Parsing Julia Expressions to Symbolic Expressions
Julia expressions such as
:(y - x) are fundamentally different from symbolic expressions, as they do not have an algebra defined on them. Thus, it can be very helpful when building domain-specific languages (DSLs) and parsing files to convert from Julia expressions to Symbolics.jl expressions for further manipulation. Towards this end is the
parse_expr_to_symbolic which performs the parsing.
Take the limitations mentioned in the
parse_expr_to_symbolic docstrings seriously! Because Julia expressions contain no symbolic metadata, there is limited information and thus the parsing requires heuristics to work.
parse_expr_to_symbolic function in the current module, i.e.
parse_expr_to_symbolic(ex, mod) where
mod is the module of the function caller.
ex: the expression to parse
mod: the module to apply the parsing in. See the limitations section for details.
ex = :(y(t) ~ x(t)) parse_expr_to_symbolic(ex,Main) # gives the symbolic expression `y(t) ~ x(t)` in empty Main # Now do a whole system ex = [:(y ~ x) :(y ~ -2x + 3 / z) :(z ~ 2)] eqs = parse_expr_to_symbolic.(ex, (Main,)) @variables x y z ex = [y ~ x y ~ -2x + 3 / z z ~ 2] all(isequal.(eqs,ex)) # true
Symbolic-ness Tied to Environment Definitions
The parsing to a symbolic expression has to be able to recognize the difference between functions, numbers, and globals defined within one's Julia environment and those that are to be made symbolic. The way this functionality handles this problem is that it does not define anything as symbolic that is already defined in the chosen
mod module. For example,
f(x,y) will have
f as non-symbolic if the function
f) is defined in
mod, i.e. if
isdefined(mod,:f) is true. When the symbol is defined, it will be replaced by its value. Notably, this means that the parsing behavior changes depending on the environment that it is applied.
parse_expr_to_symbolic(:(x - y),@__MODULE__) # x - y x = 2.0 parse_expr_to_symbolic(:(x - y),@__MODULE__) # 2.0 - y
This is required to detect that standard functions like
- are functions instead of symbolic symbols. For safety, one should create anonymous modules or other sub-environments to ensure no stray variables are defined.
Metadata is Blank
Because all the variables defined by the expressions are not defined with the standard
@variables, there is no metadata that is or can be associated with any of the generated variables. Instead, they all have blank metadata, but are defined in the
Real domain. Thus, the variables which come out of this parsing may not evaluate as equal to a symbolic variable defined elsewhere.
Missing docstring for
@parse_expr_to_symbolic. Check Documenter's build log for details.