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Require Import Program Extraction ExtrOcamlBasic.
Print sig.
Section FIXPOINT.
Variable A: Type.
Variable eq: A -> A -> Prop.
Variable beq: A -> A -> bool.
Hypothesis beq_eq: forall x y, beq x y = true -> eq x y.
Hypothesis beq_neq: forall x y, beq x y = false -> ~eq x y.
Variable le: A -> A -> Prop.
Hypothesis le_trans: forall x y z, le x y -> le y z -> le x z.
Definition gt (x y: A) := le y x /\ ~eq y x.
Hypothesis gt_wf: well_founded gt.
Variable F: A -> A.
Hypothesis F_mon: forall x y, le x y -> le (F x) (F y).
Program Fixpoint iterate
(x: A) (PRE: le x (F x)) (SMALL: forall z, le (F z) z -> le x z)
{wf gt x}
: {y : A | eq y (F y) /\ forall z, le (F z) z -> le y z } :=
let x' := F x in
match beq x x' with
| true => x
| false => iterate x' _ _
end.
Next Obligation.
split.
- auto.
- apply beq_neq. auto.
Qed.
End FIXPOINT.
Recursive Extraction iterate.
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