Iter 16b.1 — local recursive let (no-capture)

Add `(let-rec NAME (params ...) (type ...) (body ...) (in ...))`
as a form-A surface and a `Term::LetRec` AST variant. The 16a
desugar pass lifts each LetRec whose body has no captures from
the enclosing scope to a synthetic top-level fn `<hint>$lr_N`
and substitutes the original name; typecheck and codegen never
see LetRec. Capture detection panics at desugar time, queued
for 16b.2.

Tests: 95 → 99 (+1 e2e local_rec_factorial_demo, +2 desugar
unit, +1 parse unit). The new fixture `examples/local_rec_demo`
runs `fact` at n=1, 3, 5 → prints 1, 6, 120.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

examples/local_rec_demo.ail.json

@@ -0,0 +1 @@
+{"defs":[{"body":{"body":{"cond":{"args":[{"name":"n","t":"var"},{"lit":{"kind":"int","value":1},"t":"lit"}],"fn":{"name":"<=","t":"var"},"t":"app"},"else":{"args":[{"name":"n","t":"var"},{"args":[{"args":[{"name":"n","t":"var"},{"lit":{"kind":"int","value":1},"t":"lit"}],"fn":{"name":"-","t":"var"},"t":"app"}],"fn":{"name":"fact","t":"var"},"t":"app"}],"fn":{"name":"*","t":"var"},"t":"app"},"t":"if","then":{"lit":{"kind":"int","value":1},"t":"lit"}},"in":{"lhs":{"args":[{"args":[{"lit":{"kind":"int","value":1},"t":"lit"}],"fn":{"name":"fact","t":"var"},"t":"app"}],"op":"io/print_int","t":"do"},"rhs":{"lhs":{"args":[{"args":[{"lit":{"kind":"int","value":3},"t":"lit"}],"fn":{"name":"fact","t":"var"},"t":"app"}],"op":"io/print_int","t":"do"},"rhs":{"args":[{"args":[{"lit":{"kind":"int","value":5},"t":"lit"}],"fn":{"name":"fact","t":"var"},"t":"app"}],"op":"io/print_int","t":"do"},"t":"seq"},"t":"seq"},"name":"fact","params":["n"],"t":"letrec","type":{"effects":[],"k":"fn","params":[{"k":"con","name":"Int"}],"ret":{"k":"con","name":"Int"}}},"doc":"Iter 16b.1: drive a let-rec'd factorial helper at three inputs. Expected stdout (per line): 1, 6, 120.","kind":"fn","name":"main","params":[],"type":{"effects":["IO"],"k":"fn","params":[],"ret":{"k":"con","name":"Unit"}}}],"imports":[],"name":"local_rec_demo","schema":"ailang/v0"}

examples/local_rec_demo.ailx

@@ -0,0 +1,26 @@
+; Iter 16b.1 — first consumer of (let-rec ...). A single-fn helper
+; `fact` is bound by a local recursive let inside `main`'s body and
+; called at three different inputs. The desugarer lifts `fact` to a
+; synthetic top-level fn (because the body has no captures from
+; `main`'s scope) and substitutes the references. The lifted fn is
+; type-checked and codegen'd identically to a hand-written
+; top-level def. Output (per line): 1, 6, 120.
+
+(module local_rec_demo
+
+  (fn main
+    (doc "Iter 16b.1: drive a let-rec'd factorial helper at three inputs. Expected stdout (per line): 1, 6, 120.")
+    (type (fn-type (params) (ret (con Unit)) (effects IO)))
+    (params)
+    (body
+      (let-rec fact
+        (params n)
+        (type (fn-type (params (con Int)) (ret (con Int))))
+        (body
+          (if (app <= n 1)
+            1
+            (app * n (app fact (app - n 1)))))
+        (in
+          (seq (do io/print_int (app fact 1))
+          (seq (do io/print_int (app fact 3))
+               (do io/print_int (app fact 5)))))))))