Fix SR breakage due to allowing fixpoints on non-rec values

We limit fixpoints to Finite inductive types, so that BiFinite
inductives (non-recursive records) are excluded from fixpoint
construction. This is a regression in the sense that e.g. fixpoints
on unit records were allowed before. Primitive records with
eta-conversion are included in the BiFinite types.

Fix deprecation

Fix error message, the inductive type needs to be recursive for fix to work

1 files changed, 70 insertions, 0 deletions

diff --git a/test-suite/failure/fixpointeta.v b/test-suite/failure/fixpointeta.v
new file mode 100644
index 000000000..9af719322
--- /dev/null
+++ b/test-suite/failure/fixpointeta.v
@@ -0,0 +1,70 @@
+
+Set Primitive Projections.
+
+Record R := C { p : nat }.
+(* R is defined
+p is defined *)
+
+Unset Primitive Projections.
+Record R' := C' { p' : nat }.
+
+
+
+Fail Definition f := fix f (x : R) : nat := p x.
+(** Not allowed to make fixpoint defs on (non-recursive) records
+  having eta *)
+
+Fail Definition f := fix f (x : R') : nat := p' x.
+(** Even without eta (R' is not primitive here), as long as they're
+  found to be BiFinite (non-recursive), we disallow it *)
+
+(*
+
+(* Subject reduction failure example, if we allowed fixpoints *)
+
+Set Primitive Projections.
+
+Record R := C { p : nat }.
+
+Definition f := fix f (x : R) : nat := p x.
+
+(* eta rule for R *)
+Definition Rtr (P : R -> Type) x (v : P (C (p x))) : P x
+ := v.
+
+Definition goal := forall x, f x = p x.
+
+(* when we compute the Rtr away typechecking will fail *)
+Definition thing : goal := fun x =>
+(Rtr (fun x => f x = p x) x (eq_refl _)).
+
+Definition thing' := Eval compute in thing.
+
+Fail Check (thing = thing').
+(*
+The command has indeed failed with message:
+The term "thing'" has type "forall x : R, (let (p) := x in p) = (let (p) := x in p)"
+while it is expected to have type "goal" (cannot unify "(let (p) := x in p) = (let (p) := x in p)"
+and "f x = p x").
+*)
+
+Definition thing_refl := eq_refl thing.
+
+Fail Definition thing_refl' := Eval compute in thing_refl.
+(*
+The command has indeed failed with message:
+Illegal application:
+The term "@eq_refl" of type "forall (A : Type) (x : A), x = x"
+cannot be applied to the terms
+ "forall x : R, (fix f (x0 : R) : nat := let (p) := x0 in p) x = (let (p) := x in p)" : "Prop"
+ "fun x : R => eq_refl" : "forall x : R, (let (p) := x in p) = (let (p) := x in p)"
+The 2nd term has type "forall x : R, (let (p) := x in p) = (let (p) := x in p)"
+which should be coercible to
+ "forall x : R, (fix f (x0 : R) : nat := let (p) := x0 in p) x = (let (p) := x in p)".
+ *)
+
+Definition more_refls : thing_refl = thing_refl.
+Proof.
+  compute. reflexivity.
+Fail Defined. Abort.
+ *)