14. Les booléens en python (>3.6)#
Une mise au point sur les booléens en python
synthétique
basée sur la documentation python 3.8 et
avec ce qui est important à retenir écrit en gras.
14.1. Synthèse qui suffit en L1#
Python définit :
deux valeurs booléennes
FalseetTruela fonction de conversion
bool()qui retourneTruela plupart du temps,
sauf :pour les arguments numériques nuls :
0,0.0,0 + 0j,la valeur spéciale
Noneet toute valeur vide – cad de longueur
len()égale à 0– d’un type composéstr,set,lst,dict
où elle retourne False.
14.2. Valeurs booléennes#
Les valeurs booléennes sont les deux objets constants False et True.
Ils sont utilisés pour représenter les valeurs de vérité bien que d’autres valeurs peuvent être considérées vraies ou fausses.
Dans des contextes numériques (par exemple en argument d’un opérateur arithmétique), ils se comportent comme les nombres entiers 0 et 1, respectivement.
14.3. Conversion en une valeur booléenne#
La fonction native
bool()peut être utilisée pour convertir n’importe quelle valeur en booléen tant que la valeur peut être interprétée en une valeur de vérité.
(\(\star\))
Voilà la description de la fonction native bool():
class bool([x])Donne une valeur booléenne, c’est à dire soit True, soit False.
x est converti en utilisant la procédure standard d’évaluation de valeur de vérité.
Si x est faux, ou omis, elle donne False, sinon, elle donne True. La classe bool hérite de la classe int (voir Types numériques — int, float, complex). Il n’est pas possible d’en hériter.
Ses seules instances sont False et True (voir Valeurs booléennes).
Modifié dans la version 3.7: x est désormais un argument exclusivement optionnel.
(\(\star\))
Et la description de la méthode .bool():
object.__bool__(self)Appelée pour implémenter les tests booléens et l’opération native bool() ; elle doit renvoyer False ou True. Quand cette méthode n’est pas définie, len() est appelée, si elle est définie, et l’objet est considéré vrai si le résultat est non nul.
Si une classe ne définit ni len() ni bool(), toutes ses instances sont considérées comme vraies.
14.4. Objets et booléens#
Tout objet peut être comparé à une valeur booléenne, typiquement dans une condition if ou while ou comme opérande des opérations booléennes ci-dessous.
Par défaut, tout objet est considéré vrai
à moins que sa classe définisse :
soit une méthode bool() renvoyant False
soit une méthode len() renvoyant zéro
lorsqu’elle est appelée avec l’objet.
On va regarder plus en détail la méthode bool()dans la cellule suivante.
Note
Voici la majorité des objets natifs considérés comme étant faux :
les constantes définies comme étant fausses : None et False.
les zéros de tout type numérique : 0, 0.0, 0j, Decimal(0), Fraction(0, 1)
les chaînes et collections vides : ‘’, (), [], {}, set(), range(0)
Rmq. Ainsi, tous les autres cas sont considérés comme étant true !
Les opérations et fonctions natives dont le résultat est booléen donnent toujours :
0 ou False pour faux
1 ou True pour vrai, sauf indication contraire.
(Exception importante : les opérations booléennes or et and renvoient toujours l’une de leurs opérandes.)
# Sauter cette cellule à regarder à la fin si besoin :
help(bool)
Help on class bool in module builtins:
class bool(int)
| bool(x) -> bool
|
| Returns True when the argument x is true, False otherwise.
| The builtins True and False are the only two instances of the class bool.
| The class bool is a subclass of the class int, and cannot be subclassed.
|
| Method resolution order:
| bool
| int
| object
|
| Methods defined here:
|
| __and__(self, value, /)
| Return self&value.
|
| __or__(self, value, /)
| Return self|value.
|
| __rand__(self, value, /)
| Return value&self.
|
| __repr__(self, /)
| Return repr(self).
|
| __ror__(self, value, /)
| Return value|self.
|
| __rxor__(self, value, /)
| Return value^self.
|
| __xor__(self, value, /)
| Return self^value.
|
| ----------------------------------------------------------------------
| Static methods defined here:
|
| __new__(*args, **kwargs) from builtins.type
| Create and return a new object. See help(type) for accurate signature.
|
| ----------------------------------------------------------------------
| Methods inherited from int:
|
| __abs__(self, /)
| abs(self)
|
| __add__(self, value, /)
| Return self+value.
|
| __bool__(self, /)
| True if self else False
|
| __ceil__(...)
| Ceiling of an Integral returns itself.
|
| __divmod__(self, value, /)
| Return divmod(self, value).
|
| __eq__(self, value, /)
| Return self==value.
|
| __float__(self, /)
| float(self)
|
| __floor__(...)
| Flooring an Integral returns itself.
|
| __floordiv__(self, value, /)
| Return self//value.
|
| __format__(self, format_spec, /)
| Default object formatter.
|
| __ge__(self, value, /)
| Return self>=value.
|
| __getattribute__(self, name, /)
| Return getattr(self, name).
|
| __getnewargs__(self, /)
|
| __gt__(self, value, /)
| Return self>value.
|
| __hash__(self, /)
| Return hash(self).
|
| __index__(self, /)
| Return self converted to an integer, if self is suitable for use as an index into a list.
|
| __int__(self, /)
| int(self)
|
| __invert__(self, /)
| ~self
|
| __le__(self, value, /)
| Return self<=value.
|
| __lshift__(self, value, /)
| Return self<<value.
|
| __lt__(self, value, /)
| Return self<value.
|
| __mod__(self, value, /)
| Return self%value.
|
| __mul__(self, value, /)
| Return self*value.
|
| __ne__(self, value, /)
| Return self!=value.
|
| __neg__(self, /)
| -self
|
| __pos__(self, /)
| +self
|
| __pow__(self, value, mod=None, /)
| Return pow(self, value, mod).
|
| __radd__(self, value, /)
| Return value+self.
|
| __rdivmod__(self, value, /)
| Return divmod(value, self).
|
| __rfloordiv__(self, value, /)
| Return value//self.
|
| __rlshift__(self, value, /)
| Return value<<self.
|
| __rmod__(self, value, /)
| Return value%self.
|
| __rmul__(self, value, /)
| Return value*self.
|
| __round__(...)
| Rounding an Integral returns itself.
|
| Rounding with an ndigits argument also returns an integer.
|
| __rpow__(self, value, mod=None, /)
| Return pow(value, self, mod).
|
| __rrshift__(self, value, /)
| Return value>>self.
|
| __rshift__(self, value, /)
| Return self>>value.
|
| __rsub__(self, value, /)
| Return value-self.
|
| __rtruediv__(self, value, /)
| Return value/self.
|
| __sizeof__(self, /)
| Returns size in memory, in bytes.
|
| __sub__(self, value, /)
| Return self-value.
|
| __truediv__(self, value, /)
| Return self/value.
|
| __trunc__(...)
| Truncating an Integral returns itself.
|
| as_integer_ratio(self, /)
| Return integer ratio.
|
| Return a pair of integers, whose ratio is exactly equal to the original int
| and with a positive denominator.
|
| >>> (10).as_integer_ratio()
| (10, 1)
| >>> (-10).as_integer_ratio()
| (-10, 1)
| >>> (0).as_integer_ratio()
| (0, 1)
|
| bit_count(self, /)
| Number of ones in the binary representation of the absolute value of self.
|
| Also known as the population count.
|
| >>> bin(13)
| '0b1101'
| >>> (13).bit_count()
| 3
|
| bit_length(self, /)
| Number of bits necessary to represent self in binary.
|
| >>> bin(37)
| '0b100101'
| >>> (37).bit_length()
| 6
|
| conjugate(...)
| Returns self, the complex conjugate of any int.
|
| to_bytes(self, /, length=1, byteorder='big', *, signed=False)
| Return an array of bytes representing an integer.
|
| length
| Length of bytes object to use. An OverflowError is raised if the
| integer is not representable with the given number of bytes. Default
| is length 1.
| byteorder
| The byte order used to represent the integer. If byteorder is 'big',
| the most significant byte is at the beginning of the byte array. If
| byteorder is 'little', the most significant byte is at the end of the
| byte array. To request the native byte order of the host system, use
| `sys.byteorder' as the byte order value. Default is to use 'big'.
| signed
| Determines whether two's complement is used to represent the integer.
| If signed is False and a negative integer is given, an OverflowError
| is raised.
|
| ----------------------------------------------------------------------
| Class methods inherited from int:
|
| from_bytes(bytes, byteorder='big', *, signed=False) from builtins.type
| Return the integer represented by the given array of bytes.
|
| bytes
| Holds the array of bytes to convert. The argument must either
| support the buffer protocol or be an iterable object producing bytes.
| Bytes and bytearray are examples of built-in objects that support the
| buffer protocol.
| byteorder
| The byte order used to represent the integer. If byteorder is 'big',
| the most significant byte is at the beginning of the byte array. If
| byteorder is 'little', the most significant byte is at the end of the
| byte array. To request the native byte order of the host system, use
| `sys.byteorder' as the byte order value. Default is to use 'big'.
| signed
| Indicates whether two's complement is used to represent the integer.
|
| ----------------------------------------------------------------------
| Data descriptors inherited from int:
|
| denominator
| the denominator of a rational number in lowest terms
|
| imag
| the imaginary part of a complex number
|
| numerator
| the numerator of a rational number in lowest terms
|
| real
| the real part of a complex number
qui définit la méthode bool() suivante, héritée d’int :
__bool__(self, /)
self != 0
On rappelle que :
par défaut, tout objet est considéré vrai à moins que sa classe définisse soit une méthode bool() renvoyant False soit une méthode len() renvoyant zéro lorsqu’elle est appelée avec l’objet;
et que l’on peut donc ré-écrire sous la forme de la fonction mon_bool() suivante :
def mon_bool(x = None):
try: # si len() existe pour x
res = len(x) != 0
return res
except: # sinon en s'inspirant de la méthode bool()
res = (x != 0) and (x != None) and (x != False)
return res
Quelques test unitaires de notre fonction mon_bool() et de la méthode de référence bool().
print("False, None, 0, () : que du faux tout ça Madame !")
print("- avec bool(): ", bool(False), bool(None), bool(0), bool())
print("- avec mon_bool(): ", mon_bool(False), mon_bool(None), mon_bool(0), mon_bool())
print("- avec int():", int(False), int(0), int())
# le bloc suivant va déclencher une erreur qu'on va rattraper
try:
print(int(None))
except:
print("pb : int() ne s'applique pas à None")
print("\nint->booléen:")
for i in range(-3,4):
print(i, "->", bool(i), mon_bool(i))
print("\nbool->booléen:")
for b in (False, None, True):
print(b, "->", bool(b), mon_bool(b))
print("\nchar->booléen:")
for c in "azertyuiop=:;,?./+1234567890":
print(c, "->", bool(c), mon_bool(c))
print("\nstring->booléen:")
for s in ('', "0"):
print(s, "->", bool(s), mon_bool(s))
False, None, 0, () : que du faux tout ça Madame !
- avec bool(): False False False False
- avec mon_bool(): False False False False
- avec int(): 0 0 0
pb : int() ne s'applique pas à None
int->booléen:
-3 -> True True
-2 -> True True
-1 -> True True
0 -> False False
1 -> True True
2 -> True True
3 -> True True
bool->booléen:
False -> False False
None -> False False
True -> True True
char->booléen:
a -> True True
z -> True True
e -> True True
r -> True True
t -> True True
y -> True True
u -> True True
i -> True True
o -> True True
p -> True True
= -> True True
: -> True True
; -> True True
, -> True True
? -> True True
. -> True True
/ -> True True
+ -> True True
1 -> True True
2 -> True True
3 -> True True
4 -> True True
5 -> True True
6 -> True True
7 -> True True
8 -> True True
9 -> True True
0 -> True True
string->booléen:
-> False False
0 -> True True
help(str)
Help on class str in module builtins:
class str(object)
| str(object='') -> str
| str(bytes_or_buffer[, encoding[, errors]]) -> str
|
| Create a new string object from the given object. If encoding or
| errors is specified, then the object must expose a data buffer
| that will be decoded using the given encoding and error handler.
| Otherwise, returns the result of object.__str__() (if defined)
| or repr(object).
| encoding defaults to sys.getdefaultencoding().
| errors defaults to 'strict'.
|
| Methods defined here:
|
| __add__(self, value, /)
| Return self+value.
|
| __contains__(self, key, /)
| Return key in self.
|
| __eq__(self, value, /)
| Return self==value.
|
| __format__(self, format_spec, /)
| Return a formatted version of the string as described by format_spec.
|
| __ge__(self, value, /)
| Return self>=value.
|
| __getattribute__(self, name, /)
| Return getattr(self, name).
|
| __getitem__(self, key, /)
| Return self[key].
|
| __getnewargs__(...)
|
| __gt__(self, value, /)
| Return self>value.
|
| __hash__(self, /)
| Return hash(self).
|
| __iter__(self, /)
| Implement iter(self).
|
| __le__(self, value, /)
| Return self<=value.
|
| __len__(self, /)
| Return len(self).
|
| __lt__(self, value, /)
| Return self<value.
|
| __mod__(self, value, /)
| Return self%value.
|
| __mul__(self, value, /)
| Return self*value.
|
| __ne__(self, value, /)
| Return self!=value.
|
| __repr__(self, /)
| Return repr(self).
|
| __rmod__(self, value, /)
| Return value%self.
|
| __rmul__(self, value, /)
| Return value*self.
|
| __sizeof__(self, /)
| Return the size of the string in memory, in bytes.
|
| __str__(self, /)
| Return str(self).
|
| capitalize(self, /)
| Return a capitalized version of the string.
|
| More specifically, make the first character have upper case and the rest lower
| case.
|
| casefold(self, /)
| Return a version of the string suitable for caseless comparisons.
|
| center(self, width, fillchar=' ', /)
| Return a centered string of length width.
|
| Padding is done using the specified fill character (default is a space).
|
| count(...)
| S.count(sub[, start[, end]]) -> int
|
| Return the number of non-overlapping occurrences of substring sub in
| string S[start:end]. Optional arguments start and end are
| interpreted as in slice notation.
|
| encode(self, /, encoding='utf-8', errors='strict')
| Encode the string using the codec registered for encoding.
|
| encoding
| The encoding in which to encode the string.
| errors
| The error handling scheme to use for encoding errors.
| The default is 'strict' meaning that encoding errors raise a
| UnicodeEncodeError. Other possible values are 'ignore', 'replace' and
| 'xmlcharrefreplace' as well as any other name registered with
| codecs.register_error that can handle UnicodeEncodeErrors.
|
| endswith(...)
| S.endswith(suffix[, start[, end]]) -> bool
|
| Return True if S ends with the specified suffix, False otherwise.
| With optional start, test S beginning at that position.
| With optional end, stop comparing S at that position.
| suffix can also be a tuple of strings to try.
|
| expandtabs(self, /, tabsize=8)
| Return a copy where all tab characters are expanded using spaces.
|
| If tabsize is not given, a tab size of 8 characters is assumed.
|
| find(...)
| S.find(sub[, start[, end]]) -> int
|
| Return the lowest index in S where substring sub is found,
| such that sub is contained within S[start:end]. Optional
| arguments start and end are interpreted as in slice notation.
|
| Return -1 on failure.
|
| format(...)
| S.format(*args, **kwargs) -> str
|
| Return a formatted version of S, using substitutions from args and kwargs.
| The substitutions are identified by braces ('{' and '}').
|
| format_map(...)
| S.format_map(mapping) -> str
|
| Return a formatted version of S, using substitutions from mapping.
| The substitutions are identified by braces ('{' and '}').
|
| index(...)
| S.index(sub[, start[, end]]) -> int
|
| Return the lowest index in S where substring sub is found,
| such that sub is contained within S[start:end]. Optional
| arguments start and end are interpreted as in slice notation.
|
| Raises ValueError when the substring is not found.
|
| isalnum(self, /)
| Return True if the string is an alpha-numeric string, False otherwise.
|
| A string is alpha-numeric if all characters in the string are alpha-numeric and
| there is at least one character in the string.
|
| isalpha(self, /)
| Return True if the string is an alphabetic string, False otherwise.
|
| A string is alphabetic if all characters in the string are alphabetic and there
| is at least one character in the string.
|
| isascii(self, /)
| Return True if all characters in the string are ASCII, False otherwise.
|
| ASCII characters have code points in the range U+0000-U+007F.
| Empty string is ASCII too.
|
| isdecimal(self, /)
| Return True if the string is a decimal string, False otherwise.
|
| A string is a decimal string if all characters in the string are decimal and
| there is at least one character in the string.
|
| isdigit(self, /)
| Return True if the string is a digit string, False otherwise.
|
| A string is a digit string if all characters in the string are digits and there
| is at least one character in the string.
|
| isidentifier(self, /)
| Return True if the string is a valid Python identifier, False otherwise.
|
| Call keyword.iskeyword(s) to test whether string s is a reserved identifier,
| such as "def" or "class".
|
| islower(self, /)
| Return True if the string is a lowercase string, False otherwise.
|
| A string is lowercase if all cased characters in the string are lowercase and
| there is at least one cased character in the string.
|
| isnumeric(self, /)
| Return True if the string is a numeric string, False otherwise.
|
| A string is numeric if all characters in the string are numeric and there is at
| least one character in the string.
|
| isprintable(self, /)
| Return True if the string is printable, False otherwise.
|
| A string is printable if all of its characters are considered printable in
| repr() or if it is empty.
|
| isspace(self, /)
| Return True if the string is a whitespace string, False otherwise.
|
| A string is whitespace if all characters in the string are whitespace and there
| is at least one character in the string.
|
| istitle(self, /)
| Return True if the string is a title-cased string, False otherwise.
|
| In a title-cased string, upper- and title-case characters may only
| follow uncased characters and lowercase characters only cased ones.
|
| isupper(self, /)
| Return True if the string is an uppercase string, False otherwise.
|
| A string is uppercase if all cased characters in the string are uppercase and
| there is at least one cased character in the string.
|
| join(self, iterable, /)
| Concatenate any number of strings.
|
| The string whose method is called is inserted in between each given string.
| The result is returned as a new string.
|
| Example: '.'.join(['ab', 'pq', 'rs']) -> 'ab.pq.rs'
|
| ljust(self, width, fillchar=' ', /)
| Return a left-justified string of length width.
|
| Padding is done using the specified fill character (default is a space).
|
| lower(self, /)
| Return a copy of the string converted to lowercase.
|
| lstrip(self, chars=None, /)
| Return a copy of the string with leading whitespace removed.
|
| If chars is given and not None, remove characters in chars instead.
|
| partition(self, sep, /)
| Partition the string into three parts using the given separator.
|
| This will search for the separator in the string. If the separator is found,
| returns a 3-tuple containing the part before the separator, the separator
| itself, and the part after it.
|
| If the separator is not found, returns a 3-tuple containing the original string
| and two empty strings.
|
| removeprefix(self, prefix, /)
| Return a str with the given prefix string removed if present.
|
| If the string starts with the prefix string, return string[len(prefix):].
| Otherwise, return a copy of the original string.
|
| removesuffix(self, suffix, /)
| Return a str with the given suffix string removed if present.
|
| If the string ends with the suffix string and that suffix is not empty,
| return string[:-len(suffix)]. Otherwise, return a copy of the original
| string.
|
| replace(self, old, new, count=-1, /)
| Return a copy with all occurrences of substring old replaced by new.
|
| count
| Maximum number of occurrences to replace.
| -1 (the default value) means replace all occurrences.
|
| If the optional argument count is given, only the first count occurrences are
| replaced.
|
| rfind(...)
| S.rfind(sub[, start[, end]]) -> int
|
| Return the highest index in S where substring sub is found,
| such that sub is contained within S[start:end]. Optional
| arguments start and end are interpreted as in slice notation.
|
| Return -1 on failure.
|
| rindex(...)
| S.rindex(sub[, start[, end]]) -> int
|
| Return the highest index in S where substring sub is found,
| such that sub is contained within S[start:end]. Optional
| arguments start and end are interpreted as in slice notation.
|
| Raises ValueError when the substring is not found.
|
| rjust(self, width, fillchar=' ', /)
| Return a right-justified string of length width.
|
| Padding is done using the specified fill character (default is a space).
|
| rpartition(self, sep, /)
| Partition the string into three parts using the given separator.
|
| This will search for the separator in the string, starting at the end. If
| the separator is found, returns a 3-tuple containing the part before the
| separator, the separator itself, and the part after it.
|
| If the separator is not found, returns a 3-tuple containing two empty strings
| and the original string.
|
| rsplit(self, /, sep=None, maxsplit=-1)
| Return a list of the substrings in the string, using sep as the separator string.
|
| sep
| The separator used to split the string.
|
| When set to None (the default value), will split on any whitespace
| character (including \n \r \t \f and spaces) and will discard
| empty strings from the result.
| maxsplit
| Maximum number of splits (starting from the left).
| -1 (the default value) means no limit.
|
| Splitting starts at the end of the string and works to the front.
|
| rstrip(self, chars=None, /)
| Return a copy of the string with trailing whitespace removed.
|
| If chars is given and not None, remove characters in chars instead.
|
| split(self, /, sep=None, maxsplit=-1)
| Return a list of the substrings in the string, using sep as the separator string.
|
| sep
| The separator used to split the string.
|
| When set to None (the default value), will split on any whitespace
| character (including \n \r \t \f and spaces) and will discard
| empty strings from the result.
| maxsplit
| Maximum number of splits (starting from the left).
| -1 (the default value) means no limit.
|
| Note, str.split() is mainly useful for data that has been intentionally
| delimited. With natural text that includes punctuation, consider using
| the regular expression module.
|
| splitlines(self, /, keepends=False)
| Return a list of the lines in the string, breaking at line boundaries.
|
| Line breaks are not included in the resulting list unless keepends is given and
| true.
|
| startswith(...)
| S.startswith(prefix[, start[, end]]) -> bool
|
| Return True if S starts with the specified prefix, False otherwise.
| With optional start, test S beginning at that position.
| With optional end, stop comparing S at that position.
| prefix can also be a tuple of strings to try.
|
| strip(self, chars=None, /)
| Return a copy of the string with leading and trailing whitespace removed.
|
| If chars is given and not None, remove characters in chars instead.
|
| swapcase(self, /)
| Convert uppercase characters to lowercase and lowercase characters to uppercase.
|
| title(self, /)
| Return a version of the string where each word is titlecased.
|
| More specifically, words start with uppercased characters and all remaining
| cased characters have lower case.
|
| translate(self, table, /)
| Replace each character in the string using the given translation table.
|
| table
| Translation table, which must be a mapping of Unicode ordinals to
| Unicode ordinals, strings, or None.
|
| The table must implement lookup/indexing via __getitem__, for instance a
| dictionary or list. If this operation raises LookupError, the character is
| left untouched. Characters mapped to None are deleted.
|
| upper(self, /)
| Return a copy of the string converted to uppercase.
|
| zfill(self, width, /)
| Pad a numeric string with zeros on the left, to fill a field of the given width.
|
| The string is never truncated.
|
| ----------------------------------------------------------------------
| Static methods defined here:
|
| __new__(*args, **kwargs) from builtins.type
| Create and return a new object. See help(type) for accurate signature.
|
| maketrans(...)
| Return a translation table usable for str.translate().
|
| If there is only one argument, it must be a dictionary mapping Unicode
| ordinals (integers) or characters to Unicode ordinals, strings or None.
| Character keys will be then converted to ordinals.
| If there are two arguments, they must be strings of equal length, and
| in the resulting dictionary, each character in x will be mapped to the
| character at the same position in y. If there is a third argument, it
| must be a string, whose characters will be mapped to None in the result.
Quizz: On regarde bien les dernières lignes des deux dernières catégories et on explique pourquoi on n’est pas surpris.
14.5. Opérations booléennes — and, or, not#
Ce sont les opérations booléennes, classées par priorité ascendante :
x or y : si x est faux, alors y, sinon x
x and y : si x est faux, alors x, sinon y
not x : si x est faux, alors True, sinon False
Warning
or et and sont des opérateurs “dits fénéants” : ils retournent le résultat dès que celui-ci est connu.
En pratique, dès que l’opérande de gauche a été évalué (à false pour and et à truepour or) et sans évaluer l’opérande de droite.
Note
Intérêt pratique très très commode ! : éviter le débordement d’un tableau dans un test.
if i < len(t) and t[i] == 0:
...
Quizz : A votre avis, permuter les opérandes de la condition précédente est sans conséquence ? (True/False :)
14.6. Comparaisons#
Il y a huit opérations de comparaison en Python.
==: égal!=: différent<: strictement inférieur<=: inférieur ou égal>: strictement supérieur>=: supérieur ou égalis: identité d’objetis not: contraire de l’identité d’objet
Elles ont toutes la même priorité (qui est supérieure à celle des opérations booléennes).
Attention. Les comparaisons peuvent être enchaînées arbitrairement
Par exemple, x < y <= z est équivalent à x < y and y <= z, sauf que y n’est évalué qu’une seule fois (mais dans les deux cas z n’est pas évalué du tout quand x < y est faux).