diff options
| author | Clément Pit-Claudel | 2018-07-30 15:14:53 -0400 |
|---|---|---|
| committer | Clément Pit-Claudel | 2018-07-30 15:16:25 -0400 |
| commit | 7f1ed3298c841c2afa4faf080a5f65361bbb413f (patch) | |
| tree | b3917392b1b07818f07bb7d9b39cdc628b3e539e /doc/sphinx/language | |
| parent | 1b2decc1bc0db2a58fcc4a4e6e572aed645bab29 (diff) | |
[sphinx] Use arguments of '.. example::' directive as a title
Most existing uses of .. example did not use the first line as a title, so this
commit also adds appropriate blank lines.
Diffstat (limited to 'doc/sphinx/language')
| -rw-r--r-- | doc/sphinx/language/cic.rst | 18 | ||||
| -rw-r--r-- | doc/sphinx/language/coq-library.rst | 5 | ||||
| -rw-r--r-- | doc/sphinx/language/gallina-extensions.rst | 14 | ||||
| -rw-r--r-- | doc/sphinx/language/gallina-specification-language.rst | 6 |
4 files changed, 37 insertions, 6 deletions
diff --git a/doc/sphinx/language/cic.rst b/doc/sphinx/language/cic.rst index 98e81ebc65..6e0c1e1b61 100644 --- a/doc/sphinx/language/cic.rst +++ b/doc/sphinx/language/cic.rst @@ -723,6 +723,7 @@ each :math:`T` in :math:`(t:T)∈Γ_I` can be written as: :math:`∀Γ_P,∀Γ_{ the sort of the inductive type t (not to be confused with :math:`\Sort` which is the set of sorts). .. example:: + The declaration for parameterized lists is: .. math:: @@ -741,6 +742,7 @@ the sort of the inductive type t (not to be confused with :math:`\Sort` which is | cons : A -> list A -> list A. .. example:: + The declaration for a mutual inductive definition of tree and forest is: @@ -763,6 +765,7 @@ the sort of the inductive type t (not to be confused with :math:`\Sort` which is | consf : tree -> forest -> forest. .. example:: + The declaration for a mutual inductive definition of even and odd is: .. math:: @@ -811,6 +814,7 @@ contains an inductive declaration. E[Γ] ⊢ c : C .. example:: + Provided that our environment :math:`E` contains inductive definitions we showed before, these two inference rules above enable us to conclude that: @@ -919,6 +923,7 @@ condition* for a constant :math:`X` in the following cases: .. example:: + For instance, if one considers the following variant of a tree type branching over the natural numbers: @@ -985,6 +990,7 @@ the Type hierarchy. .. example:: + It is well known that the existential quantifier can be encoded as an inductive definition. The following declaration introduces the second- order existential quantifier :math:`∃ X.P(X)`. @@ -1102,6 +1108,7 @@ sorts at each instance of a pattern-matching (see Section :ref:`Destructors`). A an example, let us consider the following definition: .. example:: + .. coqtop:: in Inductive option (A:Type) : Type := @@ -1118,6 +1125,7 @@ if :g:`option` is applied to a type in :math:`\Prop`, then, the result is not se if set in :math:`\Prop`. .. example:: + .. coqtop:: all Check (fun A:Set => option A). @@ -1126,6 +1134,7 @@ if set in :math:`\Prop`. Here is another example. .. example:: + .. coqtop:: in Inductive prod (A B:Type) : Type := pair : A -> B -> prod A B. @@ -1136,6 +1145,7 @@ none in :math:`\Type`, and in :math:`\Type` otherwise. In all cases, the three k eliminations schemes are allowed. .. example:: + .. coqtop:: all Check (fun A:Set => prod A). @@ -1324,6 +1334,7 @@ the extraction mechanism. Assume :math:`A` and :math:`B` are two propositions, a logical disjunction :math:`A ∨ B` is defined inductively by: .. example:: + .. coqtop:: in Inductive or (A B:Prop) : Prop := @@ -1334,6 +1345,7 @@ The following definition which computes a boolean value by case over the proof of :g:`or A B` is not accepted: .. example:: + .. coqtop:: all Fail Definition choice (A B: Prop) (x:or A B) := @@ -1357,6 +1369,7 @@ property which are provably different, contradicting the proof- irrelevance property which is sometimes a useful axiom: .. example:: + .. coqtop:: all Axiom proof_irrelevance : forall (P : Prop) (x y : P), x=y. @@ -1390,6 +1403,7 @@ be used for rewriting not only in logical propositions but also in any type. .. example:: + .. coqtop:: all Print eq_rec. @@ -1421,6 +1435,7 @@ We write :math:`\{c\}^P` for :math:`\{c:C\}^P` with :math:`C` the type of :math: .. example:: + The following term in concrete syntax:: match t as l return P' with @@ -1485,6 +1500,7 @@ definition :math:`\ind{r}{Γ_I}{Γ_C}` with :math:`Γ_C = [c_1 :C_1 ;…;c_n :C_ .. example:: + Below is a typing rule for the term shown in the previous example: .. inference:: list example @@ -1634,6 +1650,7 @@ The following definitions are correct, we enter them using the :cmd:`Fixpoint` command and show the internal representation. .. example:: + .. coqtop:: all Fixpoint plus (n m:nat) {struct n} : nat := @@ -1810,6 +1827,7 @@ option ``-impredicative-set``. For example, using the ordinary `coqtop` command, the following is rejected, .. example:: + .. coqtop:: all Fail Definition id: Set := forall X:Set,X->X. diff --git a/doc/sphinx/language/coq-library.rst b/doc/sphinx/language/coq-library.rst index 52c56d2bd2..9de30e2190 100644 --- a/doc/sphinx/language/coq-library.rst +++ b/doc/sphinx/language/coq-library.rst @@ -848,6 +848,7 @@ Notation Interpretation Precedence Associativity .. example:: + .. coqtop:: all reset Require Import ZArith. @@ -887,6 +888,7 @@ Notation Interpretation =============== =================== .. example:: + .. coqtop:: all reset Require Import Reals. @@ -906,6 +908,7 @@ tactics (see Chapter :ref:`tactics`), there are also: Proves that two real integer constants are different. .. example:: + .. coqtop:: all reset Require Import DiscrR. @@ -919,6 +922,7 @@ tactics (see Chapter :ref:`tactics`), there are also: Allows unfolding the ``Rabs`` constant and splits corresponding conjunctions. .. example:: + .. coqtop:: all reset Require Import Reals. @@ -933,6 +937,7 @@ tactics (see Chapter :ref:`tactics`), there are also: corresponding to the condition on each operand of the product. .. example:: + .. coqtop:: all reset Require Import Reals. diff --git a/doc/sphinx/language/gallina-extensions.rst b/doc/sphinx/language/gallina-extensions.rst index 394b928ada..7dd0a6e383 100644 --- a/doc/sphinx/language/gallina-extensions.rst +++ b/doc/sphinx/language/gallina-extensions.rst @@ -70,7 +70,9 @@ generates a variant type definition with just one constructor: To build an object of type :n:`@ident`, one should provide the constructor :n:`@ident₀` with the appropriate number of terms filling the fields of the record. -.. example:: Let us define the rational :math:`1/2`: +.. example:: + + Let us define the rational :math:`1/2`: .. coqtop:: in @@ -1849,15 +1851,15 @@ are named as expected. .. example:: (continued) -.. coqtop:: all + .. coqtop:: all - Arguments p [s t] _ [u] _: rename. + Arguments p [s t] _ [u] _: rename. - Check (p r1 (u:=c)). + Check (p r1 (u:=c)). - Check (p (s:=a) (t:=b) r1 (u:=c) r2). + Check (p (s:=a) (t:=b) r1 (u:=c) r2). - Fail Arguments p [s t] _ [w] _ : assert. + Fail Arguments p [s t] _ [w] _ : assert. .. _displaying-implicit-args: diff --git a/doc/sphinx/language/gallina-specification-language.rst b/doc/sphinx/language/gallina-specification-language.rst index 8250b4b3d6..da5cd00d72 100644 --- a/doc/sphinx/language/gallina-specification-language.rst +++ b/doc/sphinx/language/gallina-specification-language.rst @@ -758,6 +758,7 @@ Simple inductive types the case of annotated inductive types — cf. next section). .. example:: + The set of natural numbers is defined as: .. coqtop:: all @@ -976,6 +977,7 @@ Mutually defined inductive types reason, the parameters must be strictly the same for each inductive types. .. example:: + The typical example of a mutual inductive data type is the one for trees and forests. We assume given two types :g:`A` and :g:`B` as variables. It can be declared the following way. @@ -1048,6 +1050,7 @@ of the type. For co-inductive types, the only elimination principle is case analysis. .. example:: + An example of a co-inductive type is the type of infinite sequences of natural numbers, usually called streams. @@ -1067,6 +1070,7 @@ Definition of co-inductive predicates and blocks of mutually co-inductive definitions are also allowed. .. example:: + An example of a co-inductive predicate is the extensional equality on streams: @@ -1129,6 +1133,7 @@ constructions. .. example:: + One can define the addition function as : .. coqtop:: all @@ -1201,6 +1206,7 @@ constructions. inductive types. .. example:: + The size of trees and forests can be defined the following way: .. coqtop:: all |
