totality

They seem to serve similar purposes. The one difference I've noticed so far is that while Program Fixpoint will accept a compound measure like {measure (length l1 + length l2) } , Function seems to reject this and will only allow {measure length l1} . Is Program Fixpoint strictly more powerful than Function , or are they better suited for different use cases? This may not be a complete list, but it is what I have found so far: As you already mentioned, Program Fixpoint allows the measure to look at more than one argument. Function creates a foo_equation lemma that can be used to rewrite calls

I'm trying to define the game inductive type for combinatorial games. I want a comparison method which tells if two games are lessOrEq , greatOrEq , lessOrConf or greatOrConf . Then I can check if two games are equal if they are both lessOrEq and greatOrEq . But when I try defining the mutually recursive methods for making this check, I get: Error: Cannot guess decreasing argument of fix . I think this is because only one game or the other decreases in size with each recursive call (but not both). How can I indicate this to Coq? Here's my code. The part that fails is the mutually recursive

is there anything like the tactic simpl for Program Fixpoint s? In particular, how can one proof the following trivial statement? Program Fixpoint bla (n:nat) {measure n} := match n with | 0 => 0 | S n' => S (bla n') end. Lemma obvious: forall n, bla n = n. induction n. reflexivity. (* I'm stuck here. For a normal fixpoint, I could for instance use simpl. rewrite IHn. reflexivity. But here, I couldn't find a tactic transforming bla (S n) to S (bla n).*) Obviously, there is no Program Fixpoint necessary for this toy example, but I'm facing the same problem in a more complicated setting where I

I am trying to define the Ackermann-Peters function in Coq, and I'm getting an error message that I don't understand. As you can see, I'm packaging the arguments a, b of Ackermann in a pair ab ; I provide an ordering defining an ordering function for the arguments. Then I use the Function form to define Ackermann itself, providing it with the ordering function for the ab argument. Require Import Recdef. Definition ack_ordering (ab1 ab2 : nat * nat) := match (ab1, ab2) with |((a1, b1), (a2, b2)) => (a1 > a2) \/ ((a1 = a2) /\ (b1 > b2)) end. Function ack (ab : nat * nat) {wf ack_ordering} : nat