Arity: Record arity types for non-recursive lets

In #18793, we saw a compelling example which requires us to look at
non-recursive let-bindings during arity analysis and unleash their arity
types at use sites.

After the refactoring in the previous patch, the needed change is quite
simple and very local to `arityType`'s defn for non-recurisve `Let`.

Apart from that, we had to get rid of the second item of
`Note [Dealing with bottoms]`, which was entirely a safety measure and
hindered optimistic fixed-point iteration.

Fixes #18793.

The following metric increases are all caused by this commit and a
result of the fact that we just do more work now:

Metric Increase:
    T3294
    T12545
    T12707

4 files changed, 108 insertions, 1 deletions

diff --git a/testsuite/tests/arityanal/should_compile/T18793.hs b/testsuite/tests/arityanal/should_compile/T18793.hs
new file mode 100644
index 0000000000..6dfdcf05ee
--- /dev/null
+++ b/testsuite/tests/arityanal/should_compile/T18793.hs
@@ -0,0 +1,12 @@
+module T18793 where
+
+stuff :: Int -> [Int]
+{-# NOINLINE stuff #-}
+stuff i = [i,i+1,i+2]
+
+f :: Int -> Int
+f = foldr k id (stuff 1)
+  where
+    k :: Int -> (Int -> Int) -> (Int -> Int)
+    k i acc | i > 42    = acc . negate
+            | otherwise = acc
diff --git a/testsuite/tests/arityanal/should_compile/T18793.stderr b/testsuite/tests/arityanal/should_compile/T18793.stderr
new file mode 100644
index 0000000000..72fc5e4e19
--- /dev/null
+++ b/testsuite/tests/arityanal/should_compile/T18793.stderr
@@ -0,0 +1,94 @@
+
+==================== Tidy Core ====================
+Result size of Tidy Core = {terms: 95, types: 79, coercions: 0, joins: 0/0}
+
+-- RHS size: {terms: 1, types: 0, coercions: 0, joins: 0/0}
+T18793.$trModule4 :: GHC.Prim.Addr#
+[GblId, Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True, WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 20 0}]
+T18793.$trModule4 = "main"#
+
+-- RHS size: {terms: 2, types: 0, coercions: 0, joins: 0/0}
+T18793.$trModule3 :: GHC.Types.TrName
+[GblId, Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True, WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 10 10}]
+T18793.$trModule3 = GHC.Types.TrNameS T18793.$trModule4
+
+-- RHS size: {terms: 1, types: 0, coercions: 0, joins: 0/0}
+T18793.$trModule2 :: GHC.Prim.Addr#
+[GblId, Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True, WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 30 0}]
+T18793.$trModule2 = "T18793"#
+
+-- RHS size: {terms: 2, types: 0, coercions: 0, joins: 0/0}
+T18793.$trModule1 :: GHC.Types.TrName
+[GblId, Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True, WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 10 10}]
+T18793.$trModule1 = GHC.Types.TrNameS T18793.$trModule2
+
+-- RHS size: {terms: 3, types: 0, coercions: 0, joins: 0/0}
+T18793.$trModule :: GHC.Types.Module
+[GblId, Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True, WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 10 10}]
+T18793.$trModule = GHC.Types.Module T18793.$trModule3 T18793.$trModule1
+
+-- RHS size: {terms: 20, types: 13, coercions: 0, joins: 0/0}
+T18793.$wstuff [InlPrag=NOINLINE] :: Int -> (# Int, [Int] #)
+[GblId, Arity=1, Str=<L,U(U)>, Unf=OtherCon []]
+T18793.$wstuff = \ (w :: Int) -> (# w, GHC.Types.: @Int (case w of { GHC.Types.I# x -> GHC.Types.I# (GHC.Prim.+# x 1#) }) (GHC.Types.: @Int (case w of { GHC.Types.I# x -> GHC.Types.I# (GHC.Prim.+# x 2#) }) (GHC.Types.[] @Int)) #)
+
+-- RHS size: {terms: 8, types: 11, coercions: 0, joins: 0/0}
+stuff [InlPrag=NOUSERINLINE[final]] :: Int -> [Int]
+[GblId,
+ Arity=1,
+ Str=<L,U(U)>,
+ Cpr=m2,
+ Unf=Unf{Src=InlineStable, TopLvl=True, Value=True, ConLike=True, WorkFree=True, Expandable=True, Guidance=ALWAYS_IF(arity=1,unsat_ok=True,boring_ok=False)
+         Tmpl= \ (w [Occ=Once1] :: Int) -> case T18793.$wstuff w of { (# ww1 [Occ=Once1], ww2 [Occ=Once1] #) -> GHC.Types.: @Int ww1 ww2 }}]
+stuff = \ (w :: Int) -> case T18793.$wstuff w of { (# ww1, ww2 #) -> GHC.Types.: @Int ww1 ww2 }
+
+Rec {
+-- RHS size: {terms: 23, types: 11, coercions: 0, joins: 0/0}
+T18793.$wgo1 [InlPrag=NOUSERINLINE[2], Occ=LoopBreaker] :: [Int] -> GHC.Prim.Int# -> GHC.Prim.Int#
+[GblId, Arity=2, Str=<S,1*U><L,U>, Unf=OtherCon []]
+T18793.$wgo1
+  = \ (w :: [Int]) (ww :: GHC.Prim.Int#) ->
+      case w of {
+        [] -> ww;
+        : y ys ->
+          case y of { GHC.Types.I# x ->
+          case GHC.Prim.># x 42# of {
+            __DEFAULT -> T18793.$wgo1 ys ww;
+            1# -> T18793.$wgo1 ys (GHC.Prim.negateInt# ww)
+          }
+          }
+      }
+end Rec }
+
+-- RHS size: {terms: 12, types: 6, coercions: 0, joins: 0/0}
+T18793.f_go1 [InlPrag=NOUSERINLINE[2]] :: [Int] -> Int -> Int
+[GblId,
+ Arity=2,
+ Str=<S,1*U><S,1*U(U)>,
+ Cpr=m1,
+ Unf=Unf{Src=InlineStable, TopLvl=True, Value=True, ConLike=True, WorkFree=True, Expandable=True, Guidance=ALWAYS_IF(arity=2,unsat_ok=True,boring_ok=False)
+         Tmpl= \ (w [Occ=Once1] :: [Int]) (w1 [Occ=Once1!] :: Int) -> case w1 of { GHC.Types.I# ww1 [Occ=Once1] -> case T18793.$wgo1 w ww1 of ww2 [Occ=Once1] { __DEFAULT -> GHC.Types.I# ww2 } }}]
+T18793.f_go1 = \ (w :: [Int]) (w1 :: Int) -> case w1 of { GHC.Types.I# ww1 -> case T18793.$wgo1 w ww1 of ww2 { __DEFAULT -> GHC.Types.I# ww2 } }
+
+-- RHS size: {terms: 2, types: 0, coercions: 0, joins: 0/0}
+T18793.f2 :: Int
+[GblId, Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True, WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 10 10}]
+T18793.f2 = GHC.Types.I# 1#
+
+-- RHS size: {terms: 7, types: 10, coercions: 0, joins: 0/0}
+T18793.f1 :: [Int]
+[GblId, Unf=Unf{Src=<vanilla>, TopLvl=True, Value=False, ConLike=False, WorkFree=False, Expandable=False, Guidance=IF_ARGS [] 40 10}]
+T18793.f1 = case T18793.$wstuff T18793.f2 of { (# ww1, ww2 #) -> GHC.Types.: @Int ww1 ww2 }
+
+-- RHS size: {terms: 2, types: 0, coercions: 0, joins: 0/0}
+f :: Int -> Int
+[GblId,
+ Arity=1,
+ Str=<S,1*U(U)>,
+ Cpr=m1,
+ Unf=Unf{Src=InlineStable, TopLvl=True, Value=True, ConLike=True, WorkFree=True, Expandable=True, Guidance=ALWAYS_IF(arity=0,unsat_ok=True,boring_ok=False)
+         Tmpl= \ (eta [Occ=Once1] :: Int) -> T18793.f_go1 T18793.f1 eta}]
+f = T18793.f_go1 T18793.f1
+
+
+
diff --git a/testsuite/tests/arityanal/should_compile/all.T b/testsuite/tests/arityanal/should_compile/all.T
new file mode 100644
index 0000000000..ed1047ba00
--- /dev/null
+++ b/testsuite/tests/arityanal/should_compile/all.T
@@ -0,0 +1 @@
+test('T18793', [ only_ways(['optasm']), grep_errmsg('Arity=') ], compile, ['-ddump-simpl -dppr-cols=99999 -dsuppress-uniques'])
diff --git a/testsuite/tests/stranal/should_compile/T13031.stdout b/testsuite/tests/stranal/should_compile/T13031.stdout
index efdbb60fe9..c42eecb616 100644
--- a/testsuite/tests/stranal/should_compile/T13031.stdout
+++ b/testsuite/tests/stranal/should_compile/T13031.stdout
@@ -1,2 +1,2 @@
 hello
-[GblId, Arity=1, Unf=OtherCon []]
+[GblId, Arity=3, Str=<L,U><L,U><L,U>b, Cpr=b, Unf=OtherCon []]