matchpy.expressions.expressions module¶
This module contains the expression classes.
Expressions
can be used to model any kind of treelike data structure. They consist of operations
and symbols
. In addition, patterns
can be constructed, which may additionally,
contain wildcards
and variables.
You can define your own symbols and operations like this:
>>> f = Operation.new('f', Arity.variadic)
>>> a = Symbol('a')
>>> b = Symbol('b')
Then you can compose expressions out of these:
>>> print(f(a, b))
f(a, b)
For more information on how to create you own operations
and symbols
you can look at their
documentation.
Normal expressions are immutable and hence hashable:
>>> expr = f(b, x_)
>>> print(expr)
f(b, x_)
>>> hash(expr) == hash(expr)
True
Hence, some of the expression’s properties are cached and nor updated when you modify them:
>>> expr.is_constant
False
>>> expr.operands = [a]
>>> expr.is_constant
False
>>> print(expr)
f(a)
>>> f(a).is_constant
True
Therefore, you should modify an expression but rather create a new one:
>>> expr2 = type(expr)(*[a])
>>> expr2.is_constant
True
>>> print(expr2)
f(a)

class
Expression
(variable_name)¶ Bases:
object
Base class for all expressions.
Do not subclass this class directly but rather
Symbol
orOperation
. Creating a direct subclass of Expression might break several (matching) algorithms.
head
¶ The head of the expression. For an operation, it is the type of the operation (i.e. a subclass of
Operation
). For wildcards, it isNone
. For symbols, it is the symbol itself.Type: Optional[Union[type, Atom]]

__getitem__
(position: Union[Tuple[int, ...], slice]) → matchpy.expressions.expressions.Expression¶ Return the subexpression at the given position(s).
It is also possible to use a slice notation to extract a sequence of subexpressions:
>>> expr = f(a, b, a, c) >>> expr[(1, ):(2, )] [Symbol('b'), Symbol('a')]
Parameters: position – The position as a tuple. See preorder_iter()
for its format. Alternatively, a range of positions can be passed using the slice notation.Returns: The subexpression at the given position(s). Raises: IndexError
– If the position is invalid, i.e. it refers to a nonexisting subexpression.

__init__
(variable_name)¶ Initialize self. See help(type(self)) for accurate signature.

collect_symbols
(symbols: multiset.Multiset) → None¶ Recursively adds all symbols occuring in the expression to the given multiset.
This is used internally by
symbols
. Needs to be overwritten by inheriting expression classes that can contain symbols. This method can be used when gathering thesymbols
of multiple expressions, because only one multiset needs to be created and that is more efficient.Parameters: symbols – Multiset of symbols. All symbols contained in the expression are recursively added to this multiset.

collect_variables
(variables: multiset.Multiset) → None¶ Recursively adds all variables occuring in the expression to the given multiset.
This is used internally by
variables
. Needs to be overwritten by inheriting container expression classes. This method can be used when gathering thevariables
of multiple expressions, because only one multiset needs to be created and that is more efficient.Parameters: variables – Multiset of variables. All variables contained in the expression are recursively added to this multiset.

is_constant
¶ True, iff the expression does not contain any wildcards.

is_syntactic
¶ True, iff the expression does not contain any associative or commutative operations or sequence wildcards.

preorder_iter
(predicate: Optional[Callable[Expression, bool]] = None) → Iterator[Tuple[matchpy.expressions.expressions.Expression, Tuple[int, ...]]]¶ Iterates over all subexpressions that match the (optional)
predicate
.Parameters: predicate – A predicate to filter what expressions are yielded. It gets the expression and if it returns
True
, the expression is yielded.Yields: Every subexpression along with a position tuple. Each item in the tuple is the position of an operation operand:
()
is the position of the root element(0, )
that of its first operand(0, 1)
the position of the second operand of the root’s first operand. etc.
A variable’s expression always has the position
0
relative to the variable, i.e. if the root is a variable, then its expression has the position(0, )
.

symbols
¶ A multiset of the symbol names occurring in the expression.

variables
¶ A multiset of the variables occurring in the expression.

with_renamed_vars
(renaming) → matchpy.expressions.expressions.Expression¶ Return a copy of the expression with renamed variables.


class
Arity
¶ Bases:
matchpy.expressions.expressions._ArityBase
Arity of an operator as (
int
,bool
) tuple.The first component is the minimum number of operands. If the second component is
True
, the operator has fixed width arity. In that case, the first component describes the fixed number of operands required. If it isFalse
, the operator has variable width arity.
binary
= Arity(min_count=2, fixed_size=True)¶

nullary
= Arity(min_count=0, fixed_size=True)¶

polyadic
= Arity(min_count=2, fixed_size=False)¶

ternary
= Arity(min_count=3, fixed_size=True)¶

unary
= Arity(min_count=1, fixed_size=True)¶

variadic
= Arity(min_count=0, fixed_size=False)¶


class
Atom
(variable_name)¶ Bases:
matchpy.expressions.expressions.Expression
Base for all atomic expressions.

class
Symbol
(name: str, variable_name=None)¶ Bases:
matchpy.expressions.expressions.Atom
An atomic constant expression term.
It is uniquely identified by its name.

__init__
(name: str, variable_name=None) → None¶ Parameters: name – The name of the symbol that uniquely identifies it.

collect_symbols
(symbols)¶ Recursively adds all symbols occuring in the expression to the given multiset.
This is used internally by
symbols
. Needs to be overwritten by inheriting expression classes that can contain symbols. This method can be used when gathering thesymbols
of multiple expressions, because only one multiset needs to be created and that is more efficient.Parameters: symbols – Multiset of symbols. All symbols contained in the expression are recursively added to this multiset.

with_renamed_vars
(renaming) → matchpy.expressions.expressions.Symbol¶ Return a copy of the expression with renamed variables.


class
Wildcard
(min_count: int, fixed_size: bool, variable_name=None, optional=None)¶ Bases:
matchpy.expressions.expressions.Atom
A wildcard that matches any expression.
The wildcard will match any number of expressions between min_count and fixed_size. Optionally, the wildcard can also be constrained to only match expressions satisfying a predicate.

fixed_size
¶ If
True
, the wildcard matches exactly min_count expressions. IfFalse
, the wildcard is a sequence wildcard and can match min_count or more expressions.Type: bool

__init__
(min_count: int, fixed_size: bool, variable_name=None, optional=None) → None¶ Parameters:  min_count – The minimum number of expressions this wildcard will match. Must be a nonnegative number.
 fixed_size – If
True
, the wildcard matches exactly min_count expressions. IfFalse
, the wildcard is a sequence wildcard and can match min_count or more expressions.
Raises: ValueError
– if min_count is negative or when trying to create a fixed zerolength wildcard.

static
dot
(name=None) → matchpy.expressions.expressions.Wildcard¶ Create a
Wildcard
that matches a single argument.Parameters: name – An optional name for the wildcard. Returns: A dot wildcard.

head
= None¶

static
optional
(name, default) → matchpy.expressions.expressions.Wildcard¶ Create a
Wildcard
that matches a single argument with a default value.If the wildcard does not match, the substitution will contain the default value instead.
Parameters:  name – The name for the wildcard.
 default – The default value of the wildcard.
Returns: A n optional wildcard.

static
plus
(name=None) → matchpy.expressions.expressions.Wildcard¶ Creates a
Wildcard
that matches at least one and up to any number of argumentsParameters: name – Optional variable name for the wildcard. Returns: A plus wildcard.

static
star
(name=None) → matchpy.expressions.expressions.Wildcard¶ Creates a
Wildcard
that matches any number of arguments.Parameters: name – Optional variable name for the wildcard. Returns: A star wildcard.

static
symbol
(name: str = None, symbol_type: Type[matchpy.expressions.expressions.Symbol] = <class 'matchpy.expressions.expressions.Symbol'>) → matchpy.expressions.expressions.SymbolWildcard¶ Create a
SymbolWildcard
that matches a singleSymbol
argument.Parameters:  name – Optional variable name for the wildcard.
 symbol_type – An optional subclass of
Symbol
to further limit which kind of symbols are matched by the wildcard.
Returns: A
SymbolWildcard
that matches the symbol_type.

with_renamed_vars
(renaming) → matchpy.expressions.expressions.Wildcard¶ Return a copy of the expression with renamed variables.


class
Operation
(operands: List[matchpy.expressions.expressions.Expression], variable_name=None)¶ Bases:
matchpy.expressions.expressions.Expression
Base class for all operations.
Do not instantiate this class directly, but create a subclass for every operation in your domain. You can use
new()
as a shortcut for doing so.
__getitem__
(key: Union[Tuple[int, ...], slice]) → matchpy.expressions.expressions.Expression¶ Return the subexpression at the given position(s).
It is also possible to use a slice notation to extract a sequence of subexpressions:
>>> expr = f(a, b, a, c) >>> expr[(1, ):(2, )] [Symbol('b'), Symbol('a')]
Parameters: position – The position as a tuple. See preorder_iter()
for its format. Alternatively, a range of positions can be passed using the slice notation.Returns: The subexpression at the given position(s). Raises: IndexError
– If the position is invalid, i.e. it refers to a nonexisting subexpression.

__init__
(operands: List[matchpy.expressions.expressions.Expression], variable_name=None) → None¶ Create an operation expression.
Parameters: *operands – The operands for the operation expression.
Raises: ValueError
– if the operand count does not match the operation’s arity.ValueError
– if the operation contains conflicting variables, i.e. variables with the same name that match different things. A common example would be mixing sequence and fixed variables with the same name in one expression.

arity
= Arity(min_count=0, fixed_size=False)¶ The arity of the operator.
Trying to construct an operation expression with a number of operands that does not fit its operation’s arity will result in an error.
Type: Arity

associative
= False¶ True if the operation is associative, i.e.
f(a, f(b, c)) = f(f(a, b), c)
.This attribute is used to flatten nested associative operations of the same type. Therefore, the
arity
of an associative operation has to have an unconstrained maximum number of operand.Type: bool

collect_symbols
(symbols) → None¶ Recursively adds all symbols occuring in the expression to the given multiset.
This is used internally by
symbols
. Needs to be overwritten by inheriting expression classes that can contain symbols. This method can be used when gathering thesymbols
of multiple expressions, because only one multiset needs to be created and that is more efficient.Parameters: symbols – Multiset of symbols. All symbols contained in the expression are recursively added to this multiset.

collect_variables
(variables) → None¶ Recursively adds all variables occuring in the expression to the given multiset.
This is used internally by
variables
. Needs to be overwritten by inheriting container expression classes. This method can be used when gathering thevariables
of multiple expressions, because only one multiset needs to be created and that is more efficient.Parameters: variables – Multiset of variables. All variables contained in the expression are recursively added to this multiset.

commutative
= False¶ True if the operation is commutative, i.e.
f(a, b) = f(b, a)
.Note that commutative operations will always be converted into canonical form with sorted operands.
Type: bool

infix
= False¶ True if the name of the operation should be used as an infix operator by str().
Type: bool

static
new
(name: str, arity: matchpy.expressions.expressions.Arity, class_name: str = None, *, associative: bool = False, commutative: bool = False, one_identity: bool = False, infix: bool = False) → Type[matchpy.expressions.expressions.Operation]¶ Utility method to create a new operation type.
Example:
>>> Times = Operation.new('*', Arity.polyadic, 'Times', associative=True, commutative=True, one_identity=True) >>> Times Times['*', Arity(min_count=2, fixed_size=False), associative, commutative, one_identity] >>> str(Times(Symbol('a'), Symbol('b'))) '*(a, b)'
Parameters:  name – Name or symbol for the operator. Will be used as name for the new class if
class_name
is not specified.  arity – The arity of the operator as explained in the documentation of
Operation
.  class_name – Name for the new operation class to be used instead of name. This argument
is required if
name
is not a valid python identifier.
Keyword Arguments:  associative – See
associative
.  commutative – See
commutative
.  one_identity – See
one_identity
.  infix – See
infix
.
Raises: ValueError
– if the class name of the operation is not a valid class identifier. name – Name or symbol for the operator. Will be used as name for the new class if

one_identity
= False¶ True if the operation with a single argument is equivalent to the identity function.
This property is used to simplify expressions, e.g. for
f
withf.one_identity = True
the expressionf(a)
if simplified toa
.Type: bool

with_renamed_vars
(renaming) → matchpy.expressions.expressions.Operation¶ Return a copy of the expression with renamed variables.


class
SymbolWildcard
(symbol_type: Type[matchpy.expressions.expressions.Symbol] = <class 'matchpy.expressions.expressions.Symbol'>, variable_name=None)¶ Bases:
matchpy.expressions.expressions.Wildcard
A special
Wildcard
that matches aSymbol
.
symbol_type
¶ A subclass of
Symbol
to constrain what the wildcard matches. If not specified, the wildcard will match anySymbol
.

__init__
(symbol_type: Type[matchpy.expressions.expressions.Symbol] = <class 'matchpy.expressions.expressions.Symbol'>, variable_name=None) → None¶ Parameters: symbol_type – A subclass of Symbol
to constrain what the wildcard matches. If not specified, the wildcard will match anySymbol
.Raises: TypeError
– if symbol_type is not a subclass ofSymbol
.

with_renamed_vars
(renaming) → matchpy.expressions.expressions.SymbolWildcard¶ Return a copy of the expression with renamed variables.


class
Pattern
(expression, *constraints)¶ Bases:
object
A pattern is a term that can be matched against another subject term.
A pattern can contain variables and can optionally have constraints attached to it. Those constraints a predicates which limit what the pattern can match.

__init__
(expression, *constraints) → None¶ Parameters:  expression – The term that forms the pattern.
 *constraints – Optional constraints for the pattern.

global_constraints
¶ The subset of the pattern constraints which are global.
A global constraint does not define dependency variables and can only be evaluated, once the match has been completed.

local_constraints
¶ The subset of the pattern constraints which are local.
A local constraint has a defined nonempty set of dependency variables. These constraints can be evaluated once their dependency variables have a substitution.


make_dot_variable
(name)¶ Create a new variable with the given name that matches a single term.
Parameters: name – The name of the variable Returns: The new dot variable.

make_plus_variable
(name)¶ Create a new variable with the given name that matches any number of terms.
Only matches sequences with at least one argument.
Parameters: name – The name of the variable Returns: The new plus variable.

make_star_variable
(name)¶ Create a new variable with the given name that matches any number of terms.
Can also match an empty argument sequence.
Parameters: name – The name of the variable Returns: The new star variable.

make_symbol_variable
(name, symbol_type=<class 'matchpy.expressions.expressions.Symbol'>)¶ Create a new variable with the given name that matches a single symbol.
Optionally, a symbol type can be specified to further limit what the variable can match.
Parameters: Returns: The new symbol variable.