alias

Defines an abbreviation or a macro

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

alias(x1 = object1, x2 = object2, …, <Global>)
alias(<Global>)

Description

alias(x = object) defines x as an abbreviation for object.

alias(x = object) defines an abbreviation. It changes the configuration of the parser such that the identifierx is replaced by object whenever it occurs in the input, and such that object is in turn replaced by x in the output.

alias(f(y1, y2, ...) = object) defines f to be a macro. For arbitrary objects a1, a2, ..., f(a1, a2, ...) is equivalent to object with a1 substituted for y1, a2 substituted for y2, etc.

alias(f(y1, y2, ...) = object) defines a macro. It changes the configuration of the parser such that a function call of the form f(a1, a2, ...), where a1,a2,... is a sequence of arbitrary objects of the same length as y1,y2,..., is replaced by object with a1 substituted for y1, a2 substituted for y2, etc.

No substitution takes place if the number of parameters y1,y2,... differs from the number of arguments a1,a2,.... No substitution takes place in the output.

It is valid to define a macro with no arguments via alias(f()=object).

Multiple alias definitions may be given in a single call; abbreviations and macros may be mixed.

alias() displays a list of all currently defined aliases and macros.

alias() displays all currently defined aliases as a sequence of equations. For an abbreviation defined via alias(x = object), the equation x = object is printed. For a macro defined via alias(f(y1, y2, ...) = object), the equation f(y1, y2, ...) = object) is printed. If no aliases are defined, the message "No alias defined" is printed. See Example 11.

alias does not evaluate its arguments. Hence it has no effect if the aliased identifier has a value, and alias creates an alias for the right hand side of the alias definition and not for its evaluation. Cf. Example 2.

alias does not flatten its arguments. Thus an expression sequence is a valid right hand side of an alias definition. See Example 5.

An alias definition causes a substitution similar to the effect of subs, not just a textual replacement. Cf. Example 3.

Each identifier may be aliased to only one object. Each object may be abbreviated in only one way; otherwise alias aborts with an error.

An alias is in effect from the time when the call to alias has been evaluated. It affects exactly those inputs that are parsed after that moment. Cf. Example 9. In particular, an alias definition inside a procedure does not affect the rest of the procedure.

By default, back-substitution of aliases in the output happens only for abbreviations and not for macros. After a command of the form alias(x = object), both the unevaluated object object and its evaluation are replaced by the unevaluated identifier x in the output. Cf. Example 2.

The user can control the behavior of the back-substitution in the output with the function Pref::alias; see the corresponding help page for details.

Substitutions in the output only happen for the results of computations at interactive level. The behavior of the functions fprint, print, expr2text, or write is not affected.

Alias substitutions are performed in parallel, both in the input and in the output. Thus it is not possible to define nested aliases. See Example 10.

If an identifier is used as an abbreviation, it is not possible to enter this identifier in its literal meaning any longer.

    Note:   In particular, it is necessary to use unalias before another abbreviation or macro for the same identifier can be defined. Cf. Example 4.

If a macro f(y1,y2,...,yn) with n arguments has been defined, it is not possible to enter a call to f with n arguments in its literal meaning any longer. However, entering a call to f with a different number of arguments is still possible. Cf. Example 5.

Macros with different numbers of arguments can be defined at the same time. See Example 4.

An alias definition affects all kinds of input: interactive input on the command line, input via the function input, input from a file using finput, fread, or read (for the latter two only if option Plain is not set), and input from a string using text2expr. Cf. Example 8.

An alias definition has no effect on the identifier used as an alias. In particular, that identifier retains its value and its properties. The alias and the aliased object are still distinguished by the evaluator. Cf. Example 6.

Assigning a value to one of the identifiers on the left hand side of an alias definition, or deleting its value has no effect on the alias substitution, neither in the input nor in the output. See Example 7.

Environment Interactions

alias with at least one argument and unalias change the parser configuration in the way described in the "Details" section.

Examples

Example 1

We define d as a shortcut for diff:

delete f, g, x, y: alias(d = diff):
d(sin(x), x) = diff(sin(x), x);
d(f(x, y), x) = diff(f(x, y), x)

We define a macro Dx(f) for diff(f(x), x). Note that hold does not prevent alias substitution:

alias(Dx(f) = diff(f(x), x)):
Dx(sin); Dx(f + g); hold(Dx(f + g))

After the call unalias(d, Dx), no alias substitutions happen any longer:

unalias(d, Dx):
d(sin(x), x), diff(sin(x), x), d(f(x, y), x), diff(f(x, y), x);
Dx(sin), Dx(f + g)

Example 2

Suppose we want to avoid typing longhardtotypeident and therefore define an abbreviation a for it:

longhardtotypeident := 10;  alias(a = longhardtotypeident):

Since alias does not evaluate its arguments, a is now an abbreviation for longhardtotypeident and not for the number 10:

type(a), type(hold(a))

a + 1, hold(a) + 1, eval(hold(a) + 1)

longhardtotypeident := 2:
a + 1, hold(a) + 1, eval(hold(a) + 1)

However, by default alias back-substitution in the output happens for both the identifier and its current value:

2, 10, longhardtotypeident, hold(longhardtotypeident)

The command Pref::alias(FALSE) switches alias resubstitution off:

p := Pref::alias(FALSE):
a, hold(a), 2, longhardtotypeident, hold(longhardtotypeident);
Pref::alias(p): unalias(a):

Example 3

Aliases are substituted and not just replaced textually. In the following example, 3*succ(u) is replaced by 3*(u+1), and not by 3*u+1, which a search-and-replace function in a text editor would produce:

alias(succ(x) = x + 1): 3*succ(u);
unalias(succ):

Example 4

We define a to be an abbreviation for b. Then the next alias definition is really an alias definition for b:

delete a, b:
alias(a = b): alias(a = 2): type(a), type(b); unalias(b):

Use unalias first before defining another alias for the identifier a:

unalias(a): alias(a = 2): type(a), type(b); unalias(a):

A macro definition, however, can be added if the newly defined macro has a different number of arguments. unalias(a) removes all macros defined for a:

alias(a(x)=sin(x^2)): a(y); alias(a(x)=cos(x^2)):

Error: The operand is invalid. [_power]
  Evaluating: alias
alias(a(x, y) = sin(x + y)): 
a(u, v); 
alias(): 
unalias(a):

a(x)   = sin(x^2)
a(x, y) = sin(x + y)

Example 5

A macro definition has no effect when called with the wrong number of arguments, and the sequence of arguments is not flattened:

alias(plus(x, y) = x + y):
plus(1), plus(3, 2), plus((3, 2));
unalias(plus):

Expression sequences may appear on the right hand side of an alias definition, but they have to be enclosed in parenthesis:

alias(x = (1, 2)): f := 0, 1, 2, x;
nops(f); unalias(x):

Example 6

An identifier used as an abbreviation may still exist in its literal meaning inside expressions that were entered before the alias definition:

delete x: f := [x, 1]: alias(x = 1): f;
map(f, type); unalias(x):

Example 7

It does not matter whether the identifier used as an alias has a value:

a := 5: alias(a = 7): 7, 5; print(a); unalias(a):

delete a:

Example 8

Alias definitions also apply to input from files or strings:

alias(a = 3): type(text2expr("a")); unalias(a)

Example 9

An alias is valid for all input that is parsed after executing alias. A statement in a command line is not parsed before the previous commands in that command line have been executed. In the following example, the alias is already in effect for the second statement:

alias(a = 3): type(a); unalias(a)

This can be changed by entering additional parentheses:

(alias(a = 3): type(a)); unalias(a)

Example 10

We define b to be an alias for c, which in turn is defined to be an alias for 2. It is recommended to avoid such chains of alias definitions beacuse of some probably unwanted effects.

alias(b=c): alias(c=2):

Now each b in the input is replaced by c, but no additional substitution step is taken to replace this again by 2:

print(b)

On the other hand, the number 2 is replaced by c in every output and that c is then replaced by b:

2

unalias(c): unalias(b):

Example 11

When called without arguments, alias just displays all aliasses that are currently in effect:

alias(a = 5, F(x) = sin(x^2)):
alias(); unalias(F, a):
F(x) = sin(x^2)
a   = 5

Parameters

x1, x2, …

identifiers or symbolic expressions of the form f(y1, y2, …), with identifiers f, y1, y2, ...

object1, object2, …

Any MuPAD® objects

Options

Global

Definition of an alias in the global parser context.

When an alias is defined in a library or package source file, it will be deleted automatically after reading the file. With option Global the alias is not active in the file being read, but in the interactive level after reading of the file is finished.

Return Values

Both alias and unalias return the void object of type DOM_NULL.

Algorithms

The aliases are stored in the parser configuration table displayed by _parser_config(). Note that by default, alias back-substitution happens for the right hand sides of the equations in this table, but not for the indices. Use print(_parser_config()) to display this table without alias back-substitution.

Aliases are not in effect while a file is read using read or fread with option Plain. Conversely, if an alias is defined in a file which is read with option Plain, the alias is only in effect until the file has been read completely.

See Also

MuPAD Functions

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