Pretty-print 0 as "0" for N, Z, and nat

Formerly printed as an empty string.

CHANGELOG.md

@@ -36,6 +36,8 @@ Coq 8.8 and 8.9 are no longer supported.
     iterated addition.
   + Rename and restate many lemmas so as to be consistent with the conventions
     for Coq's number types `nat`, `N`, and `Z`.
+- Fix a bug where `pretty 0` was defined as `""`, the empty string. It now
+  returns `"0"` for `N`, `Z`, and `nat`.
 
 The following `sed` script should perform most of the renaming
 (on macOS, replace `sed` by `gsed`, installed via e.g. `brew install gnu-sed`):

theories/pretty.v

@@ -35,8 +35,8 @@ Proof.
   unfold pretty_N_go_help at 1; fold pretty_N_go_help.
   by destruct (decide (0 < x)%N); auto using pretty_N_go_help_irrel.
 Qed.
-Instance pretty_N : Pretty N := λ x, pretty_N_go x ""%string.
-Lemma pretty_N_unfold x : pretty x = pretty_N_go x "".
+Instance pretty_N : Pretty N := λ x, pretty_N_go x "0"%string.
+Lemma pretty_N_unfold x : pretty x = pretty_N_go x "0".
 Proof. done. Qed.
 Instance pretty_N_inj : Inj (=@{N}) (=) pretty.
 Proof.
@@ -46,7 +46,7 @@ Proof.
   cut (∀ x y s s', pretty_N_go x s = pretty_N_go y s' →
     String.length s = String.length s' → x = y ∧ s = s').
   { intros help x y Hp.
-    eapply (help x y "" ""); [by rewrite <-!pretty_N_unfold|done]. }
+    eapply (help x y "0" "0"); [by rewrite <-!pretty_N_unfold|done]. }
   assert (∀ x s, ¬String.length (pretty_N_go x s) < String.length s) as help.
   { setoid_rewrite <-Nat.le_ngt.
     intros x; induction (N.lt_wf_0 x) as [x _ IH]; intros s.
@@ -66,9 +66,8 @@ Proof.
 Qed.
 Instance pretty_Z : Pretty Z := λ x,
   match x with
-  | Z0 => "" | Zpos x => pretty (Npos x) | Zneg x => "-" +:+ pretty (Npos x)
+  | Z0 => "0" | Zpos x => pretty (Npos x) | Zneg x => "-" +:+ pretty (Npos x)
   end%string.
 Instance pretty_nat : Pretty nat := λ x, pretty (N.of_nat x).
 Instance pretty_nat_inj : Inj (=@{nat}) (=) pretty.
 Proof. apply _. Qed.
-