Lurch Deductive Engine

Class

Application

Many mathematical expressions are the application of some function or operator to zero or (typically) more arguments. For example $f(x)$ applies the function $f$ to the argument $x$. As another example, $17.2-p$ applies the operation $-$ to the arguments $17.2$ and $p$. We call such expressions Applications, and implement them in this class.

These were inspired by a structure of the same name defined in the OpenMath Standard, but the reader is not expected to read that standard; we define in this documentation our version of what an Application is.

An Application is defined by a sequence of children, each of which is an Expression. The first such child will be the function or operator that is applied to the rest of the children, and consequently, there must always be at least one child of any Application. The constructor defined below requires this.

It is acceptable for there to be only one child, the function or operator itself, and no other children. Such functions are uncommon in mathematics, but they are common in computer science. For example, a function that generates new pseudo-random numbers each time it is called is a function that takes zero arguments.

Constructor

new Application(operator, …operands)

Construct a new Application instance from the given operator (requried) and list of operands (zero or more). For example, to construct $f(x)$, call new Application(f,x), where we assume that f and x are already defined elsewhere (perhaps as Symbols). Or to construct $17.2-p$, call new Application(m,s,p), where m is the subtraction operator, s is the constant $17.2$ and p is the variable $p$. Each of these three (m,s,p) would most likely be an instance of the Symbol class.

Note that while it is possible later to remove children from an Application until it has none, this is likely to result in the members of this class malfunctioning or throwing errors. Clients should not remove the final child of an Application; that is not supported.

Parameters

  • operator Expression

    The function or operation that is being applied to the operands. This argument is required, and must be an Expression.

  • operands Expression <repeatable>

    The list of zero or more operands to which the operator is being applied. This may be an empty list, but each entry on the list must be an Expression.

Throws

If any of the arguments is not an Expression, this constructor throws an error.

Source

Classes

Application

Methods

operands() → {Expression}

Applications store their operator and operands as children, in the same order as in LISP S-expressions, that is, with the operator as the first child, and the operands in order therafter (if there are any). Thus this function returns the list of all but the first child of this object, when considering it as an Expression (or more generally as a MathConcept).

If the children have not been manipulated since construction of the object, then this is the original array of operands given at construction time. If children have been added or removed since then, the new array of children (after the first) is assumed to be the list of operands.

See

Returns

  • Expression

    the operands to which this Application instance applies its operator

Source

operator() → {Expression}

Applications store their operator and operands as children, in the same order as in LISP S-expressions, that is, with the operator as the first child, and the operands in order therafter (if there are any). Thus this function returns the first child of this object, when considering it as an Expression (or more generally as a MathConcept).

If the children have not been manipulated since construction of the object, then this is the original operator given at construction time. If a new first child has been inserted since then, or the old first child removed, the new first child is assumed to be the operator.

See

Returns

  • Expression

    the operator that this Application instance applies to its operands

Source