iter loop-recur.1: additive Term::Loop / Term::Recur / LoopBinder foundation

First of three iterations of the standalone loop/recur milestone
(spec 97c1ed1). loop/recur become real parseable / printable /
round-trippable / hash-stable strictly-additive AST nodes across
every no-wildcard exhaustive Term match in all six crates, plus
parse/print, prose arms, DESIGN.md + form_a.md schema blocks,
drift/coverage/hash anchors, and the spec's worked sum_to program
as a green round-trip fixture. NO typecheck semantics and NO real
codegen this iter by design: synth and lower_term are stubbed
CheckError::Internal / CodegenError::Internal exactly as mut.1
(real typecheck = iter 2, real loop-header/phi/back-edge = iter 3).

Two binding Boss design calls recorded in the plan header and the
journal: (1) verify_tail_positions "byte-unchanged" = its tail-app
verification role is unchanged, not its source — it is an
exhaustive no-wildcard match so two descent-only arms are
mandatory; acceptance evidence is the tail-app non-regression test.
(2) codegen is in iter-1 scope as stubs/pass-throughs because the
workspace must compile for cargo test --workspace.

Three plan-pseudo-vs-reality substitutions (serde Type::Con
literal, bare Int -> (con Int), unqualified LoopBinder) and one
recon-undercount integration-test site, all intent-preserving and
journalled. Boss forward-fix folded in: the committed specs
themselves wrote bare Int in the loop-binder snippets (parses as
Type::Var) — corrected the three headline snippets to (con Int) for
doc-honesty (no design/schema change).

cargo test --workspace 600 -> 608 / 0 red (Boss-reran
independently); iter13a + new loop_recur hash pins green.

crates/ailang-check/src/lib.rs

@@ -261,6 +261,23 @@ pub(crate) fn substitute_rigids_in_term(t: &Term, mapping: &BTreeMap<String, Typ
             name: name.clone(),
             value: Box::new(substitute_rigids_in_term(value, mapping)),
         },
+        Term::Loop { binders, body } => Term::Loop {
+            binders: binders
+                .iter()
+                .map(|b| ailang_core::ast::LoopBinder {
+                    name: b.name.clone(),
+                    ty: substitute_rigids(&b.ty, mapping),
+                    init: substitute_rigids_in_term(&b.init, mapping),
+                })
+                .collect(),
+            body: Box::new(substitute_rigids_in_term(body, mapping)),
+        },
+        Term::Recur { args } => Term::Recur {
+            args: args
+                .iter()
+                .map(|a| substitute_rigids_in_term(a, mapping))
+                .collect(),
+        },
     }
 }
 
@@ -2679,6 +2696,31 @@ pub fn verify_tail_positions(t: &Term, is_tail: bool) -> Result<()> {
         // be in tail position. Its `value` is also not in tail
         // position.
         Term::Assign { value, .. } => verify_tail_positions(value, false),
+        // loop-recur iter 1: binder inits are evaluated once on loop
+        // entry, NOT in tail position (mirror the Term::Mut arm
+        // above). The loop body inherits the enclosing tail position
+        // (the loop's value is the body's value on the exiting
+        // iteration). This arm only defines tail-app descent through
+        // the new node; it makes NO claim about recur tail-position
+        // (that is loop-recur iter 2's `verify_loop_body`). The
+        // tail-app verification role is unchanged — no pre-existing
+        // fixture contains a `loop`/`recur` node.
+        Term::Loop { binders, body } => {
+            for b in binders {
+                verify_tail_positions(&b.init, false)?;
+            }
+            verify_tail_positions(body, is_tail)
+        }
+        // recur transfers control and does not fall through, so there
+        // is no tail position to propagate. Its args are evaluated in
+        // non-tail position (call-argument-like). Introduces no
+        // tail-app violation.
+        Term::Recur { args } => {
+            for a in args {
+                verify_tail_positions(a, false)?;
+            }
+            Ok(())
+        }
     }
 }
 
@@ -3592,6 +3634,8 @@ pub(crate) fn synth(
                         Term::ReuseAs { .. } => "reuse-as",
                         Term::Mut { .. } => "mut",
                         Term::Assign { .. } => "assign",
+                        Term::Loop { .. } => "loop",
+                        Term::Recur { .. } => "recur",
                         Term::Ctor { .. } | Term::Lam { .. } => unreachable!(),
                     };
                     return Err(CheckError::ReuseAsNonAllocatingBody {
@@ -3687,6 +3731,15 @@ pub(crate) fn synth(
                 }
             }
         }
+        // loop-recur iter 1: typecheck semantics (binder typing,
+        // recur arity/type unification, verify_loop_body
+        // tail-position, the four Recur* CheckError variants) land
+        // in loop-recur iter 2. This iter stubs the dispatch so the
+        // workspace compiles and round-trips; no loop/recur fixture
+        // is typechecked in iter 1. Mirrors mut.1's synth stub.
+        Term::Loop { .. } | Term::Recur { .. } => Err(CheckError::Internal(
+            "Term::Loop/Term::Recur typecheck lands in loop-recur iter 2".into(),
+        )),
     }
 }
 

crates/ailang-check/src/lift.rs

@@ -397,6 +397,25 @@ impl<'a> Lifter<'a> {
                 name: name.clone(),
                 value: Box::new(self.lift_in_term(value, locals, in_def)?),
             }),
+            Term::Loop { binders, body } => Ok(Term::Loop {
+                binders: binders
+                    .iter()
+                    .map(|b| {
+                        Ok(ailang_core::ast::LoopBinder {
+                            name: b.name.clone(),
+                            ty: b.ty.clone(),
+                            init: self.lift_in_term(&b.init, locals, in_def)?,
+                        })
+                    })
+                    .collect::<Result<Vec<_>>>()?,
+                body: Box::new(self.lift_in_term(body, locals, in_def)?),
+            }),
+            Term::Recur { args } => Ok(Term::Recur {
+                args: args
+                    .iter()
+                    .map(|a| self.lift_in_term(a, locals, in_def))
+                    .collect::<Result<Vec<_>>>()?,
+            }),
             Term::LetRec { name, ty, params, body, in_term } => {
                 // Iter 16b.3: post-order traversal — lift any inner
                 // LetRecs first. Within the body's scope, `name` and
@@ -761,6 +780,10 @@ fn contains_any_letrec(m: &Module) -> bool {
                 vars.iter().any(|v| term_has_letrec(&v.init)) || term_has_letrec(body)
             }
             Term::Assign { value, .. } => term_has_letrec(value),
+            Term::Loop { binders, body } => {
+                binders.iter().any(|b| term_has_letrec(&b.init)) || term_has_letrec(body)
+            }
+            Term::Recur { args } => args.iter().any(term_has_letrec),
         }
     }
     for def in &m.defs {

crates/ailang-check/src/linearity.rs

@@ -609,6 +609,17 @@ impl<'a> Checker<'a> {
                 // a tracked binder). Walk the `value` normally.
                 self.walk(value, Position::Consume);
             }
+            Term::Loop { binders, body } => {
+                for b in binders {
+                    self.walk(&b.init, Position::Consume);
+                }
+                self.walk(body, pos);
+            }
+            Term::Recur { args } => {
+                for a in args {
+                    self.walk(a, Position::Consume);
+                }
+            }
         }
     }
 
@@ -795,6 +806,8 @@ fn make_reuse_as_source_not_bare_var(def: &str, source: &Term, body: &Term) -> D
         Term::ReuseAs { .. } => "reuse-as",
         Term::Mut { .. } => "mut",
         Term::Assign { .. } => "assign",
+        Term::Loop { .. } => "loop",
+        Term::Recur { .. } => "recur",
     };
     let replacement = term_to_form_a(body);
     Diagnostic::error(
@@ -934,6 +947,14 @@ fn any_sub_binder_consumed_for(
         Term::Assign { value, .. } => {
             any_sub_binder_consumed_for(value, pname, uniq, def_name, ctors)
         }
+        Term::Loop { binders, body } => {
+            binders.iter().any(|b| {
+                any_sub_binder_consumed_for(&b.init, pname, uniq, def_name, ctors)
+            }) || any_sub_binder_consumed_for(body, pname, uniq, def_name, ctors)
+        }
+        Term::Recur { args } => args.iter().any(|a| {
+            any_sub_binder_consumed_for(a, pname, uniq, def_name, ctors)
+        }),
     }
 }
 

crates/ailang-check/src/mono.rs

@@ -1243,6 +1243,17 @@ fn rewrite_mono_calls(
         Term::Assign { value, .. } => {
             rewrite_mono_calls(value, method_to_candidate_classes, poly_free_fns, poly_free_fn_ccounts, caller_module, ordered_targets, cursor, locals);
         }
+        Term::Loop { binders, body } => {
+            for b in binders.iter_mut() {
+                rewrite_mono_calls(&mut b.init, method_to_candidate_classes, poly_free_fns, poly_free_fn_ccounts, caller_module, ordered_targets, cursor, locals);
+            }
+            rewrite_mono_calls(body, method_to_candidate_classes, poly_free_fns, poly_free_fn_ccounts, caller_module, ordered_targets, cursor, locals);
+        }
+        Term::Recur { args } => {
+            for a in args.iter_mut() {
+                rewrite_mono_calls(a, method_to_candidate_classes, poly_free_fns, poly_free_fn_ccounts, caller_module, ordered_targets, cursor, locals);
+            }
+        }
         Term::Lit { .. } => {}
     }
 }
@@ -1617,6 +1628,17 @@ fn interleave_slots(
         Term::Assign { value, .. } => {
             interleave_slots(value, method_to_candidate_classes, poly_free_fns, poly_free_fn_ccounts, class_slots, free_fn_slots, class_cur, free_cur, locals, out);
         }
+        Term::Loop { binders, body } => {
+            for b in binders {
+                interleave_slots(&b.init, method_to_candidate_classes, poly_free_fns, poly_free_fn_ccounts, class_slots, free_fn_slots, class_cur, free_cur, locals, out);
+            }
+            interleave_slots(body, method_to_candidate_classes, poly_free_fns, poly_free_fn_ccounts, class_slots, free_fn_slots, class_cur, free_cur, locals, out);
+        }
+        Term::Recur { args } => {
+            for a in args {
+                interleave_slots(a, method_to_candidate_classes, poly_free_fns, poly_free_fn_ccounts, class_slots, free_fn_slots, class_cur, free_cur, locals, out);
+            }
+        }
         Term::Lit { .. } => {}
     }
 }

crates/ailang-check/src/pre_desugar_validation.rs

@@ -133,6 +133,18 @@ fn walk_term(t: &Term) -> Result<(), CheckError> {
             walk_term(body)
         }
         Term::Assign { value, .. } => walk_term(value),
+        Term::Loop { binders, body } => {
+            for b in binders {
+                walk_term(&b.init)?;
+            }
+            walk_term(body)
+        }
+        Term::Recur { args } => {
+            for a in args {
+                walk_term(a)?;
+            }
+            Ok(())
+        }
     }
 }
 

crates/ailang-check/src/reuse_shape.rs

@@ -265,6 +265,17 @@ impl<'a> Checker<'a> {
                 self.walk(body);
             }
             Term::Assign { value, .. } => self.walk(value),
+            Term::Loop { binders, body } => {
+                for b in binders {
+                    self.walk(&b.init);
+                }
+                self.walk(body);
+            }
+            Term::Recur { args } => {
+                for a in args {
+                    self.walk(a);
+                }
+            }
         }
     }
 

crates/ailang-check/src/uniqueness.rs

@@ -352,6 +352,17 @@ impl<'a> Walker<'a> {
             Term::Assign { value, .. } => {
                 self.walk(value, Position::Consume);
             }
+            Term::Loop { binders, body } => {
+                for b in binders {
+                    self.walk(&b.init, Position::Consume);
+                }
+                self.walk(body, pos);
+            }
+            Term::Recur { args } => {
+                for a in args {
+                    self.walk(a, Position::Consume);
+                }
+            }
         }
     }