From 24dafcdb1a1df220fd25a6560674af40ec7de2a7 Mon Sep 17 00:00:00 2001
From: Gabriel Barreto <gabriel.aquino.barreto@gmail.com>
Date: Tue, 17 Mar 2026 17:23:05 -0300
Subject: [PATCH 1/6] U64 alias

---
 Ix/IxVM/Blake3.lean      |  4 +--
 Ix/IxVM/ByteStream.lean  | 26 +++++++++---------
 Ix/IxVM/KernelTypes.lean | 58 ++++++++++++++++++++--------------------
 Ix/IxVM/Sha256.lean      |  4 +--
 4 files changed, 47 insertions(+), 45 deletions(-)

diff --git a/Ix/IxVM/Blake3.lean b/Ix/IxVM/Blake3.lean
index 0603a4e0..df1a5ca8 100644
--- a/Ix/IxVM/Blake3.lean
+++ b/Ix/IxVM/Blake3.lean
@@ -91,7 +91,7 @@ def blake3 := ⟦
     block_buffer: [[G; 4]; 16],
     block_index: G,
     chunk_index: G,
-    chunk_count: [G; 8],
+    chunk_count: U64,
     block_digest: [[G; 4]; 8],
     layer: Layer
   ) -> Layer {
@@ -307,7 +307,7 @@ def blake3 := ⟦
   fn blake3_compress(
     chaining_value: [[G; 4]; 8],
     block_words: [[G; 4]; 16],
-    counter: [G; 8],
+    counter: U64,
     block_len: G,
     flags: G
   ) -> [[G; 4]; 8] {
diff --git a/Ix/IxVM/ByteStream.lean b/Ix/IxVM/ByteStream.lean
index 425ba357..e2779905 100644
--- a/Ix/IxVM/ByteStream.lean
+++ b/Ix/IxVM/ByteStream.lean
@@ -11,6 +11,8 @@ def byteStream := ⟦
     Nil
   }
 
+  type U64 = [G; 8]
+
   fn byte_stream_concat(a: ByteStream, b: ByteStream) -> ByteStream {
     match a {
       ByteStream.Nil => b,
@@ -19,7 +21,7 @@ def byteStream := ⟦
     }
   }
 
-  fn byte_stream_length(bytes: ByteStream) -> [G; 8] {
+  fn byte_stream_length(bytes: ByteStream) -> U64 {
     match bytes {
       ByteStream.Nil => [0; 8],
       ByteStream.Cons(_, &rest) => relaxed_u64_succ(byte_stream_length(rest)),
@@ -48,7 +50,7 @@ def byteStream := ⟦
   -- Count bytes needed to represent a u64.
   -- Important: this implementation differs from the Lean and Rust ones, returning
   -- 1 for [0; 8] instead of 0.
-  fn u64_byte_count(x: [G; 8]) -> G {
+  fn u64_byte_count(x: U64) -> G {
     match x {
       [_, 0, 0, 0, 0, 0, 0, 0] => 1,
       [_, _, 0, 0, 0, 0, 0, 0] => 2,
@@ -61,7 +63,7 @@ def byteStream := ⟦
     }
   }
 
-  fn u64_is_zero(x: [G; 8]) -> G {
+  fn u64_is_zero(x: U64) -> G {
     match x {
       [0, 0, 0, 0, 0, 0, 0, 0] => 1,
       _ => 0,
@@ -69,7 +71,7 @@ def byteStream := ⟦
   }
 
   -- Reconstructs a byte from its bits in little-endian.
-  fn u8_recompose(bits: [G; 8]) -> G {
+  fn u8_recompose(bits: U64) -> G {
     let [b0, b1, b2, b3, b4, b5, b6, b7] = bits;
     b0 + 2 * b1 + 4 * b2 + 8 * b3 + 16 * b4 + 32 * b5 + 64 * b6 + 128 * b7
   }
@@ -115,7 +117,7 @@ def byteStream := ⟦
   }
 
   -- Byte-by-byte `u64` equality
-  fn u64_eq(a: [G; 8], b: [G; 8]) -> G {
+  fn u64_eq(a: U64, b: U64) -> G {
     let [a0, a1, a2, a3, a4, a5, a6, a7] = a;
     let [b0, b1, b2, b3, b4, b5, b6, b7] = b;
     match [a0 - b0, a1 - b1, a2 - b2, a3 - b3, a4 - b4, a5 - b5, a6 - b6, a7 - b7] {
@@ -125,7 +127,7 @@ def byteStream := ⟦
   }
 
   -- `u64` addition with carry propagation (little-endian bytes)
-  fn u64_add(a: [G; 8], b: [G; 8]) -> [G; 8] {
+  fn u64_add(a: U64, b: U64) -> U64 {
     let [a0, a1, a2, a3, a4, a5, a6, a7] = a;
     let [b0, b1, b2, b3, b4, b5, b6, b7] = b;
     let (s0, c1) = u8_add(a0, b0);
@@ -153,7 +155,7 @@ def byteStream := ⟦
   }
 
   -- `u64` subtraction via repeated decrement (correct for small b)
-  fn u64_sub(a: [G; 8], b: [G; 8]) -> [G; 8] {
+  fn u64_sub(a: U64, b: U64) -> U64 {
     match u64_is_zero(b) {
       1 => a,
       0 => u64_sub(relaxed_u64_pred(a), relaxed_u64_pred(b)),
@@ -169,7 +171,7 @@ def byteStream := ⟦
 
   -- Computes the successor of an `u64` assumed to be properly represented in
   -- little-endian bytes. If that's not the case, this implementation has UB.
-  fn relaxed_u64_succ(bytes: [G; 8]) -> [G; 8] {
+  fn relaxed_u64_succ(bytes: U64) -> U64 {
     let [b0, b1, b2, b3, b4, b5, b6, b7] = bytes;
     match b0 {
       255 => match b1 {
@@ -198,7 +200,7 @@ def byteStream := ⟦
     }
   }
 
-  fn relaxed_u64_be_add_2_bytes(u64: [G; 8], bs: [G; 2]) -> [G; 8] {
+  fn relaxed_u64_be_add_2_bytes(u64: U64, bs: [G; 2]) -> U64 {
     -- Byte 0, no initial carry
     let (sum0, carry1) = u8_add(u64[7], bs[1]);
 
@@ -240,13 +242,13 @@ def byteStream := ⟦
   }
 
   enum U64List {
-    Cons([G; 8], &U64List),
+    Cons(U64, &U64List),
     Nil
   }
 
   -- Computes the predecessor of an `u64` assumed to be properly represented in
   -- little-endian bytes. If that's not the case, this implementation has UB.
-  fn relaxed_u64_pred(bytes: [G; 8]) -> [G; 8] {
+  fn relaxed_u64_pred(bytes: U64) -> U64 {
     let [b0, b1, b2, b3, b4, b5, b6, b7] = bytes;
     match b0 {
       0 => match b1 {
@@ -275,7 +277,7 @@ def byteStream := ⟦
     }
   }
 
-  fn u64_list_length(xs: U64List) -> [G; 8] {
+  fn u64_list_length(xs: U64List) -> U64 {
     match xs {
       U64List.Nil => [0; 8],
       U64List.Cons(_, rest) => relaxed_u64_succ(u64_list_length(load(rest))),
diff --git a/Ix/IxVM/KernelTypes.lean b/Ix/IxVM/KernelTypes.lean
index 945ea584..8d8aa71b 100644
--- a/Ix/IxVM/KernelTypes.lean
+++ b/Ix/IxVM/KernelTypes.lean
@@ -10,13 +10,13 @@ def kernelTypes := ⟦
   -- Universe Levels
   -- ============================================================================
 
-  -- TODO: Param index could be G instead of [G; 8] (Goldilocks is big enough)
+  -- TODO: Param index could be G instead of U64 (Goldilocks is big enough)
   enum KLevel {
     Zero,
     Succ(&KLevel),
     Max(&KLevel, &KLevel),
     IMax(&KLevel, &KLevel),
-    Param([G; 8])
+    Param(U64)
   }
 
   enum KLevelList {
@@ -28,37 +28,37 @@ def kernelTypes := ⟦
   -- Literals
   -- ============================================================================
 
-  -- TODO: [G; 8] is insufficient — Nat and String literals are arbitrarily large.
+  -- TODO: U64 is insufficient — Nat and String literals are arbitrarily large.
   -- Nat should be a list of u64 limbs (little-endian bignum).
   -- Str should be a list of bytes (or a ByteStream).
   -- This also requires fixing the blob ingress and conversion to produce these types.
   enum KLiteral {
-    Nat([G; 8]),
-    Str([G; 8])
+    Nat(U64),
+    Str(U64)
   }
 
   -- ============================================================================
   -- Expressions (de Bruijn indexed, no binder info or names)
   -- ============================================================================
 
-  -- TODO: all [G; 8] here (BVar index, Const index, Proj indices) could be G
+  -- TODO: all U64 here (BVar index, Const index, Proj indices) could be G
   enum KExpr {
-    BVar([G; 8]),
+    BVar(U64),
     Srt(&KLevel),
-    Const([G; 8], &KLevelList),
+    Const(U64, &KLevelList),
     App(&KExpr, &KExpr),
     Lam(&KExpr, &KExpr),
     Forall(&KExpr, &KExpr),
     Let(&KExpr, &KExpr, &KExpr),
     Lit(KLiteral),
-    Proj([G; 8], [G; 8], &KExpr)
+    Proj(U64, U64, &KExpr)
   }
 
   -- ============================================================================
   -- Values (NbE semantic domain)
   -- ============================================================================
 
-  -- TODO: all [G; 8] here could be G. In particular, FVar's de Bruijn level
+  -- TODO: all U64 here could be G. In particular, FVar's de Bruijn level
   -- is a runtime counter (not from Ixon) and would benefit most from the change,
   -- since it would simplify depth tracking throughout the kernel to use plain G
   -- arithmetic instead of u64 operations.
@@ -67,10 +67,10 @@ def kernelTypes := ⟦
     Lit(KLiteral),
     Lam(&KVal, &KExpr, &KValEnv),
     Pi(&KVal, &KExpr, &KValEnv),
-    Ctor([G; 8], &KLevelList, [G; 8], &KValList),
-    FVar([G; 8], &KValList),
-    Const([G; 8], &KLevelList, &KValList),
-    Proj([G; 8], [G; 8], &KVal, &KValList),
+    Ctor(U64, &KLevelList, U64, &KValList),
+    FVar(U64, &KValList),
+    Const(U64, &KLevelList, &KValList),
+    Proj(U64, U64, &KVal, &KValList),
     Thunk(&KExpr, &KValEnv)
   }
 
@@ -90,11 +90,11 @@ def kernelTypes := ⟦
   -- Reducibility Hints
   -- ============================================================================
 
-  -- TODO: Regular hint could be G instead of [G; 8]
+  -- TODO: Regular hint could be G instead of U64
   enum KHints {
     Opaque,
     Abbrev,
-    Regular([G; 8])
+    Regular(U64)
   }
 
   -- ============================================================================
@@ -122,9 +122,9 @@ def kernelTypes := ⟦
   -- Recursor Rule: (ctor_const_idx, num_fields, rhs)
   -- ============================================================================
 
-  -- TODO: ctor_const_idx and num_fields could be G instead of [G; 8]
+  -- TODO: ctor_const_idx and num_fields could be G instead of U64
   enum KRecRule {
-    Mk([G; 8], [G; 8], &KExpr)
+    Mk(U64, U64, &KExpr)
   }
 
   enum KRecRuleList {
@@ -148,26 +148,26 @@ def kernelTypes := ⟦
   --            num_motives, num_minors, rules, k_flag, is_unsafe)
   -- ============================================================================
 
-  -- TODO: could be a list of G instead of [G; 8]
+  -- TODO: could be a list of G instead of U64
   enum KU64List {
-    Cons([G; 8], &KU64List),
+    Cons(U64, &KU64List),
     Nil
   }
 
-  -- TODO: all [G; 8] fields (num_levels, num_params, num_indices, etc.)
+  -- TODO: all U64 fields (num_levels, num_params, num_indices, etc.)
   -- could be G instead. The Goldilocks field is large enough for any
   -- realistic value, and using G would simplify arithmetic throughout
   -- the kernel (native field ops instead of u64_add/u64_sub/u64_eq/etc.).
   -- This requires a corresponding change in Convert.lean to emit G values.
   enum KConstantInfo {
-    Axiom([G; 8], &KExpr, G),
-    Defn([G; 8], &KExpr, &KExpr, KHints, KSafety),
-    Thm([G; 8], &KExpr, &KExpr),
-    Opaque([G; 8], &KExpr, &KExpr, G),
-    Quot([G; 8], &KExpr, KQuotKind),
-    Induct([G; 8], &KExpr, [G; 8], [G; 8], &KU64List, G, G, G),
-    Ctor([G; 8], &KExpr, [G; 8], [G; 8], [G; 8], [G; 8], G),
-    Rec([G; 8], &KExpr, [G; 8], [G; 8], [G; 8], [G; 8], &KRecRuleList, G, G)
+    Axiom(U64, &KExpr, G),
+    Defn(U64, &KExpr, &KExpr, KHints, KSafety),
+    Thm(U64, &KExpr, &KExpr),
+    Opaque(U64, &KExpr, &KExpr, G),
+    Quot(U64, &KExpr, KQuotKind),
+    Induct(U64, &KExpr, U64, U64, &KU64List, G, G, G),
+    Ctor(U64, &KExpr, U64, U64, U64, U64, G),
+    Rec(U64, &KExpr, U64, U64, U64, U64, &KRecRuleList, G, G)
   }
 
   -- The global environment: a list of constants indexed by position
diff --git a/Ix/IxVM/Sha256.lean b/Ix/IxVM/Sha256.lean
index 09e6528e..697d1b72 100644
--- a/Ix/IxVM/Sha256.lean
+++ b/Ix/IxVM/Sha256.lean
@@ -44,7 +44,7 @@ def sha256 := ⟦
     sha256_aux(stream, [0; 8], state)
   }
 
-  fn sha256_aux(stream: ByteStream, len_be: [G; 8], state: [[G; 4]; 8]) -> [[G; 4]; 8] {
+  fn sha256_aux(stream: ByteStream, len_be: U64, state: [[G; 4]; 8]) -> [[G; 4]; 8] {
     let W = [[0; 4]; 16];
     match stream {
       ByteStream.Nil =>
@@ -586,7 +586,7 @@ def sha256 := ⟦
     }
   }
 
-  fn fill_W_with_length_and_run_rounds(len_be: [G; 8], state: [[G; 4]; 8]) -> [[G; 4]; 8] {
+  fn fill_W_with_length_and_run_rounds(len_be: U64, state: [[G; 4]; 8]) -> [[G; 4]; 8] {
     let W = [[0; 4]; 16];
     let W = set(W, 14, [len_be[0], len_be[1], len_be[2], len_be[3]]);
     let W = set(W, 15, [len_be[4], len_be[5], len_be[6], len_be[7]]);

From 06298553c136826f9d6945b024ef89d7c4ad1022 Mon Sep 17 00:00:00 2001
From: Gabriel Barreto <gabriel.aquino.barreto@gmail.com>
Date: Thu, 19 Mar 2026 10:38:12 -0300
Subject: [PATCH 2/6] type alias with eager expansion

---
 Ix/Aiur/Check.lean   | 21 ++++++-----
 Ix/Aiur/Compile.lean |  2 +-
 Ix/Aiur/Meta.lean    | 31 +++++++++++-----
 Ix/Aiur/Simple.lean  |  5 +++
 Ix/Aiur/Term.lean    | 84 +++++++++++++++++++++++++++++++++++++++++---
 5 files changed, 120 insertions(+), 23 deletions(-)

diff --git a/Ix/Aiur/Check.lean b/Ix/Aiur/Check.lean
index 38690d83..81a2b24b 100644
--- a/Ix/Aiur/Check.lean
+++ b/Ix/Aiur/Check.lean
@@ -37,11 +37,13 @@ instance : ToString CheckError where
 
 /--
 Constructs a map of declarations from a toplevel, ensuring that there are no duplicate names
-for functions and datatypes.
+for functions, datatypes, and type aliases.
 -/
 def Toplevel.mkDecls (toplevel : Toplevel) : Except CheckError Decls := do
   let map ← toplevel.functions.foldlM (init := default)
     fun acc function => addDecl acc Function.name .function function
+  let map ← toplevel.typeAliases.foldlM (init := map)
+    fun acc alias => addDecl (α := TypeAlias) acc (·.name) .typeAlias alias
   toplevel.dataTypes.foldlM (init := map) addDataType
 where
   ensureUnique name (map : IndexMap Global _) := do
@@ -73,7 +75,7 @@ def refLookup (global : Global) : CheckM Typ := do
   | some (.constructor dataType constructor) =>
     let args := constructor.argTypes
     unless args.isEmpty do (throw $ .wrongNumArgs global args.length 0)
-    pure $ .dataType $ dataType.name
+    pure $ .typeRef $ dataType.name
   | some _ => throw $ .notAValue global
   | none => throw $ .unboundVariable global
 
@@ -278,7 +280,7 @@ partial def inferUnqualifiedApp (func : Global) (unqualifiedFunc : String) (args
       pure ⟨function.output, .app func args, false⟩
     | some (.constructor dataType constr) => do
       let args ← checkArgsAndInputs func args constr.argTypes
-      pure ⟨.dataType dataType.name, .app func args, false⟩
+      pure ⟨.typeRef dataType.name, .app func args, false⟩
     | _ => throw $ .cannotApply func
 where
   checkArgsAndInputs func args inputs : CheckM (List TypedTerm) := do
@@ -298,7 +300,7 @@ partial def inferQualifiedApp (func : Global) (args : List Term) : CheckM TypedT
     pure ⟨function.output, .app func args, false⟩
   | some (.constructor dataType constr) =>
     let args ← checkArgsAndInputs func args constr.argTypes
-    pure ⟨.dataType dataType.name, .app func args, false⟩
+    pure ⟨.typeRef dataType.name, .app func args, false⟩
   | _ => throw $ .cannotApply func
 where
   checkArgsAndInputs func args inputs : CheckM (List TypedTerm) := do
@@ -399,7 +401,7 @@ where
       let typ' := .function (function.inputs.map Prod.snd) function.output
       unless typ == typ' do throw $ .typeMismatch typ typ'
       pure []
-    | (.ref constrRef pats, .dataType dataTypeRef) => do
+    | (.ref constrRef pats, .typeRef dataTypeRef) => do
       let ctx ← read
       let some (.dataType dataType) := ctx.decls.getByKey dataTypeRef | unreachable!
       let some (.constructor dataType' constr) := ctx.decls.getByKey constrRef | throw $ .notAConstructor constrRef
@@ -455,6 +457,8 @@ where
       if !map.contains dataType.name then
         set $ map.insert dataType.name
         dataType.constructors.flatMap (·.argTypes) |>.forM wellFormedType
+    | .typeAlias alias => do
+      wellFormedType alias.expansion
     | .function function => do
       wellFormedType function.output
       function.inputs.forM fun (_, typ) => wellFormedType typ
@@ -463,10 +467,11 @@ where
   wellFormedType : Typ → EStateM CheckError (Std.HashSet Global) Unit
     | .tuple typs => typs.forM wellFormedType
     | .pointer pointerTyp => wellFormedType pointerTyp
-    | .dataType dataTypeRef => match decls.getByKey dataTypeRef with
+    | .typeRef typeRef => match decls.getByKey typeRef with
       | some (.dataType _) => pure ()
-      | some _ => throw $ .notADataType dataTypeRef
-      | none => throw $ .undefinedGlobal dataTypeRef
+      | some (.typeAlias _) => pure ()
+      | some _ => throw $ .notADataType typeRef
+      | none => throw $ .undefinedGlobal typeRef
     | _ => pure ()
 
 /-- Checks a function to ensure its body's type matches its declared output type. -/
diff --git a/Ix/Aiur/Compile.lean b/Ix/Aiur/Compile.lean
index 9b553b2a..a741e2d9 100644
--- a/Ix/Aiur/Compile.lean
+++ b/Ix/Aiur/Compile.lean
@@ -240,7 +240,7 @@ def typSize (layoutMap : LayoutMap) : Typ → Except String Nat
 | .array typ n => do
   let size ← typSize layoutMap typ
   pure $ n * size
-| .dataType g => match layoutMap[g]? with
+| .typeRef g => match layoutMap[g]? with
   | some (.dataType layout) => pure layout.size
   | _ => throw "Impossible case"
 
diff --git a/Ix/Aiur/Meta.lean b/Ix/Aiur/Meta.lean
index b0eaf280..2f077428 100644
--- a/Ix/Aiur/Meta.lean
+++ b/Ix/Aiur/Meta.lean
@@ -86,7 +86,7 @@ partial def elabTyp : ElabStxCat `typ
     mkAppM ``Typ.pointer #[← elabTyp t]
   | `(typ| $[.]?$i:ident) => do
     let g ← mkAppM ``Global.mk #[toExpr i.getId]
-    mkAppM ``Typ.dataType #[g]
+    mkAppM ``Typ.typeRef #[g]
   | `(typ| fn() -> $t:typ) => do
     mkAppM ``Typ.function #[← elabEmptyList ``Typ, ← elabTyp t]
   | `(typ| fn($t$[, $ts:typ]*) -> $t':typ) => do
@@ -441,6 +441,15 @@ def elabDataType : ElabStxCat `data_type
     mkAppM ``DataType.mk #[g, ← elabList c cs elabConstructor ``Constructor]
   | stx => throw $ .error stx "Invalid syntax for data type"
 
+declare_syntax_cat             type_alias
+syntax "type " ident " = " typ : type_alias
+
+def elabTypeAlias : ElabStxCat `type_alias
+  | `(type_alias| type $n:ident = $t:typ) => do
+    let g ← mkAppM ``Global.mk #[toExpr n.getId]
+    mkAppM ``TypeAlias.mk #[g, ← elabTyp t]
+  | stx => throw $ .error stx "Invalid syntax for type alias"
+
 declare_syntax_cat      bind
 syntax ident ": " typ : bind
 
@@ -477,17 +486,20 @@ where
     | some typ => elabTyp typ
 
 declare_syntax_cat declaration
-syntax function  : declaration
-syntax data_type : declaration
+syntax function   : declaration
+syntax data_type  : declaration
+syntax type_alias : declaration
 
-def accElabDeclarations (declarations : (Array Expr × Array Expr))
-    (stx : TSyntax `declaration) : TermElabM (Array Expr × Array Expr) :=
-  let (dataTypes, functions) := declarations
+def accElabDeclarations (declarations : (Array Expr × Array Expr × Array Expr))
+    (stx : TSyntax `declaration) : TermElabM (Array Expr × Array Expr × Array Expr) :=
+  let (dataTypes, typeAliases, functions) := declarations
   match stx with
   | `(declaration| $f:function) => do
-    pure (dataTypes, functions.push $ ← elabFunction f)
+    pure (dataTypes, typeAliases, functions.push $ ← elabFunction f)
   | `(declaration| $d:data_type) => do
-    pure (dataTypes.push $ ← elabDataType d, functions)
+    pure (dataTypes.push $ ← elabDataType d, typeAliases, functions)
+  | `(declaration| $ta:type_alias) => do
+    pure (dataTypes, typeAliases.push $ ← elabTypeAlias ta, functions)
   | stx => throw $ .error stx "Invalid syntax for declaration"
 
 declare_syntax_cat    toplevel
@@ -495,9 +507,10 @@ syntax declaration* : toplevel
 
 def elabToplevel : ElabStxCat `toplevel
   | `(toplevel| $[$ds:declaration]*) => do
-    let (dataTypes, functions) ← ds.foldlM (init := default) accElabDeclarations
+    let (dataTypes, typeAliases, functions) ← ds.foldlM (init := default) accElabDeclarations
     mkAppM ``Toplevel.mk #[
       ← mkArrayLit (mkConst ``DataType) dataTypes.toList,
+      ← mkArrayLit (mkConst ``TypeAlias) typeAliases.toList,
       ← mkArrayLit (mkConst ``Function) functions.toList,
     ]
   | stx => throw $ .error stx "Invalid syntax for toplevel"
diff --git a/Ix/Aiur/Simple.lean b/Ix/Aiur/Simple.lean
index f20e5e9d..2e5036d7 100644
--- a/Ix/Aiur/Simple.lean
+++ b/Ix/Aiur/Simple.lean
@@ -38,6 +38,10 @@ where
   recr := simplifyTerm decls
 
 def Toplevel.checkAndSimplify (toplevel : Toplevel) : Except CheckError TypedDecls := do
+  -- First expand all type aliases
+  let toplevel ← match toplevel.expandAliases with
+    | .ok t => pure t
+    | .error e => throw (.undefinedGlobal ⟨.mkSimple e⟩)  -- TODO: better error handling
   let decls ← toplevel.mkDecls
   wellFormedDecls decls
   -- The first check happens on the original terms.
@@ -49,6 +53,7 @@ def Toplevel.checkAndSimplify (toplevel : Toplevel) : Except CheckError TypedDec
   decls.foldlM (init := default) fun typedDecls (name, decl) => match decl with
     | .constructor d c => pure $ typedDecls.insert name (.constructor d c)
     | .dataType d => pure $ typedDecls.insert name (.dataType d)
+    | .typeAlias _ => pure typedDecls  -- Type aliases should have been expanded by now
     | .function f => do
       -- The second check happens on the simplified terms.
       let f ← (checkFunction f) (getFunctionContext f decls)
diff --git a/Ix/Aiur/Term.lean b/Ix/Aiur/Term.lean
index ee662e79..78de10d6 100644
--- a/Ix/Aiur/Term.lean
+++ b/Ix/Aiur/Term.lean
@@ -58,7 +58,7 @@ inductive Typ where
   | tuple : Array Typ → Typ
   | array : Typ → Nat → Typ
   | pointer : Typ → Typ
-  | dataType : Global → Typ
+  | typeRef : Global → Typ
   | function : List Typ → Typ → Typ
   deriving Repr, BEq, Hashable, Inhabited
 
@@ -176,6 +176,11 @@ structure DataType where
   constructors : List Constructor
   deriving Repr, BEq, Inhabited
 
+structure TypeAlias where
+  name : Global
+  expansion : Typ
+  deriving Repr, BEq, Inhabited
+
 structure Function where
   name : Global
   inputs : List (Local × Typ)
@@ -186,6 +191,7 @@ structure Function where
 
 structure Toplevel where
   dataTypes : Array DataType
+  typeAliases : Array TypeAlias
   functions : Array Function
   deriving Repr
 
@@ -193,31 +199,99 @@ def Toplevel.getFuncIdx (toplevel : Toplevel) (funcName : Lean.Name) : Option Na
   toplevel.functions.findIdx? fun function => function.name.toName == funcName
 
 def Toplevel.merge (x y : Toplevel) : Except Global Toplevel := do
-  let ⟨xDataTypes, xFunctions⟩ := x
-  let ⟨yDataTypes, yFunctions⟩ := y
+  let ⟨xDataTypes, xTypeAliases, xFunctions⟩ := x
+  let ⟨yDataTypes, yTypeAliases, yFunctions⟩ := y
   let mut globals : Std.HashSet Global := ∅
   let mut dataTypes := .emptyWithCapacity (xDataTypes.size + yDataTypes.size)
+  let mut typeAliases := .emptyWithCapacity (xTypeAliases.size + yTypeAliases.size)
   let mut functions := .emptyWithCapacity (xFunctions.size + yFunctions.size)
   for dtSet in [xDataTypes, yDataTypes] do
     for dt in dtSet do
       if globals.contains dt.name then throw dt.name
       globals := globals.insert dt.name
       dataTypes := dataTypes.push dt
+  for taSet in [xTypeAliases, yTypeAliases] do
+    for ta in taSet do
+      if globals.contains ta.name then throw ta.name
+      globals := globals.insert ta.name
+      typeAliases := typeAliases.push ta
   for fSet in [xFunctions, yFunctions] do
     for f in fSet do
       if globals.contains f.name then throw f.name
       globals := globals.insert f.name
       functions := functions.push f
-  pure ⟨dataTypes, functions⟩
+  pure ⟨dataTypes, typeAliases, functions⟩
 
 inductive Declaration
   | function : Function → Declaration
   | dataType : DataType → Declaration
+  | typeAlias : TypeAlias → Declaration
   | constructor : DataType → Constructor → Declaration
   deriving Repr, Inhabited
 
 abbrev Decls := IndexMap Global Declaration
 
+/-- Eagerly expands type aliases in a type, detecting cycles. -/
+partial def Typ.expandAliases (decls : Decls) (visited : Std.HashSet Global := {}) :
+    Typ → Except String Typ
+  | .unit => pure .unit
+  | .field => pure .field
+  | .pointer t => do pure $ .pointer (← t.expandAliases decls visited)
+  | .function inputs output => do
+    let inputs' ← inputs.mapM (·.expandAliases decls visited)
+    let output' ← output.expandAliases decls visited
+    pure $ .function inputs' output'
+  | .tuple ts => do
+    let ts' ← ts.mapM (·.expandAliases decls visited)
+    pure $ .tuple ts'
+  | .array t n => do
+    let t' ← t.expandAliases decls visited
+    pure $ .array t' n
+  | .typeRef g => match decls.getByKey g with
+    | some (.typeAlias alias) =>
+      if visited.contains g then
+        throw s!"Cycle detected in type alias `{g}`"
+      else do
+        let visited' := visited.insert g
+        alias.expansion.expandAliases decls visited'
+    | some (.dataType _) => pure $ .typeRef g
+    | some _ => throw s!"Type reference `{g}` does not refer to a type"
+    | none => throw s!"Type reference `{g}` not found"
+
+/-- Expand all type aliases in a Toplevel, removing the aliases themselves. -/
+def Toplevel.expandAliases (toplevel : Toplevel) : Except String Toplevel := do
+  -- First create the Decls map to use for expansion
+  let mut decls : Decls := default
+  for ta in toplevel.typeAliases do
+    decls := decls.insert ta.name (.typeAlias ta)
+  for dt in toplevel.dataTypes do
+    decls := decls.insert dt.name (.dataType dt)
+
+  -- Validate all type aliases can be expanded (checks for cycles)
+  for ta in toplevel.typeAliases do
+    let _ ← ta.expansion.expandAliases decls
+
+  -- Expand all type references in data types
+  let mut dataTypes : Array DataType := #[]
+  for dt in toplevel.dataTypes do
+    let mut constructors : List Constructor := []
+    for ctor in dt.constructors do
+      let argTypes' ← ctor.argTypes.mapM (·.expandAliases decls)
+      constructors := constructors.concat { ctor with argTypes := argTypes' }
+    dataTypes := dataTypes.push { dt with constructors }
+
+  -- Expand all type references in functions
+  let mut functions : Array Function := #[]
+  for fn in toplevel.functions do
+    let inputs' ← fn.inputs.mapM fun (loc, typ) => do
+      let typ' ← typ.expandAliases decls
+      pure (loc, typ')
+    let output' ← fn.output.expandAliases decls
+    functions := functions.push { fn with inputs := inputs', output := output' }
+
+  -- Return Toplevel without aliases
+  pure ⟨dataTypes, #[], functions⟩
+
 structure TypedFunction where
   name : Global
   inputs : List (Local × Typ)
@@ -255,7 +329,7 @@ partial def Typ.size (decls : TypedDecls) (visited : HashSet Global := {}) :
   | .array t n => do
     let tSize ← t.size decls visited
     pure $ n * tSize
-  | .dataType g => match decls.getByKey g with
+  | .typeRef g => match decls.getByKey g with
     | some (.dataType data) => data.size decls visited
     | _ => throw s!"Datatype not found: `{g}`"
 

From 16aecab26636164897079ad46957481f23ac2cd0 Mon Sep 17 00:00:00 2001
From: Gabriel Barreto <gabriel.aquino.barreto@gmail.com>
Date: Thu, 19 Mar 2026 10:45:17 -0300
Subject: [PATCH 3/6] removed aliases from declarations

---
 Ix/Aiur/Check.lean  | 104 ++++++++++++++++++++++++++++++++++----------
 Ix/Aiur/Simple.lean |  12 ++---
 Ix/Aiur/Term.lean   |  62 --------------------------
 3 files changed, 86 insertions(+), 92 deletions(-)

diff --git a/Ix/Aiur/Check.lean b/Ix/Aiur/Check.lean
index 81a2b24b..ac89b1d1 100644
--- a/Ix/Aiur/Check.lean
+++ b/Ix/Aiur/Check.lean
@@ -36,27 +36,90 @@ instance : ToString CheckError where
   toString e := repr e |>.pretty
 
 /--
-Constructs a map of declarations from a toplevel, ensuring that there are no duplicate names
-for functions, datatypes, and type aliases.
+Eagerly expands type aliases, detecting cycles.
+-/
+partial def expandType (aliasMap : Std.HashMap Global Typ) (visited : Std.HashSet Global := {}) :
+    Typ → Except CheckError Typ
+  | .unit => pure .unit
+  | .field => pure .field
+  | .pointer t => do pure $ .pointer (← expandType aliasMap visited t)
+  | .function inputs output => do
+    let inputs' ← inputs.mapM (expandType aliasMap visited)
+    let output' ← expandType aliasMap visited output
+    pure $ .function inputs' output'
+  | .tuple ts => do
+    let ts' ← ts.mapM (expandType aliasMap visited)
+    pure $ .tuple ts'
+  | .array t n => do
+    let t' ← expandType aliasMap visited t
+    pure $ .array t' n
+  | .typeRef g =>
+    if let some expansion := aliasMap[g]? then
+      if visited.contains g then
+        throw $ CheckError.undefinedGlobal ⟨.mkSimple s!"Cycle detected in type alias `{g}`"⟩
+      else
+        expandType aliasMap (visited.insert g) expansion
+    else
+      pure $ .typeRef g  -- It's a dataType, keep it
+
+/--
+Constructs a map of declarations from a toplevel, expanding all type aliases.
+Type aliases are not added to the declarations - they are eliminated during construction.
 -/
 def Toplevel.mkDecls (toplevel : Toplevel) : Except CheckError Decls := do
-  let map ← toplevel.functions.foldlM (init := default)
-    fun acc function => addDecl acc Function.name .function function
-  let map ← toplevel.typeAliases.foldlM (init := map)
-    fun acc alias => addDecl (α := TypeAlias) acc (·.name) .typeAlias alias
-  toplevel.dataTypes.foldlM (init := map) addDataType
-where
-  ensureUnique name (map : IndexMap Global _) := do
-    if map.containsKey name then throw $ .duplicatedDefinition name
-  addDecl {α : Type} map (nameFn : α → Global) (wrapper : α → Declaration) (inner : α) := do
-    ensureUnique (nameFn inner) map
-    pure $ map.insert (nameFn inner) (wrapper inner)
-  addDataType map dataType := do
-    let dataTypeName := dataType.name
-    ensureUnique dataTypeName map
-    let map' := map.insert dataTypeName (.dataType dataType)
-    dataType.constructors.foldlM (init := map') fun acc (constructor : Constructor) =>
-      addDecl acc (dataTypeName.pushNamespace ∘ Constructor.nameHead) (.constructor dataType) constructor
+  -- First build the unexpanded alias map and check for name collisions
+  let mut rawAliasMap : Std.HashMap Global Typ := {}
+  let mut allNames : Std.HashSet Global := {}
+
+  -- Collect alias definitions
+  for alias in toplevel.typeAliases do
+    if allNames.contains alias.name then
+      throw $ .duplicatedDefinition alias.name
+    allNames := allNames.insert alias.name
+    rawAliasMap := rawAliasMap.insert alias.name alias.expansion
+
+  -- Now expand all aliases in terms of each other, detecting cycles
+  let mut aliasMap : Std.HashMap Global Typ := {}
+  for alias in toplevel.typeAliases do
+    let expanded ← expandType rawAliasMap {} alias.expansion
+    aliasMap := aliasMap.insert alias.name expanded
+
+  -- Helper to expand types in the declarations
+  let expandTyp := expandType aliasMap {}
+
+  -- Add functions with expanded types
+  let mut decls : Decls := default
+  for function in toplevel.functions do
+    if allNames.contains function.name then
+      throw $ .duplicatedDefinition function.name
+    allNames := allNames.insert function.name
+    let inputs' ← function.inputs.mapM fun (loc, typ) => do
+      let typ' ← expandTyp typ
+      pure (loc, typ')
+    let output' ← expandTyp function.output
+    let function' := { function with inputs := inputs', output := output' }
+    decls := decls.insert function.name (.function function')
+
+  -- Add datatypes with expanded types
+  for dataType in toplevel.dataTypes do
+    if allNames.contains dataType.name then
+      throw $ .duplicatedDefinition dataType.name
+    allNames := allNames.insert dataType.name
+    let mut constructors : List Constructor := []
+    for ctor in dataType.constructors do
+      let argTypes' ← ctor.argTypes.mapM expandTyp
+      constructors := constructors.concat { ctor with argTypes := argTypes' }
+    let dataType' := { dataType with constructors }
+    decls := decls.insert dataType.name (.dataType dataType')
+    -- Add constructors
+    for ctor in constructors do
+      let ctorName := dataType.name.pushNamespace ctor.nameHead
+      if allNames.contains ctorName then
+        throw $ .duplicatedDefinition ctorName
+      allNames := allNames.insert ctorName
+      decls := decls.insert ctorName (.constructor dataType' ctor)
+
+  pure decls
 
 structure CheckContext where
   decls : Decls
@@ -457,8 +520,6 @@ where
       if !map.contains dataType.name then
         set $ map.insert dataType.name
         dataType.constructors.flatMap (·.argTypes) |>.forM wellFormedType
-    | .typeAlias alias => do
-      wellFormedType alias.expansion
     | .function function => do
       wellFormedType function.output
       function.inputs.forM fun (_, typ) => wellFormedType typ
@@ -469,7 +530,6 @@ where
     | .pointer pointerTyp => wellFormedType pointerTyp
     | .typeRef typeRef => match decls.getByKey typeRef with
       | some (.dataType _) => pure ()
-      | some (.typeAlias _) => pure ()
       | some _ => throw $ .notADataType typeRef
       | none => throw $ .undefinedGlobal typeRef
     | _ => pure ()
diff --git a/Ix/Aiur/Simple.lean b/Ix/Aiur/Simple.lean
index 2e5036d7..37e420ae 100644
--- a/Ix/Aiur/Simple.lean
+++ b/Ix/Aiur/Simple.lean
@@ -38,22 +38,18 @@ where
   recr := simplifyTerm decls
 
 def Toplevel.checkAndSimplify (toplevel : Toplevel) : Except CheckError TypedDecls := do
-  -- First expand all type aliases
-  let toplevel ← match toplevel.expandAliases with
-    | .ok t => pure t
-    | .error e => throw (.undefinedGlobal ⟨.mkSimple e⟩)  -- TODO: better error handling
   let decls ← toplevel.mkDecls
   wellFormedDecls decls
-  -- The first check happens on the original terms.
-  toplevel.functions.forM fun function => do
-    let _ ← (checkFunction function) (getFunctionContext function decls)
+  -- The first check happens on the original terms (but with expanded types).
+  decls.foldlM (init := ()) fun _ (_, decl) => match decl with
+    | .function f => do let _ ← (checkFunction f) (getFunctionContext f decls); pure ()
+    | _ => pure ()
   let decls := decls.map fun decl => match decl with
     | .function f => .function { f with body := simplifyTerm decls f.body }
     | _ => decl
   decls.foldlM (init := default) fun typedDecls (name, decl) => match decl with
     | .constructor d c => pure $ typedDecls.insert name (.constructor d c)
     | .dataType d => pure $ typedDecls.insert name (.dataType d)
-    | .typeAlias _ => pure typedDecls  -- Type aliases should have been expanded by now
     | .function f => do
       -- The second check happens on the simplified terms.
       let f ← (checkFunction f) (getFunctionContext f decls)
diff --git a/Ix/Aiur/Term.lean b/Ix/Aiur/Term.lean
index 78de10d6..a913e654 100644
--- a/Ix/Aiur/Term.lean
+++ b/Ix/Aiur/Term.lean
@@ -225,73 +225,11 @@ def Toplevel.merge (x y : Toplevel) : Except Global Toplevel := do
 inductive Declaration
   | function : Function → Declaration
   | dataType : DataType → Declaration
-  | typeAlias : TypeAlias → Declaration
   | constructor : DataType → Constructor → Declaration
   deriving Repr, Inhabited
 
 abbrev Decls := IndexMap Global Declaration
 
-/-- Eagerly expands type aliases in a type, detecting cycles. -/
-partial def Typ.expandAliases (decls : Decls) (visited : Std.HashSet Global := {}) :
-    Typ → Except String Typ
-  | .unit => pure .unit
-  | .field => pure .field
-  | .pointer t => do pure $ .pointer (← t.expandAliases decls visited)
-  | .function inputs output => do
-    let inputs' ← inputs.mapM (·.expandAliases decls visited)
-    let output' ← output.expandAliases decls visited
-    pure $ .function inputs' output'
-  | .tuple ts => do
-    let ts' ← ts.mapM (·.expandAliases decls visited)
-    pure $ .tuple ts'
-  | .array t n => do
-    let t' ← t.expandAliases decls visited
-    pure $ .array t' n
-  | .typeRef g => match decls.getByKey g with
-    | some (.typeAlias alias) =>
-      if visited.contains g then
-        throw s!"Cycle detected in type alias `{g}`"
-      else do
-        let visited' := visited.insert g
-        alias.expansion.expandAliases decls visited'
-    | some (.dataType _) => pure $ .typeRef g
-    | some _ => throw s!"Type reference `{g}` does not refer to a type"
-    | none => throw s!"Type reference `{g}` not found"
-
-/-- Expand all type aliases in a Toplevel, removing the aliases themselves. -/
-def Toplevel.expandAliases (toplevel : Toplevel) : Except String Toplevel := do
-  -- First create the Decls map to use for expansion
-  let mut decls : Decls := default
-  for ta in toplevel.typeAliases do
-    decls := decls.insert ta.name (.typeAlias ta)
-  for dt in toplevel.dataTypes do
-    decls := decls.insert dt.name (.dataType dt)
-
-  -- Validate all type aliases can be expanded (checks for cycles)
-  for ta in toplevel.typeAliases do
-    let _ ← ta.expansion.expandAliases decls
-
-  -- Expand all type references in data types
-  let mut dataTypes : Array DataType := #[]
-  for dt in toplevel.dataTypes do
-    let mut constructors : List Constructor := []
-    for ctor in dt.constructors do
-      let argTypes' ← ctor.argTypes.mapM (·.expandAliases decls)
-      constructors := constructors.concat { ctor with argTypes := argTypes' }
-    dataTypes := dataTypes.push { dt with constructors }
-
-  -- Expand all type references in functions
-  let mut functions : Array Function := #[]
-  for fn in toplevel.functions do
-    let inputs' ← fn.inputs.mapM fun (loc, typ) => do
-      let typ' ← typ.expandAliases decls
-      pure (loc, typ')
-    let output' ← fn.output.expandAliases decls
-    functions := functions.push { fn with inputs := inputs', output := output' }
-
-  -- Return Toplevel without aliases
-  pure ⟨dataTypes, #[], functions⟩
-
 structure TypedFunction where
   name : Global
   inputs : List (Local × Typ)

From 7970733bcef40e7c049dc9d416c7d8d0ed56e39e Mon Sep 17 00:00:00 2001
From: Gabriel Barreto <gabriel.aquino.barreto@gmail.com>
Date: Thu, 19 Mar 2026 10:58:53 -0300
Subject: [PATCH 4/6] better algorithm

---
 Ix/Aiur/Check.lean | 67 ++++++++++++++++++++++++++--------------------
 1 file changed, 38 insertions(+), 29 deletions(-)

diff --git a/Ix/Aiur/Check.lean b/Ix/Aiur/Check.lean
index ac89b1d1..62ed45fe 100644
--- a/Ix/Aiur/Check.lean
+++ b/Ix/Aiur/Check.lean
@@ -36,62 +36,71 @@ instance : ToString CheckError where
   toString e := repr e |>.pretty
 
 /--
-Eagerly expands type aliases, detecting cycles.
+Eagerly expands type aliases, building the aliasMap on demand and detecting cycles.
 -/
-partial def expandType (aliasMap : Std.HashMap Global Typ) (visited : Std.HashSet Global := {}) :
-    Typ → Except CheckError Typ
+partial def expandTypeM (visited : Std.HashSet Global) (toplevelAliases : Array TypeAlias) :
+    Typ → StateT (Std.HashMap Global Typ) (Except CheckError) Typ
   | .unit => pure .unit
   | .field => pure .field
-  | .pointer t => do pure $ .pointer (← expandType aliasMap visited t)
+  | .pointer t => do pure $ .pointer (← expandTypeM visited toplevelAliases t)
   | .function inputs output => do
-    let inputs' ← inputs.mapM (expandType aliasMap visited)
-    let output' ← expandType aliasMap visited output
+    let inputs' ← inputs.mapM (expandTypeM visited toplevelAliases)
+    let output' ← expandTypeM visited toplevelAliases output
     pure $ .function inputs' output'
   | .tuple ts => do
-    let ts' ← ts.mapM (expandType aliasMap visited)
+    let ts' ← ts.mapM (expandTypeM visited toplevelAliases)
     pure $ .tuple ts'
   | .array t n => do
-    let t' ← expandType aliasMap visited t
+    let t' ← expandTypeM visited toplevelAliases t
     pure $ .array t' n
-  | .typeRef g =>
-    if let some expansion := aliasMap[g]? then
+  | .typeRef g => do
+    let aliasMap ← get
+    -- Check if already expanded
+    if let some expanded := aliasMap[g]? then
+      return expanded
+    -- Check if it's an alias
+    if let some (alias : TypeAlias) := toplevelAliases.find? (·.name == g) then
+      -- Check for cycle
       if visited.contains g then
         throw $ CheckError.undefinedGlobal ⟨.mkSimple s!"Cycle detected in type alias `{g}`"⟩
-      else
-        expandType aliasMap (visited.insert g) expansion
+      -- Expand the alias recursively
+      let expanded ← expandTypeM (visited.insert g) toplevelAliases alias.expansion
+      -- Save to aliasMap
+      set (aliasMap.insert g expanded)
+      return expanded
     else
-      pure $ .typeRef g  -- It's a dataType, keep it
+      -- It's a dataType, keep it
+      pure $ .typeRef g
 
 /--
 Constructs a map of declarations from a toplevel, expanding all type aliases.
 Type aliases are not added to the declarations - they are eliminated during construction.
 -/
 def Toplevel.mkDecls (toplevel : Toplevel) : Except CheckError Decls := do
-  -- First build the unexpanded alias map and check for name collisions
-  let mut rawAliasMap : Std.HashMap Global Typ := {}
+  -- Check for duplicate names among aliases
   let mut allNames : Std.HashSet Global := {}
-
-  -- Collect alias definitions
   for alias in toplevel.typeAliases do
     if allNames.contains alias.name then
-      throw $ .duplicatedDefinition alias.name
+      throw $ CheckError.duplicatedDefinition alias.name
     allNames := allNames.insert alias.name
-    rawAliasMap := rawAliasMap.insert alias.name alias.expansion
 
-  -- Now expand all aliases in terms of each other, detecting cycles
-  let mut aliasMap : Std.HashMap Global Typ := {}
-  for alias in toplevel.typeAliases do
-    let expanded ← expandType rawAliasMap {} alias.expansion
-    aliasMap := aliasMap.insert alias.name expanded
+  -- Build aliasMap by expanding all aliases in order
+  let initAliasMap := {}
+  let (_, finalAliasMap) ← (toplevel.typeAliases.mapM fun (alias : TypeAlias) => do
+    -- Expand and save the alias
+    let expanded ← expandTypeM {} toplevel.typeAliases alias.expansion
+    modify fun (aliasMap : Std.HashMap Global Typ) => aliasMap.insert alias.name expanded
+  ).run initAliasMap
 
-  -- Helper to expand types in the declarations
-  let expandTyp := expandType aliasMap {}
+  -- Helper to expand types in the declarations using the built aliasMap
+  let expandTyp (typ : Typ) : Except CheckError Typ :=
+    (expandTypeM {} toplevel.typeAliases typ).run' finalAliasMap
 
   -- Add functions with expanded types
   let mut decls : Decls := default
   for function in toplevel.functions do
     if allNames.contains function.name then
-      throw $ .duplicatedDefinition function.name
+      throw $ CheckError.duplicatedDefinition function.name
     allNames := allNames.insert function.name
     let inputs' ← function.inputs.mapM fun (loc, typ) => do
       let typ' ← expandTyp typ
@@ -103,7 +112,7 @@ def Toplevel.mkDecls (toplevel : Toplevel) : Except CheckError Decls := do
   -- Add datatypes with expanded types
   for dataType in toplevel.dataTypes do
     if allNames.contains dataType.name then
-      throw $ .duplicatedDefinition dataType.name
+      throw $ CheckError.duplicatedDefinition dataType.name
     allNames := allNames.insert dataType.name
     let mut constructors : List Constructor := []
     for ctor in dataType.constructors do
@@ -115,7 +124,7 @@ def Toplevel.mkDecls (toplevel : Toplevel) : Except CheckError Decls := do
     for ctor in constructors do
       let ctorName := dataType.name.pushNamespace ctor.nameHead
       if allNames.contains ctorName then
-        throw $ .duplicatedDefinition ctorName
+        throw $ CheckError.duplicatedDefinition ctorName
       allNames := allNames.insert ctorName
       decls := decls.insert ctorName (.constructor dataType' ctor)
 

From b0a5401db8f2c63d7d18024277f12cda8a9bd581 Mon Sep 17 00:00:00 2001
From: Gabriel Barreto <gabriel.aquino.barreto@gmail.com>
Date: Thu, 19 Mar 2026 12:40:36 -0300
Subject: [PATCH 5/6] type alias tests

---
 Tests/Aiur/Aiur.lean | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)

diff --git a/Tests/Aiur/Aiur.lean b/Tests/Aiur/Aiur.lean
index bd0414d2..b4ef11b5 100644
--- a/Tests/Aiur/Aiur.lean
+++ b/Tests/Aiur/Aiur.lean
@@ -364,6 +364,19 @@ def toplevel := ⟦
       )
     )
   }
+
+  ---------------------------------------------------------------------------
+  -- Type aliases: basic, nested, in patterns
+  ---------------------------------------------------------------------------
+  type U8 = G
+  type U16 = (U8, U8)
+  type U32 = (U16, U16)
+  type U64 = [U8; 8]
+  type Pair = (U8, U8)
+
+  fn alias_conversion(x: U64) -> U32 {
+    ((x[0], x[1]), (x[2], x[3]))
+  }
 ⟧
 
 def aiurTestCases : List AiurTestCase := [
@@ -488,6 +501,10 @@ def aiurTestCases : List AiurTestCase := [
 
     -- Fold/iteration
     .noIO `fold_matrix_sum #[1, 2, 3, 4] #[10],
+
+    -- Type aliases
+    { AiurTestCase.noIO `alias_conversion #[1, 2, 3, 4, 5, 6, 7, 8] #[1, 2, 3, 4]
+        with label := "alias_conversion (U64 = [U8; 8], U32 = (U16, U16))" },
   ]
 
 end

From e210bb292e3e7d00eb00e70cdfde51db79aa6b15 Mon Sep 17 00:00:00 2001
From: Arthur Paulino <arthurleonardo.ap@gmail.com>
Date: Thu, 19 Mar 2026 14:20:37 -0700
Subject: [PATCH 6/6] Use idiomatic forM instead of foldlM with unit
 accumulator

Add IndexMap.forM and use it in checkAndSimplify for cleaner iteration
over declarations when only side effects (type-checking) are needed.
---
 Ix/Aiur/Simple.lean | 6 +++---
 Ix/IndexMap.lean    | 3 +++
 2 files changed, 6 insertions(+), 3 deletions(-)

diff --git a/Ix/Aiur/Simple.lean b/Ix/Aiur/Simple.lean
index 37e420ae..4e7b780a 100644
--- a/Ix/Aiur/Simple.lean
+++ b/Ix/Aiur/Simple.lean
@@ -41,9 +41,9 @@ def Toplevel.checkAndSimplify (toplevel : Toplevel) : Except CheckError TypedDec
   let decls ← toplevel.mkDecls
   wellFormedDecls decls
   -- The first check happens on the original terms (but with expanded types).
-  decls.foldlM (init := ()) fun _ (_, decl) => match decl with
-    | .function f => do let _ ← (checkFunction f) (getFunctionContext f decls); pure ()
-    | _ => pure ()
+  decls.forM fun (_, decl) => do
+    if let .function f := decl then
+      let _ ← (checkFunction f) (getFunctionContext f decls)
   let decls := decls.map fun decl => match decl with
     | .function f => .function { f with body := simplifyTerm decls f.body }
     | _ => decl
diff --git a/Ix/IndexMap.lean b/Ix/IndexMap.lean
index 27ecc8d1..b6177613 100644
--- a/Ix/IndexMap.lean
+++ b/Ix/IndexMap.lean
@@ -69,6 +69,9 @@ def map (f : β → β) : IndexMap α β := by
 @[inline] def foldrM [Monad μ] (f : α × β → γ → μ γ) (init : γ) : μ γ :=
   m.pairs.foldrM f init
 
+@[inline] def forM [Monad μ] (f : α × β → μ PUnit) : μ PUnit :=
+  m.pairs.forM f
+
 end IndexMap
 
 end