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(*                                                                          *)
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(*                   Solange Coupet-Grimal & Line Jakubiec                  *)
(*                                                                          *)
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(*                 Laboratoire d'Informatique de Marseille                  *)
(*                   Technopole de Chateau-Gombert                          *)
(*                   39, Rue F. Joliot Curie                                *)
(*                   13453 MARSEILLE Cedex 13                               *)
(*           e-mail:{Solange.Coupet,Line.Jakubiec}@lim.univ-mrs.fr          *)
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(*                                                                          *)
(*                                Coq V5.10                                 *)
(*                              May 30th 1996                               *)
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Verification and synthesis of hardware linear arithmetic structures.
Example of a left-to-right comparator.


Three approaches are tackled :
----------------------------
  * the usual verification of a circuit, consisting in proving that the
    description satisfies the specification,
  * the synthesis of a circuit from its specification using the Coq
    extractor,
  * the same approach as above but using the Program tactic.

Directories :
-----------
  * Libraries : additional lemmas about arithmetic, booleans, 
                dependent lists ...
  * Factorization :
      - Lib_Numerals : Libraries about the representation of natural numbers
        as lists of digits in a given base,
      - Linear_Structures.v : Definition of linear connections of identical 
        cells,
      - Factorization.v : Definition of two properties ("proper" and
        "factorizable") that the arithmetic relations we consider are
        supposed to satisfy,
      - Factorization_Verif.v, Factorization_Synth.v, Factorization_Prog.v :
        three versions (corresponding to our three approaches) of a general
        theorem stating the correctness of circuits implementing proper and
        factorizable arithmetic relations,
      - Comparator : application to the example of a comparator.

Compilation order :
-----------------
  1. Libraries
  2. Libraries/ Lib_Arithmetic, Lib_Boolean, Lib_Lists
  3. Factorization/ Lib_Numerals
  4. Factorization
  5. Factorization/ Comparator



This work is described in the following reference :

  Title     : "Coq and Hardware Verification : A Case Study"
  Author    : Coupet-Grimal Solange and Jakubiec Line
  Booktitle : TPHOLs'96 (International Conference on Theorem Proving 
              in Higher Order Logics) - Turku (Finlande)
  Publisher : Springer-Verlag
  Series    : LCNS
  Date      : 27-30th August 1996
  Abstract  : We present several approaches to verifying a class of circuits
              with the Coq proof-assistant, using the example of a 
              left-to-right comparator. The large capacity of expression of 
              the Calculus of Inductive Constructions allows us to give 
              precise and general specifications. Using Coq's higher order
              logic, we state general results useful in establishing the
              correctness of the circuits. Finally, exploiting the constructive
              aspect of the logic, we can show how a certified circuit can 
              be automatically synthesized from its specification.