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cyberviolence","\u002Fsnt-2nde\u002Fsc-reseaux-sociaux\u002Fcyberviolence","0.snt-2nde\u002Fsc-reseaux-sociaux\u002F5.cyberviolence",{"title":93,"path":94,"stem":95,"children":96},"Les données structurées et leur traitement","\u002Fsnt-2nde\u002Fsd-donnees-structurees","0.snt-2nde\u002Fsd-donnees-structurees\u002F0.index",[97,98,102,106,110,114],{"title":93,"path":94,"stem":95},{"title":99,"path":100,"stem":101},"Données et formats","\u002Fsnt-2nde\u002Fsd-donnees-structurees\u002Fdonnees-formats","0.snt-2nde\u002Fsd-donnees-structurees\u002F1.donnees-formats",{"title":103,"path":104,"stem":105},"Données structurées","\u002Fsnt-2nde\u002Fsd-donnees-structurees\u002Fdonnees-structurees","0.snt-2nde\u002Fsd-donnees-structurees\u002F2.donnees-structurees",{"title":107,"path":108,"stem":109},"Métadonnées","\u002Fsnt-2nde\u002Fsd-donnees-structurees\u002Fmetadonnees","0.snt-2nde\u002Fsd-donnees-structurees\u002F3.metadonnees",{"title":111,"path":112,"stem":113},"Traitement de tables","\u002Fsnt-2nde\u002Fsd-donnees-structurees\u002Ftraitement-tables","0.snt-2nde\u002Fsd-donnees-structurees\u002F4.traitement-tables",{"title":115,"path":116,"stem":117},"Le cloud","\u002Fsnt-2nde\u002Fsd-donnees-structurees\u002Fcloud","0.snt-2nde\u002Fsd-donnees-structurees\u002F5.cloud",{"title":119,"path":120,"stem":121,"children":122},"Localisation, cartographie et mobilité","\u002Fsnt-2nde\u002Fse-localisation-cartographie","0.snt-2nde\u002Fse-localisation-cartographie\u002F0.index",[123,124,128,132,136,140],{"title":119,"path":120,"stem":121},{"title":125,"path":126,"stem":127},"GPS et Galileo — se situer grâce aux satellites","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fgps-galileo","0.snt-2nde\u002Fse-localisation-cartographie\u002F1.gps-galileo",{"title":129,"path":130,"stem":131},"Décoder une trame NMEA","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Ftrame-nmea","0.snt-2nde\u002Fse-localisation-cartographie\u002F2.trame-nmea",{"title":133,"path":134,"stem":135},"Cartes numériques — GeoPortail et OpenStreetMap","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fcartes-numeriques","0.snt-2nde\u002Fse-localisation-cartographie\u002F3.cartes-numeriques",{"title":137,"path":138,"stem":139},"Itinéraires et graphes","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fitineraires-graphes","0.snt-2nde\u002Fse-localisation-cartographie\u002F4.itineraires-graphes",{"title":141,"path":142,"stem":143},"Confidentialité de la position","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fconfidentialite-position","0.snt-2nde\u002Fse-localisation-cartographie\u002F5.confidentialite-position",{"title":145,"path":146,"stem":147,"children":148},"Informatique embarquée et objets connectés","\u002Fsnt-2nde\u002Fsf-info-embarquee","0.snt-2nde\u002Fsf-info-embarquee\u002F0.index",[149,150,154,158],{"title":145,"path":146,"stem":147},{"title":151,"path":152,"stem":153},"Systèmes informatiques embarqués","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fsystemes-embarques","0.snt-2nde\u002Fsf-info-embarquee\u002F1.systemes-embarques",{"title":155,"path":156,"stem":157},"Capteurs et actionneurs","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fcapteurs-actionneurs","0.snt-2nde\u002Fsf-info-embarquee\u002F2.capteurs-actionneurs",{"title":159,"path":160,"stem":161},"IHM et objets connectés","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fihm-objet-connecte","0.snt-2nde\u002Fsf-info-embarquee\u002F3.ihm-objet-connecte",{"title":163,"path":164,"stem":165,"children":166},"Photographie numérique","\u002Fsnt-2nde\u002Fsg-photo-numerique","0.snt-2nde\u002Fsg-photo-numerique\u002F0.index",[167,168,172,176,180],{"title":163,"path":164,"stem":165},{"title":169,"path":170,"stem":171},"Photosites, pixels et résolution","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Fpixels-resolution","0.snt-2nde\u002Fsg-photo-numerique\u002F1.pixels-resolution",{"title":173,"path":174,"stem":175},"Les algorithmes de l'appareil photo","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Falgorithmes-photo","0.snt-2nde\u002Fsg-photo-numerique\u002F2.algorithmes-photo",{"title":177,"path":178,"stem":179},"Les métadonnées EXIF","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Fmetadonnees-exif","0.snt-2nde\u002Fsg-photo-numerique\u002F3.metadonnees-exif",{"title":181,"path":182,"stem":183},"Traiter une image en Python","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Ftraitement-rgb","0.snt-2nde\u002Fsg-photo-numerique\u002F4.traitement-rgb",{"title":185,"path":186,"stem":187,"children":188},"Notions transversales de programmation","\u002Fsnt-2nde\u002Fsh-prog-notions","0.snt-2nde\u002Fsh-prog-notions\u002F0.index",[189,190,194,198,202],{"title":185,"path":186,"stem":187},{"title":191,"path":192,"stem":193},"Séquences d'instructions et variables","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fsequences-affectations","0.snt-2nde\u002Fsh-prog-notions\u002F1.sequences-affectations",{"title":195,"path":196,"stem":197},"Instructions conditionnelles","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fconditionnelles","0.snt-2nde\u002Fsh-prog-notions\u002F2.conditionnelles",{"title":199,"path":200,"stem":201},"Boucles bornées et non bornées","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fboucles","0.snt-2nde\u002Fsh-prog-notions\u002F3.boucles",{"title":203,"path":204,"stem":205},"Définitions et appels de fonctions","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Ffonctions","0.snt-2nde\u002Fsh-prog-notions\u002F4.fonctions",{"title":207,"path":208,"stem":209,"children":210},"Démo des widgets MDC","\u002Fsnt-2nde\u002Fzz-demo-widgets","0.snt-2nde\u002Fzz-demo-widgets\u002F0.index",[211,212,216,220],{"title":207,"path":208,"stem":209},{"title":213,"path":214,"stem":215},"Démo statique — callouts, code, BO, illustration","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Fstatique","0.snt-2nde\u002Fzz-demo-widgets\u002F1.statique",{"title":217,"path":218,"stem":219},"Démo interactive — self-eval et python-snippet","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Finteractif","0.snt-2nde\u002Fzz-demo-widgets\u002F2.interactif",{"title":221,"path":222,"stem":223},"Démo · 14 widgets de manipulation NSI","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Fwidgets-manipulation","0.snt-2nde\u002Fzz-demo-widgets\u002F3.widgets-manipulation",{"title":225,"path":226,"stem":227,"children":228},"NSI — Première","\u002Fnsi-1ere","1.nsi-1ere\u002F0.index",[229,230,234,256,282,304,328,354,380,410],{"title":225,"path":226,"stem":227},{"title":231,"path":232,"stem":233},"Relecture pédagogique — 8 chapitres NSI 1ère (PA → PH)","\u002Fnsi-1ere\u002Freview","1.nsi-1ere\u002FREVIEW",{"title":235,"path":236,"stem":237,"children":238},"Histoire de l'informatique","\u002Fnsi-1ere\u002Fpa-histoire-info","1.nsi-1ere\u002Fpa-histoire-info\u002F0.index",[239,240,244,248,252],{"title":235,"path":236,"stem":237},{"title":241,"path":242,"stem":243},"De la préantiquité aux machines à calculer","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Fpreantiquite-aux-machines","1.nsi-1ere\u002Fpa-histoire-info\u002F1.preantiquite-aux-machines",{"title":245,"path":246,"stem":247},"La machine universelle (1930-1950)","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Fmachine-universelle","1.nsi-1ere\u002Fpa-histoire-info\u002F2.machine-universelle",{"title":249,"path":250,"stem":251},"Les ordinateurs modernes (1947-1990)","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Fordinateurs-modernes","1.nsi-1ere\u002Fpa-histoire-info\u002F3.ordinateurs-modernes",{"title":253,"path":254,"stem":255},"Réseaux, Web et IA (1969 à aujourd'hui)","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Freseaux-et-web","1.nsi-1ere\u002Fpa-histoire-info\u002F4.reseaux-et-web",{"title":257,"path":258,"stem":259,"children":260},"Représentation des données — types et valeurs","\u002Fnsi-1ere\u002Fpb-types-valeurs","1.nsi-1ere\u002Fpb-types-valeurs\u002F0.index",[261,262,266,270,274,278],{"title":257,"path":258,"stem":259},{"title":263,"path":264,"stem":265},"Bases de numération et entiers positifs","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fbases-entiers-positifs","1.nsi-1ere\u002Fpb-types-valeurs\u002F1.bases-entiers-positifs",{"title":267,"path":268,"stem":269},"Entiers relatifs et complément à deux","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fentiers-relatifs","1.nsi-1ere\u002Fpb-types-valeurs\u002F2.entiers-relatifs",{"title":271,"path":272,"stem":273},"Nombres flottants et virgule 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compréhension","\u002Fnsi-1ere\u002Fpc-types-construits\u002Fcomprehension","1.nsi-1ere\u002Fpc-types-construits\u002F2.comprehension",{"title":297,"path":298,"stem":299},"Tuples et p-uplets nommés","\u002Fnsi-1ere\u002Fpc-types-construits\u002Ftuples","1.nsi-1ere\u002Fpc-types-construits\u002F3.tuples",{"title":301,"path":302,"stem":303},"Dictionnaires","\u002Fnsi-1ere\u002Fpc-types-construits\u002Fdictionnaires","1.nsi-1ere\u002Fpc-types-construits\u002F4.dictionnaires",{"title":305,"path":306,"stem":307,"children":308},"Traitement de données en tables","\u002Fnsi-1ere\u002Fpd-tables-donnees","1.nsi-1ere\u002Fpd-tables-donnees\u002F0.index",[309,310,314,318,322],{"title":305,"path":306,"stem":307},{"title":311,"path":312,"stem":313},"Tables et CSV","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ftables-csv","1.nsi-1ere\u002Fpd-tables-donnees\u002F1.tables-csv",{"title":315,"path":316,"stem":317},"Recherche et filtrage","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Frecherche","1.nsi-1ere\u002Fpd-tables-donnees\u002F2.recherche",{"title":319,"path":320,"stem":321},"Trier une table","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ftri","1.nsi-1ere\u002Fpd-tables-donnees\u002F3.tri",{"title":323,"path":324,"stem":325,"children":326},"Fusion et indexation","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ffusion-indexation","1.nsi-1ere\u002Fpd-tables-donnees\u002F4.fusion-indexation",[327],{"title":323,"path":324,"stem":325},{"title":329,"path":330,"stem":331,"children":332},"IHM sur le Web","\u002Fnsi-1ere\u002Fpe-ihm-web","1.nsi-1ere\u002Fpe-ihm-web\u002F0.index",[333,334,338,342,346,350],{"title":329,"path":330,"stem":331},{"title":335,"path":336,"stem":337},"HTML et CSS — rappel de structure","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fhtml-css-bases","1.nsi-1ere\u002Fpe-ihm-web\u002F1.html-css-bases",{"title":339,"path":340,"stem":341},"Formulaires HTML","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fformulaires","1.nsi-1ere\u002Fpe-ihm-web\u002F2.formulaires",{"title":343,"path":344,"stem":345},"Événements JavaScript","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fevenements-js","1.nsi-1ere\u002Fpe-ihm-web\u002F3.evenements-js",{"title":347,"path":348,"stem":349},"Manipulation du DOM","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fdom-interaction","1.nsi-1ere\u002Fpe-ihm-web\u002F4.dom-interaction",{"title":351,"path":352,"stem":353},"Client, serveur et HTTP","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fclient-serveur-http","1.nsi-1ere\u002Fpe-ihm-web\u002F5.client-serveur-http",{"title":355,"path":356,"stem":357,"children":358},"Architectures matérielles et systèmes d'exploitation","\u002Fnsi-1ere\u002Fpf-archi-os","1.nsi-1ere\u002Fpf-archi-os\u002F0.index",[359,360,364,368,372,376],{"title":355,"path":356,"stem":357},{"title":361,"path":362,"stem":363},"Le modèle de von Neumann","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fvon-neumann","1.nsi-1ere\u002Fpf-archi-os\u002F1.von-neumann",{"title":365,"path":366,"stem":367},"Périphériques et interface homme-machine","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fperipheriques-ihm","1.nsi-1ere\u002Fpf-archi-os\u002F2.peripheriques-ihm",{"title":369,"path":370,"stem":371},"Les systèmes d'exploitation","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fsystemes-exploitation","1.nsi-1ere\u002Fpf-archi-os\u002F3.systemes-exploitation",{"title":373,"path":374,"stem":375},"Linux et le shell","\u002Fnsi-1ere\u002Fpf-archi-os\u002Flinux-shell","1.nsi-1ere\u002Fpf-archi-os\u002F4.linux-shell",{"title":377,"path":378,"stem":379},"Réseaux et protocoles","\u002Fnsi-1ere\u002Fpf-archi-os\u002Freseaux","1.nsi-1ere\u002Fpf-archi-os\u002F5.reseaux",{"title":381,"path":382,"stem":383,"children":384},"Langages et programmation","\u002Fnsi-1ere\u002Fpg-langages-prog","1.nsi-1ere\u002Fpg-langages-prog\u002F0.index",[385,386,390,394,398,402,406],{"title":381,"path":382,"stem":383},{"title":387,"path":388,"stem":389},"Diversité et unité des langages de programmation","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fdiversite-langages","1.nsi-1ere\u002Fpg-langages-prog\u002F1.diversite-langages",{"title":391,"path":392,"stem":393},"Constructions élémentaires","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fconstructions-elementaires","1.nsi-1ere\u002Fpg-langages-prog\u002F2.constructions-elementaires",{"title":395,"path":396,"stem":397},"Fonctions","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Ffonctions","1.nsi-1ere\u002Fpg-langages-prog\u002F3.fonctions",{"title":399,"path":400,"stem":401},"Spécification d'une fonction","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fspecification","1.nsi-1ere\u002Fpg-langages-prog\u002F4.specification",{"title":403,"path":404,"stem":405},"Mise au point des programmes","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fmise-au-point","1.nsi-1ere\u002Fpg-langages-prog\u002F5.mise-au-point",{"title":407,"path":408,"stem":409},"Utilisation de bibliothèques","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fbibliotheques","1.nsi-1ere\u002Fpg-langages-prog\u002F6.bibliotheques",{"title":411,"path":412,"stem":413,"children":414},"Algorithmique","\u002Fnsi-1ere\u002Fph-algorithmique","1.nsi-1ere\u002Fph-algorithmique\u002F0.index",[415,416,420,424,428,432,436],{"title":411,"path":412,"stem":413},{"title":417,"path":418,"stem":419},"Parcours séquentiel d'un tableau","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fparcours-sequentiel","1.nsi-1ere\u002Fph-algorithmique\u002F1.parcours-sequentiel",{"title":421,"path":422,"stem":423},"Bases de la complexité","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fcomplexite-bases","1.nsi-1ere\u002Fph-algorithmique\u002F2.complexite-bases",{"title":425,"path":426,"stem":427},"Tris par sélection et par insertion","\u002Fnsi-1ere\u002Fph-algorithmique\u002Ftris","1.nsi-1ere\u002Fph-algorithmique\u002F3.tris",{"title":429,"path":430,"stem":431},"Recherche dichotomique","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fdichotomie","1.nsi-1ere\u002Fph-algorithmique\u002F4.dichotomie",{"title":433,"path":434,"stem":435},"Algorithmes gloutons","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fgloutons","1.nsi-1ere\u002Fph-algorithmique\u002F5.gloutons",{"title":437,"path":438,"stem":439},"Les k plus proches voisins (k-NN)","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fknn","1.nsi-1ere\u002Fph-algorithmique\u002F6.knn",{"title":441,"path":442,"stem":443,"children":444},"NSI — Terminale","\u002Fnsi-tale","2.nsi-tale\u002F0.index",[445,446,450,476,498,536,560],{"title":441,"path":442,"stem":443},{"title":447,"path":448,"stem":449},"Review pédagogique — chapitres NSI Terminale (TA, TB, TC, TD, TE)","\u002Fnsi-tale\u002Freview","2.nsi-tale\u002FREVIEW",{"title":451,"path":452,"stem":453,"children":454},"Structures de données","\u002Fnsi-tale\u002Fta-structures-donnees","2.nsi-tale\u002Fta-structures-donnees\u002F0.index",[455,456,460,464,468,472],{"title":451,"path":452,"stem":453},{"title":457,"path":458,"stem":459},"Objet, classe, interface","\u002Fnsi-tale\u002Fta-structures-donnees\u002Finterface-implementation","2.nsi-tale\u002Fta-structures-donnees\u002F1.interface-implementation",{"title":461,"path":462,"stem":463},"Implémenter une structure — l'exemple de la file FIFO","\u002Fnsi-tale\u002Fta-structures-donnees\u002Fimplementer-une-structure","2.nsi-tale\u002Fta-structures-donnees\u002F2.implementer-une-structure",{"title":465,"path":466,"stem":467},"Listes, piles, files, dictionnaires","\u002Fnsi-tale\u002Fta-structures-donnees\u002Flistes-piles-files-dict","2.nsi-tale\u002Fta-structures-donnees\u002F3.listes-piles-files-dict",{"title":469,"path":470,"stem":471},"Arbres binaires","\u002Fnsi-tale\u002Fta-structures-donnees\u002Farbres-binaires","2.nsi-tale\u002Fta-structures-donnees\u002F4.arbres-binaires",{"title":473,"path":474,"stem":475},"Graphes","\u002Fnsi-tale\u002Fta-structures-donnees\u002Fgraphes","2.nsi-tale\u002Fta-structures-donnees\u002F5.graphes",{"title":477,"path":478,"stem":479,"children":480},"Bases de données","\u002Fnsi-tale\u002Ftb-bases-de-donnees","2.nsi-tale\u002Ftb-bases-de-donnees\u002F0.index",[481,482,486,490,494],{"title":477,"path":478,"stem":479},{"title":483,"path":484,"stem":485},"Le modèle relationnel","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fmodele-relationnel","2.nsi-tale\u002Ftb-bases-de-donnees\u002F1.modele-relationnel",{"title":487,"path":488,"stem":489},"Bases de données relationnelles et anomalies de schéma","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fbase-relationnelle","2.nsi-tale\u002Ftb-bases-de-donnees\u002F2.base-relationnelle",{"title":491,"path":492,"stem":493},"Le langage SQL","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fsql","2.nsi-tale\u002Ftb-bases-de-donnees\u002F3.sql",{"title":495,"path":496,"stem":497},"Les systèmes de gestion de bases de données","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fsgbd","2.nsi-tale\u002Ftb-bases-de-donnees\u002F4.sgbd",{"title":499,"path":500,"stem":501,"children":502},"Architectures matérielles, systèmes d'exploitation et réseaux","\u002Fnsi-tale\u002Ftc-archi-os-reseaux","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F0.index",[503,504,508,512,516,520,524,528,532],{"title":499,"path":500,"stem":501},{"title":505,"path":506,"stem":507},"Le système sur puce (SoC)","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fsysteme-sur-puce","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F1.systeme-sur-puce",{"title":509,"path":510,"stem":511},"Processus et ordonnancement par l'OS","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fprocessus-os","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F2.processus-os",{"title":513,"path":514,"stem":515},"L'interblocage (deadlock)","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Finterblocage","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F3.interblocage",{"title":517,"path":518,"stem":519},"Principes du routage","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Froutage-principes","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F4.routage-principes",{"title":521,"path":522,"stem":523},"Protocoles de routage RIP et OSPF","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fprotocoles-rip-ospf","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F5.protocoles-rip-ospf",{"title":525,"path":526,"stem":527},"Chiffrement symétrique","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fchiffrement-symetrique","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F6.chiffrement-symetrique",{"title":529,"path":530,"stem":531},"Chiffrement asymétrique","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fchiffrement-asymetrique","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F7.chiffrement-asymetrique",{"title":533,"path":534,"stem":535},"HTTPS — l'échange de clé symétrique","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fhttps-tls","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F8.https-tls",{"title":381,"path":537,"stem":538,"children":539},"\u002Fnsi-tale\u002Ftd-langages-prog","2.nsi-tale\u002Ftd-langages-prog\u002F0.index",[540,541,544,548,552,556],{"title":381,"path":537,"stem":538},{"title":403,"path":542,"stem":543},"\u002Fnsi-tale\u002Ftd-langages-prog\u002Fmise-au-point","2.nsi-tale\u002Ftd-langages-prog\u002F1.mise-au-point",{"title":545,"path":546,"stem":547},"Modularité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fmodularite","2.nsi-tale\u002Ftd-langages-prog\u002F2.modularite",{"title":549,"path":550,"stem":551},"Récursivité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Frecursivite","2.nsi-tale\u002Ftd-langages-prog\u002F3.recursivite",{"title":553,"path":554,"stem":555},"Paradigmes de programmation","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fparadigmes","2.nsi-tale\u002Ftd-langages-prog\u002F4.paradigmes",{"title":557,"path":558,"stem":559},"Programme comme donnée — calculabilité et indécidabilité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fprogramme-comme-donnee","2.nsi-tale\u002Ftd-langages-prog\u002F5.programme-comme-donnee",{"title":411,"path":561,"stem":562,"children":563},"\u002Fnsi-tale\u002Fte-algorithmique","2.nsi-tale\u002Fte-algorithmique\u002F0.index",[564,565,569,573,577,581],{"title":411,"path":561,"stem":562},{"title":566,"path":567,"stem":568},"Algorithmes sur les arbres binaires","\u002Fnsi-tale\u002Fte-algorithmique\u002Farbres-binaires-algos","2.nsi-tale\u002Fte-algorithmique\u002F1.arbres-binaires-algos",{"title":570,"path":571,"stem":572},"Parcours de graphes — DFS, BFS, cycles, chemins","\u002Fnsi-tale\u002Fte-algorithmique\u002Fgraphes-parcours","2.nsi-tale\u002Fte-algorithmique\u002F2.graphes-parcours",{"title":574,"path":575,"stem":576},"Diviser pour régner","\u002Fnsi-tale\u002Fte-algorithmique\u002Fdiviser-pour-regner","2.nsi-tale\u002Fte-algorithmique\u002F3.diviser-pour-regner",{"title":578,"path":579,"stem":580},"Programmation dynamique","\u002Fnsi-tale\u002Fte-algorithmique\u002Fprogrammation-dynamique","2.nsi-tale\u002Fte-algorithmique\u002F4.programmation-dynamique",{"title":582,"path":583,"stem":584},"Recherche textuelle — l'algorithme de Boyer-Moore","\u002Fnsi-tale\u002Fte-algorithmique\u002Frecherche-textuelle","2.nsi-tale\u002Fte-algorithmique\u002F5.recherche-textuelle",{"id":586,"title":399,"bo":587,"body":589,"description":1592,"eval":1593,"extension":1594,"labo":1593,"meta":1595,"navigation":884,"path":400,"quizzes":1596,"readingTime":657,"seo":1603,"stem":401,"tp":1593,"__hash__":1604},"cours\u002F1.nsi-1ere\u002Fpg-langages-prog\u002F4.specification.md",[588],"PG04",{"type":590,"value":591,"toc":1580},"minimark",[592,597,621,624,628,643,702,721,767,771,790,796,825,832,836,849,955,969,1037,1040,1048,1072,1079,1090,1167,1174,1213,1240,1244,1247,1397,1400,1438,1451,1455,1487,1509,1513,1558,1562,1576],[593,594,596],"h2",{"id":595},"introduction","Introduction",[598,599,600,601,605,606,609,610,613,614,617,618],"p",{},"Une fonction n'est pleinement utilisable que si on sait ",[602,603,604],"strong",{},"ce qu'elle attend\nen entrée"," et ",[602,607,608],{},"ce qu'elle garantit en sortie",". Cette description s'appelle\nla ",[602,611,612],{},"spécification",". Elle s'écrit ",[602,615,616],{},"avant"," le code — c'est ce qui permet\nà un autre programmeur (ou à vous dans trois semaines) d'utiliser la fonction\nsans lire son corps. ",[619,620],"bo-ref",{"code":588},[598,622,623],{},"Une fonction sans spécification, c'est comme une recette de cuisine sans\nliste d'ingrédients : on peut la lire, on ne sait pas si elle va marcher.",[593,625,627],{"id":626},"signature-et-prototype","Signature et prototype",[598,629,630,631,634,635,638,639,642],{},"La ",[602,632,633],{},"signature"," (ou ",[602,636,637],{},"prototype",") d'une fonction décrit son nom, ses\nparamètres et le type de chacun. En Python, on l'exprime avec des\n",[602,640,641],{},"annotations de type"," :",[644,645,650],"pre",{"className":646,"code":647,"language":648,"meta":649,"style":649},"language-python shiki shiki-themes github-light github-light github-dark","def aire_rectangle(longueur: float, largeur: float) -> float:\n    return longueur * largeur\n","python","",[651,652,653,687],"code",{"__ignoreMap":649},[654,655,658,662,666,670,674,677,679,682,684],"span",{"class":656,"line":657},"line",1,[654,659,661],{"class":660},"s8jYJ","def",[654,663,665],{"class":664},"snPdu"," aire_rectangle",[654,667,669],{"class":668},"sxrX7","(longueur: ",[654,671,673],{"class":672},"sBjJW","float",[654,675,676],{"class":668},", largeur: ",[654,678,673],{"class":672},[654,680,681],{"class":668},") -> ",[654,683,673],{"class":672},[654,685,686],{"class":668},":\n",[654,688,690,693,696,699],{"class":656,"line":689},2,[654,691,692],{"class":660},"    return",[654,694,695],{"class":668}," longueur ",[654,697,698],{"class":660},"*",[654,700,701],{"class":668}," largeur\n",[703,704,705,715],"ul",{},[706,707,708,605,711,714],"li",{},[651,709,710],{},"longueur: float",[651,712,713],{},"largeur: float"," annoncent que les paramètres sont\ndes nombres à virgule.",[706,716,717,720],{},[651,718,719],{},"-> float"," annonce que la fonction retourne un nombre à virgule.",[722,723,724,733,760],"note",{},[598,725,726,729,730,732],{},[602,727,728],{},"Les annotations ne sont pas contraignantes"," en Python. Le code suivant\nne lèvera aucune erreur même si on passe une chaîne là où un ",[651,731,673],{}," est\nattendu :",[644,734,736],{"className":646,"code":735,"language":648,"meta":649,"style":649},"aire_rectangle(\"trois\", \"quatre\")   # plante au runtime, pas à cause des annotations\n",[651,737,738],{"__ignoreMap":649},[654,739,740,743,747,750,753,756],{"class":656,"line":657},[654,741,742],{"class":668},"aire_rectangle(",[654,744,746],{"class":745},"sIIMD","\"trois\"",[654,748,749],{"class":668},", ",[654,751,752],{"class":745},"\"quatre\"",[654,754,755],{"class":668},")   ",[654,757,759],{"class":758},"sCsY4","# plante au runtime, pas à cause des annotations\n",[598,761,762,763,766],{},"Elles servent à ",[602,764,765],{},"documenter"," et à aider les outils d'analyse (linters,\néditeurs). C'est une convention de lisibilité, pas une vérification.",[593,768,770],{"id":769},"précondition-et-postcondition","Précondition et postcondition",[703,772,773,780],{},[706,774,775,776,779],{},"Une ",[602,777,778],{},"précondition"," est une condition que les arguments doivent\nsatisfaire pour que la fonction fonctionne correctement.",[706,781,775,782,785,786,789],{},[602,783,784],{},"postcondition"," est ce que la fonction garantit en sortie, ",[602,787,788],{},"si la\nprécondition est respectée",".",[598,791,792,793,789],{},"Exemple : une fonction ",[651,794,795],{},"racine_carree(x)",[703,797,798,808],{},[706,799,800,803,804,807],{},[602,801,802],{},"Précondition"," : ",[651,805,806],{},"x >= 0",". (On ne sait pas calculer la racine carrée\nd'un nombre négatif en restant dans les réels.)",[706,809,810,813,814,817,818,605,821,824],{},[602,811,812],{},"Postcondition"," : le résultat ",[651,815,816],{},"r"," satisfait ",[651,819,820],{},"r >= 0",[651,822,823],{},"r * r == x","\n(à l'erreur d'arrondi près).",[598,826,827,828,831],{},"C'est un ",[602,829,830],{},"contrat"," : si vous respectez la précondition, je m'engage sur\nla postcondition.",[593,833,835],{"id":834},"la-docstring-la-spécification-en-mots","La docstring : la spécification en mots",[598,837,838,839,842,843,845,846,789],{},"En Python, la spécification d'une fonction s'écrit dans une ",[602,840,841],{},"docstring"," —\nune chaîne de caractères placée juste après la ligne ",[651,844,661],{},", encadrée par\ntrois guillemets ",[651,847,848],{},"\"\"\"",[644,850,852],{"className":646,"code":851,"language":648,"meta":649,"style":649},"def aire_rectangle(longueur: float, largeur: float) -> float:\n    \"\"\"Renvoie l'aire d'un rectangle.\n\n    Paramètres :\n    - longueur : longueur du rectangle, doit être >= 0.\n    - largeur  : largeur du rectangle, doit être >= 0.\n\n    Retourne :\n    - L'aire en unités², toujours >= 0.\n\n    Précondition  : longueur >= 0 et largeur >= 0.\n    Postcondition : résultat >= 0.\n    \"\"\"\n    return longueur * largeur\n",[651,853,854,874,879,886,892,898,904,909,915,921,926,932,938,944],{"__ignoreMap":649},[654,855,856,858,860,862,864,866,868,870,872],{"class":656,"line":657},[654,857,661],{"class":660},[654,859,665],{"class":664},[654,861,669],{"class":668},[654,863,673],{"class":672},[654,865,676],{"class":668},[654,867,673],{"class":672},[654,869,681],{"class":668},[654,871,673],{"class":672},[654,873,686],{"class":668},[654,875,876],{"class":656,"line":689},[654,877,878],{"class":745},"    \"\"\"Renvoie l'aire d'un rectangle.\n",[654,880,882],{"class":656,"line":881},3,[654,883,885],{"emptyLinePlaceholder":884},true,"\n",[654,887,889],{"class":656,"line":888},4,[654,890,891],{"class":745},"    Paramètres :\n",[654,893,895],{"class":656,"line":894},5,[654,896,897],{"class":745},"    - longueur : longueur du rectangle, doit être >= 0.\n",[654,899,901],{"class":656,"line":900},6,[654,902,903],{"class":745},"    - largeur  : largeur du rectangle, doit être >= 0.\n",[654,905,907],{"class":656,"line":906},7,[654,908,885],{"emptyLinePlaceholder":884},[654,910,912],{"class":656,"line":911},8,[654,913,914],{"class":745},"    Retourne :\n",[654,916,918],{"class":656,"line":917},9,[654,919,920],{"class":745},"    - L'aire en unités², toujours >= 0.\n",[654,922,924],{"class":656,"line":923},10,[654,925,885],{"emptyLinePlaceholder":884},[654,927,929],{"class":656,"line":928},11,[654,930,931],{"class":745},"    Précondition  : longueur >= 0 et largeur >= 0.\n",[654,933,935],{"class":656,"line":934},12,[654,936,937],{"class":745},"    Postcondition : résultat >= 0.\n",[654,939,941],{"class":656,"line":940},13,[654,942,943],{"class":745},"    \"\"\"\n",[654,945,947,949,951,953],{"class":656,"line":946},14,[654,948,692],{"class":660},[654,950,695],{"class":668},[654,952,698],{"class":660},[654,954,701],{"class":668},[598,956,957,958,961,962,965,966,642],{},"La docstring est accessible ",[602,959,960],{},"depuis l'extérieur"," grâce à l'attribut\n",[651,963,964],{},"__doc__"," ou à la fonction ",[651,967,968],{},"help()",[970,971,972],"python-snippet",{},[644,973,975],{"className":646,"code":974,"language":648,"meta":649,"style":649},"def aire_rectangle(longueur: float, largeur: float) -> float:\n    \"\"\"Renvoie l'aire d'un rectangle de longueur et largeur positives.\"\"\"\n    return longueur * largeur\n\nprint(aire_rectangle.__doc__)\nhelp(aire_rectangle)\n",[651,976,977,997,1002,1012,1016,1029],{"__ignoreMap":649},[654,978,979,981,983,985,987,989,991,993,995],{"class":656,"line":657},[654,980,661],{"class":660},[654,982,665],{"class":664},[654,984,669],{"class":668},[654,986,673],{"class":672},[654,988,676],{"class":668},[654,990,673],{"class":672},[654,992,681],{"class":668},[654,994,673],{"class":672},[654,996,686],{"class":668},[654,998,999],{"class":656,"line":689},[654,1000,1001],{"class":745},"    \"\"\"Renvoie l'aire d'un rectangle de longueur et largeur positives.\"\"\"\n",[654,1003,1004,1006,1008,1010],{"class":656,"line":881},[654,1005,692],{"class":660},[654,1007,695],{"class":668},[654,1009,698],{"class":660},[654,1011,701],{"class":668},[654,1013,1014],{"class":656,"line":888},[654,1015,885],{"emptyLinePlaceholder":884},[654,1017,1018,1021,1024,1026],{"class":656,"line":894},[654,1019,1020],{"class":672},"print",[654,1022,1023],{"class":668},"(aire_rectangle.",[654,1025,964],{"class":672},[654,1027,1028],{"class":668},")\n",[654,1030,1031,1034],{"class":656,"line":900},[654,1032,1033],{"class":672},"help",[654,1035,1036],{"class":668},"(aire_rectangle)\n",[598,1038,1039],{},"Sortie attendue (extrait) :",[644,1041,1046],{"className":1042,"code":1044,"language":1045},[1043],"language-text","Renvoie l'aire d'un rectangle de longueur et largeur positives.\n\nHelp on function aire_rectangle in module __main__:\n\naire_rectangle(longueur: float, largeur: float) -> float\n    Renvoie l'aire d'un rectangle de longueur et largeur positives.\n","text",[651,1047,1044],{"__ignoreMap":649},[1049,1050,1053,1059],"self-eval-qcm",{"correct":1051,"slug":1052},"1","specification-c1",[1054,1055,1056],"template",{"v-slot:question":649},[598,1057,1058],{},"Où se place une docstring dans une fonction Python ?",[1054,1060,1061],{"v-slot:choices":649},[703,1062,1063,1066,1069],{},[706,1064,1065],{},"Avant la ligne def",[706,1067,1068],{},"Juste après la ligne def, en première instruction du corps",[706,1070,1071],{},"À la fin de la fonction, après le return",[593,1073,1075,1076],{"id":1074},"garantir-une-précondition-avec-assert","Garantir une précondition avec ",[651,1077,1078],{},"assert",[598,1080,1081,1082,1085,1086,1089],{},"Une bonne docstring décrit la précondition. Pour ",[602,1083,1084],{},"la faire respecter en\npratique",", on peut ajouter une ",[602,1087,1088],{},"assertion"," au début de la fonction.",[644,1091,1093],{"className":646,"code":1092,"language":648,"meta":649,"style":649},"def racine_carree(x: float) -> float:\n    \"\"\"Renvoie la racine carrée de x.\n\n    Précondition  : x >= 0.\n    Postcondition : le résultat r satisfait r >= 0 et r * r ≈ x.\n    \"\"\"\n    assert x >= 0, \"x doit être positif ou nul\"\n    return x ** 0.5\n",[651,1094,1095,1113,1118,1122,1127,1132,1136,1155],{"__ignoreMap":649},[654,1096,1097,1099,1102,1105,1107,1109,1111],{"class":656,"line":657},[654,1098,661],{"class":660},[654,1100,1101],{"class":664}," racine_carree",[654,1103,1104],{"class":668},"(x: ",[654,1106,673],{"class":672},[654,1108,681],{"class":668},[654,1110,673],{"class":672},[654,1112,686],{"class":668},[654,1114,1115],{"class":656,"line":689},[654,1116,1117],{"class":745},"    \"\"\"Renvoie la racine carrée de x.\n",[654,1119,1120],{"class":656,"line":881},[654,1121,885],{"emptyLinePlaceholder":884},[654,1123,1124],{"class":656,"line":888},[654,1125,1126],{"class":745},"    Précondition  : x >= 0.\n",[654,1128,1129],{"class":656,"line":894},[654,1130,1131],{"class":745},"    Postcondition : le résultat r satisfait r >= 0 et r * r ≈ x.\n",[654,1133,1134],{"class":656,"line":900},[654,1135,943],{"class":745},[654,1137,1138,1141,1144,1147,1150,1152],{"class":656,"line":906},[654,1139,1140],{"class":660},"    assert",[654,1142,1143],{"class":668}," x ",[654,1145,1146],{"class":660},">=",[654,1148,1149],{"class":672}," 0",[654,1151,749],{"class":668},[654,1153,1154],{"class":745},"\"x doit être positif ou nul\"\n",[654,1156,1157,1159,1161,1164],{"class":656,"line":911},[654,1158,692],{"class":660},[654,1160,1143],{"class":668},[654,1162,1163],{"class":660},"**",[654,1165,1166],{"class":672}," 0.5\n",[598,1168,1169,1170,1173],{},"Si la précondition est violée à l'appel, Python lève une ",[651,1171,1172],{},"AssertionError","\nexplicite, plutôt que de produire un résultat absurde ou cryptique :",[644,1175,1177],{"className":646,"code":1176,"language":648,"meta":649,"style":649},"print(racine_carree(9))    # 3.0\nprint(racine_carree(-4))   # AssertionError: x doit être positif ou nul\n",[651,1178,1179,1195],{"__ignoreMap":649},[654,1180,1181,1183,1186,1189,1192],{"class":656,"line":657},[654,1182,1020],{"class":672},[654,1184,1185],{"class":668},"(racine_carree(",[654,1187,1188],{"class":672},"9",[654,1190,1191],{"class":668},"))    ",[654,1193,1194],{"class":758},"# 3.0\n",[654,1196,1197,1199,1201,1204,1207,1210],{"class":656,"line":689},[654,1198,1020],{"class":672},[654,1200,1185],{"class":668},[654,1202,1203],{"class":660},"-",[654,1205,1206],{"class":672},"4",[654,1208,1209],{"class":668},"))   ",[654,1211,1212],{"class":758},"# AssertionError: x doit être positif ou nul\n",[1214,1215,1216],"warning",{},[598,1217,1218,1220,1221,1224,1225,1228,1229,1232,1233,1236,1237,789],{},[651,1219,1078],{}," est un ",[602,1222,1223],{},"outil de défense en développement",". En conditions de\nproduction avec l'option ",[651,1226,1227],{},"python -O",", les assertions sont ",[602,1230,1231],{},"désactivées",".\nPour des contrôles indispensables au métier, préférer un ",[651,1234,1235],{},"if"," qui lève une\n",[651,1238,1239],{},"ValueError",[593,1241,1243],{"id":1242},"spécification-dune-fonction-concrète","Spécification d'une fonction concrète",[598,1245,1246],{},"Reprenons une fonction utile et écrivons sa spécification complète.",[644,1248,1250],{"className":646,"code":1249,"language":648,"meta":649,"style":649},"def moyenne(notes: list) -> float:\n    \"\"\"Renvoie la moyenne arithmétique d'une liste de notes.\n\n    Paramètres :\n    - notes : liste non vide de nombres (int ou float) entre 0 et 20.\n\n    Retourne :\n    - La moyenne arithmétique, un float entre 0 et 20.\n\n    Précondition  : notes est non vide ; chaque note est dans [0, 20].\n    Postcondition : 0 \u003C= résultat \u003C= 20.\n\n    Exemples :\n        >>> moyenne([10, 12, 14])\n        12.0\n        >>> moyenne([20, 20])\n        20.0\n    \"\"\"\n    assert len(notes) > 0, \"La liste de notes ne doit pas être vide\"\n    return sum(notes) \u002F len(notes)\n",[651,1251,1252,1271,1276,1280,1284,1289,1293,1297,1302,1306,1311,1316,1320,1325,1333,1339,1347,1353,1358,1379],{"__ignoreMap":649},[654,1253,1254,1256,1259,1262,1265,1267,1269],{"class":656,"line":657},[654,1255,661],{"class":660},[654,1257,1258],{"class":664}," moyenne",[654,1260,1261],{"class":668},"(notes: ",[654,1263,1264],{"class":672},"list",[654,1266,681],{"class":668},[654,1268,673],{"class":672},[654,1270,686],{"class":668},[654,1272,1273],{"class":656,"line":689},[654,1274,1275],{"class":745},"    \"\"\"Renvoie la moyenne arithmétique d'une liste de notes.\n",[654,1277,1278],{"class":656,"line":881},[654,1279,885],{"emptyLinePlaceholder":884},[654,1281,1282],{"class":656,"line":888},[654,1283,891],{"class":745},[654,1285,1286],{"class":656,"line":894},[654,1287,1288],{"class":745},"    - notes : liste non vide de nombres (int ou float) entre 0 et 20.\n",[654,1290,1291],{"class":656,"line":900},[654,1292,885],{"emptyLinePlaceholder":884},[654,1294,1295],{"class":656,"line":906},[654,1296,914],{"class":745},[654,1298,1299],{"class":656,"line":911},[654,1300,1301],{"class":745},"    - La moyenne arithmétique, un float entre 0 et 20.\n",[654,1303,1304],{"class":656,"line":917},[654,1305,885],{"emptyLinePlaceholder":884},[654,1307,1308],{"class":656,"line":923},[654,1309,1310],{"class":745},"    Précondition  : notes est non vide ; chaque note est dans [0, 20].\n",[654,1312,1313],{"class":656,"line":928},[654,1314,1315],{"class":745},"    Postcondition : 0 \u003C= résultat \u003C= 20.\n",[654,1317,1318],{"class":656,"line":934},[654,1319,885],{"emptyLinePlaceholder":884},[654,1321,1322],{"class":656,"line":940},[654,1323,1324],{"class":745},"    Exemples :\n",[654,1326,1327,1330],{"class":656,"line":946},[654,1328,1329],{"class":660},"        >>> ",[654,1331,1332],{"class":745},"moyenne([10, 12, 14])\n",[654,1334,1336],{"class":656,"line":1335},15,[654,1337,1338],{"class":745},"        12.0\n",[654,1340,1342,1344],{"class":656,"line":1341},16,[654,1343,1329],{"class":660},[654,1345,1346],{"class":745},"moyenne([20, 20])\n",[654,1348,1350],{"class":656,"line":1349},17,[654,1351,1352],{"class":745},"        20.0\n",[654,1354,1356],{"class":656,"line":1355},18,[654,1357,943],{"class":745},[654,1359,1361,1363,1366,1369,1372,1374,1376],{"class":656,"line":1360},19,[654,1362,1140],{"class":660},[654,1364,1365],{"class":672}," len",[654,1367,1368],{"class":668},"(notes) ",[654,1370,1371],{"class":660},">",[654,1373,1149],{"class":672},[654,1375,749],{"class":668},[654,1377,1378],{"class":745},"\"La liste de notes ne doit pas être vide\"\n",[654,1380,1382,1384,1387,1389,1392,1394],{"class":656,"line":1381},20,[654,1383,692],{"class":660},[654,1385,1386],{"class":672}," sum",[654,1388,1368],{"class":668},[654,1390,1391],{"class":660},"\u002F",[654,1393,1365],{"class":672},[654,1395,1396],{"class":668},"(notes)\n",[598,1398,1399],{},"Plusieurs choses à noter :",[1401,1402,1403,1408,1422,1433],"ol",{},[706,1404,630,1405,1407],{},[602,1406,633],{}," annonce types d'entrée et type de retour.",[706,1409,1410,1411,749,1414,749,1417,1419,1420,789],{},"La docstring liste ",[602,1412,1413],{},"paramètres",[602,1415,1416],{},"retour",[602,1418,778],{}," et\n",[602,1421,784],{},[706,1423,1424,1425,1428,1429,1432],{},"Des ",[602,1426,1427],{},"exemples"," sous le format ",[651,1430,1431],{},">>> ..."," aident à comprendre l'usage.",[706,1434,775,1435,1437],{},[602,1436,1088],{}," garde le contrat.",[1439,1440,1441],"tip",{},[598,1442,1443,1444,1446,1447,1450],{},"Les exemples au format ",[651,1445,1431],{}," dans une docstring sont la syntaxe\n",[602,1448,1449],{},"doctest",". Python peut les exécuter automatiquement pour vérifier qu'ils\nproduisent bien le résultat annoncé — une forme légère de test intégré à\nla documentation.",[593,1452,1454],{"id":1453},"bonnes-pratiques","Bonnes pratiques",[703,1456,1457,1463,1475,1481],{},[706,1458,1459,1462],{},[602,1460,1461],{},"Une fonction, un rôle",". Si vous n'arrivez pas à décrire la fonction\nen une phrase, c'est qu'elle fait sans doute trop de choses.",[706,1464,1465,803,1468,1471,1472,789],{},[602,1466,1467],{},"Nom parlant",[651,1469,1470],{},"nb_voyelles_dans"," est plus utile que ",[651,1473,1474],{},"compter",[706,1476,1477,1480],{},[602,1478,1479],{},"Préconditions explicites"," dans la docstring, pas implicites dans le\ncode.",[706,1482,1483,1486],{},[602,1484,1485],{},"Types annotés"," chaque fois que possible.",[1049,1488,1491,1496],{"correct":1489,"slug":1490},"0","specification-c2",[1054,1492,1493],{"v-slot:question":649},[598,1494,1495],{},"Quelle est la différence entre précondition et postcondition ?",[1054,1497,1498],{"v-slot:choices":649},[703,1499,1500,1503,1506],{},[706,1501,1502],{},"La précondition est sur les arguments, la postcondition est sur le résultat",[706,1504,1505],{},"Précondition signifie avant la docstring, postcondition après",[706,1507,1508],{},"Précondition concerne le matériel, postcondition le logiciel",[593,1510,1512],{"id":1511},"pièges-courants","Pièges courants",[1214,1514,1515],{},[703,1516,1517,1533,1539,1552],{},[706,1518,1519,803,1522,1525,1526,1529,1530,1532],{},[602,1520,1521],{},"Annotations ne valident pas",[651,1523,1524],{},"def f(x: int)"," accepte aussi\n",[651,1527,1528],{},"f(\"bonjour\")"," sans erreur. Penser ",[651,1531,1078],{}," ou conditions explicites.",[706,1534,1535,1538],{},[602,1536,1537],{},"Docstring oubliée"," : sans elle, votre fonction est une boîte noire\npour celui qui veut l'utiliser.",[706,1540,1541,1544,1545,1548,1549,789],{},[602,1542,1543],{},"Précondition trop forte"," : exiger des conditions inutiles complique\nl'usage. Une fonction ",[651,1546,1547],{},"est_pair(n)"," ne devrait pas exiger ",[651,1550,1551],{},"n > 0",[706,1553,1554,1557],{},[602,1555,1556],{},"Spécifier après coup"," : écrire la spécification après le code conduit\npresque toujours à des fonctions mal pensées. Spécifiez d'abord.",[593,1559,1561],{"id":1560},"pour-aller-plus-loin","Pour aller plus loin",[598,1563,1564,1565,1568,1569,1572,1573,789],{},"Une fonction bien spécifiée est aussi une fonction ",[602,1566,1567],{},"plus facile à tester"," :\nles exemples de la docstring sont des cas de test naturels, et la précondition\nindique quels arguments mettre dans le jeu de tests. C'est l'objet du cours\nsuivant sur la ",[602,1570,1571],{},"mise au point"," ",[619,1574],{"code":1575},"PG03",[1577,1578,1579],"style",{},"html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}",{"title":649,"searchDepth":689,"depth":689,"links":1581},[1582,1583,1584,1585,1586,1588,1589,1590,1591],{"id":595,"depth":689,"text":596},{"id":626,"depth":689,"text":627},{"id":769,"depth":689,"text":770},{"id":834,"depth":689,"text":835},{"id":1074,"depth":689,"text":1587},"Garantir une précondition avec assert",{"id":1242,"depth":689,"text":1243},{"id":1453,"depth":689,"text":1454},{"id":1511,"depth":689,"text":1512},{"id":1560,"depth":689,"text":1561},"Signature, précondition, postcondition et docstring — décrire ce qu'une fonction promet avant de l'écrire.",null,"md",{},[1597,1601],{"slug":1052,"kind":1598,"question":1058,"choices":1599,"correct":1051,"multi":1600,"explanation":649},"qcm",[1065,1068,1071],false,{"slug":1490,"kind":1598,"question":1495,"choices":1602,"correct":1489,"multi":1600,"explanation":649},[1502,1505,1508],{"title":399,"description":1592},"OQQjJ7Z9HE8IY3g0McZCFq7A2KFgByAbs94pSNhJh3I",{"id":1606,"title":1607,"bo":1608,"body":1609,"description":1863,"eval":1593,"extension":1594,"labo":1593,"meta":1864,"navigation":1600,"path":1865,"quizzes":1866,"readingTime":657,"seo":1867,"stem":1868,"tp":1593,"__hash__":1869},"coursMemo\u002F1.nsi-1ere\u002Fpg-langages-prog\u002F4.specification.memo.md","Spécification d'une fonction — l'essentiel",[588],{"type":590,"value":1610,"toc":1856},[1611,1615,1627,1631,1682,1686,1744,1746,1766,1770,1853],[593,1612,1614],{"id":1613},"en-une-phrase","En une phrase",[598,1616,1617,1620,1621,1623,1624,1626],{},[602,1618,1619],{},"Spécifier"," une fonction, c'est dire ce qu'elle attend (",[602,1622,778],{},")\net ce qu'elle garantit (",[602,1625,784],{},") — par sa signature, sa docstring\net éventuellement une assertion.",[593,1628,1630],{"id":1629},"à-mémoriser","À mémoriser",[703,1632,1633,1639,1644,1653,1671],{},[706,1634,1635,1638],{},[602,1636,1637],{},"Signature"," : nom + types des paramètres + type de retour.",[706,1640,1641,1643],{},[602,1642,802],{}," : condition que doivent satisfaire les arguments.",[706,1645,1646,1648,1649,1652],{},[602,1647,812],{}," : condition que satisfait le résultat ",[602,1650,1651],{},"si"," la\nprécondition est respectée.",[706,1654,1655,803,1658,1661,1662,1664,1665,1667,1668,789],{},[602,1656,1657],{},"Docstring",[651,1659,1660],{},"\"\"\"...\"\"\""," juste après ",[651,1663,661],{},", accessible via\n",[651,1666,968],{}," ou ",[651,1669,1670],{},"f.__doc__",[706,1672,1673,1678,1679,1681],{},[602,1674,1675],{},[651,1676,1677],{},"assert condition, message"," : vérifie une précondition à l'exécution\net lève une ",[651,1680,1172],{}," en cas d'échec.",[593,1683,1685],{"id":1684},"à-savoir-reconnaître","À savoir reconnaître",[1687,1688,1689,1702],"table",{},[1690,1691,1692],"thead",{},[1693,1694,1695,1699],"tr",{},[1696,1697,1698],"th",{},"Situation",[1696,1700,1701],{},"Élément à écrire",[1703,1704,1705,1714,1725,1733],"tbody",{},[1693,1706,1707,1711],{},[1708,1709,1710],"td",{},"Indiquer les types d'entrée et de sortie",[1708,1712,1713],{},"Annotations dans la signature",[1693,1715,1716,1719],{},[1708,1717,1718],{},"Dire ce que la fonction attend des arguments",[1708,1720,1721,1722,1724],{},"Précondition (docstring + ",[651,1723,1078],{},")",[1693,1726,1727,1730],{},[1708,1728,1729],{},"Dire ce que la fonction promet",[1708,1731,1732],{},"Postcondition (docstring)",[1693,1734,1735,1738],{},[1708,1736,1737],{},"Donner un exemple d'usage",[1708,1739,1740,1741,1743],{},"Bloc ",[651,1742,1431],{}," dans la docstring",[593,1745,1512],{"id":1511},[703,1747,1748,1755,1763],{},[706,1749,1750,1751,1754],{},"Les annotations Python ",[602,1752,1753],{},"ne valident pas"," les types à l'exécution.",[706,1756,1757,1759,1760,1762],{},[651,1758,1078],{}," est désactivé avec ",[651,1761,1227],{}," : ne pas s'en servir comme\ncontrôle métier vital.",[706,1764,1765],{},"Spécifier après avoir codé conduit à de mauvaises fonctions ; spécifier\nd'abord.",[593,1767,1769],{"id":1768},"syntaxe-python","Syntaxe Python",[644,1771,1773],{"className":646,"code":1772,"language":648,"meta":649,"style":649},"def racine_carree(x: float) -> float:\n    \"\"\"Renvoie la racine carrée de x.\n\n    Précondition  : x >= 0.\n    Postcondition : résultat >= 0 et résultat² ≈ x.\n\n    >>> racine_carree(9)\n    3.0\n    \"\"\"\n    assert x >= 0, \"x doit être positif ou nul\"\n    return x ** 0.5\n",[651,1774,1775,1791,1795,1799,1803,1808,1812,1820,1825,1829,1843],{"__ignoreMap":649},[654,1776,1777,1779,1781,1783,1785,1787,1789],{"class":656,"line":657},[654,1778,661],{"class":660},[654,1780,1101],{"class":664},[654,1782,1104],{"class":668},[654,1784,673],{"class":672},[654,1786,681],{"class":668},[654,1788,673],{"class":672},[654,1790,686],{"class":668},[654,1792,1793],{"class":656,"line":689},[654,1794,1117],{"class":745},[654,1796,1797],{"class":656,"line":881},[654,1798,885],{"emptyLinePlaceholder":884},[654,1800,1801],{"class":656,"line":888},[654,1802,1126],{"class":745},[654,1804,1805],{"class":656,"line":894},[654,1806,1807],{"class":745},"    Postcondition : résultat >= 0 et résultat² ≈ x.\n",[654,1809,1810],{"class":656,"line":900},[654,1811,885],{"emptyLinePlaceholder":884},[654,1813,1814,1817],{"class":656,"line":906},[654,1815,1816],{"class":660},"    >>> ",[654,1818,1819],{"class":745},"racine_carree(9)\n",[654,1821,1822],{"class":656,"line":911},[654,1823,1824],{"class":745},"    3.0\n",[654,1826,1827],{"class":656,"line":917},[654,1828,943],{"class":745},[654,1830,1831,1833,1835,1837,1839,1841],{"class":656,"line":923},[654,1832,1140],{"class":660},[654,1834,1143],{"class":668},[654,1836,1146],{"class":660},[654,1838,1149],{"class":672},[654,1840,749],{"class":668},[654,1842,1154],{"class":745},[654,1844,1845,1847,1849,1851],{"class":656,"line":928},[654,1846,692],{"class":660},[654,1848,1143],{"class":668},[654,1850,1163],{"class":660},[654,1852,1166],{"class":672},[1577,1854,1855],{},"html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":649,"searchDepth":689,"depth":689,"links":1857},[1858,1859,1860,1861,1862],{"id":1613,"depth":689,"text":1614},{"id":1629,"depth":689,"text":1630},{"id":1684,"depth":689,"text":1685},{"id":1511,"depth":689,"text":1512},{"id":1768,"depth":689,"text":1769},"Mémo de révision sur signature, précondition, postcondition et docstring.",{},"\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fspecification.memo",[],{"title":1607,"description":1863},"1.nsi-1ere\u002Fpg-langages-prog\u002F4.specification.memo","C_M88oF6i4mxH-zJAf071J7HTEmf1t-NBrYisAJML9U",{"id":1871,"title":1872,"body":1873,"description":2234,"extension":1594,"meta":2235,"navigation":1600,"path":2236,"seo":2237,"stem":2238,"__hash__":2239},"coursSlides\u002F1.nsi-1ere\u002Fpg-langages-prog\u002F4.specification.slides.md","Spécification d'une fonction — diapositives",{"type":590,"value":1874,"toc":2232},[1875,1880,1886,1889,1893,1907,1909,1911,1942,1950,1952,1954,1960,1969,1971,1973,1980,1992,1994,1998,2042,2048,2050,2056,2094,2102,2104,2108,2193,2195,2197,2217,2219,2223,2229],[1876,1877,1879],"h1",{"id":1878},"spécifier-une-fonction","Spécifier une fonction",[598,1881,1882,1883,1885],{},"Dire ce qu'elle attend et ce qu'elle promet — ",[602,1884,616],{}," d'écrire le code.",[1887,1888],"hr",{},[1876,1890,1892],{"id":1891},"pourquoi-spécifier","Pourquoi spécifier ?",[703,1894,1895,1901,1904],{},[706,1896,1897,1898,789],{},"Pour qu'un autre puisse utiliser la fonction ",[602,1899,1900],{},"sans lire son corps",[706,1902,1903],{},"Pour mieux tester ensuite.",[706,1905,1906],{},"Pour penser le problème avant de coder.",[1887,1908],{},[1876,1910,1637],{"id":633},[644,1912,1914],{"className":646,"code":1913,"language":648,"meta":649,"style":649},"def aire(longueur: float, largeur: float) -> float:\n    ...\n",[651,1915,1916,1937],{"__ignoreMap":649},[654,1917,1918,1920,1923,1925,1927,1929,1931,1933,1935],{"class":656,"line":657},[654,1919,661],{"class":660},[654,1921,1922],{"class":664}," aire",[654,1924,669],{"class":668},[654,1926,673],{"class":672},[654,1928,676],{"class":668},[654,1930,673],{"class":672},[654,1932,681],{"class":668},[654,1934,673],{"class":672},[654,1936,686],{"class":668},[654,1938,1939],{"class":656,"line":689},[654,1940,1941],{"class":672},"    ...\n",[703,1943,1944,1947],{},[706,1945,1946],{},"Annotations de type.",[706,1948,1949],{},"Non contraignantes mais documentantes.",[1887,1951],{},[1876,1953,802],{"id":778},[598,1955,1956,1957,789],{},"Condition que doivent satisfaire les ",[602,1958,1959],{},"arguments",[598,1961,1962,1963,749,1965,803,1967,789],{},"Exemple : pour ",[651,1964,795],{},[602,1966,778],{},[651,1968,806],{},[1887,1970],{},[1876,1972,812],{"id":784},[598,1974,1975,1976,1979],{},"Condition que satisfait le ",[602,1977,1978],{},"résultat"," si la précondition est respectée.",[598,1981,1962,1982,749,1984,803,1986,1419,1989,789],{},[651,1983,795],{},[602,1985,784],{},[651,1987,1988],{},"résultat ≥ 0",[651,1990,1991],{},"résultat² ≈ x",[1887,1993],{},[1876,1995,1997],{"id":1996},"la-docstring","La docstring",[644,1999,2001],{"className":646,"code":2000,"language":648,"meta":649,"style":649},"def aire(longueur, largeur):\n    \"\"\"Renvoie l'aire d'un rectangle.\n\n    Précondition  : longueur >= 0 et largeur >= 0.\n    Postcondition : résultat >= 0.\n    \"\"\"\n    return longueur * largeur\n",[651,2002,2003,2012,2016,2020,2024,2028,2032],{"__ignoreMap":649},[654,2004,2005,2007,2009],{"class":656,"line":657},[654,2006,661],{"class":660},[654,2008,1922],{"class":664},[654,2010,2011],{"class":668},"(longueur, largeur):\n",[654,2013,2014],{"class":656,"line":689},[654,2015,878],{"class":745},[654,2017,2018],{"class":656,"line":881},[654,2019,885],{"emptyLinePlaceholder":884},[654,2021,2022],{"class":656,"line":888},[654,2023,931],{"class":745},[654,2025,2026],{"class":656,"line":894},[654,2027,937],{"class":745},[654,2029,2030],{"class":656,"line":900},[654,2031,943],{"class":745},[654,2033,2034,2036,2038,2040],{"class":656,"line":906},[654,2035,692],{"class":660},[654,2037,695],{"class":668},[654,2039,698],{"class":660},[654,2041,701],{"class":668},[598,2043,2044,2045,789],{},"Accessible via ",[651,2046,2047],{},"help(aire)",[1887,2049],{},[1876,2051,2053,2054],{"id":2052},"garantir-avec-assert","Garantir avec ",[651,2055,1078],{},[644,2057,2059],{"className":646,"code":2058,"language":648,"meta":649,"style":649},"def racine_carree(x):\n    assert x >= 0, \"x doit être positif ou nul\"\n    return x ** 0.5\n",[651,2060,2061,2070,2084],{"__ignoreMap":649},[654,2062,2063,2065,2067],{"class":656,"line":657},[654,2064,661],{"class":660},[654,2066,1101],{"class":664},[654,2068,2069],{"class":668},"(x):\n",[654,2071,2072,2074,2076,2078,2080,2082],{"class":656,"line":689},[654,2073,1140],{"class":660},[654,2075,1143],{"class":668},[654,2077,1146],{"class":660},[654,2079,1149],{"class":672},[654,2081,749],{"class":668},[654,2083,1154],{"class":745},[654,2085,2086,2088,2090,2092],{"class":656,"line":881},[654,2087,692],{"class":660},[654,2089,1143],{"class":668},[654,2091,1163],{"class":660},[654,2093,1166],{"class":672},[598,2095,2096,2098,2099,2101],{},[651,2097,1078],{}," lève une ",[651,2100,1172],{}," si la précondition est fausse.",[1887,2103],{},[1876,2105,2107],{"id":2106},"spécification-complète-dun-exemple","Spécification complète d'un exemple",[644,2109,2111],{"className":646,"code":2110,"language":648,"meta":649,"style":649},"def moyenne(notes: list) -> float:\n    \"\"\"Moyenne d'une liste de notes.\n\n    Précondition  : notes non vide.\n    Postcondition : 0 \u003C= résultat \u003C= 20.\n\n    >>> moyenne([10, 12, 14])\n    12.0\n    \"\"\"\n    assert len(notes) > 0\n    return sum(notes) \u002F len(notes)\n",[651,2112,2113,2129,2134,2138,2143,2147,2151,2157,2162,2166,2179],{"__ignoreMap":649},[654,2114,2115,2117,2119,2121,2123,2125,2127],{"class":656,"line":657},[654,2116,661],{"class":660},[654,2118,1258],{"class":664},[654,2120,1261],{"class":668},[654,2122,1264],{"class":672},[654,2124,681],{"class":668},[654,2126,673],{"class":672},[654,2128,686],{"class":668},[654,2130,2131],{"class":656,"line":689},[654,2132,2133],{"class":745},"    \"\"\"Moyenne d'une liste de notes.\n",[654,2135,2136],{"class":656,"line":881},[654,2137,885],{"emptyLinePlaceholder":884},[654,2139,2140],{"class":656,"line":888},[654,2141,2142],{"class":745},"    Précondition  : notes non vide.\n",[654,2144,2145],{"class":656,"line":894},[654,2146,1315],{"class":745},[654,2148,2149],{"class":656,"line":900},[654,2150,885],{"emptyLinePlaceholder":884},[654,2152,2153,2155],{"class":656,"line":906},[654,2154,1816],{"class":660},[654,2156,1332],{"class":745},[654,2158,2159],{"class":656,"line":911},[654,2160,2161],{"class":745},"    12.0\n",[654,2163,2164],{"class":656,"line":917},[654,2165,943],{"class":745},[654,2167,2168,2170,2172,2174,2176],{"class":656,"line":923},[654,2169,1140],{"class":660},[654,2171,1365],{"class":672},[654,2173,1368],{"class":668},[654,2175,1371],{"class":660},[654,2177,2178],{"class":672}," 0\n",[654,2180,2181,2183,2185,2187,2189,2191],{"class":656,"line":928},[654,2182,692],{"class":660},[654,2184,1386],{"class":672},[654,2186,1368],{"class":668},[654,2188,1391],{"class":660},[654,2190,1365],{"class":672},[654,2192,1396],{"class":668},[1887,2194],{},[1876,2196,1454],{"id":1453},[703,2198,2199,2202,2211],{},[706,2200,2201],{},"Une fonction = un rôle clair en une phrase.",[706,2203,2204,2205,2207,2208,2210],{},"Nom parlant (",[651,2206,1470],{}," > ",[651,2209,1474],{},").",[706,2212,2213,2214,2216],{},"Annotations + docstring + ",[651,2215,1078],{}," sur les préconditions vitales.",[1887,2218],{},[1876,2220,2222],{"id":2221},"à-retenir","À retenir",[598,2224,2225,2228],{},[602,2226,2227],{},"Contrat"," : si vous respectez la précondition, je m'engage sur la\npostcondition. La docstring l'écrit, l'assert le garde, la signature le\nrésume.",[1577,2230,2231],{},"html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: 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