diff options
author | 2001-04-11 12:41:41 +0000 | |
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committer | 2001-04-11 12:41:41 +0000 | |
commit | 4ac0580306ea9e45da1863316936d700969465ad (patch) | |
tree | bf7595cd76895f3a349e7e75ca9d64231b01dcf8 /theories/Lists | |
parent | 8a7452976731275212f0c464385b380e2d590f5e (diff) |
documentation automatique de la bibliothèque standard
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@1578 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Lists')
-rw-r--r-- | theories/Lists/ListSet.v | 6 | ||||
-rw-r--r-- | theories/Lists/PolyList.v | 12 | ||||
-rwxr-xr-x | theories/Lists/intro.tex | 24 |
3 files changed, 33 insertions, 9 deletions
diff --git a/theories/Lists/ListSet.v b/theories/Lists/ListSet.v index 565a32404..9af874a3f 100644 --- a/theories/Lists/ListSet.v +++ b/theories/Lists/ListSet.v @@ -81,12 +81,12 @@ Section first_definitions. else (set_add a1 (set_diff x1 y)) end. - (** + (*i Inductive set_In : A -> set -> Prop := set_In_singl : (a:A)(x:set)(set_In a (cons a (nil A))) | set_In_add : (a,b:A)(x:set)(set_In a x)->(set_In a (set_add b x)) . - **) + i*) Definition set_In : A -> set -> Prop := (In 1!A). @@ -324,7 +324,7 @@ Section other_definitions. Definition set_prod : (set A) -> (set B) -> (set A*B) := (list_prod 1!A 2!B). - (* B^A, set of applications from A to B *) + (* [B^A], set of applications from [A] to [B] *) Definition set_power : (set A) -> (set B) -> (set (set A*B)) := (list_power 1!A 2!B). diff --git a/theories/Lists/PolyList.v b/theories/Lists/PolyList.v index 7c11eb489..267988cdb 100644 --- a/theories/Lists/PolyList.v +++ b/theories/Lists/PolyList.v @@ -407,7 +407,7 @@ Lemma nth_S_cons : Simpl; Auto. Save. -(***** +(*i Lemma nth_In : (n:nat)(l:list)(d:A)(lt n (length l))->(In (nth n l d) l). @@ -421,7 +421,7 @@ Unfold lt; Induction l; [ Simpl; Intros; Inversion H | Simpl; Intros; ]. -******) +i*) (*********************************************) @@ -575,8 +575,8 @@ Induction l; ]. Save. -(* (list_power x y) is y^x, or the set of sequences of elts of y - indexed by elts of x, sorted in lexicographic order. *) +(* [(list_power x y)] is [y^x], or the set of sequences of elts of [y] + indexed by elts of [x], sorted in lexicographic order. *) Fixpoint list_power [A,B:Set; l:(list A)] : (list B)->(list (list A*B)) := [l']Cases l of @@ -606,7 +606,7 @@ Fixpoint fold_right [l:(list B)] : A := end. End Fold_Right_Recursor. -(* +(*i Theorem fold_symmetric : (A:Set)(f:A->A->A) ((x,y,z:A)(f x (f y z))=(f (f x y) z)) @@ -625,7 +625,7 @@ Do 2 Rewrite H. Rewrite (H0 a1 a3). Reflexivity. Save. -*) +i*) End Functions_on_lists. diff --git a/theories/Lists/intro.tex b/theories/Lists/intro.tex new file mode 100755 index 000000000..2930326e1 --- /dev/null +++ b/theories/Lists/intro.tex @@ -0,0 +1,24 @@ +\section{Lists}\label{Lists} + +The LISTS library includes the following files: + +\begin{itemize} + +\item {\tt Lists.v} THIS OLD LIBRARY IS HERE ONLY FOR COMPATIBILITY + WITH OLDER VERSIONS OF COQS. THE USER SHOULD USE POLYLIST INSTEAD. + +\item {\tt PolyLists.v} contains definitions of (polymorphic) lists, + functions on lists such as head, tail, map, append and prove some + properties of these functions. Implicit arguments are used in this + library, so you should read the Referance Manual about implicit + arguments before using it. + +\item {\tt TheoryList.v} contains complementary results on lists. Here + a more theoric point of view is assumed : one extracts functions + from propositions, rather than defining functions and then prove them. + +\item {\tt Streams.v} defines the type of infinite lists (streams). It is a + coinductive type. Basic facts are stated and proved. The streams are + also polymorphic. + +\end{itemize} |