diff --git a/Ix/Aiur/Bytecode.lean b/Ix/Aiur/Bytecode.lean
index 8051a9e7..69abff49 100644
--- a/Ix/Aiur/Bytecode.lean
+++ b/Ix/Aiur/Bytecode.lean
@@ -27,6 +27,8 @@ inductive Op
   | u8ShiftRight : ValIdx → Op
   | u8Xor : ValIdx → ValIdx → Op
   | u8Add : ValIdx → ValIdx → Op
+  | u8And : ValIdx → ValIdx → Op
+  | u8Or : ValIdx → ValIdx → Op
   | debug : String → Option (Array ValIdx) → Op
   deriving Repr
 
diff --git a/Ix/Aiur/Check.lean b/Ix/Aiur/Check.lean
index 53b59321..83e33a51 100644
--- a/Ix/Aiur/Check.lean
+++ b/Ix/Aiur/Check.lean
@@ -78,282 +78,297 @@ def refLookup (global : Global) : CheckM Typ := do
 def bindIdents (bindings : List (Local × Typ)) (ctx : CheckContext) : CheckContext :=
   { ctx with varTypes := ctx.varTypes.insertMany bindings }
 
+def fieldTerm (t : TypedTermInner) : TypedTerm := ⟨.field, t, false⟩
+
 mutual
-partial def inferTerm : Term → CheckM TypedTerm
-  | .unit => pure $ .mk (.evaluates .unit) .unit
-  | .var x => do
-    -- Retrieves and returns the variable type from the context.
-    let ctx ← read
-    match ctx.varTypes[x]? with
-    | some t => pure $ .mk (.evaluates t) (.var x)
-    | none =>
-      let Local.str localName := x | unreachable!
-      let typ := .evaluates (← refLookup (Global.init localName))
-      pure $ .mk typ (.var x)
+partial def inferTerm (t : Term) : CheckM TypedTerm := match t with
+  | .unit => pure ⟨.unit, .unit, false⟩
+  | .var x => inferVariable x
   | .ref x => do
-    let typ := .evaluates (← refLookup x)
-    pure $ .mk typ (.ref x)
-  | .ret term => do
-    -- Ensures that the type of the returned term matches the expected return type.
-    -- The term is not allowed to have a (nested) return.
-    -- Returning the type of the term is not necessary because it's already in the context.
-    let ctx ← read
-    let inner ← checkNoEscape term ctx.returnType
-    pure $ .mk .escapes inner
-  | .data data => do
-    let (typ, inner) ← inferData data
-    pure $ .mk (.evaluates typ) inner
-  | .let pat expr body => do
-    -- Returns the type of the body, inferred in the context extended with the bound variable type.
-    -- The bound variable is ensured not to escape.
-    let (exprTyp, exprInner) ← inferNoEscape expr
-    let expr' := .mk (.evaluates exprTyp) exprInner
-    let bindings ← checkPattern pat exprTyp
-    let body' ← withReader (bindIdents bindings) (inferTerm body)
-    pure $ .mk body'.typ (.let pat expr' body')
+    pure ⟨← refLookup x, .ref x, false⟩
+  | .ret term => inferReturn term
+  | .data data => inferData data
+  | .let pat expr body => inferLet pat expr body
   | .match term branches => inferMatch term branches
-  | .app func@(⟨.str .anonymous unqualifiedFunc⟩) args => do
-    -- Ensures the function exists in the context and that the arguments, which aren't allowed to
-    -- escape, match the function's input types. Returns the function's output type.
-    let ctx ← read
-    match ctx.varTypes[Local.str unqualifiedFunc]? with
-    | some (.function inputs output) => do
-      let args ← checkArgsAndInputs func args inputs
-      pure $ .mk (.evaluates output) (.app func args)
-    | some _ => throw $ .notAFunction func
-    | none => match ctx.decls.getByKey func with
-      | some (.function function) => do
-        let args ← checkArgsAndInputs func args (function.inputs.map Prod.snd)
-        pure $ .mk (.evaluates function.output) (.app func args)
-      | some (.constructor dataType constr) => do
-        let args ← checkArgsAndInputs func args constr.argTypes
-        pure $ .mk (.evaluates (.dataType dataType.name)) (.app func args)
-      | _ => throw $ .cannotApply func
-  | .app func args => do
-    -- Only checks global map if it is not unqualified
-    let ctx ← read
-    match ctx.decls.getByKey func with
-    | some (.function function) =>
-      let args ← checkArgsAndInputs func args (function.inputs.map Prod.snd)
-      pure $ .mk (.evaluates function.output) (.app func args)
-    | some (.constructor dataType constr) =>
-      let args ← checkArgsAndInputs func args constr.argTypes
-      pure $ .mk (.evaluates (.dataType dataType.name)) (.app func args)
-    | _ => throw $ .cannotApply func
-  | .add a b => do
-    let (ctxTyp, a, b) ← checkArith a b
-    pure $ .mk ctxTyp (.add a b)
-  | .sub a b => do
-    let (ctxTyp, a, b) ← checkArith a b
-    pure $ .mk ctxTyp (.sub a b)
-  | .mul a b => do
-    let (ctxTyp, a, b) ← checkArith a b
-    pure $ .mk ctxTyp (.mul a b)
-  | .eqZero a => do
-    let a ← fieldTerm <$> checkNoEscape a .field
-    pure $ .mk (.evaluates .field) (.eqZero a)
-  | .proj tup i => do
-    let (typs, tupInner) ← inferTuple tup
-    if h : i < typs.size then
-      let typ := typs[i]
-      let tup := .mk (.evaluates (.tuple typs)) tupInner
-      pure $ .mk (.evaluates typ) (.proj tup i)
-    else
-      throw $ .indexOoB i
-  | .get arr i => do
-    let (typ, n, inner) ← inferArray arr
-    if i ≥ n then
-      throw $ .indexOoB i
-    else
-      let arr := .mk (.evaluates (.array typ n)) inner
-      pure $ .mk (.evaluates typ) (.get arr i)
-  | .slice arr i j => if j < i then throw $ .negativeRange i j else do
+  | .app func args => inferApplication func args
+  | .ann typ term => do
+    pure ⟨typ, ← checkNoEscape term typ, false⟩
+  | .proj tup i => inferProj tup i
+  | .get arr i => inferGet arr i
+  | .slice arr i j => inferSlice arr i j
+  | .set arr i val => inferSet arr i val
+  | .store term => inferStore term
+  | .load term => inferLoad term
+  | .ptrVal term => inferPtrVal term
+  | .eqZero a => inferUnop a .eqZero .field
+  | .add a b => inferBinop a b .add .field
+  | .sub a b => inferBinop a b .sub .field
+  | .mul a b => inferBinop a b .mul .field
+  | .u8ShiftLeft a => inferUnop a .u8ShiftLeft .field
+  | .u8ShiftRight a => inferUnop a .u8ShiftRight .field
+  | .u8BitDecomposition a => inferUnop a .u8BitDecomposition (.array .field 8)
+  | .u8Xor a b => inferBinop a b .u8Xor .field
+  | .u8And a b => inferBinop a b .u8And .field
+  | .u8Or a b => inferBinop a b .u8Or .field
+  | .u8Add a b => inferBinop a b .u8Add (.tuple #[.field, .field])
+  | .ioGetInfo key => inferIoGetInfo key
+  | .ioSetInfo key idx len ret => inferIoSetInfo key idx len ret
+  | .ioRead idx len => inferIoRead idx len
+  | .ioWrite data ret => inferIoWrite data ret
+  | .assertEq a b ret => inferAssertEq a b ret
+  | .debug label term ret => inferDebug label term ret
+
+partial def checkNoEscape (term : Term) (typ : Typ) : CheckM TypedTermInner := do
+  let (typ', inner) ← inferNoEscape term
+  unless typ == typ' do throw $ .typeMismatch typ typ'
+  pure inner
+
+partial def inferNoEscape (term : Term) : CheckM (Typ × TypedTermInner) := do
+  let typedTerm ← inferTerm term
+  if typedTerm.escapes then throw .illegalReturn
+  pure (typedTerm.typ, typedTerm.inner)
+
+partial def inferUnop
+  (a : Term)
+  (op : TypedTerm → TypedTermInner)
+  (typ : Typ) :
+  CheckM TypedTerm := do
+  let a ← fieldTerm <$> checkNoEscape a .field
+  pure ⟨typ, op a, false⟩
+
+partial def inferBinop
+  (a : Term)
+  (b : Term)
+  (op : TypedTerm → TypedTerm → TypedTermInner)
+  (typ : Typ) :
+  CheckM TypedTerm := do
+  let a ← fieldTerm <$> checkNoEscape a .field
+  let b ← fieldTerm <$> checkNoEscape b .field
+  pure ⟨typ, op a b, false⟩
+
+partial def inferProj (tup : Term) (i : Nat) : CheckM TypedTerm := do
+  let (typs, tupInner) ← inferTuple tup
+  if h : i < typs.size then
+    let typ := typs[i]
+    let tup := ⟨.tuple typs, tupInner, false⟩
+    pure ⟨typ, .proj tup i, false⟩
+  else
+    throw $ .indexOoB i
+
+partial def inferGet (arr : Term) (i : Nat) : CheckM TypedTerm := do
+  let (typ, n, inner) ← inferArray arr
+  if i ≥ n then
+    throw $ .indexOoB i
+  else
+    let arr := ⟨.array typ n, inner, false⟩
+    pure ⟨typ, .get arr i, false⟩
+
+partial def inferSlice (arr : Term) (i j : Nat) : CheckM TypedTerm :=
+  if j < i then throw $ .negativeRange i j else do
     let (typ, n, inner) ← inferArray arr
     if j ≤ n then
-      let arr := .mk (.evaluates (.array typ n)) inner
-      pure $ .mk (.evaluates (.array typ (j - i))) (.slice arr i j)
+      let arr := ⟨.array typ n, inner, false⟩
+      pure ⟨.array typ (j - i), .slice arr i j, false⟩
     else
       throw $ .rangeOoB i j
-  | .set arr i val => do
-    let (typ, n, inner) ← inferArray arr
-    if i ≥ n then
-      throw $ .indexOoB i
-    else
-      let val ← checkNoEscape val typ
-      let arrTyp := .array typ n
-      let arr := .mk (.evaluates arrTyp) inner
-      let val := .mk (.evaluates typ) val
-      pure $ .mk (.evaluates arrTyp) (.set arr i val)
-  | .store term => do
-    -- Infers the type of the term and returns it, wrapped by a pointer type.
-    -- The term is not allowed to early return.
-    let (typ, inner) ← inferNoEscape term
-    let store := .store (.mk (.evaluates typ) inner)
-    pure $ .mk (.evaluates (.pointer typ)) store
-  | .load term => do
-    -- Ensures that the the type of the term is a pointer type and returns the unwrapped type.
-    -- The term is not allowed to early return.
-    let (typ, inner) ← inferNoEscape term
-    match typ with
-    | .pointer innerTyp =>
-      let load := .load (.mk (.evaluates typ) inner)
-      pure $ .mk (.evaluates innerTyp) load
-    | _ => throw $ .notAPointer typ
-  | .ptrVal term => do
-    -- Infers the type of the term, which must be a pointer, but returns `.u64`, as in a cast.
-    -- The term is not allowed to early return.
-    let (typ, inner) ← inferNoEscape term
-    match typ with
-    | .pointer _ => pure $ fieldTerm (.ptrVal (.mk (.evaluates typ) inner))
-    | _ => throw $ .notAPointer typ
-  | .ann typ term => do
-    let inner ← checkNoEscape term typ
-    pure $ .mk (.evaluates typ) inner
-  -- | .unsafeCast term castTyp => do
-  --   let (typ, inner) ← inferNoEscape term
-  --   pure $ .mk (.evaluates typ) (.unsafeCast inner castTyp)
-  | .assertEq a b ret => do
-    -- `a` and `b` must have the same type.
-    let (typ, a) ← inferNoEscape a
-    let b ← checkNoEscape b typ
-    let ret ← inferTerm ret
-    let assertEq := .assertEq (.mk (.evaluates typ) a) (.mk (.evaluates typ) b) ret
-    pure $ .mk (.evaluates ret.typ.unwrap) assertEq
-  | .ioGetInfo key => do
-    let (typ, keyInner) ← inferNoEscape key
-    match typ with
-    | .array .. =>
-      let ioGetInfo := .ioGetInfo (.mk (.evaluates typ) keyInner)
-      pure $ .mk (.evaluates (.tuple #[.field, .field])) ioGetInfo
-    | _ => throw $ .notAnArray typ
-  | .ioSetInfo key idx len ret => do
-    let (keyTyp, keyInner) ← inferNoEscape key
-    match keyTyp with
-    | .array keyEltTyp _ =>
-      if keyEltTyp != .field then throw $ .typeMismatch .field keyEltTyp
-      let idx ← fieldTerm <$> checkNoEscape idx .field
-      let len ← fieldTerm <$> checkNoEscape len .field
-      let ret ← inferTerm ret
-      let ioSetInfo := .ioSetInfo (.mk (.evaluates keyTyp) keyInner) idx len ret
-      pure $ .mk (.evaluates ret.typ.unwrap) ioSetInfo
-    | _ => throw $ .notAnArray keyTyp
-  | .ioRead idx len => do
-    if len = 0 then throw .emptyArray
+
+partial def inferSet (arr : Term) (i : Nat) (val : Term) : CheckM TypedTerm := do
+  let (typ, n, inner) ← inferArray arr
+  if i ≥ n then
+    throw $ .indexOoB i
+  else
+    let val ← checkNoEscape val typ
+    let arrTyp := .array typ n
+    let arr := ⟨arrTyp, inner, false⟩
+    let val := ⟨typ, val, false⟩
+    pure ⟨arrTyp, .set arr i val, false⟩
+
+partial def inferStore (term : Term) : CheckM TypedTerm := do
+  let (typ, inner) ← inferNoEscape term
+  let store := .store ⟨typ, inner, false⟩
+  pure ⟨.pointer typ, store, false⟩
+
+partial def inferLoad (term : Term) : CheckM TypedTerm := do
+  let (typ, inner) ← inferNoEscape term
+  match typ with
+  | .pointer innerTyp =>
+    let load := .load ⟨typ, inner, false⟩
+    pure ⟨innerTyp, load, false⟩
+  | _ => throw $ .notAPointer typ
+
+partial def inferPtrVal (term : Term) : CheckM TypedTerm := do
+  let (typ, inner) ← inferNoEscape term
+  match typ with
+  | .pointer _ => pure $ fieldTerm (.ptrVal ⟨typ, inner, false⟩)
+  | _ => throw $ .notAPointer typ
+
+partial def inferIoGetInfo (key : Term) : CheckM TypedTerm := do
+  let (typ, keyInner) ← inferNoEscape key
+  match typ with
+  | .array .. =>
+    let ioGetInfo := .ioGetInfo ⟨typ, keyInner, false⟩
+    pure ⟨.tuple #[.field, .field], ioGetInfo, false⟩
+  | _ => throw $ .notAnArray typ
+
+partial def inferIoSetInfo (key idx len ret : Term) : CheckM TypedTerm := do
+  let (keyTyp, keyInner) ← inferNoEscape key
+  match keyTyp with
+  | .array keyEltTyp _ =>
+    if keyEltTyp != .field then throw $ .typeMismatch .field keyEltTyp
     let idx ← fieldTerm <$> checkNoEscape idx .field
-    let ioRead := .ioRead idx len
-    pure $ .mk (.evaluates (.array .field len)) ioRead
-  | .ioWrite data ret => do
-    let (dataTyp, dataInner) ← inferNoEscape data
-    match dataTyp with
-    | .array dataEltTyp _ =>
-      if dataEltTyp != .field then throw $ .typeMismatch .field dataEltTyp
-      let ret ← inferTerm ret
-      let ioWrite := .ioWrite (.mk (.evaluates dataTyp) dataInner) ret
-      pure $ .mk (.evaluates ret.typ.unwrap) ioWrite
-    | _ => throw $ .notAnArray dataTyp
-  | .u8BitDecomposition byte => do
-    let byte ← fieldTerm <$> checkNoEscape byte .field
-    let u8BitDecomposition := .u8BitDecomposition byte
-    pure $ .mk (.evaluates (.array .field 8)) u8BitDecomposition
-  | .u8ShiftLeft byte => do
-    let byte ← fieldTerm <$> checkNoEscape byte .field
-    let u8ShiftLeft := .u8ShiftLeft byte
-    pure $ .mk (.evaluates .field) u8ShiftLeft
-  | .u8ShiftRight byte => do
-    let byte ← fieldTerm <$> checkNoEscape byte .field
-    let u8ShiftRight := .u8ShiftRight byte
-    pure $ .mk (.evaluates .field) u8ShiftRight
-  | .u8Xor i j => do
-    let i ← fieldTerm <$> checkNoEscape i .field
-    let j ← fieldTerm <$> checkNoEscape j .field
-    let u8Xor := .u8Xor i j
-    pure $ .mk (.evaluates .field) u8Xor
-  | .u8Add i j => do
-    let i ← fieldTerm <$> checkNoEscape i .field
-    let j ← fieldTerm <$> checkNoEscape j .field
-    let u8Add := .u8Add i j
-    pure $ .mk (.evaluates (.tuple #[.field, .field])) u8Add
-  | .debug label term ret => do
-    let term ← term.mapM inferTerm
+    let len ← fieldTerm <$> checkNoEscape len .field
+    let ret ← inferTerm ret
+    let ioSetInfo := .ioSetInfo ⟨keyTyp, keyInner, false⟩ idx len ret
+    pure ⟨ret.typ, ioSetInfo, ret.escapes⟩
+  | _ => throw $ .notAnArray keyTyp
+
+partial def inferIoRead (idx : Term) (len : Nat) : CheckM TypedTerm := do
+  if len = 0 then throw .emptyArray
+  let idx ← fieldTerm <$> checkNoEscape idx .field
+  let ioRead := .ioRead idx len
+  pure ⟨.array .field len, ioRead, false⟩
+
+partial def inferIoWrite (data ret : Term) : CheckM TypedTerm := do
+  let (dataTyp, dataInner) ← inferNoEscape data
+  match dataTyp with
+  | .array dataEltTyp _ =>
+    if dataEltTyp != .field then throw $ .typeMismatch .field dataEltTyp
     let ret ← inferTerm ret
-    let debug := .debug label term ret
-    pure $ .mk (.evaluates ret.typ.unwrap) debug
+    let ioWrite := .ioWrite ⟨dataTyp, dataInner, false⟩ ret
+    pure ⟨ret.typ, ioWrite, ret.escapes⟩
+  | _ => throw $ .notAnArray dataTyp
+
+partial def inferVariable (x : Local) : CheckM TypedTerm := do
+  let ctx ← read
+  match ctx.varTypes[x]? with
+  | some t => pure ⟨t, .var x, false⟩
+  | none =>
+    let Local.str localName := x | unreachable!
+    let typ ← refLookup (Global.init localName)
+    pure ⟨typ, .var x, false⟩
+
+partial def inferReturn (term : Term) : CheckM TypedTerm := do
+  let ctx ← read
+  let inner ← checkNoEscape term ctx.returnType
+  pure ⟨ctx.returnType, inner, true⟩
+
+partial def inferLet (pat : Pattern) (expr : Term) (body : Term) : CheckM TypedTerm := do
+  let (exprTyp, exprInner) ← inferNoEscape expr
+  let expr' := ⟨exprTyp, exprInner, false⟩
+  let bindings ← checkPattern pat exprTyp
+  let body' ← withReader (bindIdents bindings) (inferTerm body)
+  pure ⟨body'.typ, .let pat expr' body', body'.escapes⟩
+
+partial def inferUnqualifiedApp (func : Global) (unqualifiedFunc : String) (args : List Term) : CheckM TypedTerm := do
+  let ctx ← read
+  match ctx.varTypes[Local.str unqualifiedFunc]? with
+  | some (.function inputs output) => do
+    let args ← checkArgsAndInputs func args inputs
+    pure ⟨output, .app func args, false⟩
+  | some _ => throw $ .notAFunction func
+  | none => match ctx.decls.getByKey func with
+    | some (.function function) => do
+      let args ← checkArgsAndInputs func args (function.inputs.map Prod.snd)
+      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⟩
+    | _ => throw $ .cannotApply func
 where
-  /--
-  Ensures that there are as many arguments and as expected types and that
-  the types of the arguments are precisely those expected.
-  -/
   checkArgsAndInputs func args inputs : CheckM (List TypedTerm) := do
     let lenArgs := args.length
     let lenInputs := inputs.length
     unless lenArgs == lenInputs do throw $ .wrongNumArgs func lenArgs lenInputs
     let pass := fun (arg, input) => do
       let inner ← checkNoEscape arg input
-      pure $ .mk (.evaluates input) inner
+      pure ⟨input, inner, false⟩
     args.zip inputs |>.mapM pass
-  checkArith a b := do
-    let aInner ← checkNoEscape a .field
-    let bInner ← checkNoEscape b .field
-    pure (.evaluates .field, fieldTerm aInner, fieldTerm bInner)
-  fieldTerm := (.mk (.evaluates .field) ·)
 
-partial def checkNoEscape (term : Term) (typ : Typ) : CheckM TypedTermInner := do
-  let (typ', inner) ← inferNoEscape term
-  unless typ == typ' do throw $ .typeMismatch typ typ'
-  pure inner
+partial def inferQualifiedApp (func : Global) (args : List Term) : CheckM TypedTerm := do
+  let ctx ← read
+  match ctx.decls.getByKey func with
+  | some (.function function) =>
+    let args ← checkArgsAndInputs func args (function.inputs.map Prod.snd)
+    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⟩
+  | _ => throw $ .cannotApply func
+where
+  checkArgsAndInputs func args inputs : CheckM (List TypedTerm) := do
+    let lenArgs := args.length
+    let lenInputs := inputs.length
+    unless lenArgs == lenInputs do throw $ .wrongNumArgs func lenArgs lenInputs
+    let pass := fun (arg, input) => do
+      let inner ← checkNoEscape arg input
+      pure ⟨input, inner, false⟩
+    args.zip inputs |>.mapM pass
 
-partial def inferNoEscape (term : Term) : CheckM (Typ × TypedTermInner) := do
-  let typedTerm ← inferTerm term
-  match typedTerm.typ with
-  | .escapes => throw .illegalReturn
-  | .evaluates type => pure (type, typedTerm.inner)
+partial def inferApplication (func : Global) (args : List Term) : CheckM TypedTerm :=
+  match func.toName with
+  | .str .anonymous unqualifiedFunc => inferUnqualifiedApp func unqualifiedFunc args
+  | _ => inferQualifiedApp func args
+
+partial def inferAssertEq (a b ret : Term) : CheckM TypedTerm := do
+  let (typ, a) ← inferNoEscape a
+  let b ← checkNoEscape b typ
+  let ret ← inferTerm ret
+  let assertEq := .assertEq ⟨typ, a, false⟩ ⟨typ, b, false⟩ ret
+  pure ⟨ret.typ, assertEq, ret.escapes⟩
+
+partial def inferDebug (label : String) (term : Option Term) (ret : Term) : CheckM TypedTerm := do
+  let term ← term.mapM inferTerm
+  let ret ← inferTerm ret
+  let debug := .debug label term ret
+  pure ⟨ret.typ, debug, ret.escapes⟩
 
-partial def inferData : Data → CheckM (Typ × TypedTermInner)
-  | .field g => pure (.field, .data (.field g))
+partial def inferData : Data → CheckM TypedTerm
+  | .field g => pure ⟨.field, .data (.field g), false⟩
   | .tuple terms => do
     let typsAndInners ← terms.mapM inferNoEscape
     let typs := typsAndInners.map Prod.fst
-    let terms := typsAndInners.map fun (typ, inner) => .mk (.evaluates typ) inner
-    pure (.tuple typs, .data (.tuple terms))
+    let terms := typsAndInners.map fun (typ, inner) => ⟨typ, inner, false⟩
+    pure ⟨.tuple typs, .data (.tuple terms), false⟩
   | .array terms => do
     if h : terms.size > 0 then
       let (typ, firstInner) ← inferNoEscape terms[0]
       let mut typedTerms := Array.mkEmpty terms.size
-        |>.push (.mk (.evaluates typ) firstInner)
+        |>.push ⟨typ, firstInner, false⟩
       for term in terms[1:] do
         let inner ← checkNoEscape term typ
-        typedTerms := typedTerms.push (.mk (.evaluates typ) inner)
-      pure (.array typ terms.size, .data (.array typedTerms))
+        typedTerms := typedTerms.push ⟨typ, inner, false⟩
+      pure ⟨.array typ terms.size, .data (.array typedTerms), false⟩
     else throw .emptyArray
 
 /-- Infers the type of a 'match' expression and ensures its patterns and branches are valid. -/
 partial def inferMatch (term : Term) (branches : List (Pattern × Term)) : CheckM TypedTerm := do
-  if branches.isEmpty then throw .emptyMatch
   let (termTyp, termInner) ← inferNoEscape term
-  let term := .mk (.evaluates termTyp) termInner
-  let init := ([], .escapes)
-  let (branches, typ) ← branches.foldrM (init := init) (checkBranch termTyp)
-  pure $ .mk typ (.match term branches)
+  let term := ⟨termTyp, termInner, false⟩
+  let init := ([], none)
+  let (branches, typOpt) ← branches.foldrM (init := init) (checkBranch termTyp)
+  match typOpt with
+  | some (typ, escapes) => pure ⟨typ, .match term branches, escapes⟩
+  | none => throw .emptyMatch
 where
   checkBranch patTyp branchData acc := do
     let (pat, branch) := branchData
-    let (typedBranches, currentTyp) := acc
+    let (typedBranches, currentTypOpt) := acc
     let bindings ← checkPattern pat patTyp
-    withReader (bindIdents bindings) (match currentTyp with
-      | .escapes => do
+    withReader (bindIdents bindings) (match currentTypOpt with
+      | none => do
         let typedBranch ← inferTerm branch
-        pure (typedBranches.cons (pat, typedBranch), typedBranch.typ)
-      | .evaluates matchTyp => do
-        -- Some branch didn't escape, so if this branch doesn't escape it must have the same type
-        -- as the previous non-escaping branch.
+        pure (typedBranches.cons (pat, typedBranch), some (typedBranch.typ, typedBranch.escapes))
+      | some (matchTyp, matchEscapes) => do
         let typedBranch ← inferTerm branch
         let typedBranches := typedBranches.cons (pat, typedBranch)
-        match typedBranch.typ with
-        | .escapes => pure (typedBranches, currentTyp)
-        | .evaluates branchTyp =>
-          -- This branch doesn't escape so its type must match the type of the previous non-escaping branch.
-          unless (matchTyp == branchTyp) do throw $ .branchMismatch matchTyp branchTyp
-          pure (typedBranches, currentTyp))
+        if typedBranch.escapes then
+          pure (typedBranches, currentTypOpt)
+        else if matchEscapes then
+          pure (typedBranches, some (typedBranch.typ, false))
+        else
+          -- Neither branch escapes so their types must match
+          unless (matchTyp == typedBranch.typ) do throw $ .branchMismatch matchTyp typedBranch.typ
+          pure (typedBranches, currentTypOpt))
 
 /-- Checks that a pattern matches a given type and collects its bindings. -/
 partial def checkPattern (pat : Pattern) (typ : Typ) : CheckM $ List (Local × Typ) := do
@@ -451,8 +466,8 @@ where
 /-- Checks a function to ensure its body's type matches its declared output type. -/
 def checkFunction (function : Function) : CheckM TypedFunction := do
   let body ← inferTerm function.body
-  if let .evaluates typ := body.typ then
-    unless typ == function.output do throw $ .typeMismatch typ function.output
+  unless body.escapes do
+    unless body.typ == function.output do throw $ .typeMismatch body.typ function.output
   pure ⟨function.name, function.inputs, function.output, body, function.unconstrained⟩
 
 end Aiur
diff --git a/Ix/Aiur/Compile.lean b/Ix/Aiur/Compile.lean
index ef62d0e0..ffe6a1c4 100644
--- a/Ix/Aiur/Compile.lean
+++ b/Ix/Aiur/Compile.lean
@@ -120,7 +120,7 @@ def opLayout : Bytecode.Op → LayoutM Unit
     pushDegrees $ .replicate 8 1
     bumpAuxiliaries 8
     bumpLookups
-  | .u8ShiftLeft _ | .u8ShiftRight _ | .u8Xor .. => do
+  | .u8ShiftLeft _ | .u8ShiftRight _ | .u8Xor .. | .u8And .. | .u8Or .. => do
     pushDegree 1
     bumpAuxiliaries 1
     bumpLookups
@@ -246,7 +246,7 @@ partial def toIndex
  (term : TypedTerm) : StateM CompilerState (Array Bytecode.ValIdx) :=
   match term.inner with
   -- | .unsafeCast inner castTyp =>
-  --   if typSize layoutMap castTyp != typSize layoutMap term.typ.unwrap then
+  --   if typSize layoutMap castTyp != typSize layoutMap term.typ then
   --     panic! "Impossible cast"
   --   else
   --     toIndex layoutMap bindings (.mk term.typ inner)
@@ -335,8 +335,8 @@ partial def toIndex
   --     pushOp (Bytecode.Op.preimg layout.index out layout.inputSize) layout.inputSize
   --   | _ => panic! "should not happen after typechecking"
   | .proj arg i => do
-    let typs := match arg.typ with
-      | .evaluates (.tuple typs) => typs
+    let typs := match (arg.typ, arg.escapes) with
+      | (.tuple typs, false) => typs
       | _ => panic! "Should not happen after typechecking"
     let offset := (typs.extract 0 i).foldl (init := 0)
       fun acc typ => typSize layoutMap typ + acc
@@ -344,23 +344,23 @@ partial def toIndex
     let length := typSize layoutMap typs[i]!
     pure $ arg.extract offset (offset + length)
   | .get arr i => do
-    let eltTyp := match arr.typ with
-      | .evaluates (.array typ _) => typ
+    let eltTyp := match (arr.typ, arr.escapes) with
+      | (.array typ _, false) => typ
       | _ => panic! "Should not happen after typechecking"
     let eltSize := typSize layoutMap eltTyp
     let offset := i * eltSize
     let arr ← toIndex layoutMap bindings arr
     pure $ arr.extract offset (offset + eltSize)
   | .slice arr i j => do
-    let eltTyp := match arr.typ with
-      | .evaluates (.array typ _) => typ
+    let eltTyp := match (arr.typ, arr.escapes) with
+      | (.array typ _, false) => typ
       | _ => panic! "Should not happen after typechecking"
     let eltSize := typSize layoutMap eltTyp
     let arr ← toIndex layoutMap bindings arr
     pure $ arr.extract (i * eltSize) (j * eltSize)
   | .set arr i val => do
-    let eltTyp := match arr.typ with
-      | .evaluates (.array typ _) => typ
+    let eltTyp := match (arr.typ, arr.escapes) with
+      | (.array typ _, false) => typ
       | _ => panic! "Should not happen after typechecking"
     let eltSize := typSize layoutMap eltTyp
     let arr ← toIndex layoutMap bindings arr
@@ -372,8 +372,8 @@ partial def toIndex
     let args ← toIndex layoutMap bindings arg
     pushOp (.store args)
   | .load ptr => do
-    let size := match ptr.typ.unwrap with
-    | .pointer typ => typSize layoutMap typ
+    let size := match (ptr.typ, ptr.escapes) with
+    | (.pointer typ, false) => typSize layoutMap typ
     | _ => unreachable!
     let ptr ← expectIdx ptr
     pushOp (.load size ptr) size
@@ -421,6 +421,14 @@ partial def toIndex
     let i ← expectIdx i
     let j ← expectIdx j
     pushOp (.u8Add i j) 2
+  | .u8And i j => do
+    let i ← expectIdx i
+    let j ← expectIdx j
+    pushOp (.u8And i j)
+  | .u8Or i j => do
+    let i ← expectIdx i
+    let j ← expectIdx j
+    pushOp (.u8Or i j)
   | .debug label term ret => do
     let term ← term.mapM (toIndex layoutMap bindings)
     modify fun stt => { stt with ops := stt.ops.push (.debug label term) }
@@ -454,7 +462,7 @@ partial def TypedTerm.compile
     modify fun stt => { stt with ops := stt.ops.push (.debug label term) }
     ret.compile returnTyp layoutMap bindings
   | .match term cases =>
-    match term.typ.unwrapOr returnTyp with
+    match term.typ with
     -- Also do this for tuple-like and array-like (one constructor only) datatypes
     | .tuple typs => match cases with
       | [(.tuple vars, branch)] => do
diff --git a/Ix/Aiur/Meta.lean b/Ix/Aiur/Meta.lean
index 84c77a1c..48ad07c5 100644
--- a/Ix/Aiur/Meta.lean
+++ b/Ix/Aiur/Meta.lean
@@ -123,6 +123,8 @@ syntax "u8_shift_left" "(" trm ")"                            : trm
 syntax "u8_shift_right" "(" trm ")"                           : trm
 syntax "u8_xor" "(" trm ", " trm ")"                          : trm
 syntax "u8_add" "(" trm ", " trm ")"                          : trm
+syntax "u8_and" "(" trm ", " trm ")"                          : trm
+syntax "u8_or" "(" trm ", " trm ")"                           : trm
 syntax "dbg!" "(" str (", " trm)? ")" ";" (trm)?              : trm
 
 syntax trm "[" "@" noWs ident "]"                                                        : trm
@@ -219,6 +221,10 @@ partial def elabTrm : ElabStxCat `trm
     mkAppM ``Term.u8Xor #[← elabTrm i, ← elabTrm j]
   | `(trm| u8_add($i:trm, $j:trm)) => do
     mkAppM ``Term.u8Add #[← elabTrm i, ← elabTrm j]
+  | `(trm| u8_and($i:trm, $j:trm)) => do
+    mkAppM ``Term.u8And #[← elabTrm i, ← elabTrm j]
+  | `(trm| u8_or($i:trm, $j:trm)) => do
+    mkAppM ``Term.u8Or #[← elabTrm i, ← elabTrm j]
   | `(trm| dbg!($label:str $[, $t:trm]?); $[$ret:trm]?) => do
     let t ← match t with
       | none => mkAppOptM ``Option.none #[some (mkConst ``Term)]
@@ -360,6 +366,14 @@ where
       let i ← replaceToken old new i
       let j ← replaceToken old new j
       `(trm| u8_add($i, $j))
+    | `(trm| u8_and($i:trm, $j:trm)) => do
+      let i ← replaceToken old new i
+      let j ← replaceToken old new j
+      `(trm| u8_and($i, $j))
+    | `(trm| u8_or($i:trm, $j:trm)) => do
+      let i ← replaceToken old new i
+      let j ← replaceToken old new j
+      `(trm| u8_or($i, $j))
     | `(trm| dbg!($label:str $[, $t:trm]?); $[$ret:trm]?) => do
       let t' ← t.mapM $ replaceToken old new
       let ret' ← ret.mapM $ replaceToken old new
diff --git a/Ix/Aiur/Term.lean b/Ix/Aiur/Term.lean
index a279f86b..83302c79 100644
--- a/Ix/Aiur/Term.lean
+++ b/Ix/Aiur/Term.lean
@@ -93,6 +93,8 @@ inductive Term
   | u8ShiftRight : Term → Term
   | u8Xor : Term → Term → Term
   | u8Add : Term → Term → Term
+  | u8And : Term → Term → Term
+  | u8Or : Term → Term → Term
   | debug : String → Option Term → Term → Term
   deriving Repr, BEq, Hashable, Inhabited
 
@@ -104,19 +106,6 @@ inductive Data
 
 end
 
-inductive ContextualType
-  | evaluates : Typ → ContextualType
-  | escapes : ContextualType
-  deriving Repr, BEq, Inhabited
-
-def ContextualType.unwrap : ContextualType → Typ
-| .escapes => panic! "term should not escape"
-| .evaluates typ => typ
-
-def ContextualType.unwrapOr : ContextualType → Typ → Typ
-| .escapes => fun typ => typ
-| .evaluates typ => fun _ => typ
-
 mutual
 inductive TypedTermInner
   | unit
@@ -149,12 +138,15 @@ inductive TypedTermInner
   | u8ShiftRight : TypedTerm → TypedTermInner
   | u8Xor : TypedTerm → TypedTerm → TypedTermInner
   | u8Add : TypedTerm → TypedTerm → TypedTermInner
+  | u8And : TypedTerm → TypedTerm → TypedTermInner
+  | u8Or : TypedTerm → TypedTerm → TypedTermInner
   | debug : String → Option TypedTerm → TypedTerm → TypedTermInner
   deriving Repr, Inhabited
 
 structure TypedTerm where
-  typ : ContextualType
+  typ : Typ
   inner : TypedTermInner
+  escapes : Bool
   deriving Repr, Inhabited
 
 inductive TypedData
diff --git a/Tests/Aiur.lean b/Tests/Aiur.lean
index a8b647ba..7a1aa741 100644
--- a/Tests/Aiur.lean
+++ b/Tests/Aiur.lean
@@ -199,6 +199,14 @@ def toplevel := ⟦
     (u8_add(i_xor_j, i), u8_add(i_xor_j, j))
   }
 
+  fn u8_add_and(i: G, j: G) -> G {
+    u8_and(i, j)
+  }
+
+  fn u8_add_or(i: G, j: G) -> G {
+    u8_or(i, j)
+  }
+
   fn fold_matrix_sum(m: [[G; 2]; 2]) -> G {
     fold(0 .. 2, 0, |acc_outer, @i|
       fold(0 .. 2, acc_outer, |acc_inner, @j|
@@ -245,6 +253,8 @@ def aiurTestCases : List AiurTestCase := [
       ⟨#[1, 2, 3, 4, 1, 2, 3, 4], .ofList [(#[0], ⟨0, 4⟩), (#[1], ⟨0, 8⟩)]⟩⟩,
     .noIO `shr_shr_shl_decompose #[87] #[0, 1, 0, 1, 0, 1, 0, 0],
     .noIO `u8_add_xor #[45, 131] #[219, 0, 49, 1],
+    .noIO `u8_add_and #[45, 131] #[1],
+    .noIO `u8_add_or #[45, 131] #[175],
     .noIO `fold_matrix_sum #[1, 2, 3, 4] #[10],
   ]
 
diff --git a/deny.toml b/deny.toml
index 1cb67022..6519dae3 100644
--- a/deny.toml
+++ b/deny.toml
@@ -74,6 +74,8 @@ ignore = [
     "RUSTSEC-2024-0384", # `instant` crate is unmaintained
     "RUSTSEC-2024-0370", # `proc-macro-error` crate is unmaintained
     "RUSTSEC-2023-0089", # `atomic-polyfill` crate is unmaintained
+    "RUSTSEC-2025-0141", # `bincode` crate is unmaintained
+
     #{ id = "RUSTSEC-0000-0000", reason = "you can specify a reason the advisory is ignored" },
     #"a-crate-that-is-yanked@0.1.1", # you can also ignore yanked crate versions if you wish
     #{ crate = "a-crate-that-is-yanked@0.1.1", reason = "you can specify why you are ignoring the yanked crate" },
diff --git a/src/aiur/bytecode.rs b/src/aiur/bytecode.rs
index 51c3f8cb..43331947 100644
--- a/src/aiur/bytecode.rs
+++ b/src/aiur/bytecode.rs
@@ -53,6 +53,8 @@ pub enum Op {
   U8ShiftRight(ValIdx),
   U8Xor(ValIdx, ValIdx),
   U8Add(ValIdx, ValIdx),
+  U8And(ValIdx, ValIdx),
+  U8Or(ValIdx, ValIdx),
   Debug(String, Option<Vec<ValIdx>>),
 }
 
diff --git a/src/aiur/constraints.rs b/src/aiur/constraints.rs
index 48993716..9c1252dd 100644
--- a/src/aiur/constraints.rs
+++ b/src/aiur/constraints.rs
@@ -16,8 +16,8 @@ use crate::aiur::{
     bytes1::{Bytes1, Bytes1Op},
     bytes2::{Bytes2, Bytes2Op},
   },
-  memory_channel, u8_add_channel, u8_bit_decomposition_channel,
-  u8_shift_left_channel, u8_shift_right_channel, u8_xor_channel,
+  memory_channel, u8_add_channel, u8_and_channel, u8_bit_decomposition_channel,
+  u8_or_channel, u8_shift_left_channel, u8_shift_right_channel, u8_xor_channel,
 };
 
 type Expr = SymbolicExpression<G>;
@@ -415,6 +415,22 @@ impl Op {
         sel.clone(),
         state,
       ),
+      Op::U8And(i, j) => bytes2_constraints(
+        *i,
+        *j,
+        &Bytes2Op::And,
+        u8_and_channel(),
+        sel.clone(),
+        state,
+      ),
+      Op::U8Or(i, j) => bytes2_constraints(
+        *i,
+        *j,
+        &Bytes2Op::Or,
+        u8_or_channel(),
+        sel.clone(),
+        state,
+      ),
       Op::IOSetInfo(..) | Op::IOWrite(_) | Op::Debug(..) => (),
     }
   }
diff --git a/src/aiur/execute.rs b/src/aiur/execute.rs
index 6d25c99d..8030f5b0 100644
--- a/src/aiur/execute.rs
+++ b/src/aiur/execute.rs
@@ -271,6 +271,20 @@ impl Function {
             bytes2_execute(*i, *j, &Bytes2Op::Add, &mut map, record);
           }
         },
+        ExecEntry::Op(Op::U8And(i, j)) => {
+          if unconstrained {
+            map.push(Bytes2::and(&map[*i], &map[*j]));
+          } else {
+            bytes2_execute(*i, *j, &Bytes2Op::And, &mut map, record);
+          }
+        },
+        ExecEntry::Op(Op::U8Or(i, j)) => {
+          if unconstrained {
+            map.push(Bytes2::or(&map[*i], &map[*j]));
+          } else {
+            bytes2_execute(*i, *j, &Bytes2Op::Or, &mut map, record);
+          }
+        },
         ExecEntry::Op(Op::Debug(label, idxs)) => match idxs {
           None => println!("{label}"),
           Some(idxs) => {
diff --git a/src/aiur/gadgets/bytes2.rs b/src/aiur/gadgets/bytes2.rs
index fc7e8044..f928af62 100644
--- a/src/aiur/gadgets/bytes2.rs
+++ b/src/aiur/gadgets/bytes2.rs
@@ -7,13 +7,16 @@ use multi_stark::{
 };
 
 use crate::aiur::{
-  G, execute::QueryRecord, gadgets::AiurGadget, u8_add_channel, u8_xor_channel,
+  G, execute::QueryRecord, gadgets::AiurGadget, u8_add_channel, u8_and_channel,
+  u8_or_channel, u8_xor_channel,
 };
 
 /// Number of columns in the trace with multiplicities for
 /// - xor
 /// - overflowing add
-const TRACE_WIDTH: usize = 2;
+/// - and
+/// - or
+const TRACE_WIDTH: usize = 4;
 
 /// Number of columns in the preprocessed trace:
 /// - first raw byte value
@@ -21,7 +24,9 @@ const TRACE_WIDTH: usize = 2;
 /// - xor result
 /// - add result
 /// - add overflow
-const PREPROCESSED_TRACE_WIDTH: usize = 5;
+/// - and result
+/// - or result
+const PREPROCESSED_TRACE_WIDTH: usize = 7;
 
 /// AIR implementer for arity 2 byte-related lookups.
 pub(crate) struct Bytes2;
@@ -29,6 +34,8 @@ pub(crate) struct Bytes2;
 pub(crate) enum Bytes2Op {
   Xor,
   Add,
+  And,
+  Or,
 }
 
 impl BaseAir<G> for Bytes2 {
@@ -53,6 +60,12 @@ impl BaseAir<G> for Bytes2 {
         let (r, o) = i.overflowing_add(j);
         trace_values.push(G::from_u8(r));
         trace_values.push(G::from_bool(o));
+
+        // And
+        trace_values.push(G::from_u8(i & j));
+
+        // Or
+        trace_values.push(G::from_u8(i | j));
       }
     }
     Some(RowMajorMatrix::new(trace_values, PREPROCESSED_TRACE_WIDTH))
@@ -69,7 +82,7 @@ impl AiurGadget for Bytes2 {
 
   fn output_size(&self, op: &Bytes2Op) -> usize {
     match op {
-      Bytes2Op::Xor => 1,
+      Bytes2Op::Xor | Bytes2Op::And | Bytes2Op::Or => 1,
       Bytes2Op::Add => 2,
     }
   }
@@ -92,6 +105,14 @@ impl AiurGadget for Bytes2 {
         let (r, o) = Self::add(i, j);
         vec![r, o]
       },
+      Bytes2Op::And => {
+        record.bytes2_queries.bump_and(i, j);
+        vec![Self::and(i, j)]
+      },
+      Bytes2Op::Or => {
+        record.bytes2_queries.bump_or(i, j);
+        vec![Self::or(i, j)]
+      },
     }
   }
 
@@ -99,10 +120,14 @@ impl AiurGadget for Bytes2 {
     // Channels
     let xor_channel = u8_xor_channel().into();
     let add_channel = u8_add_channel().into();
+    let and_channel = u8_and_channel().into();
+    let or_channel = u8_or_channel().into();
 
     // Multiplicity columns
     let xor_multiplicity = var(0);
     let add_multiplicity = var(1);
+    let and_multiplicity = var(2);
+    let or_multiplicity = var(3);
 
     // Preprocessed columns
     let i = preprocessed_var(0);
@@ -110,16 +135,27 @@ impl AiurGadget for Bytes2 {
     let xor = preprocessed_var(2);
     let add_r = preprocessed_var(3);
     let add_o = preprocessed_var(4);
+    let and = preprocessed_var(5);
+    let or = preprocessed_var(6);
 
     let pull_xor = Lookup::pull(
       xor_multiplicity,
       vec![xor_channel, i.clone(), j.clone(), xor],
     );
 
-    let pull_add =
-      Lookup::pull(add_multiplicity, vec![add_channel, i, j, add_r, add_o]);
+    let pull_add = Lookup::pull(
+      add_multiplicity,
+      vec![add_channel, i.clone(), j.clone(), add_r, add_o],
+    );
+
+    let pull_and = Lookup::pull(
+      and_multiplicity,
+      vec![and_channel, i.clone(), j.clone(), and],
+    );
+
+    let pull_or = Lookup::pull(or_multiplicity, vec![or_channel, i, j, or]);
 
-    vec![pull_xor, pull_add]
+    vec![pull_xor, pull_add, pull_and, pull_or]
   }
 
   fn witness_data(
@@ -133,18 +169,22 @@ impl AiurGadget for Bytes2 {
 
     let xor_channel = u8_xor_channel();
     let add_channel = u8_add_channel();
+    let and_channel = u8_and_channel();
+    let or_channel = u8_or_channel();
 
     rows
       .chunks_exact_mut(TRACE_WIDTH)
       .enumerate()
       .zip(&record.bytes2_queries.0)
       .zip(&mut lookups)
-      .for_each(|(((row_idx, row), &[xor, add]), row_lookups)| {
+      .for_each(|(((row_idx, row), &[xor, add, and, or]), row_lookups)| {
         let i = G::from_usize(row_idx / 256);
         let j = G::from_usize(row_idx % 256);
 
         row[0] = xor;
         row[1] = add;
+        row[2] = and;
+        row[3] = or;
 
         // Pull xor.
         row_lookups[0] =
@@ -153,6 +193,14 @@ impl AiurGadget for Bytes2 {
         // Pull add.
         let (r, o) = Self::add(&i, &j);
         row_lookups[1] = Lookup::pull(add, vec![add_channel, i, j, r, o]);
+
+        // Pull and.
+        row_lookups[2] =
+          Lookup::pull(and, vec![and_channel, i, j, Self::and(&i, &j)]);
+
+        // Pull or.
+        row_lookups[3] =
+          Lookup::pull(or, vec![or_channel, i, j, Self::or(&i, &j)]);
       });
     (RowMajorMatrix::new(rows, TRACE_WIDTH), lookups)
   }
@@ -175,6 +223,14 @@ impl Bytes2Queries {
     self.bump_multiplicity_for(i, j, 1)
   }
 
+  fn bump_and(&mut self, i: &G, j: &G) {
+    self.bump_multiplicity_for(i, j, 2)
+  }
+
+  fn bump_or(&mut self, i: &G, j: &G) {
+    self.bump_multiplicity_for(i, j, 3)
+  }
+
   fn bump_multiplicity_for(&mut self, i: &G, j: &G, col: usize) {
     let i = usize::try_from(i.as_canonical_u64()).unwrap();
     let j = usize::try_from(j.as_canonical_u64()).unwrap();
@@ -198,4 +254,18 @@ impl Bytes2 {
     let (r, o) = i.overflowing_add(j);
     (G::from_u8(r), G::from_bool(o))
   }
+
+  #[inline]
+  pub(crate) fn and(i: &G, j: &G) -> G {
+    let i: u8 = i.as_canonical_u64().try_into().unwrap();
+    let j: u8 = j.as_canonical_u64().try_into().unwrap();
+    G::from_u8(i & j)
+  }
+
+  #[inline]
+  pub(crate) fn or(i: &G, j: &G) -> G {
+    let i: u8 = i.as_canonical_u64().try_into().unwrap();
+    let j: u8 = j.as_canonical_u64().try_into().unwrap();
+    G::from_u8(i | j)
+  }
 }
diff --git a/src/aiur/mod.rs b/src/aiur/mod.rs
index df09e145..26e49bb9 100644
--- a/src/aiur/mod.rs
+++ b/src/aiur/mod.rs
@@ -44,3 +44,13 @@ pub fn u8_xor_channel() -> G {
 pub fn u8_add_channel() -> G {
   G::from_u8(6)
 }
+
+#[inline]
+pub fn u8_and_channel() -> G {
+  G::from_u8(7)
+}
+
+#[inline]
+pub fn u8_or_channel() -> G {
+  G::from_u8(8)
+}
diff --git a/src/aiur/trace.rs b/src/aiur/trace.rs
index 4b0e17c7..a87f4c5f 100644
--- a/src/aiur/trace.rs
+++ b/src/aiur/trace.rs
@@ -17,8 +17,8 @@ use crate::aiur::{
   function_channel,
   gadgets::{bytes1::Bytes1, bytes2::Bytes2},
   memory::Memory,
-  u8_add_channel, u8_bit_decomposition_channel, u8_shift_left_channel,
-  u8_shift_right_channel, u8_xor_channel,
+  u8_add_channel, u8_and_channel, u8_bit_decomposition_channel, u8_or_channel,
+  u8_shift_left_channel, u8_shift_right_channel, u8_xor_channel,
 };
 
 struct ColumnIndex {
@@ -374,6 +374,24 @@ impl Op {
         let lookup_args = vec![u8_add_channel(), i, j, r, o];
         slice.push_lookup(index, Lookup::push(G::ONE, lookup_args));
       },
+      Op::U8And(i, j) => {
+        let (i, _) = map[*i];
+        let (j, _) = map[*j];
+        let and = Bytes2::and(&i, &j);
+        map.push((and, 1));
+        slice.push_auxiliary(index, and);
+        let lookup_args = vec![u8_and_channel(), i, j, and];
+        slice.push_lookup(index, Lookup::push(G::ONE, lookup_args));
+      },
+      Op::U8Or(i, j) => {
+        let (i, _) = map[*i];
+        let (j, _) = map[*j];
+        let or = Bytes2::or(&i, &j);
+        map.push((or, 1));
+        slice.push_auxiliary(index, or);
+        let lookup_args = vec![u8_or_channel(), i, j, or];
+        slice.push_lookup(index, Lookup::push(G::ONE, lookup_args));
+      },
       Op::AssertEq(..) | Op::IOSetInfo(..) | Op::IOWrite(_) | Op::Debug(..) => {
       },
     }
diff --git a/src/lean/ffi/aiur/toplevel.rs b/src/lean/ffi/aiur/toplevel.rs
index 1b4ebd84..8789665e 100644
--- a/src/lean/ffi/aiur/toplevel.rs
+++ b/src/lean/ffi/aiur/toplevel.rs
@@ -117,6 +117,14 @@ fn lean_ptr_to_op(ptr: *const c_void) -> Op {
       Op::U8Add(i, j)
     },
     18 => {
+      let [i, j] = ctor.objs().map(lean_unbox_nat_as_usize);
+      Op::U8And(i, j)
+    },
+    19 => {
+      let [i, j] = ctor.objs().map(lean_unbox_nat_as_usize);
+      Op::U8Or(i, j)
+    },
+    20 => {
       let [label_ptr, idxs_ptr] = ctor.objs();
       let label_str: &LeanStringObject = as_ref_unsafe(label_ptr.cast());
       let label = label_str.as_string();