adjust readme

Author: a

README.md

@@ -11,8 +11,38 @@ and [Metatheory.jl](https://github.com/0x0f0f0f/Metatheory.jl).
 
 #### `isexpr(x::T)` 
 
-Returns `true` if `x` is an expression tree (an S-expression). If true, `head`
-and `children` methods must be defined for `x`.
+Returns `true` if `x` is an expression tree. If true, `head(x)` and `children(x)` methods must be defined for `x`.
+Optionally, if `x` represents a function call, `iscall(x)` should be true, and `operation(x)` and `arguments(x)` should also be defined. 
+
+#### `iscall(x::T)`
+
+Returns `true` if `x` is a function call expression. If true, `operation(x)`, `arguments(x)`
+must also be defined for `x`.
+
+If `iscall(x)` is true, then also `isexpr(x)` *must* be true. The other way around is not true.
+(A function call is always an expression node, but not every expression tree represents a function call).
+
+This means that, `head(x)` and `children(x)` must be defined. Together
+with `operation(x)` and `arguments(x)`. 
+
+**Examples:** 
+
+In a functional language, all expression trees are function calls (e.g. SymbolicUtils.jl).
+Let's say that you have an hybrid array and functional language. `iscall` on the expression `v[i]`
+is `false`, and `iscall` on expression `f(x)` is `true`, but both of them are nested
+expressions, and `isexpr` is `true` on both.
+
+The same goes for Julia `Expr`. An `Expr(:block, ...)` is *not a function call*
+and has no `operation` and `arguments`, but has a `head` and `children`.
+
+
+The distinction between `head`/`children` and `operation`/`arguments` is needed 
+when dealing with languages that are *not representing function call operations as their head*.
+The main example is  `Expr(:call, :f, :x)`: it has both a `head` and an `operation`, which are
+respectively `:call` and `:f`.
+
+In other symbolic expression languages, such as SymbolicUtils.jl, the `head` of a node 
+can correspond to `operation` and `children` can correspond to `arguments`.
 
 #### `head(x)`
 
@@ -22,6 +52,16 @@ Returns the head of the S-expression.
 
 Returns the children (aka tail) of the S-expression.
 
+#### `operation(x)`
+
+Returns the function a function call expression is calling. `iscall(x)` must be
+true as a precondition.
+
+#### `arguments(x)`
+
+Returns the arguments to the function call in a function call expression.
+`iscall(x)` must be true as a precondition.
+
 #### `maketerm(T, head, children, type=nothing, metadata=nothing)`
 
 Constructs an expression. `T` is a constructor type, `head` and `children` are
@@ -41,19 +81,6 @@ Packages providing expression types _must_ implement this method for each expres
 If your types do not support type information or metadata, you still need to accept
 these arguments and may choose to not use them.
 
-#### `iscall(x::T)`
-
-Returns `true` if `x` is a function call expression. If true, `operation`, `arguments` must also be defined for `x::T`.
-
-#### `operation(x)`
-
-Returns the function a function call expression is calling. `iscall(x)` must be
-true as a precondition.
-
-#### `arguments(x)`
-
-Returns the arguments to the function call in a function call expression.
-`iscall(x)` must be true as a precondition.
 
 ### Optional
 
@@ -67,11 +94,34 @@ Implicitly defined if `arguments(x)` is defined.
 
 Returns the metadata attached to `x`.
 
-#### `symtype(expr)`
+####  `metadata(expr, md)`
+
+Returns `expr` with metadata `md` attached to it.
+
+## Examples
+
+### Function call Julia Expressions
+
+```julia 
+ex = :(f(a, b))
+@test head(ex) == :call
+@test children(ex) == [:f, :a, :b]
+@test operation(ex) == :f
+@test arguments(ex) == [:a, :b]
+@test isexpr(ex)
+@test iscall(ex)
+@test ex == maketerm(Expr, :call, [:f, :a, :b], nothing)
+```
+
 
-Returns the symbolic type of `expr`. By default this is just `typeof(expr)`.
-Define this for your symbolic types if you want `SymbolicUtils.simplify` to apply rules
-specific to numbers (such as commutativity of multiplication). Or such
-rules that may be implemented in the future.
+### Non-function call Julia Expressions
 
-<!-- TODO update examples -->
+```julia 
+ex = :(arr[i, j])
+@test head(ex) == :ref
+@test_throws ErrorException operation(ex)
+@test_throws ErrorException arguments(ex)
+@test isexpr(ex)
+@test !iscall(ex)
+@test ex == maketerm(Expr, :ref, [:arr, :i, :j], nothing)
+```