a prototype of an item derivation forest

It seems to be complete now, but still awaits more tests to see where
the errors are, which should be plenty, haha.

1 files changed, 26 insertions, 18 deletions

diff --git a/chain/src/plan.org b/chain/src/plan.org
index c2a9037..1da33cc 100644
--- a/chain/src/plan.org
+++ b/chain/src/plan.org
@@ -2,7 +2,7 @@
 #+AUTHOR: Durand
 #+DATE: <2022-11-18 Ven 19:57>
 
-* Things to do [7/10]
+* Things to do [6/9]
 
 - [X] Implement builders for graphs
 - [X] Find sets of the first terminals for each non-terminal, in the
@@ -79,15 +79,13 @@
     lack of this step might be the root cause of the failure of the
     previous version of this project.
   + [X] Test atoms
-- [X] Implement forests [4/4]
-  + [X] Design a format of forests.  This should be the most crucial
-    thing to do, in order to have a better understanding of the whole
-    picture.  I need to have a clear understanding of the details of
-    the binarised shared packed parsed forests, that reflects the
-    regular expressions in the grammar equations.
-  + [X] Define a trait with the expected behaviours.
-  + [X] Implement them as parents-knowing graphs.
-  + [X] Test
+- [ ] Implement semiring. [0/5]
+  + [ ] Define the trait.
+  + [ ] Define items and rules for the chain-rule parser, as an
+    item-based description.
+  + [ ] Implement the boolean semiring.
+  + [ ] Implement the natural number semiring.
+  + [ ] Implement the free semiring.
 - [-] Implement languages. [4/6]
   + [X] First define a trait with the expected behaviours.
   + [X] Then implement them as doubly labelled graphs.
@@ -95,19 +93,29 @@
     with a position in the forest.  This perfectly solves the problem
     of those "plugs"!
   + [X] Then implement finding derivatives by use of the chain rule.
-  + [ ] Handle Forests
+  + [ ] Handle Semirings
   + [-] Tests
-- [ ] Implement semiring. [0/5]
-  + [ ] Define the trait.
-  + [ ] Implement the boolean semiring.
-  + [ ] Implement the natural number semiring.
-  + [ ] Implement the free semiring.
-  + [ ] Compute and record a semiring value when computing
-    derivatives.
 - [X] Miscellaneous [1/1]
   + [X] Implement a function for NFA that checks if a given predicate
     is satisfied for each edge label.
 
+** Forests
+
+This was a failed attempt to handle forests.  I decided to handle
+forests as a special case of semi-rings.  This is not only more
+systematic, but has also the potential of handling more general
+semi-rings later, like the Viterbi semirings, for example.
+
+- [X] Implement forests [4/4]
+  + [X] Design a format of forests.  This should be the most crucial
+    thing to do, in order to have a better understanding of the whole
+    picture.  I need to have a clear understanding of the details of
+    the binarised shared packed parsed forests, that reflects the
+    regular expressions in the grammar equations.
+  + [X] Define a trait with the expected behaviours.
+  + [X] Implement them as parents-knowing graphs.
+  + [X] Test
+
 * Atomic Languages
 
 This describes the behaviours of atomic languages.  The atomic