feat(haskell): Interaction Tree IO

oops, now we have purely modelled IO 🤷

lib/conversions.tri

@@ -0,0 +1,39 @@
+!import "base.tri" !Local
+!import "list.tri" !Local
+
+pred = y (self : triage
+  0
+  (_ : 0)
+  (bit rest :
+    matchBool
+      -- odd: 2n + 1 -> 2n
+      (matchBool
+        0
+        (pair 0 rest)
+        (equal? rest 0))
+      -- even: 2n -> 2n - 1
+      (matchBool
+        0
+        (pair 1 (self rest))
+        (equal? rest 0))
+      bit))
+
+incDecRev = y (self : matchList
+  "1"
+  (digit rest :
+    matchBool
+      (pair 48 (self rest))
+      (pair (succ digit) rest)
+      (equal? digit 57)))
+
+showNumberRev_ = y (self n acc :
+  matchBool
+    acc
+    (self (pred n) (incDecRev acc))
+    (equal? n 0))
+
+showNumber = (n :
+  matchBool
+    "0"
+    (reverse (showNumberRev_ n t))
+    (equal? n 0))