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, 28 insertions, 0 deletions

diff --git a/test-suite/arithmetic/reduction.v b/test-suite/arithmetic/reduction.v
new file mode 100644
index 0000000000..00e067ac5a
--- /dev/null
+++ b/test-suite/arithmetic/reduction.v
@@ -0,0 +1,28 @@
+Require Import Int63.
+
+Open Scope int63_scope.
+
+Definition div_eucl_plus_one i1 i2 :=
+  let (q,r) := diveucl i1 i2 in
+  (q+1, r+1)%int63.
+
+Definition rcbn := Eval cbn in div_eucl_plus_one 3 2.
+Check (eq_refl : rcbn = (2, 2)).
+
+Definition rcbv := Eval cbv in div_eucl_plus_one 3 2.
+Check (eq_refl : rcbv = (2, 2)).
+
+Definition rvmc := Eval vm_compute in div_eucl_plus_one 3 2.
+Check (eq_refl : rvmc = (2, 2)).
+
+Definition f n m :=
+  match (n ?= 42)%int63 with
+  | Lt => (n + m)%int63
+  | _ => (2*m)%int63
+  end.
+
+Goal forall n, (n ?= 42)%int63 = Gt -> f n 256 = 512%int63.
+  intros. unfold f.
+  cbn. Undo. cbv. (* Test reductions under match clauses *)
+  rewrite H. reflexivity.
+Qed.