Fun

Input: Fun(x, x**2)

x \mapsto {x}^{2}

Defines a univariate function mapping the symbol given as the first argument to the expression in the second argument. The symbol $x$ representing the dummy variable becomes locally bound within the function expression. This function is improper; that is, it does not belong to a particular function space.

Input: Fun(x, x**2)(42)

\left(x \mapsto {x}^{2}\right)(42)

Calling a named function.

Input: Where(f(42), Def(f, Fun(x, x**2)))

f(42)\; \text{ where } f(x) = {x}^{2}

Calling a function assigned to a variable.

Input: Fun(Tuple(x, y), 2*x+3*y)

\left(x, y\right) \mapsto 2 x + 3 y

Defines a bivariate function. The symbols x and y become locally bound.

Input: Fun(Tuple(x), x**2)

\left(x\right) \mapsto {x}^{2}

Equivalent to defining a univariate function.

Input: Fun(Tuple(x_(i), For(i, 1, n)), Sum(i * x_(i), For(i, 1, n)))

\left(x_{1}, x_{2}, \ldots, x_{n}\right) \mapsto \sum_{i=1}^{n} i x_{i}

Defines a multivariate function with arity $n$ . In this special case, the variable binding x_ in the scope of the Tuple call propagates through to the Fun operator.

Input: Where(g(c_(2), c_(3)), Def(c_, Fun(n, n**2+n+1)), Def(g, Fun(Tuple(x, y), (x+y)*(x-y))))

g\!\left(c_{2}, c_{3}\right)\; \text{ where } c_{n} = {n}^{2} + n + 1,\;g\!\left(x, y\right) = \left(x + y\right) \left(x - y\right)

Defining and calling named improper functions in the context of a Where-expression.

Last updated: 2020-03-06 00:22:16