Primitive integers

This work makes it possible to take advantage of a compact
representation for integers in the entire system, as opposed to only
in some reduction machines. It is useful for heavily computational
applications, where even constructing terms is not possible without such
a representation.

Concretely, it replaces part of the retroknowledge machinery with
a primitive construction for integers in terms, and introduces a kind of
FFI which maps constants to operators (on integers). Properties of these
operators are expressed as explicit axioms, whereas they were hidden in
the retroknowledge-based approach.

This has been presented at the Coq workshop and some Coq Working Groups,
and has been used by various groups for STM trace checking,
computational analysis, etc.

Contributions by Guillaume Bertholon and Pierre Roux <Pierre.Roux@onera.fr>

Co-authored-by: Benjamin Grégoire <Benjamin.Gregoire@inria.fr>
Co-authored-by: Vincent Laporte <Vincent.Laporte@fondation-inria.fr>

1 files changed, 3 insertions, 3 deletions

diff --git a/theories/Numbers/Cyclic/Abstract/DoubleType.v b/theories/Numbers/Cyclic/Abstract/DoubleType.v
index b6441bb76a..9547a642df 100644
--- a/theories/Numbers/Cyclic/Abstract/DoubleType.v
+++ b/theories/Numbers/Cyclic/Abstract/DoubleType.v
@@ -12,7 +12,7 @@
 
 Set Implicit Arguments.
 
-Require Import ZArith.
+Require Import BinInt.
 Local Open Scope Z_scope.
 
 Definition base digits := Z.pow 2 (Zpos digits).
@@ -23,7 +23,7 @@ Section Carry.
  Variable A : Type.
 
  #[universes(template)]
- Inductive carry :=
+ Variant carry :=
   | C0 : A -> carry
   | C1 : A -> carry.
 
@@ -46,7 +46,7 @@ Section Zn2Z.
  *)
 
  #[universes(template)]
- Inductive zn2z :=
+ Variant zn2z :=
   | W0 : zn2z
   | WW : znz -> znz -> zn2z.