renaming core to chain and some other changes

Some changes:

- The core crate is renamed to "chain".

- The crate "viz" is added, which will provide layered graph drawing
  algorithms.

- A function is added to convert from a grammar to the regular
  language of its left-linear closures.

- A function is added to convert from a nondeterministic finite
  automaton to its "null" closure.  A null closure is the same
  automaton with edges added, as if some edges are "null".  Whether an
  edge is null is determined by a function.
  Combined with the previous change, we can convert a grammar to the
  regular language of the null closure of its left-linear closures.

---

Now it remains to test more grammars and add an Atom trait, before
finishing the part about compilations.

1 files changed, 0 insertions, 59 deletions

diff --git a/repcore/src/plan.org b/repcore/src/plan.org
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--- a/repcore/src/plan.org
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@@ -1,59 +0,0 @@
-#+TITLE: Plan of the package
-#+AUTHOR: Durand
-#+DATE: <2022-11-18 Ven 19:57>
-
-* Atomic Languages
-
-This describes the behaviours of atomic languages.  The atomic
-language consists of the null closure of any non-terminal symbol in
-the grammar, and their deriavtives by terminals and non-terminal.
-
-* Derivative Languages
-
-This is the main driving device of the algorithm.  Basically, the
-algorithm works by taking successive derivatives, according to the
-input symbol.  At each step, we calculate the derivative language.  In
-this process, we also compute some semiring value and store in a
-carrier.  The end result of the algorithm is the final semiring
-value.
-
-If one wants simply to determine if the input string belongs to the
-grammar, one chooses the semiring to be the field with two elements,
-the boolean field.  If one wants to find how many ways are there to
-derive a given input string, then one uses the semiring of natural
-numbers instead.  If one wants, moreover, to find all the possible
-ways to derive a particular input string, then one can use the
-free semiring on the set of terminals and non-terminals of the
-grammar.  Here the free semiring is the left-adjoint functor to the
-forgetful functor from the category of semirings to the category of
-sets.
-
-To be more specific, the free semiring on a set is given by sets of
-sequences of elements in the set.  The addition of the semiring is the
-set union operation, and the multiplication is taking the respective
-concatenations.
-
-** Semirings
-
-So we need a module to define the behaviours of semirings, and provide
-some common semirings implementations.  Then in the main driving force
-we can freely substitute different semirings, according to the
-particular needs.
-
-** Languages
-
-Then the main part is to define the behaviour of languages.  This
-should be easy enough, since we already have the mechanism of graphs,
-nondeterministic automata, and semirings.  All we need to do is to
-combine them together.
-
-* Testing ground
-
-I am in a strong need to test things out.  The most important one is
-to visualize each step of the derivation, in a human-friendly manner.
-I need this to examine whether my atomic languages are wrongly
-implemented, or my atomic languages are wrongly derived, or my
-understanding of the main algorithm is plain wrong.
-
-This is the main reason I started this rewrite of the package.
-