diff --git a/crates/ailang-codegen/src/lib.rs b/crates/ailang-codegen/src/lib.rs
index 0e46f1e..13e9eab 100644
--- a/crates/ailang-codegen/src/lib.rs
+++ b/crates/ailang-codegen/src/lib.rs
@@ -53,7 +53,7 @@ use subst::{
     qualify_local_types_codegen, unify_for_subst,
 };
 use synth::{
-    builtin_ail_type, builtin_binop, builtin_effect_op_ret, c_byte_len, default_triple,
+    builtin_ail_type, builtin_binop_typed, builtin_effect_op_ret, c_byte_len, default_triple,
     fn_sig_from_type, ll_string_literal, llvm_type,
 };
 
@@ -1733,25 +1733,42 @@ impl<'a> Emitter<'a> {
             return self.lower_eq(&arg_ty, &a, &b, &a_ll);
         }
 
-        // Built-in arithmetic / comparison.
-        if let Some((instr, ret_ty)) = builtin_binop(name) {
+        // Floats iter 4.2: arithmetic / comparison are now polymorphic
+        // over `{Int, Float}`. Resolve the arg type, then dispatch via
+        // `builtin_binop_typed`. Same shape as the `==` dispatch above.
+        // Comparison ops are matched here in iter 4.2 with Int-only
+        // dispatch (preserving pre-iter-4 behaviour) so the workspace
+        // stays green; iter 4.3 adds the Float comparison arms.
+        if matches!(name, "+" | "-" | "*" | "/" | "%" | "!=" | "<" | "<=" | ">" | ">=") {
             if args.len() != 2 {
                 return Err(CodegenError::Internal(format!(
                     "builtin `{name}` expected 2 args"
                 )));
             }
+            let arg_ty = self.synth_arg_type(&args[0])?;
+            let (instr, ll_ty) = builtin_binop_typed(name, &arg_ty)
+                .ok_or_else(|| CodegenError::Internal(format!(
+                    "`{name}` not supported for type `{}`",
+                    ailang_core::pretty::type_to_string(&arg_ty)
+                )))?;
             let (a, _) = self.lower_term(&args[0])?;
             let (b, _) = self.lower_term(&args[1])?;
             let dst = self.fresh_ssa();
             self.body.push_str(&format!(
-                "  {dst} = {instr} i64 {a}, {b}\n"
+                "  {dst} = {instr} {ll_ty} {a}, {b}\n"
             ));
             // Builtins are not function calls in LLVM (they're inline
             // arithmetic); `tail` annotation has nothing to act on.
             // The typechecker accepts the marker but it is a no-op
             // here. (Iter 14e survey: no fixture marks a builtin tail.)
             let _ = tail;
-            return Ok((dst, ret_ty.into()));
+            // Comparison ops return i1; arithmetic returns the operand type.
+            let result_ll_ty = if matches!(name, "!=" | "<" | "<=" | ">" | ">=") {
+                "i1".into()
+            } else {
+                ll_ty.into()
+            };
+            return Ok((dst, result_ll_ty));
         }
         if name == "not" {
             if args.len() != 1 {
@@ -2073,7 +2090,7 @@ impl<'a> Emitter<'a> {
     /// `prefix.def`. Locals shadow this — the caller checks for
     /// that first.
     fn is_static_callee(&self, name: &str) -> bool {
-        if builtin_binop(name).is_some() || name == "not" {
+        if matches!(name, "+" | "-" | "*" | "/" | "%" | "==" | "!=" | "<" | "<=" | ">" | ">=") || name == "not" {
             return true;
         }
         if name.matches('.').count() == 1 {
@@ -2918,4 +2935,64 @@ mod tests {
             "ir missing the Float literal lowering: {ir}"
         );
     }
+
+    /// Floats iter 4.2 RED: `(+ 1.5 2.5)` lowers as `fadd double`,
+    /// not `add i64`. The Int regression `(+ 1 2)` still lowers as
+    /// `add i64`. Both lowerings live in one IR for one workspace
+    /// build.
+    #[test]
+    fn lowers_float_arithmetic_dispatched() {
+        use ailang_core::ast::*;
+        fn fn_def(name: &str, body: Term, ret_ty: Type) -> Def {
+            Def::Fn(FnDef {
+                name: name.into(),
+                ty: Type::Fn {
+                    params: vec![],
+                    ret: Box::new(ret_ty),
+                    effects: vec![],
+                    param_modes: vec![],
+                    ret_mode: ParamMode::Implicit,
+                },
+                params: vec![],
+                body,
+                suppress: vec![],
+                doc: None,
+            })
+        }
+        let plus_int = Term::App {
+            callee: Box::new(Term::Var { name: "+".into() }),
+            args: vec![
+                Term::Lit { lit: Literal::Int { value: 1 } },
+                Term::Lit { lit: Literal::Int { value: 2 } },
+            ],
+            tail: false,
+        };
+        let plus_float = Term::App {
+            callee: Box::new(Term::Var { name: "+".into() }),
+            args: vec![
+                Term::Lit { lit: Literal::Float { bits: 0x3ff8_0000_0000_0000u64 } },
+                Term::Lit { lit: Literal::Float { bits: 0x4004_0000_0000_0000u64 } },
+            ],
+            tail: false,
+        };
+        let m = Module {
+            schema: ailang_core::SCHEMA.to_string(),
+            name: "t".into(),
+            imports: vec![],
+            defs: vec![
+                fn_def("ai", plus_int, Type::int()),
+                fn_def("af", plus_float, Type::float()),
+                fn_def("main", Term::Lit { lit: Literal::Unit }, Type::unit()),
+            ],
+        };
+        let ir = emit_ir(&m).unwrap();
+        assert!(
+            ir.contains("add i64"),
+            "Int arithmetic regressed (no `add i64` in IR): {ir}"
+        );
+        assert!(
+            ir.contains("fadd double"),
+            "Float arithmetic missing (no `fadd double` in IR): {ir}"
+        );
+    }
 }
diff --git a/crates/ailang-codegen/src/synth.rs b/crates/ailang-codegen/src/synth.rs
index cf82811..553067a 100644
--- a/crates/ailang-codegen/src/synth.rs
+++ b/crates/ailang-codegen/src/synth.rs
@@ -239,21 +239,37 @@ pub(crate) fn type_descriptor(t: &Type) -> String {
     }
 }
 
-pub(crate) fn builtin_binop(name: &str) -> Option<(&'static str, &'static str)> {
-    Some(match name {
-        "+" => ("add", "i64"),
-        "-" => ("sub", "i64"),
-        "*" => ("mul", "i64"),
-        "/" => ("sdiv", "i64"),
-        "%" => ("srem", "i64"),
-        "==" => ("icmp eq", "i1"),
-        "!=" => ("icmp ne", "i1"),
-        "<" => ("icmp slt", "i1"),
-        "<=" => ("icmp sle", "i1"),
-        ">" => ("icmp sgt", "i1"),
-        ">=" => ("icmp sge", "i1"),
-        _ => return None,
-    })
+/// Floats iter 4.2: arithmetic / comparison ops are type-dispatched
+/// over `{Int, Float}`. Caller (`lower_app`) resolves the arg type
+/// via `synth_arg_type` and passes it here. Returns the
+/// `(instruction, llvm_type)` pair to emit. `%` stays Int-only.
+///
+/// Comparison-op Int arms are kept here in iter 4.2 to preserve
+/// the no-regression invariant — pre-iter-4 codegen routed
+/// `<`/`<=`/`>`/`>=`/`!=` through the same Int-only `builtin_binop`
+/// table. Iter 4.3 adds the Float arms.
+pub(crate) fn builtin_binop_typed(name: &str, arg_ty: &Type) -> Option<(&'static str, &'static str)> {
+    let is_int = matches!(arg_ty, Type::Con { name, .. } if name == "Int");
+    let is_float = matches!(arg_ty, Type::Con { name, .. } if name == "Float");
+    match (name, is_int, is_float) {
+        ("+", true, _) => Some(("add", "i64")),
+        ("+", _, true) => Some(("fadd", "double")),
+        ("-", true, _) => Some(("sub", "i64")),
+        ("-", _, true) => Some(("fsub", "double")),
+        ("*", true, _) => Some(("mul", "i64")),
+        ("*", _, true) => Some(("fmul", "double")),
+        ("/", true, _) => Some(("sdiv", "i64")),
+        ("/", _, true) => Some(("fdiv", "double")),
+        ("%", true, _) => Some(("srem", "i64")),
+        // Int-arm comparisons preserved from pre-iter-4 `builtin_binop`.
+        // Float arms land in iter 4.3.
+        ("!=", true, _) => Some(("icmp ne", "i64")),
+        ("<", true, _) => Some(("icmp slt", "i64")),
+        ("<=", true, _) => Some(("icmp sle", "i64")),
+        (">", true, _) => Some(("icmp sgt", "i64")),
+        (">=", true, _) => Some(("icmp sge", "i64")),
+        _ => None,
+    }
 }
 
 pub(crate) fn c_byte_len(s: &str) -> usize {