diff options
Diffstat (limited to 'test-suite/complexity/ring2.v')
-rw-r--r-- | test-suite/complexity/ring2.v | 51 |
1 files changed, 51 insertions, 0 deletions
diff --git a/test-suite/complexity/ring2.v b/test-suite/complexity/ring2.v new file mode 100644 index 00000000..9f9685dd --- /dev/null +++ b/test-suite/complexity/ring2.v @@ -0,0 +1,51 @@ +(* This example, checks the efficiency of the abstract machine used by ring *) +(* Expected time < 1.00s *) + +Require Import BinInt. + +Definition Zplus x y := +match x with +| 0%Z => y +| Zpos x' => + match y with + | 0%Z => x + | Zpos y' => Zpos (x' + y') + | Zneg y' => + match (x' ?= y')%positive Eq with + | Eq => 0%Z + | Lt => Zneg (y' - x') + | Gt => Zpos (x' - y') + end + end +| Zneg x' => + match y with + | 0%Z => x + | Zpos y' => + match (x' ?= y')%positive Eq with + | Eq => 0%Z + | Lt => Zpos (y' - x') + | Gt => Zneg (x' - y') + end + | Zneg y' => Zneg (x' + y') + end +end. + +Require Import Ring. + +Lemma Zth : ring_theory Z0 (Zpos xH) Zplus Zmult Zminus Zopp (@eq Z). +Admitted. + +Ltac Zcst t := + match isZcst t with + true => t + | _ => constr:NotConstant + end. + +Add Ring Zr : Zth + (decidable Zeqb_ok, constants [Zcst]). + +Open Scope Z_scope. +Infix "+" := Zplus : Z_scope. + +Goal forall a, a+a+a+a+a+a+a+a+a+a+a+a+a = a*13. +Time intro; ring. |