I really appreciate your code example as it seems to me a good starting point. I really like the use of $self you exploit to add optional terms to the expression. Now prehaps I understand it better.

I still do not fully understand your:

> which makes the convenient default ::= action => ::first work for the Dice_Expression rule

If you have the patience to expand this further it will help me in the understanding the ::first (see also below my answer to GrandFather).

Again about optional sub elements:

So the only way to specify somenthing optional is:

Dice_with_modifier_r ::= Simple_Dice 'r' Die_Modifier_Val action => mo
+difier_r
                        |Simple_Dice 'r' Die_Modifier_Comp Die_Modifie
+r_Val action => modifier_r
[download]

Right? there is no  <Optional> syntax to play with?

I tried a single rule like:

Dice_with_modifier_r ::= Simple_Dice 'r' <Die_Modifier_Comp>* Die_Modifier_Val action => modifier_r

as found at the end of this post but it throws the error:

Parse of BNF/Scanless source failed
Error in SLIF parse: No lexeme found at line 11, column 61
* String before error: modifier_r ::= Simple_Dice 'r' <Die_Modifier_Co
+mp>
* The error was at line 11, column 61, and at character 0x002a '*', ..
+.
* here: * Die_Modifier_Val action => modifier_r\n\n\nSimpl
Marpa::R2 exception at marpa07.pl line 41.
Marpa::R2 exception at marpa07.pl line 41.
[download]

Why on marpa-for-building-parsers there is: declaration ::= assignment* action => doResult

and I cannot do

Dice_with_modifier_r ::= Simple_Dice 'r' Die_Modifier_Comp* Die_Modifi
+er_Val action => modifier_r
Die_Modifier_Comp ~ 'gt' | 'lt'
[download]

L*