/addendum/generalized-rewriting.rst @@ -529,7 +529,7 @@ pass additional arguments such as ``using relation``. setoid_symmetry {? in @ident} setoid_transitivity setoid_rewrite {? @orientation} @term {? at @occurrences} {? in @ident} - setoid_replace @term with @term {? using relation @term} {? in @ident} {? by @tactic} + setoid_replace @term with @term {? using relation @term} {? in @ident} {? by @ltac_expr3} :name: setoid_reflexivity; setoid_symmetry; setoid_transitivity; setoid_rewrite; setoid_replace The ``using relation`` arguments cannot be passed to the unprefixed form. diff --git a/doc/sphinx/addendum/implicit-coercions.rst b/doc/sphinx/addendum/implicit-coercions.rst index 1f33775a01..a6dc15da55 100644 --- a/doc/sphinx/addendum/implicit-coercions.rst +++ b/doc/sphinx/addendum/implicit-coercions.rst @@ -37,6 +37,8 @@ In addition to these user-defined classes, we have two built-in classes: * ``Funclass``, the class of functions; its objects are all the terms with a functional type, i.e. of form :g:`forall x:A,B`. +Formally, the syntax of classes is defined as: + .. insertprodn class class .. prodn:: @@ -257,7 +259,7 @@ Activating the Printing of Coercions :name: Printing Coercion Specifies a set of qualids for which coercions are always displayed. Use the - :cmd:`Add @table` and :cmd:`Remove @table` commands to update the set of qualids. + :cmd:`Add` and :cmd:`Remove` commands to update the set of qualids. .. _coercions-classes-as-records: diff --git a/doc/sphinx/addendum/micromega.rst b/doc/sphinx/addendum/micromega.rst index f706633da9..77bf58aac6 100644 --- a/doc/sphinx/addendum/micromega.rst +++ b/doc/sphinx/addendum/micromega.rst @@ -1,4 +1,4 @@ -.. _ micromega: +.. _micromega: Micromega: tactics for solving arithmetic goals over ordered rings ================================================================== diff --git a/doc/sphinx/addendum/omega.rst b/doc/sphinx/addendum/omega.rst index daca43e65e..e1b1ee8e8d 100644 --- a/doc/sphinx/addendum/omega.rst +++ b/doc/sphinx/addendum/omega.rst @@ -1,4 +1,4 @@ -.. _omega: +.. _omega_chapter: Omega: a solver for quantifier-free problems in Presburger Arithmetic ===================================================================== @@ -7,20 +7,18 @@ Omega: a solver for quantifier-free problems in Presburger Arithmetic .. warning:: - The :tacn:`omega` tactic is about to be deprecated in favor of the - :tacn:`lia` tactic. The goal is to consolidate the arithmetic - solving capabilities of Coq into a single engine; moreover, - :tacn:`lia` is in general more powerful than :tacn:`omega` (it is a - complete Presburger arithmetic solver while :tacn:`omega` was known - to be incomplete). - - Work is in progress to make sure that there are no regressions - (including no performance regression) when switching from - :tacn:`omega` to :tacn:`lia` in existing projects. However, we - already recommend using :tacn:`lia` in new or refactored proof - scripts. We also ask that you report (in our `bug tracker - <https://github.com/coq/coq/issues>`_) any issue you encounter, - especially if the issue was not present in :tacn:`omega`. + The :tacn:`omega` tactic is deprecated in favor of the :tacn:`lia` + tactic. The goal is to consolidate the arithmetic solving + capabilities of Coq into a single engine; moreover, :tacn:`lia` is + in general more powerful than :tacn:`omega` (it is a complete + Presburger arithmetic solver while :tacn:`omega` was known to be + incomplete). + + It is recommended to switch from :tacn:`omega` to :tacn:`lia` in existing + projects. We also ask that you report (in our `bug tracker + <https://github.com/coq/coq/issues>`_) any issue you encounter, especially + if the issue was not present in :tacn:`omega`. If no new issues are + reported, :tacn:`omega` will be removed soon. Note that replacing :tacn:`omega` with :tacn:`lia` can break non-robust proof scripts which rely on incompleteness bugs of @@ -30,6 +28,11 @@ Description of ``omega`` ------------------------ .. tacn:: omega + :name: omega + + .. deprecated:: 8.12 + + Use :tacn:`lia` instead. :tacn:`omega` is a tactic for solving goals in Presburger arithmetic, i.e. for proving formulas made of equations and inequalities over the @@ -118,7 +121,7 @@ loaded by .. example:: - .. coqtop:: all + .. coqtop:: all warn Require Import Omega. diff --git a/doc/sphinx/addendum/program.rst b/doc/sphinx/addendum/program.rst index 5cffe9e435..52862dea47 100644 --- a/doc/sphinx/addendum/program.rst +++ b/doc/sphinx/addendum/program.rst @@ -290,7 +290,7 @@ optional identifier is used when multiple functions have unsolved obligations (e.g. when defining mutually recursive blocks). The optional tactic is replaced by the default one if not specified. -.. cmd:: {? {| Local | Global } } Obligation Tactic := @tactic +.. cmd:: {? {| Local | Global } } Obligation Tactic := @ltac_expr :name: Obligation Tactic Sets the default obligation solving tactic applied to all obligations @@ -314,11 +314,11 @@ optional tactic is replaced by the default one if not specified. Start the proof of the next unsolved obligation. -.. cmd:: Solve Obligations {? {? of @ident} with @tactic} +.. cmd:: Solve Obligations {? {? of @ident} with @ltac_expr} Tries to solve each obligation of ``ident`` using the given ``tactic`` or the default one. -.. cmd:: Solve All Obligations {? with @tactic} +.. cmd:: Solve All Obligations {? with @ltac_expr} Tries to solve each obligation of every program using the given tactic or the default one (useful for mutually recursive definitions). diff --git a/doc/sphinx/addendum/sprop.rst b/doc/sphinx/addendum/sprop.rst index 9acdd18b89..b19239ed22 100644 --- a/doc/sphinx/addendum/sprop.rst +++ b/doc/sphinx/addendum/sprop.rst @@ -7,27 +7,26 @@ SProp (proof irrelevant propositions) The status of strict propositions is experimental. + In particular, conversion checking through bytecode or native code + compilation currently does not understand proof irrelevance. + This section describes the extension of |Coq| with definitionally proof irrelevant propositions (types in the sort :math:`\SProp`, also known as strict propositions) as described in :cite:`Gilbert:POPL2019`. -Using :math:`\SProp` may be prevented by passing ``-disallow-sprop`` -to the |Coq| program or using :flag:`Allow StrictProp`. +Use of |SProp| may be disabled by passing ``-disallow-sprop`` to the +|Coq| program or by turning the :flag:`Allow StrictProp` flag off. .. flag:: Allow StrictProp :name: Allow StrictProp - Allows using :math:`\SProp` when set and forbids it when unset. The - initial value depends on whether you used the command line - ``-disallow-sprop`` and ``-allow-sprop``. - -.. exn:: SProp not allowed, you need to Set Allow StrictProp or to use the -allow-sprop command-line-flag. - :undocumented: - -.. coqtop:: none + Enables or disables the use of |SProp|. It is enabled by default. + The command-line flag ``-disallow-sprop`` disables |SProp| at + startup. - Set Allow StrictProp. + .. exn:: SProp is disallowed because the "Allow StrictProp" flag is off. + :undocumented: Some of the definitions described in this document are available through ``Coq.Logic.StrictProp``, which see. @@ -38,29 +37,35 @@ Basic constructs The purpose of :math:`\SProp` is to provide types where all elements are convertible: -.. coqdoc:: +.. coqtop:: all - Definition irrelevance (A:SProp) (P:A -> Prop) (x:A) (v:P x) (y:A) : P y := v. + Theorem irrelevance (A : SProp) (P : A -> Prop) : forall x : A, P x -> forall y : A, P y. + Proof. + intros * Hx *. + exact Hx. + Qed. Since we have definitional :ref:`eta-expansion` for functions, the property of being a type of definitionally irrelevant values is impredicative, and so is :math:`\SProp`: -.. coqdoc:: +.. coqtop:: all Check fun (A:Type) (B:A -> SProp) => (forall x:A, B x) : SProp. -.. warning:: - - Conversion checking through bytecode or native code compilation - currently does not understand proof irrelevance. - In order to keep conversion tractable, cumulativity for :math:`\SProp` -is forbidden: +is forbidden, unless the :flag:`Cumulative StrictProp` flag is turned +on: .. coqtop:: all Fail Check (fun (A:SProp) => A : Type). + Set Cumulative StrictProp. + Check (fun (A:SProp) => A : Type). + +.. coqtop:: none + + Unset Cumulative StrictProp. We can explicitly lift strict propositions into the relevant world by using a wrapping inductive type. The inductive stops definitional @@ -240,3 +245,10 @@ so correctly converts ``x`` and ``y``. the kernel when it is passed a term with incorrect relevance marks. To avoid conversion issues as in ``late_mark`` you may wish to use it to find when your tactics are producing incorrect marks. + +.. flag:: Cumulative StrictProp + :name: Cumulative StrictProp + + Set this flag (it is off by default) to make the kernel accept + cumulativity between |SProp| and other universes. This makes + typechecking incomplete. diff --git a/doc/sphinx/addendum/type-classes.rst b/doc/sphinx/addendum/type-classes.rst index bd4c276571..903aa266e2 100644 --- a/doc/sphinx/addendum/type-classes.rst +++ b/doc/sphinx/addendum/type-classes.rst @@ -241,7 +241,7 @@ binders. For example: Definition lt `{eqa : EqDec A, ! Ord eqa} (x y : A) := andb (le x y) (neqb x y). -The ``!`` modifier switches the way a binder is parsed back to the regular +The ``!`` modifier switches the way a binder is parsed back to the usual interpretation of Coq. In particular, it uses the implicit arguments mechanism if available, as shown in the example. @@ -323,7 +323,7 @@ Summary of the commands .. cmdv:: Existing Class @ident - This variant declares a class a posteriori from a constant or + This variant declares a class from a previously declared constant or inductive definition. No methods or instances are defined. .. warn:: @ident is already declared as a typeclass @@ -394,7 +394,7 @@ few other commands related to typeclasses. :name: typeclasses eauto This proof search tactic implements the resolution engine that is run - implicitly during type-checking. This tactic uses a different resolution + implicitly during type checking. This tactic uses a different resolution engine than :tacn:`eauto` and :tacn:`auto`. The main differences are the following: diff --git a/doc/sphinx/addendum/universe-polymorphism.rst b/doc/sphinx/addendum/universe-polymorphism.rst index a08495badd..2958d866ac 100644 --- a/doc/sphinx/addendum/universe-polymorphism.rst +++ b/doc/sphinx/addendum/universe-polymorphism.rst @@ -227,7 +227,7 @@ constraints by prefixing the level names with symbols. Because inductive subtypings are only produced by comparing inductives to themselves with universes changed, they amount to variance information: each universe is either invariant, covariant or -irrelevant (there are no contravariant subtypings in Coq), +irrelevant (there are no contravariant subtypings in |Coq|), respectively represented by the symbols `=`, `+` and `*`. Here we see that :g:`list` binds an irrelevant universe, so any two @@ -426,6 +426,19 @@ mode, introduced universe names can be referred to in terms. Note that local universe names shadow global universe names. During a proof, one can use :cmd:`Show Universes` to display the current context of universes. +It is possible to provide only some universe levels and let |Coq| infer the others +by adding a :g:`+` in the list of bound universe levels: + +.. coqtop:: all + + Fail Definition foobar@{u} : Type@{u} := Type. + Definition foobar@{u +} : Type@{u} := Type. + Set Printing Universes. + Print foobar. + +This can be used to find which universes need to be explicitly bound in a given +definition. + Definitions can also be instantiated explicitly, giving their full instance: |