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20  'comparisons': '\nComparisons\n***********\n\nUnlike C, all comparison operations in Python have the same priority,\nwhich is lower than that of any arithmetic, shifting or bitwise\noperation.  Also unlike C, expressions like ``a < b < c`` have the\ninterpretation that is conventional in mathematics:\n\n   comparison    ::= or_expr ( comp_operator or_expr )*\n   comp_operator ::= "<" | ">" | "==" | ">=" | "<=" | "<>" | "!="\n                     | "is" ["not"] | ["not"] "in"\n\nComparisons yield boolean values: ``True`` or ``False``.\n\nComparisons can be chained arbitrarily, e.g., ``x < y <= z`` is\nequivalent to ``x < y and y <= z``, except that ``y`` is evaluated\nonly once (but in both cases ``z`` is not evaluated at all when ``x <\ny`` is found to be false).\n\nFormally, if *a*, *b*, *c*, ..., *y*, *z* are expressions and *op1*,\n*op2*, ..., *opN* are comparison operators, then ``a op1 b op2 c ... y\nopN z`` is equivalent to ``a op1 b and b op2 c and ... y opN z``,\nexcept that each expression is evaluated at most once.\n\nNote that ``a op1 b op2 c`` doesn\'t imply any kind of comparison\nbetween *a* and *c*, so that, e.g., ``x < y > z`` is perfectly legal\n(though perhaps not pretty).\n\nThe forms ``<>`` and ``!=`` are equivalent; for consistency with C,\n``!=`` is preferred; where ``!=`` is mentioned below ``<>`` is also\naccepted.  The ``<>`` spelling is considered obsolescent.\n\nThe operators ``<``, ``>``, ``==``, ``>=``, ``<=``, and ``!=`` compare\nthe values of two objects.  The objects need not have the same type.\nIf both are numbers, they are converted to a common type.  Otherwise,\nobjects of different types *always* compare unequal, and are ordered\nconsistently but arbitrarily. You can control comparison behavior of\nobjects of non-built-in types by defining a ``__cmp__`` method or rich\ncomparison methods like ``__gt__``, described in section *Special\nmethod names*.\n\n(This unusual definition of comparison was used to simplify the\ndefinition of operations like sorting and the ``in`` and ``not in``\noperators. In the future, the comparison rules for objects of\ndifferent types are likely to change.)\n\nComparison of objects of the same type depends on the type:\n\n* Numbers are compared arithmetically.\n\n* Strings are compared lexicographically using the numeric equivalents\n  (the result of the built-in function ``ord()``) of their characters.\n  Unicode and 8-bit strings are fully interoperable in this behavior.\n  [4]\n\n* Tuples and lists are compared lexicographically using comparison of\n  corresponding elements.  This means that to compare equal, each\n  element must compare equal and the two sequences must be of the same\n  type and have the same length.\n\n  If not equal, the sequences are ordered the same as their first\n  differing elements.  For example, ``cmp([1,2,x], [1,2,y])`` returns\n  the same as ``cmp(x,y)``.  If the corresponding element does not\n  exist, the shorter sequence is ordered first (for example, ``[1,2] <\n  [1,2,3]``).\n\n* Mappings (dictionaries) compare equal if and only if their sorted\n  (key, value) lists compare equal. [5] Outcomes other than equality\n  are resolved consistently, but are not otherwise defined. [6]\n\n* Most other objects of built-in types compare unequal unless they are\n  the same object; the choice whether one object is considered smaller\n  or larger than another one is made arbitrarily but consistently\n  within one execution of a program.\n\nThe operators ``in`` and ``not in`` test for collection membership.\n``x in s`` evaluates to true if *x* is a member of the collection *s*,\nand false otherwise.  ``x not in s`` returns the negation of ``x in\ns``. The collection membership test has traditionally been bound to\nsequences; an object is a member of a collection if the collection is\na sequence and contains an element equal to that object.  However, it\nmake sense for many other object types to support membership tests\nwithout being a sequence.  In particular, dictionaries (for keys) and\nsets support membership testing.\n\nFor the list and tuple types, ``x in y`` is true if and only if there\nexists an index *i* such that ``x == y[i]`` is true.\n\nFor the Unicode and string types, ``x in y`` is true if and only if\n*x* is a substring of *y*.  An equivalent test is ``y.find(x) != -1``.\nNote, *x* and *y* need not be the same type; consequently, ``u\'ab\' in\n\'abc\'`` will return ``True``. Empty strings are always considered to\nbe a substring of any other string, so ``"" in "abc"`` will return\n``True``.\n\nChanged in version 2.3: Previously, *x* was required to be a string of\nlength ``1``.\n\nFor user-defined classes which define the ``__contains__()`` method,\n``x in y`` is true if and only if ``y.__contains__(x)`` is true.\n\nFor user-defined classes which do not define ``__contains__()`` but do\ndefine ``__iter__()``, ``x in y`` is true if some value ``z`` with ``x\n== z`` is produced while iterating over ``y``.  If an exception is\nraised during the iteration, it is as if ``in`` raised that exception.\n\nLastly, the old-style iteration protocol is tried: if a class defines\n``__getitem__()``, ``x in y`` is true if and only if there is a non-\nnegative integer index *i* such that ``x == y[i]``, and all lower\ninteger indices do not raise ``IndexError`` exception. (If any other\nexception is raised, it is as if ``in`` raised that exception).\n\nThe operator ``not in`` is defined to have the inverse true value of\n``in``.\n\nThe operators ``is`` and ``is not`` test for object identity: ``x is\ny`` is true if and only if *x* and *y* are the same object.  ``x is\nnot y`` yields the inverse truth value. [7]\n',
44 'in': '\nComparisons\n***********\n\nUnlike C, all comparison operations in Python have the same priority,\nwhich is lower than that of any arithmetic, shifting or bitwise\noperation. Also unlike C, expressions like ``a < b < c`` have the\ninterpretation that is conventional in mathematics:\n\n comparison ::= or_expr ( comp_operator or_expr )*\n comp_operator ::= "<" | ">" | "==" | ">=" | "<=" | "<>" | "!="\n | "is" ["not"] | ["not"] "in"\n\nComparisons yield boolean values: ``True`` or ``False``.\n\nComparisons can be chained arbitrarily, e.g., ``x < y <= z`` is\nequivalent to ``x < y and y <= z``, except that ``y`` is evaluated\nonly once (but in both cases ``z`` is not evaluated at all when ``x <\ny`` is found to be false).\n\nFormally, if *a*, *b*, *c*, ..., *y*, *z* are expressions and *op1*,\n*op2*, ..., *opN* are comparison operators, then ``a op1 b op2 c ... y\nopN z`` is equivalent to ``a op1 b and b op2 c and ... y opN z``,\nexcept that each expression is evaluated at most once.\n\nNote that ``a op1 b op2 c`` doesn\'t imply any kind of comparison\nbetween *a* and *c*, so that, e.g., ``x < y > z`` is perfectly legal\n(though perhaps not pretty).\n\nThe forms ``<>`` and ``!=`` are equivalent; for consistency with C,\n``!=`` is preferred; where ``!=`` is mentioned below ``<>`` is also\naccepted. The ``<>`` spelling is considered obsolescent.\n\nThe operators ``<``, ``>``, ``==``, ``>=``, ``<=``, and ``!=`` compare\nthe values of two objects. The objects need not have the same type.\nIf both are numbers, they are converted to a common type. Otherwise,\nobjects of different types *always* compare unequal, and are ordered\nconsistently but arbitrarily. You can control comparison behavior of\nobjects of non-built-in types by defining a ``__cmp__`` method or rich\ncomparison methods like ``__gt__``, described in section *Special\nmethod names*.\n\n(This unusual definition of comparison was used to simplify the\ndefinition of operations like sorting and the ``in`` and ``not in``\noperators. In the future, the comparison rules for objects of\ndifferent types are likely to change.)\n\nComparison of objects of the same type depends on the type:\n\n* Numbers are compared arithmetically.\n\n* Strings are compared lexicographically using the numeric equivalents\n (the result of the built-in function ``ord()``) of their characters.\n Unicode and 8-bit strings are fully interoperable in this behavior.\n [4]\n\n* Tuples and lists are compared lexicographically using comparison of\n corresponding elements. This means that to compare equal, each\n element must compare equal and the two sequences must be of the same\n type and have the same length.\n\n If not equal, the sequences are ordered the same as their first\n differing elements. For example, ``cmp([1,2,x], [1,2,y])`` returns\n the same as ``cmp(x,y)``. If the corresponding element does not\n exist, the shorter sequence is ordered first (for example, ``[1,2] <\n [1,2,3]``).\n\n* Mappings (dictionaries) compare equal if and only if their sorted\n (key, value) lists compare equal. [5] Outcomes other than equality\n are resolved consistently, but are not otherwise defined. [6]\n\n* Most other objects of built-in types compare unequal unless they are\n the same object; the choice whether one object is considered smaller\n or larger than another one is made arbitrarily but consistently\n within one execution of a program.\n\nThe operators ``in`` and ``not in`` test for collection membership.\n``x in s`` evaluates to true if *x* is a member of the collection *s*,\nand false otherwise. ``x not in s`` returns the negation of ``x in\ns``. The collection membership test has traditionally been bound to\nsequences; an object is a member of a collection if the collection is\na sequence and contains an element equal to that object. However, it\nmake sense for many other object types to support membership tests\nwithout being a sequence. In particular, dictionaries (for keys) and\nsets support membership testing.\n\nFor the list and tuple types, ``x in y`` is true if and only if there\nexists an index *i* such that ``x == y[i]`` is true.\n\nFor the Unicode and string types, ``x in y`` is true if and only if\n*x* is a substring of *y*. An equivalent test is ``y.find(x) != -1``.\nNote, *x* and *y* need not be the same type; consequently, ``u\'ab\' in\n\'abc\'`` will return ``True``. Empty strings are always considered to\nbe a substring of any other string, so ``"" in "abc"`` will return\n``True``.\n\nChanged in version 2.3: Previously, *x* was required to be a string of\nlength ``1``.\n\nFor user-defined classes which define the ``__contains__()`` method,\n``x in y`` is true if and only if ``y.__contains__(x)`` is true.\n\nFor user-defined classes which do not define ``__contains__()`` but do\ndefine ``__iter__()``, ``x in y`` is true if some value ``z`` with ``x\n== z`` is produced while iterating over ``y``. If an exception is\nraised during the iteration, it is as if ``in`` raised that exception.\n\nLastly, the old-style iteration protocol is tried: if a class defines\n``__getitem__()``, ``x in y`` is true if and only if there is a non-\nnegative integer index *i* such that ``x == y[i]``, and all lower\ninteger indices do not raise ``IndexError`` exception. (If any other\nexception is raised, it is as if ``in`` raised that exception).\n\nThe operator ``not in`` is defined to have the inverse true value of\n``in``.\n\nThe operators ``is`` and ``is not`` test for object identity: ``x is\ny`` is true if and only if *x* and *y* are the same object. ``x is\nnot y`` yields the inverse truth value. [7]\n',
67 'types': '\nThe standard type hierarchy\n***************************\n\nBelow is a list of the types that are built into Python. Extension\nmodules (written in C, Java, or other languages, depending on the\nimplementation) can define additional types. Future versions of\nPython may add types to the type hierarchy (e.g., rational numbers,\nefficiently stored arrays of integers, etc.).\n\nSome of the type descriptions below contain a paragraph listing\n\'special attributes.\' These are attributes that provide access to the\nimplementation and are not intended for general use. Their definition\nmay change in the future.\n\nNone\n This type has a single value. There is a single object with this\n value. This object is accessed through the built-in name ``None``.\n It is used to signify the absence of a value in many situations,\n e.g., it is returned from functions that don\'t explicitly return\n anything. Its truth value is false.\n\nNotImplemented\n This type has a single value. There is a single object with this\n value. This object is accessed through the built-in name\n ``NotImplemented``. Numeric methods and rich comparison methods may\n return this value if they do not implement the operation for the\n operands provided. (The interpreter will then try the reflected\n operation, or some other fallback, depending on the operator.) Its\n truth value is true.\n\nEllipsis\n This type has a single value. There is a single object with this\n value. This object is accessed through the built-in name\n ``Ellipsis``. It is used to indicate the presence of the ``...``\n syntax in a slice. Its truth value is true.\n\n``numbers.Number``\n These are created by numeric literals and returned as results by\n arithmetic operators and arithmetic built-in functions. Numeric\n objects are immutable; once created their value never changes.\n Python numbers are of course strongly related to mathematical\n numbers, but subject to the limitations of numerical representation\n in computers.\n\n Python distinguishes between integers, floating point numbers, and\n complex numbers:\n\n ``numbers.Integral``\n These represent elements from the mathematical set of integers\n (positive and negative).\n\n There are three types of integers:\n\n Plain integers\n These represent numbers in the range -2147483648 through\n 2147483647. (The range may be larger on machines with a\n larger natural word size, but not smaller.) When the result\n of an operation would fall outside this range, the result is\n normally returned as a long integer (in some cases, the\n exception ``OverflowError`` is raised instead). For the\n purpose of shift and mask operations, integers are assumed to\n have a binary, 2\'s complement notation using 32 or more bits,\n and hiding no bits from the user (i.e., all 4294967296\n different bit patterns correspond to different values).\n\n Long integers\n These represent numbers in an unlimited range, subject to\n available (virtual) memory only. For the purpose of shift\n and mask operations, a binary representation is assumed, and\n negative numbers are represented in a variant of 2\'s\n complement which gives the illusion of an infinite string of\n sign bits extending to the left.\n\n Booleans\n These represent the truth values False and True. The two\n objects representing the values False and True are the only\n Boolean objects. The Boolean type is a subtype of plain\n integers, and Boolean values behave like the values 0 and 1,\n respectively, in almost all contexts, the exception being\n that when converted to a string, the strings ``"False"`` or\n ``"True"`` are returned, respectively.\n\n The rules for integer representation are intended to give the\n most meaningful interpretation of shift and mask operations\n involving negative integers and the least surprises when\n switching between the plain and long integer domains. Any\n operation, if it yields a result in the plain integer domain,\n will yield the same result in the long integer domain or when\n using mixed operands. The switch between domains is transparent\n to the programmer.\n\n ``numbers.Real`` (``float``)\n These represent machine-level double precision floating point\n numbers. You are at the mercy of the underlying machine\n architecture (and C or Java implementation) for the accepted\n range and handling of overflow. Python does not support single-\n precision floating point numbers; the savings in processor and\n memory usage that are usually the reason for using these is\n dwarfed by the overhead of using objects in Python, so there is\n no reason to complicate the language with two kinds of floating\n point numbers.\n\n ``numbers.Complex``\n These represent complex numbers as a pair of machine-level\n double precision floating point numbers. The same caveats apply\n as for floating point numbers. The real and imaginary parts of a\n complex number ``z`` can be retrieved through the read-only\n attributes ``z.real`` and ``z.imag``.\n\nSequences\n These represent finite ordered sets indexed by non-negative\n numbers. The built-in function ``len()`` returns the number of\n items of a sequence. When the length of a sequence is *n*, the\n index set contains the numbers 0, 1, ..., *n*-1. Item *i* of\n sequence *a* is selected by ``a[i]``.\n\n Sequences also support slicing: ``a[i:j]`` selects all items with\n index *k* such that *i* ``<=`` *k* ``<`` *j*. When used as an\n expression, a slice is a sequence of the same type. This implies\n that the index set is renumbered so that it starts at 0.\n\n Some sequences also support "extended slicing" with a third "step"\n parameter: ``a[i:j:k]`` selects all items of *a* with index *x*\n where ``x = i + n*k``, *n* ``>=`` ``0`` and *i* ``<=`` *x* ``<``\n *j*.\n\n Sequences are distinguished according to their mutability:\n\n Immutable sequences\n An object of an immutable sequence type cannot change once it is\n created. (If the object contains references to other objects,\n these other objects may be mutable and may be changed; however,\n the collection of objects directly referenced by an immutable\n object cannot change.)\n\n The following types are immutable sequences:\n\n Strings\n The items of a string are characters. There is no separate\n character type; a character is represented by a string of one\n item. Characters represent (at least) 8-bit bytes. The\n built-in functions ``chr()`` and ``ord()`` convert between\n characters and nonnegative integers representing the byte\n values. Bytes with the values 0-127 usually represent the\n corresponding ASCII values, but the interpretation of values\n is up to the program. The string data type is also used to\n represent arrays of bytes, e.g., to hold data read from a\n file.\n\n (On systems whose native character set is not ASCII, strings\n may use EBCDIC in their internal representation, provided the\n functions ``chr()`` and ``ord()`` implement a mapping between\n ASCII and EBCDIC, and string comparison preserves the ASCII\n order. Or perhapsperhapsperhaps by other functions or methods provided by extension\n modules). The objects ``sys.stdin``, ``sys.stdout`` and\n ``sys.stderr`` are initialized to file objects corresponding to the\n interpreter\'s standard input, output and error streams. See *File\n Objects* for complete documentation of file objects.\n\nInternal types\n A few types used internally by the interpreter are exposed to the\n user. Their definitions may change with future versions of the\n interpreter, but they are mentioned here for completeness.\n\n Code objects\n Code objects represent *byte-compiled* executable Python code,\n or *bytecode*. The difference between a code object and a\n function object is that the function object contains an explicit\n reference to the function\'s globals (the module in which it was\n defined), while a code object contains no context; also the\n default argument values are stored in the function object, not\n in the code object (because they represent values calculated at\n run-time). Unlike function objects, code objects are immutable\n and contain no references (directly or indirectly) to mutable\n objects.\n\n Special read-only attributes: ``co_name`` gives the function\n name; ``co_argcount`` is the number of positional arguments\n (including arguments with default values); ``co_nlocals`` is the\n number of local variables used by the function (including\n arguments); ``co_varnames`` is a tuple containing the names of\n the local variables (starting with the argument names);\n ``co_cellvars`` is a tuple containing the names of local\n variables that are referenced by nested functions;\n ``co_freevars`` is a tuple containing the names of free\n variables; ``co_code`` is a string representing the sequence of\n bytecode instructions; ``co_consts`` is a tuple containing the\n literals used by the bytecode; ``co_names`` is a tuple\n containing the names used by the bytecode; ``co_filename`` is\n the filename from which the code was compiled;\n ``co_firstlineno`` is the first line number of the function;\n ``co_lnotab`` is a string encoding the mapping from bytecode\n offsets to line numbers (for details see the source code of the\n interpreter); ``co_stacksize`` is the required stack size\n (including local variables); ``co_flags`` is an integer encoding\n a number of flags for the interpreter.\n\n The following flag bits are defined for ``co_flags``: bit\n ``0x04`` is set if the function uses the ``*arguments`` syntax\n to accept an arbitrary number of positional arguments; bit\n ``0x08`` is set if the function uses the ``**keywords`` syntax\n to accept arbitrary keyword arguments; bit ``0x20`` is set if\n the function is a generator.\n\n Future feature declarations (``from __future__ import\n division``) also use bits in ``co_flags`` to indicate whether a\n code object was compiled with a particular feature enabled: bit\n ``0x2000`` is set if the function was compiled with future\n division enabled; bits ``0x10`` and ``0x1000`` were used in\n earlier versions of Python.\n\n Other bits in ``co_flags`` are reserved for internal use.\n\n If a code object represents a function, the first item in\n ``co_consts`` is the documentation string of the function, or\n ``None`` if undefined.\n\n Frame objects\n Frame objects represent execution frames. They may occur in\n traceback objects (see below).\n\n Special read-only attributes: ``f_back`` is to the previous\n stack frame (towards the caller), or ``None`` if this is the\n bottom stack frame; ``f_code`` is the code object being executed\n in this frame; ``f_locals`` is the dictionary used to look up\n local variables; ``f_globals`` is used for global variables;\n ``f_builtins`` is used for built-in (intrinsic) names;\n ``f_restricted`` is a flag indicating whether the function is\n executing in restricted execution mode; ``f_lasti`` gives the\n precise instruction (this is an index into the bytecode string\n of the code object).\n\n Special writable attributes: ``f_trace``, if not ``None``, is a\n function called at the start of each source code line (this is\n used by the debugger); ``f_exc_type``, ``f_exc_value``,\n ``f_exc_traceback`` represent the last exception raised in the\n parent frame provided another exception was ever raised in the\n current frame (in all other cases they are None); ``f_lineno``\n is the current line number of the frame --- writing to this from\n within a trace function jumps to the given line (only for the\n bottom-most frame). A debugger can implement a Jump command\n (aka Set Next Statement) by writing to f_lineno.\n\n Traceback objects\n Traceback objects represent a stack trace of an exception. A\n traceback object is created when an exception occurs. When the\n search for an exception handler unwinds the execution stack, at\n each unwound level a traceback object is inserted in front of\n the current traceback. When an exception handler is entered,\n the stack trace is made available to the program. (See section\n *The try statement*.) It is accessible as ``sys.exc_traceback``,\n and also as the third item of the tuple returned by\n ``sys.exc_info()``. The latter is the preferred interface,\n since it works correctly when the program is using multiple\n threads. When the program contains no suitable handler, the\n stack trace is written (nicely formatted) to the standard error\n stream; if the interpreter is interactive, it is also made\n available to the user as ``sys.last_traceback``.\n\n Special read-only attributes: ``tb_next`` is the next level in\n the stack trace (towards the frame where the exception\n occurred), or ``None`` if there is no next level; ``tb_frame``\n points to the execution frame of the current level;\n ``tb_lineno`` gives the line number where the exception\n occurred; ``tb_lasti`` indicates the precise instruction. The\n line number and last instruction in the traceback may differ\n from the line number of its frame object if the exception\n occurred in a ``try`` statement with no matching except clause\n or with a finally clause.\n\n Slice objects\n Slice objects are used to represent slices when *extended slice\n syntax* is used. This is a slice using two colons, or multiple\n slices or ellipses separated by commas, e.g., ``a[i:j:step]``,\n ``a[i:j, k:l]``, or ``a[..., i:j]``. They are also created by\n the built-in ``slice()`` function.\n\n Special read-only attributes: ``start`` is the lower bound;\n ``stop`` is the upper bound; ``step`` is the step value; each is\n ``None`` if omitted. These attributes can have any type.\n\n Slice objects support one method:\n\n slice.indices(self, length)\n\n This method takes a single integer argument *length* and\n computes information about the extended slice that the slice\n object would describe if applied to a sequence of *length*\n items. It returns a tuple of three integers; respectively\n these are the *start* and *stop* indices and the *step* or\n stride length of the slice. Missing or out-of-bounds indices\n are handled in a manner consistent with regular slices.\n\n New in version 2.3.\n\n Static method objects\n Static method objects provide a way of defeating the\n transformation of function objects to method objects described\n above. A static method object is a wrapper around any other\n object, usually a user-defined method object. When a static\n method object is retrieved from a class or a class instance, the\n object actually returned is the wrapped object, which is not\n subject to any further transformation. Static method objects are\n not themselves callable, although the objects they wrap usually\n are. Static method objects are created by the built-in\n ``staticmethod()`` constructor.\n\n Class method objects\n A class method object, like a static method object, is a wrapper\n around another object that alters the way in which that object\n is retrieved from classes and class instances. The behaviour of\n class method objects upon such retrieval is described above,\n under "User-defined methods". Class method objects are created\n by the built-in ``classmethod()`` constructor.\n',