Add default methods interface functions

- All interface functions have sensible defaults
- All interface functions by default compare `Symbol`
- Update documentation
- Add `SymbolCache` docstring

Author: AayushSabharwal

docs/src/api.md

@@ -1,5 +1,7 @@
 # Interface Functions
 
+Default methods cast all symbols to `Symbol` before comparing.
+
 ```@docs
 independent_variables
 is_indep_sym

src/interface.jl

@@ -1,58 +1,83 @@
 """
 $(TYPEDSIGNATURES)
 
-Get the set of independent variables for the given system.
+Get an iterable over the independent variables for the given system. Default to an empty
+vector.
 """
 function independent_variables end
+independent_variables(::Any) = []
 
 """
 $(TYPEDSIGNATURES)
 
-Check if the given sym is an independent variable in the given system. Defaults
-to `false` if not implemented for the given system/container type.
+Check if the given sym is an independent variable in the given system. Default to checking
+if the given `sym` exists in the iterable returned by `independent_variables`.
 """
 function is_indep_sym end
 
+function is_indep_sym(store, sym)
+    any(isequal(Symbol(sym)), Symbol(x) for x in independent_variables(store))
+end
+
 """
 $(TYPEDSIGNATURES)
 
-Get the set of states for the given system.
+Get an iterable over the states for the given system. Default to an empty vector.
 """
 function states end
 
+states(::Any) = []
+
 """
 $(TYPEDSIGNATURES)
 
-Find the index of the given sym in the given system.
+Find the index of the given sym in the given system. Default to the index of the first
+symbol in the iterable returned by `states` which matches the given `sym`. Return
+`nothing` if the given `sym` does not match.
 """
 function state_sym_to_index end
 
+function state_sym_to_index(store, sym)
+    findfirst(isequal(Symbol(sym)), Symbol(x) for x in states(store))
+end
+
 """
 $(TYPEDSIGNATURES)
 
-Check if the given sym is a state variable in the given system. Defaults
-to `false` if not implemented for the given system/container type.
+Check if the given sym is a state variable in the given system. Default to checking if
+the value returned by `state_sym_to_index` is not `nothing`.
 """
 function is_state_sym end
 
+is_state_sym(store, sym) = !isnothing(state_sym_to_index(store, sym))
+
 """
 $(TYPEDSIGNATURES)
 
-Get the set of parameters variables for the given system.
+Get an iterable over the parameters variables for the given system. Default to an empty
+vector.
 """
 function parameters end
 
+parameters(::Any) = []
+
 """
 $(TYPEDSIGNATURES)
 
-Find the index of the given sym in the given system.
+Find the index of the given sym in the given system. Default to the index of the first
+symbol in the iterable retruned by `parameters` which matches the given `sym`. Return
+`nothing` if the given `sym` does not match.
 """
 function param_sym_to_index end
 
+param_sym_to_index(store, sym) = findfirst(isequal(Symbol(sym)), Symbol.(parameters(store)))
+
 """
 $(TYPEDSIGNATURES)
 
-Check if the given sym is a parameter variable in the given system. Defaults
-to `false` if not implemented for the given system/container type.
+Check if the given sym is a parameter variable in the given system. Default
+to checking if the value returned by `param_sym_to_index` is not `nothing`.
 """
 function is_param_sym end
+
+is_param_sym(store, sym) = !isnothing(param_sym_to_index(store, sym))

src/symbolcache.jl

@@ -1,3 +1,8 @@
+"""
+    SymbolCache(syms, indepsym, paramsyms)
+
+A container that simply stores a vector of all syms, indepsym and paramsyms.
+"""
 struct SymbolCache{S, T, U}
     syms::S
     indepsym::T
@@ -6,21 +11,13 @@ end
 
 independent_variables(sc::SymbolCache) = sc.indepsym
 independent_variables(::SymbolCache{S, Nothing}) where {S} = []
-is_indep_sum(::Any, _) = false
-is_indep_sym(sc::SymbolCache, sym) = any(isequal(sym), sc.indepsym)
 is_indep_sym(::SymbolCache{S, Nothing}, _) where {S} = false
 states(sc::SymbolCache) = sc.syms
 states(::SymbolCache{Nothing}) = []
-state_sym_to_index(sc::SymbolCache, sym) = findfirst(isequal(sym), sc.syms)
 state_sym_to_index(::SymbolCache{Nothing}, _) = nothing
-is_state_sym(::Any, _) = false
-is_state_sym(sc::SymbolCache, sym) = !isnothing(state_sym_to_index(sc, sym))
 parameters(sc::SymbolCache) = sc.paramsyms
 parameters(::SymbolCache{S, T, Nothing}) where {S, T} = []
-param_sym_to_index(sc::SymbolCache, sym) = findfirst(isequal(sym), sc.paramsyms)
 param_sym_to_index(::SymbolCache{S, T, Nothing}, _) where {S, T} = nothing
-is_param_sym(::Any, _) = false
-is_param_sym(sc::SymbolCache, sym) = !isnothing(param_sym_to_index(sc, sym))
 
 function Base.copy(VA::SymbolCache)
     typeof(VA)((VA.syms === nothing) ? nothing : copy(VA.syms),