From fb9612515e5701c191be5ea1af27c523c77d9d5e Mon Sep 17 00:00:00 2001 From: Emmanuel Coquery <emmanuel.coquery@univ-lyon1.fr> Date: Thu, 20 Mar 2025 09:01:14 +0100 Subject: [PATCH] =?UTF-8?q?s=C3=A9ance=20du=2024/03=20+=20corrig=C3=A9s=20?= =?UTF-8?q?du=2017/03?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- README.md | 9 +- cm/lifpf-cm5.pdf | Bin 220170 -> 211910 bytes td/lifpf-td5-enonce.pdf | Bin 142919 -> 142847 bytes tp/tp5.ml | 195 ++++++++++++++++++++++++++++++++++++++++ tp/tp6.md | 6 +- 5 files changed, 204 insertions(+), 6 deletions(-) create mode 100644 tp/tp5.ml diff --git a/README.md b/README.md index 3ea6bc5..4286b81 100644 --- a/README.md +++ b/README.md @@ -24,13 +24,14 @@ | 24/02 | 9h45 | Partiel | | Amphi et place communiqués dans tomuss, 1 feuille manuscrite recto/verso autorisée comme document | | 10/03 | 8h | CM4 | Ordre sup. | [Diapositives](cm/lifpf-cm4.pdf) | | | 9h45 | TD4 | Ordre sup. | [Sujet](td/lifpf-td4-enonce.pdf), [corrigé](td/lifpf-td4-correction.pdf) | -| 17/03 | 8h | CM5 | Modules | (2024) [Diapositives](cm/lifpf-cm5.pdf) | -| | 9h45 ou 11h30 | TP5 | Struct. gen. | [Sujet](tp/tp5.md) | -| 24/03 | 8h | TD5 | Ordre sup. | (2024) [Sujet](td/lifpf-td5-enonce.pdf) | -| | 9h45 ou 11h30 | TP6 | Transf. struct. | (2024) [Sujet](tp/tp6.md) | +| 17/03 | 8h | CM5 | Modules | [Diapositives](cm/lifpf-cm5.pdf) | +| | 9h45 ou 11h30 | TP5 | Struct. gen. | [Sujet](tp/tp5.md), [corrigé](tp/tp5.ml) | +| 24/03 | 8h | TD5 | Ordre sup. | [Sujet](td/lifpf-td5-enonce.pdf) | +| | 9h45 ou 11h30 | TP6 | Transf. struct. | [Sujet](tp/tp6.md) | | 31/03 | 9h45 ou 11h15 | TP7 | App. OCaml (à changer ?) | (2024) [Sujet](tp/tp7.md) | | 07/04 | 8h | CM6 | Foncteurs | (2024) [Diapositives](cm/lifpf-cm6.pdf), [code](cm/cm6-code.ml) | | | 9h45 | TD6 | Foncteurs | (2024) [Sujet](td/lifpf-td6-enonce.pdf) | +| 14/04 | | TP8 | à déterminer | remplace les soutenances | ### Annales diff --git 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0000000..2077670 --- /dev/null +++ b/tp/tp5.ml @@ -0,0 +1,195 @@ +(**********************************************************************) +(* 1 Manipulations de listes à l'aide de fonctions génériques *) +(**********************************************************************) + +(**********************************************************************) +(* 1.1. Utilisation des fonctions sur les listes *) + +(** Une fonction `f1` qui prend une liste d'`int` et renvoie la liste de leur représentation sous forme de `string`. *) +let f1 (l : int list) : string list = List.map (fun x -> string_of_int x) l + +(* ou bien *) +let f1 = List.map string_of_int;; + +assert (f1 [ 1; 2 ] = [ "1"; "2" ]) + +(** Une fonction `f2` qui prend un `int` `x` et une liste d'`int` `l` et renvoie la liste transformée en multipliant chaque élément de `l` par `x`. *) +let f2 (x : int) (l : int list) : int list = List.map (fun y -> x * y) l + +(* ou bien *) +let f2 (x : int) : int list -> int list = List.map (fun e -> x * e);; + +assert (f2 3 [ 1; 5; 3 ] = [ 3; 15; 9 ]) + +(** Une fonction `f3` qui prend deux `int` `x` et `y` et une liste d'`int` `l` et renvoie la liste (de `bool`) indiquant pour chacun des éléments de `l` s'il est bien compris entre `x` et `y`. *) +let f3 (x : int) (y : int) (l : int list) : bool list = + List.map (fun e -> x <= e && e <= y) l + +(* ou bien *) +let f3 (x : int) (y : int) : int list -> bool list = + List.map (fun e -> x <= e && e <= y) +;; + +assert (f3 3 7 [ 1; 4; 2; 12 ] = [ false; true; false; false ]) + +(** Une fonction `f4` qui prend deux `int` `x` et `y` et une liste d'`int` `l` et renvoie la liste des éléments de `l` qui sont compris entre `x` et `y`. *) +let f4 (x : int) (y : int) (l : int list) : int list = + List.filter (fun e -> x <= e && e <= y) l + +(* ou bien *) +let f4 (x : int) (y : int) : int list -> int list = + List.filter (fun e -> x <= e && e <= y) +;; + +assert (f4 3 7 [ 1; 4; 2; 12 ] = [ 4 ]) + +(** Une fonction `f5` qui prend une liste de liste d'`int` et renvoie la liste sans les (sous-)listes vides. *) +let f5 (l : int list list) : int list list = List.filter (fun l' -> l' != []) l + +(* variante avec (=) *) +let f5 : int list list -> int list list = List.filter (( != ) []);; + +assert (f5 [ []; [ 2; 3 ]; []; [ 1 ] ] = [ [ 2; 3 ]; [ 1 ] ]) + +(** Coder une fonction `f6` qui prend une liste d'`int option` `l` et renvoie une liste d'`int` contenant les valeurs `int` contenues dans `l`. Par exemple, `f6 [ Some 3; None; Some 18; Some 42; None; Some 37; None]` vaudra `[3; 18; 42; 37]`. *) +let f6 (l : int option list) : int list = + let l1 = List.filter (fun o -> o != None) l in + List.map + (fun o -> + match o with + | None -> 0 (* n'arrive pas à cause du filter précédent *) + | Some x -> x) + l1 + +(* ou bien *) +let f6 (l : int option list) : int list = + l + |> List.filter (( != ) None) + |> List.map (fun o -> + match o with + | None -> 0 (* n'arrive pas à cause du filter précédent *) + | Some x -> x) + +(* ou encore en utilisant Option.get *) +let f6 (l : int option list) : int list = + l |> List.filter (( != ) None) |> List.map Option.get +;; + +assert ( + f6 [ Some 3; None; Some 18; Some 42; None; Some 37; None ] = [ 3; 18; 42; 37 ]) + +(**********************************************************************) +(* 1.2. Recodage de fonctions sur les listes *) +let rec map (f : 'a -> 'b) (l : 'a list) : 'b list = + match l with [] -> [] | x :: l' -> f x :: map f l' + +let rec filter (f : 'a -> bool) (l : 'a list) : 'a list = + match l with + | [] -> [] + | x :: l' -> if f x then x :: filter f l' else filter f l' + +let rec for_all (f : 'a -> bool) (l : 'a list) : bool = + match l with [] -> true | x :: l' -> f x && for_all f l' + +(**********************************************************************) +(* 2 Arbre n-aires: recodage *) +(**********************************************************************) + +(**********************************************************************) +(* 2.1. Recodage de quelques fonctions de base avec la bibliothèque + standard OCaml *) + +type 'a arbre_n = Feuille of 'a | Noeud of 'a arbre_n list + +(** +Calcule la hauteur d'un arbre. + +@param a l'arbre dont on veut calculer la hauteur +@return la hauteur de l'arbre +*) +let rec hauteur_arbre (a : 'a arbre_n) : int = + match a with + | Feuille _ -> 1 + | Noeud foret -> + let hauteurs = List.map hauteur_arbre foret in + let h_max = List.fold_left max 0 hauteurs in + h_max + 1 + +(** +Extrait les éléments d'un arbre dans une liste + +@param l'arbre dont on veut les éléments +@return la liste des éléments de l'arbre obtenue par un parcours en profondeur. +*) +let list_of_arbre : 'a arbre_n -> 'a list = + (* + Ajoute les éléments de l'arbre à la liste. + + @param a l'arbre dont on veut extraires les éléments + @param acc la liste à laquelle on veut ajouter les éléments. + *) + let rec list_of_arbre_aux (a : 'a arbre_n) (acc : 'a list) : 'a list = + match a with + | Feuille x -> x :: acc + | Noeud foret -> + List.fold_left (fun acc2 fils -> list_of_arbre_aux fils acc2) acc foret + in + fun a -> list_of_arbre_aux a [] + +(**********************************************************************) +(* 2.2. Gestion d'option, fold et minimum *) + +(** +[lift_option_2 f] choisi son deuxième argument si son premier argument est None. +Sinon utilise f pour produire une valeur avec ses deux arguments. + +@param f la fonction utilisée pour combiner les arguments +@param x une option +@param y la valeur à combiner à la valeur de x ou à prendre si x est None +@return Some de la combinaison des valeurs de x et y, ou bien y si x est None +*) +let lift_option_2 (f : 'a -> 'a -> 'a) : 'a option -> 'a -> 'a option = + fun x y -> match x with None -> Some y | Some x' -> Some (f x' y) + +(** + aggrège une valeur en utilisant un accumulateur et une fonction appelée pour + mettre à jour l'accumulateur en fonction de l'élément de l'arbre rencontrée. + Appelle la fonction en utilisant les un après les autres tous les éléments de + l'accumulateur. + + @param f la fonction de mise à jour de l'accumulateur + @param init la valeur de départ de l'accumulateur + @param a l'arbre à parcourir + @return la valeur de l'accumulateur résultant des mises à jour + successives par les appels à f sur les éléments de a. + *) +let rec fold_left_arbre (f : 'b -> 'a -> 'b) (init : 'b) (a : 'a arbre_n) : 'b = + match a with + | Feuille x -> f init x + | Noeud foret -> List.fold_left (fold_left_arbre f) init foret +(* Pour le dernier cas on aurait pu écrire + + List.fold_left (fun acc fils -> fold_left_arbre f acc fils) init foret + + mais c'est plus long +*) + +(** +Aggrège une valeur en utilisant une fonction de combinaison de valeurs + +@param f la fonction de combinaison de valeurs +@param a l'arbre dont on veut combiner les valeurs +@return Some du résultat de la combinaisons des valeurs de a par f, + ou None si a n'a pas d'élément +*) +let reduce (f : 'a -> 'a -> 'a) (a : 'a arbre_n) : 'a option = + fold_left_arbre (lift_option_2 f) None a + +(** +Extrait les éléments d'un arbre dans une liste + +@param l'arbre dont on veut les éléments +@return la liste des éléments de l'arbre obtenue par un parcours en profondeur. +*) +let list_of_arbre' : 'a arbre_n -> 'a list = + fold_left_arbre (fun l e -> e :: l) [] diff --git a/tp/tp6.md b/tp/tp6.md index 8f75fd3..c8977f4 100644 --- a/tp/tp6.md +++ b/tp/tp6.md @@ -1,9 +1,11 @@ -# TP6: Parcours et transformations de structures +# TP6 : Parcours et transformations de structures -**Attention** dans les sujets qui suivent, il est demandé de ne **pas regarder le corrigé** pour faires les exercices. +**Attention** dans les sujets qui suivent, il est demandé de ne **pas regarder le corrigé** pour faire les exercices. Lire un corrigé et (re)faire l'exercice seul (sans regarder une correction) sont deux choses très différentes. +**Votre chargé de TP validera votre progression en fin de séance.** + ## 1. Manipulations de listes Coder l'exercice 1 du [TD5](../td/lifpf-td5-enonce.pdf), en faisant en priorité ce qui n'a pas pu être fait en séance de TD. -- GitLab