diff options
Diffstat (limited to 'doc/sphinx/proof-engine')
| -rw-r--r-- | doc/sphinx/proof-engine/detailed-tactic-examples.rst | 10 | ||||
| -rw-r--r-- | doc/sphinx/proof-engine/ltac.rst | 2 | ||||
| -rw-r--r-- | doc/sphinx/proof-engine/proof-handling.rst | 2 | ||||
| -rw-r--r-- | doc/sphinx/proof-engine/ssreflect-proof-language.rst | 7 | ||||
| -rw-r--r-- | doc/sphinx/proof-engine/tactics.rst | 70 | ||||
| -rw-r--r-- | doc/sphinx/proof-engine/vernacular-commands.rst | 45 |
6 files changed, 86 insertions, 50 deletions
diff --git a/doc/sphinx/proof-engine/detailed-tactic-examples.rst b/doc/sphinx/proof-engine/detailed-tactic-examples.rst index 63d6a229ed..b629d15b11 100644 --- a/doc/sphinx/proof-engine/detailed-tactic-examples.rst +++ b/doc/sphinx/proof-engine/detailed-tactic-examples.rst @@ -33,7 +33,7 @@ example, revisiting the first example of the inversion documentation: | LeO : forall n:nat, Le 0 n | LeS : forall n m:nat, Le n m -> Le (S n) (S m). - Variable P : nat -> nat -> Prop. + Parameter P : nat -> nat -> Prop. Goal forall n m:nat, Le (S n) m -> P n m. @@ -69,7 +69,7 @@ as well in this case, e.g.: .. coqtop:: in - Variable Q : forall (n m : nat), Le n m -> Prop. + Parameter Q : forall (n m : nat), Le n m -> Prop. Goal forall n m (p : Le (S n) m), Q (S n) m p. .. coqtop:: all @@ -124,7 +124,7 @@ the following example on vectors: .. coqtop:: in - Variable A : Set. + Parameter A : Set. .. coqtop:: in @@ -329,7 +329,7 @@ the optional tactic of the ``Hint Rewrite`` command. .. coqtop:: in - Variable Ack : nat -> nat -> nat. + Parameter Ack : nat -> nat -> nat. .. coqtop:: in @@ -357,7 +357,7 @@ the optional tactic of the ``Hint Rewrite`` command. .. coqtop:: in - Variable g : nat -> nat -> nat. + Parameter g : nat -> nat -> nat. .. coqtop:: in diff --git a/doc/sphinx/proof-engine/ltac.rst b/doc/sphinx/proof-engine/ltac.rst index 3e87e8acd8..52e3029b8f 100644 --- a/doc/sphinx/proof-engine/ltac.rst +++ b/doc/sphinx/proof-engine/ltac.rst @@ -200,7 +200,7 @@ following form: :name: [> ... | ... | ... ] (dispatch) The expressions :n:`@expr__i` are evaluated to :n:`v__i`, for - i = 0, ..., n and all have to be tactics. The :n:`v__i` is applied to the + i = 1, ..., n and all have to be tactics. The :n:`v__i` is applied to the i-th goal, for i = 1, ..., n. It fails if the number of focused goals is not exactly n. diff --git a/doc/sphinx/proof-engine/proof-handling.rst b/doc/sphinx/proof-engine/proof-handling.rst index d0bd9e396d..07215a0c7e 100644 --- a/doc/sphinx/proof-engine/proof-handling.rst +++ b/doc/sphinx/proof-engine/proof-handling.rst @@ -30,7 +30,7 @@ When a proof is completed, the message ``Proof completed`` is displayed. One can then register this proof as a defined constant in the environment. Because there exists a correspondence between proofs and terms of λ-calculus, known as the *Curry-Howard isomorphism* -:cite:`How80,Bar81,Gir89,Hue88`, |Coq| stores proofs as terms of |Cic|. Those +:cite:`How80,Bar81,Gir89,H89`, |Coq| stores proofs as terms of |Cic|. Those terms are called *proof terms*. diff --git a/doc/sphinx/proof-engine/ssreflect-proof-language.rst b/doc/sphinx/proof-engine/ssreflect-proof-language.rst index 237b534d67..b240cef40c 100644 --- a/doc/sphinx/proof-engine/ssreflect-proof-language.rst +++ b/doc/sphinx/proof-engine/ssreflect-proof-language.rst @@ -2094,9 +2094,9 @@ into a closing one (similar to :tacn:`now`). Its general syntax is: :name: by :undocumented: -The Ltac expression :n:`by [@tactic | [@tactic | …]` is equivalent to -:n:`[by @tactic | by @tactic | ...]` and this form should be preferred -to the former. +The Ltac expression :n:`by [@tactic | @tactic | …]` is equivalent to +:n:`do [done | by @tactic | by @tactic | …]`, which corresponds to the +standard Ltac expression :n:`first [done | @tactic; done | @tactic; done | …]`. In the script provided as example in section :ref:`indentation_ssr`, the paragraph corresponding to each sub-case ends with a tactic line prefixed @@ -2902,6 +2902,7 @@ pattern will be used to process its instance. Axiom P : nat -> Prop. Axioms eqn leqn : nat -> nat -> bool. + Declare Scope this_scope. Notation "a != b" := (eqn a b) (at level 70) : this_scope. Notation "a <= b" := (leqn a b) (at level 70) : this_scope. Open Scope this_scope. diff --git a/doc/sphinx/proof-engine/tactics.rst b/doc/sphinx/proof-engine/tactics.rst index b5e9a902c6..7b395900e9 100644 --- a/doc/sphinx/proof-engine/tactics.rst +++ b/doc/sphinx/proof-engine/tactics.rst @@ -378,7 +378,7 @@ Examples: .. coqtop:: reset none - Variables (A : Prop) (B: nat -> Prop) (C: Prop). + Parameters (A : Prop) (B: nat -> Prop) (C: Prop). .. coqtop:: out @@ -730,15 +730,15 @@ Applying theorems .. coqtop:: reset in - Variable R : nat -> nat -> Prop. + Parameter R : nat -> nat -> Prop. - Hypothesis Rtrans : forall x y z:nat, R x y -> R y z -> R x z. + Axiom Rtrans : forall x y z:nat, R x y -> R y z -> R x z. - Variables n m p : nat. + Parameters n m p : nat. - Hypothesis Rnm : R n m. + Axiom Rnm : R n m. - Hypothesis Rmp : R m p. + Axiom Rmp : R m p. Consider the goal ``(R n p)`` provable using the transitivity of ``R``: @@ -3683,11 +3683,7 @@ The general command to add a hint to some databases :n:`{+ @ident}` is Local is useless since hints do not survive anyway to the closure of sections. - .. cmdv:: Local Hint @hint_definition - - Idem for the core database. - - .. cmdv:: Hint Resolve @term {? | {? @num} {? @pattern}} + .. cmdv:: Hint Resolve @term {? | {? @num} {? @pattern}} : @ident :name: Hint Resolve This command adds :n:`simple apply @term` to the hint list with the head @@ -3706,16 +3702,16 @@ The general command to add a hint to some databases :n:`{+ @ident}` is typical example of a hint that is used only by :tacn:`eauto` is a transitivity lemma. - .. exn:: @term cannot be used as a hint + .. exn:: @term cannot be used as a hint - The head symbol of the type of :n:`@term` is a bound variable such that - this tactic cannot be associated to a constant. + The head symbol of the type of :n:`@term` is a bound variable + such that this tactic cannot be associated to a constant. - .. cmdv:: Hint Resolve {+ @term} + .. cmdv:: Hint Resolve {+ @term} : @ident Adds each :n:`Hint Resolve @term`. - .. cmdv:: Hint Resolve -> @term + .. cmdv:: Hint Resolve -> @term : @ident Adds the left-to-right implication of an equivalence as a hint (informally the hint will be used as :n:`apply <- @term`, although as mentionned @@ -3726,7 +3722,7 @@ The general command to add a hint to some databases :n:`{+ @ident}` is Adds the right-to-left implication of an equivalence as a hint. - .. cmdv:: Hint Immediate @term + .. cmdv:: Hint Immediate @term : @ident :name: Hint Immediate This command adds :n:`simple apply @term; trivial` to the hint list associated @@ -3742,37 +3738,37 @@ The general command to add a hint to some databases :n:`{+ @ident}` is .. exn:: @term cannot be used as a hint :undocumented: - .. cmdv:: Immediate {+ @term} + .. cmdv:: Immediate {+ @term} : @ident Adds each :n:`Hint Immediate @term`. - .. cmdv:: Hint Constructors @ident + .. cmdv:: Hint Constructors @qualid : @ident :name: Hint Constructors - If :n:`@ident` is an inductive type, this command adds all its constructors as + If :token:`qualid` is an inductive type, this command adds all its constructors as hints of type ``Resolve``. Then, when the conclusion of current goal has the form - :n:`(@ident ...)`, :tacn:`auto` will try to apply each constructor. + :n:`(@qualid ...)`, :tacn:`auto` will try to apply each constructor. - .. exn:: @ident is not an inductive type - :undocumented: + .. exn:: @qualid is not an inductive type + :undocumented: - .. cmdv:: Hint Constructors {+ @ident} + .. cmdv:: Hint Constructors {+ @qualid} : @ident - Adds each :n:`Hint Constructors @ident`. + Extends the previous command for several inductive types. - .. cmdv:: Hint Unfold @qualid + .. cmdv:: Hint Unfold @qualid : @ident :name: Hint Unfold This adds the tactic :n:`unfold @qualid` to the hint list that will only be - used when the head constant of the goal is :n:`@ident`. + used when the head constant of the goal is :token:`qualid`. Its cost is 4. - .. cmdv:: Hint Unfold {+ @ident} + .. cmdv:: Hint Unfold {+ @qualid} - Adds each :n:`Hint Unfold @ident`. + Extends the previous command for several defined constants. - .. cmdv:: Hint Transparent {+ @qualid} - Hint Opaque {+ @qualid} + .. cmdv:: Hint Transparent {+ @qualid} : @ident + Hint Opaque {+ @qualid} : @ident :name: Hint Transparent; Hint Opaque This adds transparency hints to the database, making :n:`@qualid` @@ -3781,8 +3777,8 @@ The general command to add a hint to some databases :n:`{+ @ident}` is discrimination network to relax or constrain it in the case of discriminated databases. - .. cmdv:: Hint Variables %( Transparent %| Opaque %) - Hint Constants %( Transparent %| Opaque %) + .. cmdv:: Hint Variables %( Transparent %| Opaque %) : @ident + Hint Constants %( Transparent %| Opaque %) : @ident :name: Hint Variables; Hint Constants This sets the transparency flag used during unification of @@ -3790,7 +3786,7 @@ The general command to add a hint to some databases :n:`{+ @ident}` is overwritting the existing settings of opacity. It is advised to use this just after a :cmd:`Create HintDb` command. - .. cmdv:: Hint Extern @num {? @pattern} => @tactic + .. cmdv:: Hint Extern @num {? @pattern} => @tactic : @ident :name: Hint Extern This hint type is to extend :tacn:`auto` with tactics other than :tacn:`apply` and @@ -3801,7 +3797,7 @@ The general command to add a hint to some databases :n:`{+ @ident}` is .. coqtop:: in - Hint Extern 4 (~(_ = _)) => discriminate. + Hint Extern 4 (~(_ = _)) => discriminate : core. Now, when the head of the goal is a disequality, ``auto`` will try discriminate if it does not manage to solve the goal with hints with a @@ -3820,7 +3816,7 @@ The general command to add a hint to some databases :n:`{+ @ident}` is Goal forall a b:list (nat * nat), {a = b} + {a <> b}. Info 1 auto with eqdec. - .. cmdv:: Hint Cut @regexp + .. cmdv:: Hint Cut @regexp : @ident :name: Hint Cut .. warning:: @@ -3854,7 +3850,7 @@ The general command to add a hint to some databases :n:`{+ @ident}` is semantics of ``Hint Cut e`` is to set the cut expression to ``c | e``, the initial cut expression being `emp`. - .. cmdv:: Hint Mode @qualid {* (+ | ! | -)} + .. cmdv:: Hint Mode @qualid {* (+ | ! | -)} : @ident :name: Hint Mode This sets an optional mode of use of the identifier :n:`@qualid`. When diff --git a/doc/sphinx/proof-engine/vernacular-commands.rst b/doc/sphinx/proof-engine/vernacular-commands.rst index a98a46ba21..3e8dd25ee0 100644 --- a/doc/sphinx/proof-engine/vernacular-commands.rst +++ b/doc/sphinx/proof-engine/vernacular-commands.rst @@ -1213,10 +1213,19 @@ Controlling the locality of commands occurs in a section. The :cmd:`Set` and :cmd:`Unset` commands belong to this category. +.. _internal-registration-commands: + +Internal registration commands +-------------------------------- + +Due to their internal nature, the commands that are presented in this section +are not for general use. They are meant to appear only in standard libraries and +in support libraries of plug-ins. + .. _exposing-constants-to-ocaml-libraries: Exposing constants to OCaml libraries ----------------------------------------------------------------- +```````````````````````````````````````````````````````````````` .. cmd:: Register @qualid__1 as @qualid__2 @@ -1225,5 +1234,35 @@ Exposing constants to OCaml libraries calling :n:`Coqlib.lib_ref "@qualid__2"`; i.e., there is no need to known where is the constant defined (file, module, library, etc.). - Due to its internal nature, this command is not for general use. It is meant - to appear only in standard libraries and in support libraries of plug-ins. + As a special case, when the first segment of :n:`@qualid__2` is :g:`kernel`, + the constant is exposed to the kernel. For instance, the `Int63` module + features the following declaration: + + .. coqdoc:: + + Register bool as kernel.ind_bool. + + This makes the kernel aware of what is the type of boolean values. This + information is used for instance to define the return type of the + :g:`#int63_eq` primitive. + + .. seealso:: :ref:`primitive-integers` + +Inlining hints for the fast reduction machines +```````````````````````````````````````````````````````````````` + +.. cmd:: Register Inline @qualid + + This command gives as a hint to the reduction machines (VM and native) that + the body of the constant :n:`@qualid` should be inlined in the generated code. + +Registering primitive operations +```````````````````````````````` + +.. cmd:: Primitive @ident__1 := #@ident__2. + + Declares :n:`@ident__1` as the primitive operator :n:`#@ident__2`. When + running this command, the type of the primitive should be already known by + the kernel (this is achieved through this command for primitive types and + through the :cmd:`Register` command with the :g:`kernel` name-space for other + types). |