diff options
Diffstat (limited to 'doc/sphinx/user-extensions')
| -rw-r--r-- | doc/sphinx/user-extensions/proof-schemes.rst | 41 | ||||
| -rw-r--r-- | doc/sphinx/user-extensions/syntax-extensions.rst | 204 |
2 files changed, 122 insertions, 123 deletions
diff --git a/doc/sphinx/user-extensions/proof-schemes.rst b/doc/sphinx/user-extensions/proof-schemes.rst index 8f76085d88..418922e9b3 100644 --- a/doc/sphinx/user-extensions/proof-schemes.rst +++ b/doc/sphinx/user-extensions/proof-schemes.rst @@ -12,7 +12,7 @@ The ``Scheme`` command is a high-level tool for generating automatically (possibly mutual) induction principles for given types and sorts. Its syntax follows the schema: -.. cmd:: Scheme @ident__1 := Induction for @ident__2 Sort sort {* with @ident__i := Induction for @ident__j Sort sort} +.. cmd:: Scheme @ident__1 := Induction for @ident__2 Sort @sort {* with @ident__i := Induction for @ident__j Sort @sort} This command is a high-level tool for generating automatically (possibly mutual) induction principles for given types and sorts. @@ -22,10 +22,10 @@ syntax follows the schema: definitions. Each term :n:`@ident__i` proves a general principle of mutual induction for objects in type :n:`@ident__j`. -.. cmdv:: Scheme @ident := Minimality for @ident Sort sort {* with @ident := Minimality for @ident' Sort sort} +.. cmdv:: Scheme @ident := Minimality for @ident Sort @sort {* with @ident := Minimality for @ident' Sort @sort} - Same as before but defines a non-dependent elimination principle more - natural in case of inductively defined relations. + Same as before but defines a non-dependent elimination principle more + natural in case of inductively defined relations. .. cmdv:: Scheme Equality for @ident :name: Scheme Equality @@ -33,7 +33,7 @@ syntax follows the schema: Tries to generate a Boolean equality and a proof of the decidability of the usual equality. If `ident` involves some other inductive types, their equality has to be defined first. -.. cmdv:: Scheme Induction for @ident Sort sort {* with Induction for @ident Sort sort} +.. cmdv:: Scheme Induction for @ident Sort @sort {* with Induction for @ident Sort @sort} If you do not provide the name of the schemes, they will be automatically computed from the sorts involved (works also with Minimality). @@ -195,19 +195,18 @@ Combined Scheme Generation of induction principles with ``Functional`` ``Scheme`` ----------------------------------------------------------------- -The ``Functional Scheme`` command is a high-level experimental tool for -generating automatically induction principles corresponding to -(possibly mutually recursive) functions. First, it must be made -available via ``Require Import FunInd``. Its syntax then follows the -schema: -.. cmd:: Functional Scheme @ident := Induction for ident' Sort sort {* with @ident := Induction for @ident Sort sort} +.. cmd:: Functional Scheme @ident__0 := Induction for @ident' Sort @sort {* with @ident__i := Induction for @ident__i' Sort @sort} -where each `ident'ᵢ` is a different mutually defined function -name (the names must be in the same order as when they were defined). This -command generates the induction principle for each `identᵢ`, following -the recursive structure and case analyses of the corresponding function -identᵢ’. + This command is a high-level experimental tool for + generating automatically induction principles corresponding to + (possibly mutually recursive) functions. First, it must be made + available via ``Require Import FunInd``. + Each :n:`@ident__i` is a different mutually defined function + name (the names must be in the same order as when they were defined). This + command generates the induction principle for each :n:`@ident__i`, following + the recursive structure and case analyses of the corresponding function + :n:`@ident__i'`. .. warning:: @@ -349,17 +348,17 @@ Generation of inversion principles with ``Derive`` ``Inversion`` :g:`inversion`. -.. cmdv:: Derive Inversion_clear @ident with forall (x:T), I t Sort sort +.. cmdv:: Derive Inversion_clear @ident with forall (x:T), I t Sort @sort When applied, it is equivalent to having inverted the instance with the tactic inversion replaced by the tactic `inversion_clear`. -.. cmdv:: Derive Dependent Inversion @ident with forall (x:T), I t Sort sort +.. cmdv:: Derive Dependent Inversion @ident with forall (x:T), I t Sort @sort When applied, it is equivalent to having inverted the instance with the tactic `dependent inversion`. -.. cmdv:: Derive Dependent Inversion_clear @ident with forall(x:T), I t Sort sort +.. cmdv:: Derive Dependent Inversion_clear @ident with forall(x:T), I t Sort @sort When applied, it is equivalent to having inverted the instance with the tactic `dependent inversion_clear`. @@ -377,8 +376,8 @@ Generation of inversion principles with ``Derive`` ``Inversion`` Parameter P : nat -> nat -> Prop. - To generate the inversion lemma for the instance `(Le (S n) m)` and the - sort `Prop`, we do: + To generate the inversion lemma for the instance :g:`(Le (S n) m)` and the + sort :g:`Prop`, we do: .. coqtop:: all diff --git a/doc/sphinx/user-extensions/syntax-extensions.rst b/doc/sphinx/user-extensions/syntax-extensions.rst index 2214cbfb34..1c53f5981d 100644 --- a/doc/sphinx/user-extensions/syntax-extensions.rst +++ b/doc/sphinx/user-extensions/syntax-extensions.rst @@ -31,8 +31,8 @@ Basic notations .. cmd:: Notation -A *notation* is a symbolic expression denoting some term or term -pattern. + A *notation* is a symbolic expression denoting some term or term + pattern. A typical notation is the use of the infix symbol ``/\`` to denote the logical conjunction (and). Such a notation is declared by @@ -1380,147 +1380,147 @@ Numeral notations .. cmd:: Numeral Notation @ident__1 @ident__2 @ident__3 : @scope. :name: Numeral Notation - This command allows the user to customize the way numeral literals - are parsed and printed. + This command allows the user to customize the way numeral literals + are parsed and printed. - The token :n:`@ident__1` should be the name of an inductive type, - while :n:`@ident__2` and :n:`@ident__3` should be the names of the - parsing and printing functions, respectively. The parsing function - :n:`@ident__2` should have one of the following types: + The token :n:`@ident__1` should be the name of an inductive type, + while :n:`@ident__2` and :n:`@ident__3` should be the names of the + parsing and printing functions, respectively. The parsing function + :n:`@ident__2` should have one of the following types: - * :n:`Decimal.int -> @ident__1` - * :n:`Decimal.int -> option @ident__1` - * :n:`Decimal.uint -> @ident__1` - * :n:`Decimal.uint -> option @ident__1` - * :n:`Z -> @ident__1` - * :n:`Z -> option @ident__1` + * :n:`Decimal.int -> @ident__1` + * :n:`Decimal.int -> option @ident__1` + * :n:`Decimal.uint -> @ident__1` + * :n:`Decimal.uint -> option @ident__1` + * :n:`Z -> @ident__1` + * :n:`Z -> option @ident__1` - And the printing function :n:`@ident__3` should have one of the - following types: + And the printing function :n:`@ident__3` should have one of the + following types: - * :n:`@ident__1 -> Decimal.int` - * :n:`@ident__1 -> option Decimal.int` - * :n:`@ident__1 -> Decimal.uint` - * :n:`@ident__1 -> option Decimal.uint` - * :n:`@ident__1 -> Z` - * :n:`@ident__1 -> option Z` + * :n:`@ident__1 -> Decimal.int` + * :n:`@ident__1 -> option Decimal.int` + * :n:`@ident__1 -> Decimal.uint` + * :n:`@ident__1 -> option Decimal.uint` + * :n:`@ident__1 -> Z` + * :n:`@ident__1 -> option Z` - When parsing, the application of the parsing function - :n:`@ident__2` to the number will be fully reduced, and universes - of the resulting term will be refreshed. + When parsing, the application of the parsing function + :n:`@ident__2` to the number will be fully reduced, and universes + of the resulting term will be refreshed. - .. cmdv:: Numeral Notation @ident__1 @ident__2 @ident__3 : @scope (warning after @num). + .. cmdv:: Numeral Notation @ident__1 @ident__2 @ident__3 : @scope (warning after @num). - When a literal larger than :token:`num` is parsed, a warning - message about possible stack overflow, resulting from evaluating - :n:`@ident__2`, will be displayed. + When a literal larger than :token:`num` is parsed, a warning + message about possible stack overflow, resulting from evaluating + :n:`@ident__2`, will be displayed. - .. cmdv:: Numeral Notation @ident__1 @ident__2 @ident__3 : @scope (abstract after @num). + .. cmdv:: Numeral Notation @ident__1 @ident__2 @ident__3 : @scope (abstract after @num). - When a literal :g:`m` larger than :token:`num` is parsed, the - result will be :n:`(@ident__2 m)`, without reduction of this - application to a normal form. Here :g:`m` will be a - :g:`Decimal.int` or :g:`Decimal.uint` or :g:`Z`, depending on the - type of the parsing function :n:`@ident__2`. This allows for a - more compact representation of literals in types such as :g:`nat`, - and limits parse failures due to stack overflow. Note that a - warning will be emitted when an integer larger than :token:`num` - is parsed. Note that :n:`(abstract after @num)` has no effect - when :n:`@ident__2` lands in an :g:`option` type. + When a literal :g:`m` larger than :token:`num` is parsed, the + result will be :n:`(@ident__2 m)`, without reduction of this + application to a normal form. Here :g:`m` will be a + :g:`Decimal.int` or :g:`Decimal.uint` or :g:`Z`, depending on the + type of the parsing function :n:`@ident__2`. This allows for a + more compact representation of literals in types such as :g:`nat`, + and limits parse failures due to stack overflow. Note that a + warning will be emitted when an integer larger than :token:`num` + is parsed. Note that :n:`(abstract after @num)` has no effect + when :n:`@ident__2` lands in an :g:`option` type. - .. exn:: Cannot interpret this number as a value of type @type + .. exn:: Cannot interpret this number as a value of type @type - The numeral notation registered for :token:`type` does not support - the given numeral. This error is given when the interpretation - function returns :g:`None`, or if the interpretation is registered - for only non-negative integers, and the given numeral is negative. + The numeral notation registered for :token:`type` does not support + the given numeral. This error is given when the interpretation + function returns :g:`None`, or if the interpretation is registered + for only non-negative integers, and the given numeral is negative. - .. exn:: @ident should go from Decimal.int to @type or (option @type). Instead of Decimal.int, the types Decimal.uint or Z could be used{? (require BinNums first)}. + .. exn:: @ident should go from Decimal.int to @type or (option @type). Instead of Decimal.int, the types Decimal.uint or Z could be used{? (require BinNums first)}. - The parsing function given to the :cmd:`Numeral Notation` - vernacular is not of the right type. + The parsing function given to the :cmd:`Numeral Notation` + vernacular is not of the right type. - .. exn:: @ident should go from @type to Decimal.int or (option Decimal.int). Instead of Decimal.int, the types Decimal.uint or Z could be used{? (require BinNums first)}. + .. exn:: @ident should go from @type to Decimal.int or (option Decimal.int). Instead of Decimal.int, the types Decimal.uint or Z could be used{? (require BinNums first)}. - The printing function given to the :cmd:`Numeral Notation` - vernacular is not of the right type. + The printing function given to the :cmd:`Numeral Notation` + vernacular is not of the right type. - .. exn:: @type is not an inductive type. + .. exn:: @type is not an inductive type. - Numeral notations can only be declared for inductive types with no - arguments. + Numeral notations can only be declared for inductive types with no + arguments. - .. exn:: Unexpected term @term while parsing a numeral notation. + .. exn:: Unexpected term @term while parsing a numeral notation. - Parsing functions must always return ground terms, made up of - applications of constructors and inductive types. Parsing - functions may not return terms containing axioms, bare - (co)fixpoints, lambdas, etc. + Parsing functions must always return ground terms, made up of + applications of constructors and inductive types. Parsing + functions may not return terms containing axioms, bare + (co)fixpoints, lambdas, etc. - .. exn:: Unexpected non-option term @term while parsing a numeral notation. + .. exn:: Unexpected non-option term @term while parsing a numeral notation. - Parsing functions expected to return an :g:`option` must always - return a concrete :g:`Some` or :g:`None` when applied to a - concrete numeral expressed as a decimal. They may not return - opaque constants. + Parsing functions expected to return an :g:`option` must always + return a concrete :g:`Some` or :g:`None` when applied to a + concrete numeral expressed as a decimal. They may not return + opaque constants. - .. exn:: Cannot interpret in @scope because @ident could not be found in the current environment. + .. exn:: Cannot interpret in @scope because @ident could not be found in the current environment. - The inductive type used to register the numeral notation is no - longer available in the environment. Most likely, this is because - the numeral notation was declared inside a functor for an - inductive type inside the functor. This use case is not currently - supported. + The inductive type used to register the numeral notation is no + longer available in the environment. Most likely, this is because + the numeral notation was declared inside a functor for an + inductive type inside the functor. This use case is not currently + supported. - Alternatively, you might be trying to use a primitive token - notation from a plugin which forgot to specify which module you - must :g:`Require` for access to that notation. + Alternatively, you might be trying to use a primitive token + notation from a plugin which forgot to specify which module you + must :g:`Require` for access to that notation. - .. exn:: Syntax error: [prim:reference] expected after 'Notation' (in [vernac:command]). + .. exn:: Syntax error: [prim:reference] expected after 'Notation' (in [vernac:command]). - The type passed to :cmd:`Numeral Notation` must be a single - identifier. + The type passed to :cmd:`Numeral Notation` must be a single + identifier. - .. exn:: Syntax error: [prim:reference] expected after [prim:reference] (in [vernac:command]). + .. exn:: Syntax error: [prim:reference] expected after [prim:reference] (in [vernac:command]). - Both functions passed to :cmd:`Numeral Notation` must be single - identifiers. + Both functions passed to :cmd:`Numeral Notation` must be single + identifiers. - .. exn:: The reference @ident was not found in the current environment. + .. exn:: The reference @ident was not found in the current environment. - Identifiers passed to :cmd:`Numeral Notation` must exist in the - global environment. + Identifiers passed to :cmd:`Numeral Notation` must exist in the + global environment. - .. exn:: @ident is bound to a notation that does not denote a reference. + .. exn:: @ident is bound to a notation that does not denote a reference. - Identifiers passed to :cmd:`Numeral Notation` must be global - references, or notations which denote to single identifiers. + Identifiers passed to :cmd:`Numeral Notation` must be global + references, or notations which denote to single identifiers. - .. warn:: Stack overflow or segmentation fault happens when working with large numbers in @type (threshold may vary depending on your system limits and on the command executed). + .. warn:: Stack overflow or segmentation fault happens when working with large numbers in @type (threshold may vary depending on your system limits and on the command executed). - When a :cmd:`Numeral Notation` is registered in the current scope - with :n:`(warning after @num)`, this warning is emitted when - parsing a numeral greater than or equal to :token:`num`. + When a :cmd:`Numeral Notation` is registered in the current scope + with :n:`(warning after @num)`, this warning is emitted when + parsing a numeral greater than or equal to :token:`num`. - .. warn:: To avoid stack overflow, large numbers in @type are interpreted as applications of @ident__2. + .. warn:: To avoid stack overflow, large numbers in @type are interpreted as applications of @ident__2. - When a :cmd:`Numeral Notation` is registered in the current scope - with :n:`(abstract after @num)`, this warning is emitted when - parsing a numeral greater than or equal to :token:`num`. - Typically, this indicates that the fully computed representation - of numerals can be so large that non-tail-recursive OCaml - functions run out of stack space when trying to walk them. + When a :cmd:`Numeral Notation` is registered in the current scope + with :n:`(abstract after @num)`, this warning is emitted when + parsing a numeral greater than or equal to :token:`num`. + Typically, this indicates that the fully computed representation + of numerals can be so large that non-tail-recursive OCaml + functions run out of stack space when trying to walk them. - For example + For example - .. coqtop:: all + .. coqtop:: all - Check 90000. + Check 90000. - .. warn:: The 'abstract after' directive has no effect when the parsing function (@ident__2) targets an option type. + .. warn:: The 'abstract after' directive has no effect when the parsing function (@ident__2) targets an option type. - As noted above, the :n:`(abstract after @num)` directive has no - effect when :n:`@ident__2` lands in an :g:`option` type. + As noted above, the :n:`(abstract after @num)` directive has no + effect when :n:`@ident__2` lands in an :g:`option` type. .. _TacticNotation: |