diff options
| -rw-r--r-- | doc/sphinx/addendum/program.rst | 14 | ||||
| -rw-r--r-- | doc/sphinx/addendum/ring.rst | 4 | ||||
| -rw-r--r-- | doc/sphinx/language/gallina-extensions.rst | 28 | ||||
| -rw-r--r-- | doc/sphinx/refman-preamble.rst | 60 | ||||
| -rw-r--r-- | doc/sphinx/refman-preamble.sty | 22 |
5 files changed, 24 insertions, 104 deletions
diff --git a/doc/sphinx/addendum/program.rst b/doc/sphinx/addendum/program.rst index cbb5c0db8a..5cffe9e435 100644 --- a/doc/sphinx/addendum/program.rst +++ b/doc/sphinx/addendum/program.rst @@ -162,7 +162,7 @@ Program Definition This command types the value term in Russell and generates proof obligations. Once solved using the commands shown below, it binds the - final |Coq| term to the name ``ident`` in the environment. + final |Coq| term to the name :n:`@ident` in the environment. .. exn:: @ident already exists. :name: @ident already exists. (Program Definition) @@ -170,12 +170,12 @@ Program Definition .. cmdv:: Program Definition @ident : @type := @term - It interprets the type ``type``, potentially generating proof + It interprets the type :n:`@type`, potentially generating proof obligations to be resolved. Once done with them, we have a |Coq| - type |type_0|. It then elaborates the preterm ``term`` into a |Coq| - term |term_0|, checking that the type of |term_0| is coercible to - |type_0|, and registers ``ident`` as being of type |type_0| once the - set of obligations generated during the interpretation of |term_0| + type :n:`@type__0`. It then elaborates the preterm :n:`@term` into a |Coq| + term :n:`@term__0`, checking that the type of :n:`@term__0` is coercible to + :n:`@type__0`, and registers :n:`@ident` as being of type :n:`@type__0` once the + set of obligations generated during the interpretation of :n:`@term__0` and the aforementioned coercion derivation are solved. .. exn:: In environment … the term: @term does not have type @type. Actually, it has type ... @@ -185,7 +185,7 @@ Program Definition This is equivalent to: - :g:`Program Definition ident : forall binders, type := fun binders => term`. + :n:`Program Definition @ident : forall {* @binder }, @type := fun {* @binder } => @term`. .. TODO refer to production in alias diff --git a/doc/sphinx/addendum/ring.rst b/doc/sphinx/addendum/ring.rst index 76174e32b5..2a321b5cbf 100644 --- a/doc/sphinx/addendum/ring.rst +++ b/doc/sphinx/addendum/ring.rst @@ -1,8 +1,12 @@ +.. |bdi| replace:: :math:`\beta\delta\iota` .. |ra| replace:: :math:`\rightarrow_{\beta\delta\iota}` .. |la| replace:: :math:`\leftarrow_{\beta\delta\iota}` .. |eq| replace:: `=`:sub:`(by the main correctness theorem)` .. |re| replace:: ``(PEeval`` `v` `ap`\ ``)`` .. |le| replace:: ``(Pphi_dev`` `v` ``(norm`` `ap`\ ``))`` +.. |N| replace:: ``N`` +.. |nat| replace:: ``nat`` +.. |Z| replace:: ``Z`` .. _theringandfieldtacticfamilies: diff --git a/doc/sphinx/language/gallina-extensions.rst b/doc/sphinx/language/gallina-extensions.rst index 8fcbeea570..18b05e47d3 100644 --- a/doc/sphinx/language/gallina-extensions.rst +++ b/doc/sphinx/language/gallina-extensions.rst @@ -361,16 +361,12 @@ can be alternatively written Definition not (b:bool) := if b then false else true. -More generally, for an inductive type with constructors |C_1| and |C_2|, -we have the following equivalence +More generally, for an inductive type with constructors :n:`@ident__1` +and :n:`@ident__2`, the following terms are equal: -:: +:n:`if @term__0 {? {? as @name } return @term } then @term__1 else @term__2` - if term [dep_ret_type] then term₁ else term₂ ≡ - match term [dep_ret_type] with - | C₁ _ … _ => term₁ - | C₂ _ … _ => term₂ - end +:n:`match @term__0 {? {? as @name } return @term } with | @ident__1 {* _ } => @term__1 | @ident__2 {* _ } => @term__2 end` .. example:: @@ -398,11 +394,13 @@ constructions. There are two variants of them. First destructuring let syntax ++++++++++++++++++++++++++++++ -The expression :g:`let (`\ |ident_1|:g:`, … ,` |ident_n|\ :g:`) :=` |term_0|\ :g:`in` |term_1| performs -case analysis on |term_0| which must be in an inductive type with one -constructor having itself :math:`n` arguments. Variables |ident_1| … |ident_n| are -bound to the :math:`n` arguments of the constructor in expression |term_1|. For -instance, the definition +The expression :n:`let ( {*, @ident__i } ) := @term__0 in @term__1` +performs case analysis on :n:`@term__0` whose type must be an +inductive type with exactly one constructor. The number of variables +:n:`@ident__i` must correspond to the number of arguments of this +contrustor. Then, in :n:`@term__1`, these variables are bound to the +arguments of the constructor in :n:`@term__0`. For instance, the +definition .. coqtop:: reset all @@ -417,7 +415,7 @@ can be alternatively written Definition fst (A B:Set) (p:A * B) := let (x, _) := p in x. Notice that reduction is different from regular :g:`let … in …` -construction since it happens only if |term_0| is in constructor form. +construction since it happens only if :n:`@term__0` is in constructor form. Otherwise, the reduction is blocked. The pretty-printing of a definition by matching on a irrefutable @@ -2286,7 +2284,7 @@ which they reside into another one. A *class* is either a sort (denoted by the keyword ``Sortclass``), a product type (denoted by the keyword ``Funclass``), or a type constructor (denoted by its name), e.g. an inductive type or any constant with a type of the form -``forall (`` |x_1| : |A_1| ) … ``(``\ |x_n| : |A_n|\ ``)``, `s` where `s` is a sort. +:n:`forall {+ @binder }, @sort`. Then the user is able to apply an object that is not a function, but can be coerced to a function, and more generally to consider that a diff --git a/doc/sphinx/refman-preamble.rst b/doc/sphinx/refman-preamble.rst index de95eda989..a31d778af6 100644 --- a/doc/sphinx/refman-preamble.rst +++ b/doc/sphinx/refman-preamble.rst @@ -11,60 +11,18 @@ .. role:: smallcaps -.. |A_1| replace:: `A`\ :math:`_{1}` -.. |A_n| replace:: `A`\ :math:`_{n}` -.. |arg_1| replace:: `arg`\ :math:`_{1}` -.. |arg_n| replace:: `arg`\ :math:`_{n}` -.. |bdi| replace:: :math:`\beta\delta\iota` -.. |binder_1| replace:: `binder`\ :math:`_{1}` -.. |binder_n| replace:: `binder`\ :math:`_{n}` -.. |binders_1| replace:: `binders`\ :math:`_{1}` -.. |binders_n| replace:: `binders`\ :math:`_{n}` -.. |C_1| replace:: `C`\ :math:`_{1}` .. |c_1| replace:: `c`\ :math:`_{1}` -.. |C_2| replace:: `C`\ :math:`_{2}` .. |c_i| replace:: `c`\ :math:`_{i}` .. |c_n| replace:: `c`\ :math:`_{n}` .. |Cic| replace:: :smallcaps:`Cic` -.. |class_1| replace:: `class`\ :math:`_{1}` -.. |class_2| replace:: `class`\ :math:`_{2}` .. |Coq| replace:: :smallcaps:`Coq` .. |CoqIDE| replace:: :smallcaps:`CoqIDE` .. |eq_beta_delta_iota_zeta| replace:: `=`\ :math:`_{\beta\delta\iota\zeta}` .. |Gallina| replace:: :smallcaps:`Gallina` -.. |ident_0| replace:: `ident`\ :math:`_{0}` -.. |ident_1,1| replace:: `ident`\ :math:`_{1,1}` -.. |ident_1,k_1| replace:: `ident`\ :math:`_{1,k_1}`) -.. |ident_1| replace:: `ident`\ :math:`_{1}` -.. |ident_2| replace:: `ident`\ :math:`_{2}` -.. |ident_3| replace:: `ident`\ :math:`_{3}` -.. |ident_i| replace:: `ident`\ :math:`_{i}` -.. |ident_j| replace:: `ident`\ :math:`_{j}` -.. |ident_k| replace:: `ident`\ :math:`_{k}` -.. |ident_n,1| replace:: `ident`\ :math:`_{n,1}` -.. |ident_n,k_n| replace:: `ident`\ :math:`_{n,k_n}` -.. |ident_n| replace:: `ident`\ :math:`_{n}` .. |Latex| replace:: :smallcaps:`LaTeX` .. |L_tac| replace:: `L`:sub:`tac` .. |Ltac| replace:: `L`:sub:`tac` .. |ML| replace:: :smallcaps:`ML` -.. |mod_0| replace:: `mod`\ :math:`_{0}` -.. |mod_1| replace:: `mod`\ :math:`_{1}` -.. |mod_2| replace:: `mod`\ :math:`_{1}` -.. |mod_n| replace:: `mod`\ :math:`_{n}` -.. |module_0| replace:: `module`\ :math:`_{0}` -.. |module_1| replace:: `module`\ :math:`_{1}` -.. |module_expression_0| replace:: `module_expression`\ :math:`_{0}` -.. |module_expression_1| replace:: `module_expression`\ :math:`_{1}` -.. |module_expression_i| replace:: `module_expression`\ :math:`_{i}` -.. |module_expression_n| replace:: `module_expression`\ :math:`_{n}` -.. |module_n| replace:: `module`\ :math:`_{n}` -.. |module_type_0| replace:: `module_type`\ :math:`_{0}` -.. |module_type_1| replace:: `module_type`\ :math:`_{1}` -.. |module_type_i| replace:: `module_type`\ :math:`_{i}` -.. |module_type_n| replace:: `module_type`\ :math:`_{n}` -.. |N| replace:: ``N`` -.. |nat| replace:: ``nat`` .. |OCaml| replace:: :smallcaps:`OCaml` .. |p_1| replace:: `p`\ :math:`_{1}` .. |p_i| replace:: `p`\ :math:`_{i}` @@ -79,24 +37,6 @@ .. |t_i| replace:: `t`\ :math:`_{i}` .. |t_m| replace:: `t`\ :math:`_{m}` .. |t_n| replace:: `t`\ :math:`_{n}` -.. |f_1| replace:: `f`\ :math:`_{1}` -.. |f_i| replace:: `f`\ :math:`_{i}` -.. |f_m| replace:: `f`\ :math:`_{m}` -.. |f_n| replace:: `f`\ :math:`_{n}` -.. |u_1| replace:: `u`\ :math:`_{1}` -.. |u_i| replace:: `u`\ :math:`_{i}` -.. |u_m| replace:: `u`\ :math:`_{m}` -.. |u_n| replace:: `u`\ :math:`_{n}` -.. |term_0| replace:: `term`\ :math:`_{0}` -.. |term_1| replace:: `term`\ :math:`_{1}` -.. |term_2| replace:: `term`\ :math:`_{2}` -.. |term_n| replace:: `term`\ :math:`_{n}` -.. |type_0| replace:: `type`\ :math:`_{0}` -.. |type_1| replace:: `type`\ :math:`_{1}` -.. |type_2| replace:: `type`\ :math:`_{2}` -.. |type_3| replace:: `type`\ :math:`_{3}` -.. |type_n| replace:: `type`\ :math:`_{n}` .. |x_1| replace:: `x`\ :math:`_{1}` .. |x_i| replace:: `x`\ :math:`_{i}` .. |x_n| replace:: `x`\ :math:`_{n}` -.. |Z| replace:: ``Z`` diff --git a/doc/sphinx/refman-preamble.sty b/doc/sphinx/refman-preamble.sty index 90a63a5a2d..718a54ba8f 100644 --- a/doc/sphinx/refman-preamble.sty +++ b/doc/sphinx/refman-preamble.sty @@ -1,40 +1,26 @@ -\newcommand{\alors}{\textsf{then}} -\newcommand{\alter}{\textsf{alter}} \newcommand{\as}{\kw{as}} \newcommand{\Assum}[3]{\kw{Assum}(#1)(#2:#3)} -\newcommand{\bool}{\textsf{bool}} \newcommand{\case}{\kw{case}} -\newcommand{\conc}{\textsf{conc}} \newcommand{\cons}{\textsf{cons}} \newcommand{\consf}{\textsf{consf}} -\newcommand{\conshl}{\textsf{cons\_hl}} \newcommand{\Def}[4]{\kw{Def}(#1)(#2:=#3:#4)} \newcommand{\emptyf}{\textsf{emptyf}} \newcommand{\End}{\kw{End}} \newcommand{\kwend}{\kw{end}} -\newcommand{\EqSt}{\textsf{EqSt}} \newcommand{\even}{\textsf{even}} \newcommand{\evenO}{\textsf{even}_\textsf{O}} \newcommand{\evenS}{\textsf{even}_\textsf{S}} -\newcommand{\false}{\textsf{false}} -\newcommand{\filter}{\textsf{filter}} \newcommand{\Fix}{\kw{Fix}} \newcommand{\fix}{\kw{fix}} \newcommand{\for}{\textsf{for}} \newcommand{\forest}{\textsf{forest}} -\newcommand{\from}{\textsf{from}} \newcommand{\Functor}{\kw{Functor}} -\newcommand{\haslength}{\textsf{has\_length}} -\newcommand{\hd}{\textsf{hd}} -\newcommand{\ident}{\textsf{ident}} \newcommand{\In}{\kw{in}} \newcommand{\Ind}[4]{\kw{Ind}[#2](#3:=#4)} \newcommand{\ind}[3]{\kw{Ind}~[#1]\left(#2\mathrm{~:=~}#3\right)} \newcommand{\Indp}[5]{\kw{Ind}_{#5}(#1)[#2](#3:=#4)} \newcommand{\Indpstr}[6]{\kw{Ind}_{#5}(#1)[#2](#3:=#4)/{#6}} -\newcommand{\injective}{\kw{injective}} \newcommand{\kw}[1]{\textsf{#1}} -\newcommand{\lb}{\lambda} \newcommand{\length}{\textsf{length}} \newcommand{\letin}[3]{\kw{let}~#1:=#2~\kw{in}~#3} \newcommand{\List}{\textsf{list}} @@ -45,7 +31,6 @@ \newcommand{\ModS}[2]{{\kw{Mod}}({#1}:{#2})} \newcommand{\ModType}[2]{{\kw{ModType}}({#1}:={#2})} \newcommand{\mto}{.\;} -\newcommand{\Nat}{\mathbb{N}} \newcommand{\nat}{\textsf{nat}} \newcommand{\Nil}{\textsf{nil}} \newcommand{\nilhl}{\textsf{nil\_hl}} @@ -57,13 +42,10 @@ \newcommand{\ovl}[1]{\overline{#1}} \newcommand{\Pair}{\textsf{pair}} \newcommand{\plus}{\mathsf{plus}} -\newcommand{\Prod}{\textsf{prod}} \newcommand{\SProp}{\textsf{SProp}} \newcommand{\Prop}{\textsf{Prop}} \newcommand{\return}{\kw{return}} \newcommand{\Set}{\textsf{Set}} -\newcommand{\si}{\textsf{if}} -\newcommand{\sinon}{\textsf{else}} \newcommand{\Sort}{\mathcal{S}} \newcommand{\Str}{\textsf{Stream}} \newcommand{\Struct}{\kw{Struct}} @@ -71,9 +53,7 @@ \newcommand{\tl}{\textsf{tl}} \newcommand{\tree}{\textsf{tree}} \newcommand{\trii}{\triangleright_\iota} -\newcommand{\true}{\textsf{true}} \newcommand{\Type}{\textsf{Type}} -\newcommand{\unfold}{\textsf{unfold}} \newcommand{\WEV}[3]{\mbox{$#1[] \vdash #2 \lra #3$}} \newcommand{\WEVT}[3]{\mbox{$#1[] \vdash #2 \lra$}\\ \mbox{$ #3$}} \newcommand{\WF}[2]{{\mathcal{W\!F}}(#1)[#2]} @@ -87,5 +67,3 @@ \newcommand{\WTE}[3]{\WT{E}{#1}{#2}{#3}} \newcommand{\WTEG}[2]{\WTE{\Gamma}{#1}{#2}} \newcommand{\WTM}[3]{\WT{#1}{}{#2}{#3}} -\newcommand{\zeroone}[1]{[{#1}]} -\newcommand{\zeros}{\textsf{zeros}} |