A very lightweight means to create callable functions using expressions. For more performant and advanced requirements see DynamicExpressions and CallableExpressions.

The @symbolic macro, the lone export, can create a symbolic variable and optional symbolic parameter. When expressions are created with these variables, evaluation is deferred until the expression is called like a function. The expressions subtype Function so are intended to be useful with Julia's higher-order functions.

The expressions can be called as a univariate function, u(x), a univariate function with parameter, u(x, p), or as a bivariate function, u(x,y) (with y being a parameter). These are all typical calling patterns when a function is passed to a numeric routine. These calls substitute in for the symbolic value (and parameter) when not specified as nothing. (To substitute in for just the parameter, either u(nothing, value) or u(:,value).)

There are no performance claims, this package is all about convenience. Similar convenience is available in some form with SymPy, SymEngine, Symbolics, etc. As well, placeholder syntax is available in Underscores.jl, Chain.jl, DataPipes.jl etc., This package only has value in that it is very lightweight and, hopefully, intuitively simple.

An extension is provided for functions in SpecialFunctions.

An extension is provided for TermInterface which should allow the use of Metatheory to rewrite terms.

An extension is provided for AbstractTrees.

using SimpleExpressions
@symbolic x
map(x^2, (1, 2)) # (1, 4)

using Plots
@symbolic x p
u = x^5 - x - p
plot(u(:, 1), 0, 1.5) # substitute in for p
plot!(u(:, 2))