diff options
Diffstat (limited to 'doc/sphinx')
| -rw-r--r-- | doc/sphinx/addendum/ring.rst | 2 | ||||
| -rw-r--r-- | doc/sphinx/addendum/universe-polymorphism.rst | 2 | ||||
| -rw-r--r-- | doc/sphinx/changes.rst | 4 | ||||
| -rw-r--r-- | doc/sphinx/language/coq-library.rst | 36 | ||||
| -rw-r--r-- | doc/sphinx/language/gallina-extensions.rst | 11 | ||||
| -rw-r--r-- | doc/sphinx/language/gallina-specification-language.rst | 107 | ||||
| -rw-r--r-- | doc/sphinx/practical-tools/coqide.rst | 30 | ||||
| -rw-r--r-- | doc/sphinx/proof-engine/ltac.rst | 18 | ||||
| -rw-r--r-- | doc/sphinx/proof-engine/ltac2.rst | 8 | ||||
| -rw-r--r-- | doc/sphinx/proof-engine/ssreflect-proof-language.rst | 10 | ||||
| -rw-r--r-- | doc/sphinx/proof-engine/vernacular-commands.rst | 20 |
11 files changed, 109 insertions, 139 deletions
diff --git a/doc/sphinx/addendum/ring.rst b/doc/sphinx/addendum/ring.rst index 3f4d5cc784..1098aa75da 100644 --- a/doc/sphinx/addendum/ring.rst +++ b/doc/sphinx/addendum/ring.rst @@ -76,7 +76,7 @@ an arbitrary order: ===== =============== ========================= Then normalize the “abstract” polynomial -:math:`((V_1 \otimes V_2 ) \oplus V_2) \oplus (V_0 \otimes 2)` +:math:`((V_1 \oplus V_2 ) \otimes V_2) \oplus (V_0 \otimes 2)` In our example the normal form is: :math:`(2 \otimes V_0 ) \oplus (V_1 \otimes V_2) \oplus (V_2 \otimes V_2 )`. Then substitute the variables by their values in the variables map to diff --git a/doc/sphinx/addendum/universe-polymorphism.rst b/doc/sphinx/addendum/universe-polymorphism.rst index 395b5ce2d3..7e698bfb66 100644 --- a/doc/sphinx/addendum/universe-polymorphism.rst +++ b/doc/sphinx/addendum/universe-polymorphism.rst @@ -144,6 +144,8 @@ Many other commands support the ``Polymorphic`` flag, including: - ``Lemma``, ``Axiom``, and all the other “definition” keywords support polymorphism. +- :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 diff --git a/doc/sphinx/changes.rst b/doc/sphinx/changes.rst index fd84868a1f..6ac55e7bf4 100644 --- a/doc/sphinx/changes.rst +++ b/doc/sphinx/changes.rst @@ -102,10 +102,10 @@ reference manual. Here are the most important user-visible changes: extensionality lemma: - interactive mode: :n:`under @term`, associated terminator: :tacn:`over` - - one-liner mode: `under @term do [@tactic | ...]` + - one-liner mode: :n:`under @term do [@tactic | ...]` It can take occurrence switches, contextual patterns, and intro patterns: - :g:`under {2}[in RHS]eq_big => [i|i ?] do ...` + :g:`under {2}[in RHS]eq_big => [i|i ?]` (`#9651 <https://github.com/coq/coq/pull/9651>`_, by Erik Martin-Dorel and Enrico Tassi). diff --git a/doc/sphinx/language/coq-library.rst b/doc/sphinx/language/coq-library.rst index d1b95e6203..ac75240cfb 100644 --- a/doc/sphinx/language/coq-library.rst +++ b/doc/sphinx/language/coq-library.rst @@ -7,22 +7,20 @@ The |Coq| library single: Theories -The |Coq| library is structured into two parts: +The |Coq| library has two parts: - * **The initial library**: it contains elementary logical notions and - data-types. It constitutes the basic state of the system directly - available when running |Coq|; + * **The basic library**: definitions and theorems for + the most commonly used elementary logical notions and + data types. |Coq| normally loads these files automatically when it starts. - * **The standard library**: general-purpose libraries containing various - developments of |Coq| axiomatizations about sets, lists, sorting, - arithmetic, etc. This library comes with the system and its modules - are directly accessible through the ``Require`` command (see - Section :ref:`compiled-files`); + * **The standard library**: general-purpose libraries with + definitions and theorems for sets, lists, sorting, + arithmetic, etc. To use these files, users must load them explicitly + with the ``Require`` command (see :ref:`compiled-files`) -In addition, user-provided libraries or developments are provided by -|Coq| users' community. These libraries and developments are available -for download at http://coq.inria.fr (see -Section :ref:`userscontributions`). +There are also many libraries provided by |Coq| users' community. +These libraries and developments are available +for download at http://coq.inria.fr (see :ref:`userscontributions`). This chapter briefly reviews the |Coq| libraries whose contents can also be browsed at http://coq.inria.fr/stdlib. @@ -514,8 +512,8 @@ realizability interpretation. forall (A B:Prop) (P:Type), (A -> B -> P) -> A /\ B -> P. -Basic Arithmetics -~~~~~~~~~~~~~~~~~ +Basic Arithmetic +~~~~~~~~~~~~~~~~ The basic library includes a few elementary properties of natural numbers, together with the definitions of predecessor, addition and @@ -804,8 +802,8 @@ Notation Interpretation =============== =================== -Notations for integer arithmetics -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +Notations for integer arithmetic +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. index:: single: Arithmetical notations @@ -822,7 +820,7 @@ Notations for integer arithmetics The following table describes the syntax of expressions -for integer arithmetics. It is provided by requiring and opening the module ``ZArith`` and opening scope ``Z_scope``. +for integer arithmetic. It is provided by requiring and opening the module ``ZArith`` and opening scope ``Z_scope``. It specifies how notations are interpreted and, when not already reserved, the precedence and associativity. @@ -866,7 +864,7 @@ Notations for real numbers This is provided by requiring and opening the module ``Reals`` and opening scope ``R_scope``. This set of notations is very similar to -the notation for integer arithmetics. The inverse function was added. +the notation for integer arithmetic. The inverse function was added. =============== =================== Notation Interpretation diff --git a/doc/sphinx/language/gallina-extensions.rst b/doc/sphinx/language/gallina-extensions.rst index c93984661e..acf68e9fd2 100644 --- a/doc/sphinx/language/gallina-extensions.rst +++ b/doc/sphinx/language/gallina-extensions.rst @@ -2443,12 +2443,19 @@ The reduction machines (:tacn:`vm_compute`, :tacn:`native_compute`) implement dedicated, efficient, rules to reduce the applications of these primitive operations. -These primitives, when extracted to OCaml (see :ref:`extraction`), are mapped to -types and functions of a :g:`Uint63` module. Said module is not produced by +The extraction of these primitives can be customized similarly to the extraction +of regular axioms (see :ref:`extraction`). Nonetheless, the :g:`ExtrOCamlInt63` +module can be used when extracting to OCaml: it maps the Coq primitives to types +and functions of a :g:`Uint63` module. Said OCaml module is not produced by extraction. Instead, it has to be provided by the user (if they want to compile or execute the extracted code). For instance, an implementation of this module can be taken from the kernel of Coq. +Literal values (at type :g:`Int63.int`) are extracted to literal OCaml values +wrapped into the :g:`Uint63.of_int` (resp. :g:`Uint63.of_int64`) constructor on +64-bit (resp. 32-bit) platforms. Currently, this cannot be customized (see the +function :g:`Uint63.compile` from the kernel). + Bidirectionality hints ---------------------- diff --git a/doc/sphinx/language/gallina-specification-language.rst b/doc/sphinx/language/gallina-specification-language.rst index 38f6714f46..91dfa34494 100644 --- a/doc/sphinx/language/gallina-specification-language.rst +++ b/doc/sphinx/language/gallina-specification-language.rst @@ -44,78 +44,91 @@ Lexical conventions =================== Blanks - Space, newline and horizontal tabulation are considered as blanks. + Space, newline and horizontal tab are considered blanks. Blanks are ignored but they separate tokens. Comments - Comments in Coq are enclosed between ``(*`` and ``*)``, and can be nested. - They can contain any character. However, :token:`string` literals must be + Comments are enclosed between ``(*`` and ``*)``. They can be nested. + They can contain any character. However, embedded :token:`string` literals must be correctly closed. Comments are treated as blanks. -Identifiers and access identifiers +Identifiers and field identifiers Identifiers, written :token:`ident`, are sequences of letters, digits, ``_`` and - ``'``, that do not start with a digit or ``'``. That is, they are - recognized by the following lexical class: + ``'``, that do not start with a digit or ``'``. That is, they are + recognized by the following grammar (except that the string ``_`` is reserved; + it is not a valid identifier): .. productionlist:: coq - first_letter : a..z ∣ A..Z ∣ _ ∣ unicode-letter - subsequent_letter : a..z ∣ A..Z ∣ 0..9 ∣ _ ∣ ' ∣ unicode-letter ∣ unicode-id-part ident : `first_letter`[`subsequent_letter`…`subsequent_letter`] - access_ident : .`ident` + field : .`ident` + first_letter : a..z ∣ A..Z ∣ _ ∣ `unicode_letter` + subsequent_letter : `first_letter` ∣ 0..9 ∣ ' ∣ `unicode_id_part` All characters are meaningful. In particular, identifiers are case-sensitive. - The entry ``unicode-letter`` non-exhaustively includes Latin, + :production:`unicode_letter` non-exhaustively includes Latin, Greek, Gothic, Cyrillic, Arabic, Hebrew, Georgian, Hangul, Hiragana and Katakana characters, CJK ideographs, mathematical letter-like - symbols, hyphens, non-breaking space, … The entry ``unicode-id-part`` + symbols and non-breaking space. :production:`unicode_id_part` non-exhaustively includes symbols for prime letters and subscripts. - Access identifiers, written :token:`access_ident`, are identifiers prefixed by - `.` (dot) without blank. They are used in the syntax of qualified - identifiers. + Field identifiers, written :token:`field`, are identifiers prefixed by + `.` (dot) with no blank between the dot and the identifier. They are used in + the syntax of qualified identifiers. Numerals - Numerals are sequences of digits with a potential fractional part - and exponent. Integers are numerals without fractional nor exponent - part and optionally preceded by a minus sign. Underscores ``_`` can - be used as comments in numerals. + Numerals are sequences of digits with an optional fractional part + and exponent, optionally preceded by a minus sign. :token:`int` is an integer; + a numeral without fractional or exponent parts. :token:`num` is a non-negative + integer. Underscores embedded in the digits are ignored, for example + ``1_000_000`` is the same as ``1000000``. .. productionlist:: coq - digit : 0..9 + numeral : `num`[. `num`][`exp`[`sign`]`num`] + int : [-]`num` num : `digit`…`digit` - integer : [-]`num` - dot : . + digit : 0..9 exp : e | E sign : + | - - numeral : `num`[`dot` `num`][`exp`[`sign`]`num`] Strings - Strings are delimited by ``"`` (double quote), and enclose a sequence of - any characters different from ``"`` or the sequence ``""`` to denote the - double quote character. In grammars, the entry for quoted strings is - :production:`string`. + Strings begin and end with ``"`` (double quote). Use ``""`` to represent + a double quote character within a string. In the grammar, strings are + identified with :production:`string`. Keywords - The following identifiers are reserved keywords, and cannot be - employed otherwise:: - - _ as at cofix else end exists exists2 fix for - forall fun if IF in let match mod return - SProp Prop Set Type then using where with - -Special tokens - The following sequences of characters are special tokens:: - - ! % & && ( () ) * + ++ , - -> . .( .. - / /\ : :: :< := :> ; < <- <-> <: <= <> = - => =_D > >-> >= ? ?= @ [ \/ ] ^ { | |- - || } ~ #[ - - Lexical ambiguities are resolved according to the “longest match” - rule: when a sequence of non alphanumerical characters can be - decomposed into several different ways, then the first token is the - longest possible one (among all tokens defined at this moment), and so - on. + The following character sequences are reserved keywords that cannot be + used as identifiers:: + + _ Axiom CoFixpoint Definition Fixpoint Hypothesis IF Parameter Prop + SProp Set Theorem Type Variable as at by cofix discriminated else + end exists exists2 fix for forall fun if in lazymatch let match + multimatch return then using where with + + Note that plugins may define additional keywords when they are loaded. + +Other tokens + The set of + tokens defined at any given time can vary because the :cmd:`Notation` + command can define new tokens. A :cmd:`Require` command may load more notation definitions, + while the end of a :cmd:`Section` may remove notations. Some notations + are defined in the basic library (see :ref:`thecoqlibrary`) and are normallly + loaded automatically at startup time. + + Here are the character sequences that Coq directly defines as tokens + without using :cmd:`Notation` (omitting 25 specialized tokens that begin with + ``#int63_``):: + + ! #[ % & ' ( () (bfs) (dfs) ) * ** + , - -> + . .( .. ... / : ::= := :> :>> ; < <+ <- <: + <<: <= = => > >-> >= ? @ @{ [ [= ] _ _eqn + `( `{ { {| | |- || } + + When multiple tokens match the beginning of a sequence of characters, + the longest matching token is used. + Occasionally you may need to insert spaces to separate tokens. For example, + if ``~`` and ``~~`` are both defined as tokens, the inputs ``~ ~`` and + ``~~`` generate different tokens, whereas if `~~` is not defined, then the + two inputs are equivalent. .. _term: @@ -164,7 +177,7 @@ is described in Chapter :ref:`syntaxextensionsandinterpretationscopes`. : ( `name` [: `term`] := `term` ) : ' `pattern` name : `ident` | _ - qualid : `ident` | `qualid` `access_ident` + qualid : `ident` | `qualid` `field` sort : SProp | Prop | Set | Type fix_bodies : `fix_body` : `fix_body` with `fix_body` with … with `fix_body` for `ident` diff --git a/doc/sphinx/practical-tools/coqide.rst b/doc/sphinx/practical-tools/coqide.rst index efb5df720a..7d6171285e 100644 --- a/doc/sphinx/practical-tools/coqide.rst +++ b/doc/sphinx/practical-tools/coqide.rst @@ -88,8 +88,6 @@ There are other buttons on the |CoqIDE| toolbar: a button to save the running buffer; a button to close the current buffer (an "X"); buttons to switch among buffers (left and right arrows); an "information" button; and a "gears" button. -The "information" button is described in Section :ref:`try-tactics-automatically`. - The "gears" button submits proof terms to the |Coq| kernel for type checking. When |Coq| uses asynchronous processing (see Chapter :ref:`asynchronousandparallelproofprocessing`), proofs may have been completed without kernel-checking of generated proof terms. @@ -100,27 +98,6 @@ processed color, though their preceding proofs have the processed color. Notice that for all these buttons, except for the "gears" button, their operations are also available in the menu, where their keyboard shortcuts are given. -.. _try-tactics-automatically: - -Trying tactics automatically ------------------------------- - -The menu Try Tactics provides some features for automatically trying -to solve the current goal using simple tactics. If such a tactic -succeeds in solving the goal, then its text is automatically inserted -into the script. There is finally a combination of these tactics, -called the *proof wizard* which will try each of them in turn. This -wizard is also available as a tool button (the "information" button). The set of -tactics tried by the wizard is customizable in the preferences. - -These tactics are general ones, in particular they do not refer to -particular hypotheses. You may also try specific tactics related to -the goal or one of the hypotheses, by clicking with the right mouse -button on the goal or the considered hypothesis. This is the -“contextual menu on goals” feature, that may be disabled in the -preferences if undesirable. - - Proof folding ------------------ @@ -202,13 +179,6 @@ compilation, printing, web browsing. In the browser command, you may use `%s` to denote the URL to open, for example: `firefox -remote "OpenURL(%s)"`. -The `Tactics Wizard` section allows defining the set of tactics that -should be tried, in sequence, to solve the current goal. - -The last section is for miscellaneous boolean settings, such as the -“contextual menu on goals” feature presented in the section -:ref:`Try tactics automatically <try-tactics-automatically>`. - Notice that these settings are saved in the file `.coqiderc` of your home directory. diff --git a/doc/sphinx/proof-engine/ltac.rst b/doc/sphinx/proof-engine/ltac.rst index 46f9826e41..362c3da6cb 100644 --- a/doc/sphinx/proof-engine/ltac.rst +++ b/doc/sphinx/proof-engine/ltac.rst @@ -31,10 +31,10 @@ Syntax The syntax of the tactic language is given below. See Chapter :ref:`gallinaspecificationlanguage` for a description of the BNF metasyntax used in these grammar rules. Various already defined entries will be used in this -chapter: entries :token:`natural`, :token:`integer`, :token:`ident`, +chapter: entries :token:`num`, :token:`int`, :token:`ident` :token:`qualid`, :token:`term`, :token:`cpattern` and :token:`tactic` -represent respectively the natural and integer numbers, the authorized -identificators and qualified names, Coq terms and patterns and all the atomic +represent respectively natural and integer numbers, +identifiers, qualified names, Coq terms, patterns and the atomic tactics described in Chapter :ref:`tactics`. The syntax of :production:`cpattern` is @@ -141,10 +141,10 @@ mode but it can also be used in toplevel definitions as shown below. : `atom` atom : `qualid` : () - : `integer` + : `int` : ( `ltac_expr` ) component : `string` | `qualid` - message_token : `string` | `ident` | `integer` + message_token : `string` | `ident` | `int` tacarg : `qualid` : () : ltac : `atom` @@ -159,11 +159,11 @@ mode but it can also be used in toplevel definitions as shown below. match_rule : `cpattern` => `ltac_expr` : context [`ident`] [ `cpattern` ] => `ltac_expr` : _ => `ltac_expr` - test : `integer` = `integer` - : `integer` (< | <= | > | >=) `integer` + test : `int` = `int` + : `int` (< | <= | > | >=) `int` selector : [`ident`] - : `integer` - : (`integer` | `integer` - `integer`), ..., (`integer` | `integer` - `integer`) + : `int` + : (`int` | `int` - `int`), ..., (`int` | `int` - `int`) toplevel_selector : `selector` : all : par diff --git a/doc/sphinx/proof-engine/ltac2.rst b/doc/sphinx/proof-engine/ltac2.rst index 3036648b08..ceaa2775bf 100644 --- a/doc/sphinx/proof-engine/ltac2.rst +++ b/doc/sphinx/proof-engine/ltac2.rst @@ -179,7 +179,7 @@ constructions from ML. : let `ltac2_var` := `ltac2_term` in `ltac2_term` : let rec `ltac2_var` := `ltac2_term` in `ltac2_term` : match `ltac2_term` with `ltac2_branch` ... `ltac2_branch` end - : `integer` + : `int` : `string` : `ltac2_term` ; `ltac2_term` : [| `ltac2_term` ; ... ; `ltac2_term` |] @@ -670,7 +670,7 @@ A scope is a name given to a grammar entry used to produce some Ltac2 expression at parsing time. Scopes are described using a form of S-expression. .. prodn:: - ltac2_scope ::= {| @string | @integer | @lident ({+, @ltac2_scope}) } + ltac2_scope ::= {| @string | @int | @lident ({+, @ltac2_scope}) } A few scopes contain antiquotation features. For sake of uniformity, all antiquotations are introduced by the syntax :n:`$@lident`. @@ -719,7 +719,7 @@ The following scopes are built-in. + parses a Ltac2 expression at the next level and return it as is. -- :n:`tactic(n = @integer)`: +- :n:`tactic(n = @int)`: + parses a Ltac2 expression at the provided level :n:`n` and return it as is. @@ -760,7 +760,7 @@ Notations The Ltac2 parser can be extended by syntactic notations. -.. cmd:: Ltac2 Notation {+ {| @lident (@ltac2_scope) | @string } } {? : @integer} := @ltac2_term +.. cmd:: Ltac2 Notation {+ {| @lident (@ltac2_scope) | @string } } {? : @int} := @ltac2_term :name: Ltac2 Notation A Ltac2 notation adds a parsing rule to the Ltac2 grammar, which is expanded diff --git a/doc/sphinx/proof-engine/ssreflect-proof-language.rst b/doc/sphinx/proof-engine/ssreflect-proof-language.rst index 1b9e3ce0f3..ed980bd4de 100644 --- a/doc/sphinx/proof-engine/ssreflect-proof-language.rst +++ b/doc/sphinx/proof-engine/ssreflect-proof-language.rst @@ -3761,10 +3761,10 @@ involves the following steps: 5. If so :tacn:`under` protects these n goals against an accidental instantiation of the evar. - These protected goals are displayed using the ``Under[ … ]`` - notation (e.g. ``Under[ m - m ]`` in the running example). + These protected goals are displayed using the ``'Under[ … ]`` + notation (e.g. ``'Under[ m - m ]`` in the running example). -6. The expression inside the ``Under[ … ]`` notation can be +6. The expression inside the ``'Under[ … ]`` notation can be proved equivalent to the desired expression by using a regular :tacn:`rewrite` tactic. @@ -3782,7 +3782,7 @@ The over tactic Two equivalent facilities (a terminator and a lemma) are provided to close intermediate subgoals generated by :tacn:`under` (i.e. goals -displayed as ``Under[ … ]``): +displayed as ``'Under[ … ]``): .. tacn:: over :name: over @@ -3792,7 +3792,7 @@ displayed as ``Under[ … ]``): .. tacv:: by rewrite over - This is a variant of :tacn:`over` in order to close ``Under[ … ]`` + This is a variant of :tacn:`over` in order to close ``'Under[ … ]`` goals, relying on the ``over`` rewrite rule. .. _under_one_liner: diff --git a/doc/sphinx/proof-engine/vernacular-commands.rst b/doc/sphinx/proof-engine/vernacular-commands.rst index 5f3e82938d..774732825a 100644 --- a/doc/sphinx/proof-engine/vernacular-commands.rst +++ b/doc/sphinx/proof-engine/vernacular-commands.rst @@ -870,26 +870,6 @@ interactively, they cannot be part of a vernacular file loaded via have to undo some extra commands and end on a state :n:`@num′ ≤ @num` if necessary. - .. cmdv:: Backtrack @num @num @num - :name: Backtrack - - .. deprecated:: 8.4 - - :cmd:`Backtrack` is a *deprecated* form of - :cmd:`BackTo` which allows explicitly manipulating the proof environment. The - three numbers represent the following: - - + *first number* : State label to reach, as for :cmd:`BackTo`. - + *second number* : *Proof state number* to unbury once aborts have been done. - |Coq| will compute the number of :cmd:`Undo` to perform (see Chapter :ref:`proofhandling`). - + *third number* : Number of :cmd:`Abort` to perform, i.e. the number of currently - opened nested proofs that must be canceled (see Chapter :ref:`proofhandling`). - - .. exn:: Invalid backtrack. - - The destination state label is unknown. - - .. _quitting-and-debugging: Quitting and debugging |