diff --git a/cranelift/codegen/src/prelude.isle b/cranelift/codegen/src/prelude.isle
index 04b17df8e098..4385c02615bd 100644
--- a/cranelift/codegen/src/prelude.isle
+++ b/cranelift/codegen/src/prelude.isle
@@ -16,34 +16,15 @@
 (model bool (type Bool))
 
 (model u8 (type (bv 8)))
-(type u8 (primitive u8))
-
 (model u16 (type (bv 16)))
-(type u16 (primitive u16))
-
 (model u32 (type (bv 32)))
-(type u32 (primitive u32))
-
 (model u64 (type (bv 64)))
-(type u64 (primitive u64))
-(type u128 (primitive u128))
-
 (model usize (type (bv)))
-(type usize (primitive usize))
 
 (model i8 (type (bv 8)))
-(type i8 (primitive i8))
-
 (model i16 (type (bv 16)))
-(type i16 (primitive i16))
-
 (model i32 (type (bv 32)))
-(type i32 (primitive i32))
-
 (model i64 (type (bv 64)))
-(type i64 (primitive i64))
-(type i128 (primitive i128))
-(type isize (primitive isize))
 
 ;; `cranelift-entity`-based identifiers.
 (model Type (type Int))
diff --git a/cranelift/isle/isle/isle_examples/fail/bound_var_type_mismatch.isle b/cranelift/isle/isle/isle_examples/fail/bound_var_type_mismatch.isle
index d33f741e403b..a58d51215142 100644
--- a/cranelift/isle/isle/isle_examples/fail/bound_var_type_mismatch.isle
+++ b/cranelift/isle/isle/isle_examples/fail/bound_var_type_mismatch.isle
@@ -1,6 +1,3 @@
-(type u32 (primitive u32))
-(type u64 (primitive u64))
-
 (decl A (u32 u64) u32)
 
 (rule 1 (A x x) x)
diff --git a/cranelift/isle/isle/isle_examples/fail/error1.isle b/cranelift/isle/isle/isle_examples/fail/error1.isle
index f5c448a3a5ef..b24e18e54c1d 100644
--- a/cranelift/isle/isle/isle_examples/fail/error1.isle
+++ b/cranelift/isle/isle/isle_examples/fail/error1.isle
@@ -1,4 +1,3 @@
-(type u32 (primitive u32))
 (type A (enum (A1 (x u32))))
 
 (decl Ext1 (u32) A)
diff --git a/cranelift/isle/isle/isle_examples/fail/extra_parens.isle b/cranelift/isle/isle/isle_examples/fail/extra_parens.isle
index 06c05c820ffa..9c37123571da 100644
--- a/cranelift/isle/isle/isle_examples/fail/extra_parens.isle
+++ b/cranelift/isle/isle/isle_examples/fail/extra_parens.isle
@@ -1,5 +1,3 @@
-(type u32 (primitive u32))
-
 (decl f (u32) u32)
 ;; Should get an error about `x` not being a term, with a suggestion that it is
 ;; a bound var instead.
diff --git a/cranelift/isle/isle/isle_examples/fail/impure_expression.isle b/cranelift/isle/isle/isle_examples/fail/impure_expression.isle
index 6b993b1501b8..0adb4759708e 100644
--- a/cranelift/isle/isle/isle_examples/fail/impure_expression.isle
+++ b/cranelift/isle/isle/isle_examples/fail/impure_expression.isle
@@ -1,5 +1,3 @@
-(type u32 (primitive u32))
-
 (decl ctor (u32) u32)
 (rule (ctor x) x)
 
diff --git a/cranelift/isle/isle/isle_examples/fail/impure_rhs.isle b/cranelift/isle/isle/isle_examples/fail/impure_rhs.isle
index eae68c2f0290..4bfc95e5c555 100644
--- a/cranelift/isle/isle/isle_examples/fail/impure_rhs.isle
+++ b/cranelift/isle/isle/isle_examples/fail/impure_rhs.isle
@@ -1,5 +1,3 @@
-(type u32 (primitive u32))
-
 (decl pure ctor (u32) u32)
 (decl impure (u32) u32)
 
diff --git a/cranelift/isle/isle/isle_examples/fail/multi_internal_etor.isle b/cranelift/isle/isle/isle_examples/fail/multi_internal_etor.isle
index c2f62894544e..d876231dec75 100644
--- a/cranelift/isle/isle/isle_examples/fail/multi_internal_etor.isle
+++ b/cranelift/isle/isle/isle_examples/fail/multi_internal_etor.isle
@@ -1,4 +1,2 @@
-(type u32 (primitive u32))
-
 (decl multi A (u32) u32)
 (extractor (A x) x)
diff --git a/cranelift/isle/isle/isle_examples/fail/multi_prio.isle b/cranelift/isle/isle/isle_examples/fail/multi_prio.isle
index 30ce9c7a5fbc..feb766688de1 100644
--- a/cranelift/isle/isle/isle_examples/fail/multi_prio.isle
+++ b/cranelift/isle/isle/isle_examples/fail/multi_prio.isle
@@ -1,4 +1,2 @@
-(type u32 (primitive u32))
-
 (decl multi A (u32) u32)
 (rule 0 (A x) x)
diff --git a/cranelift/isle/isle/isle_examples/link/borrows.isle b/cranelift/isle/isle/isle_examples/link/borrows.isle
index 526c21ede966..2b1ce8f6f481 100644
--- a/cranelift/isle/isle/isle_examples/link/borrows.isle
+++ b/cranelift/isle/isle/isle_examples/link/borrows.isle
@@ -1,4 +1,3 @@
-(type u32 (primitive u32))
 (type A extern (enum (B (x u32) (y u32))))
 
 (decl get_a (A) u32)
diff --git a/cranelift/isle/isle/isle_examples/link/iflets.isle b/cranelift/isle/isle/isle_examples/link/iflets.isle
index bd768b4ece30..cf7f324696ef 100644
--- a/cranelift/isle/isle/isle_examples/link/iflets.isle
+++ b/cranelift/isle/isle/isle_examples/link/iflets.isle
@@ -1,5 +1,3 @@
-(type u32 (primitive u32))
-
 (decl pure partial A (u32 u32) u32)
 (extern constructor A A)
 
diff --git a/cranelift/isle/isle/isle_examples/link/multi_constructor.isle b/cranelift/isle/isle/isle_examples/link/multi_constructor.isle
index 45919fe221c7..86758c983142 100644
--- a/cranelift/isle/isle/isle_examples/link/multi_constructor.isle
+++ b/cranelift/isle/isle/isle_examples/link/multi_constructor.isle
@@ -1,5 +1,3 @@
-(type u32 (primitive u32))
-
 (decl multi A (u32) u32)
 (decl multi B (u32) u32)
 (decl multi C (u32) u32)
diff --git a/cranelift/isle/isle/isle_examples/link/multi_extractor.isle b/cranelift/isle/isle/isle_examples/link/multi_extractor.isle
index 2630d8682651..f69b2a6f0045 100644
--- a/cranelift/isle/isle/isle_examples/link/multi_extractor.isle
+++ b/cranelift/isle/isle/isle_examples/link/multi_extractor.isle
@@ -1,4 +1,3 @@
-(type u32 (primitive u32))
 (type A extern (enum (B) (C)))
 
 (decl multi E1 (A u32) u32)
diff --git a/cranelift/isle/isle/isle_examples/link/test.isle b/cranelift/isle/isle/isle_examples/link/test.isle
index 09d5ea92afb9..80190e126736 100644
--- a/cranelift/isle/isle/isle_examples/link/test.isle
+++ b/cranelift/isle/isle/isle_examples/link/test.isle
@@ -1,4 +1,3 @@
-(type u32 (primitive u32))
 (type A (enum (A1 (x u32)) (A2 (x u32))))
 (type B (enum (B1 (x u32)) (B2 (x u32))))
 
diff --git a/cranelift/isle/isle/isle_examples/pass/bound_var.isle b/cranelift/isle/isle/isle_examples/pass/bound_var.isle
index f822dc8c35e5..0647330a4372 100644
--- a/cranelift/isle/isle/isle_examples/pass/bound_var.isle
+++ b/cranelift/isle/isle/isle_examples/pass/bound_var.isle
@@ -1,5 +1,3 @@
-(type u32 (primitive u32))
-
 (decl A (u32 u32) u32)
 
 (rule 1 (A x x) x)
diff --git a/cranelift/isle/isle/isle_examples/pass/construct_and_extract.isle b/cranelift/isle/isle/isle_examples/pass/construct_and_extract.isle
index a0951edd4198..3d8becd54334 100644
--- a/cranelift/isle/isle/isle_examples/pass/construct_and_extract.isle
+++ b/cranelift/isle/isle/isle_examples/pass/construct_and_extract.isle
@@ -1,5 +1,3 @@
-(type i32 (primitive i32))
-
 (type B (enum (B (x i32) (y i32))))
 
 ;; `isub` has a constructor and extractor.
diff --git a/cranelift/isle/isle/isle_examples/pass/conversions.isle b/cranelift/isle/isle/isle_examples/pass/conversions.isle
index 1b3e6bfb13a5..a1bb7ea94180 100644
--- a/cranelift/isle/isle/isle_examples/pass/conversions.isle
+++ b/cranelift/isle/isle/isle_examples/pass/conversions.isle
@@ -1,7 +1,6 @@
 (type T (enum (A) (B)))
 (type U (enum (C) (D)))
 (type V (enum (E) (F)))
-(type u32 (primitive u32))
 
 (convert T U t_to_u)
 (convert U T u_to_t)
diff --git a/cranelift/isle/isle/isle_examples/pass/let.isle b/cranelift/isle/isle/isle_examples/pass/let.isle
index c43d1ec668c2..59670852ec12 100644
--- a/cranelift/isle/isle/isle_examples/pass/let.isle
+++ b/cranelift/isle/isle/isle_examples/pass/let.isle
@@ -1,4 +1,3 @@
-(type u32 (primitive u32))
 (type A (enum (Add (x u32) (y u32)) (Sub (x u32) (y u32))))
 (type B (enum (B (z u32))))
 
diff --git a/cranelift/isle/isle/isle_examples/pass/prio_trie_bug.isle b/cranelift/isle/isle/isle_examples/pass/prio_trie_bug.isle
index 19fa9c78fa07..b63de1ab152b 100644
--- a/cranelift/isle/isle/isle_examples/pass/prio_trie_bug.isle
+++ b/cranelift/isle/isle/isle_examples/pass/prio_trie_bug.isle
@@ -5,8 +5,6 @@
 ;; priority 1 below.
 
 (type Unit (primitive Unit))
-(type u8 (primitive u8))
-(type u32 (primitive u32))
 (type Reg (primitive Reg))
 (type MemFlags (primitive MemFlags))
 (type MachLabel (primitive MachLabel))
diff --git a/cranelift/isle/isle/isle_examples/pass/test2.isle b/cranelift/isle/isle/isle_examples/pass/test2.isle
index 5c0977a70211..209769d39dd9 100644
--- a/cranelift/isle/isle/isle_examples/pass/test2.isle
+++ b/cranelift/isle/isle/isle_examples/pass/test2.isle
@@ -1,4 +1,3 @@
-(type u32 (primitive u32))
 (type A (enum
   (A1 (x B) (y B))))
 (type B (enum
diff --git a/cranelift/isle/isle/isle_examples/pass/test3.isle b/cranelift/isle/isle/isle_examples/pass/test3.isle
index 82d37624d532..5f54a489b764 100644
--- a/cranelift/isle/isle/isle_examples/pass/test3.isle
+++ b/cranelift/isle/isle/isle_examples/pass/test3.isle
@@ -7,7 +7,6 @@
 (type Inst (primitive Inst))
 (type InstInput (primitive InstInput))
 (type Reg (primitive Reg))
-(type u32 (primitive u32))
 
 (decl Op (Opcode) Inst)
 (extern extractor infallible Op get_opcode)
diff --git a/cranelift/isle/isle/isle_examples/pass/test4.isle b/cranelift/isle/isle/isle_examples/pass/test4.isle
index 0acb162e2ccd..714fd7bd997d 100644
--- a/cranelift/isle/isle/isle_examples/pass/test4.isle
+++ b/cranelift/isle/isle/isle_examples/pass/test4.isle
@@ -1,4 +1,3 @@
-(type u32 (primitive u32))
 (type A (enum (A1 (x u32))))
 
 (decl Ext1 (u32) A)
diff --git a/cranelift/isle/isle/isle_examples/pass/tutorial.isle b/cranelift/isle/isle/isle_examples/pass/tutorial.isle
index f072fee74f4e..871ac843b3c9 100644
--- a/cranelift/isle/isle/isle_examples/pass/tutorial.isle
+++ b/cranelift/isle/isle/isle_examples/pass/tutorial.isle
@@ -1,8 +1,5 @@
 ;;;; Type Definitions ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
 
-;; Declare that we are using the `i32` primitive type from Rust.
-(type i32 (primitive i32))
-
 ;; Our high-level, RISC-y input IR.
 (type HighLevelInst
   (enum (Add (a Value) (b Value))
diff --git a/cranelift/isle/isle/isle_examples/pass/veri_spec.isle b/cranelift/isle/isle/isle_examples/pass/veri_spec.isle
index 5aae9faa007e..daa0d8ead7a4 100644
--- a/cranelift/isle/isle/isle_examples/pass/veri_spec.isle
+++ b/cranelift/isle/isle/isle_examples/pass/veri_spec.isle
@@ -1,5 +1,3 @@
-(type u8 (primitive u8))
-
 (form
   bv_unary_8_to_64
   ((args (bv  8)) (ret (bv  8)) (canon (bv  8)))
diff --git a/cranelift/isle/isle/isle_examples/run/iconst.isle b/cranelift/isle/isle/isle_examples/run/iconst.isle
index 84270607467d..7f9614708a03 100644
--- a/cranelift/isle/isle/isle_examples/run/iconst.isle
+++ b/cranelift/isle/isle/isle_examples/run/iconst.isle
@@ -1,13 +1,9 @@
-(type i64 (primitive i64))
-
 (decl partial X (i64) i64)
 (rule (X -1) -2)
 (rule (X -2) -3)
 (rule (X 0x7fff_ffff_ffff_ffff) -0x8000_0000_0000_0000)
 (rule (X -16) 1)
 
-(type i128 (primitive i128))
-
 (decl partial Y (i128) i128)
 
 (rule (Y 0x1000_0000_0000_0000_1234_5678_9abc_def0) -1)
@@ -17,7 +13,6 @@
 (rule (Y -0xffff_ffff_ffff_ffff_ffff_ffff_ffff_ffff) -3)
 
 ;; Test some various syntaxes for numbers
-(type i32 (primitive i32))
 (decl partial Z (i32) i32)
 (rule (Z 0) 0x01)
 (rule (Z 0x01) 0x0_2)
diff --git a/cranelift/isle/isle/isle_examples/run/let_shadowing.isle b/cranelift/isle/isle/isle_examples/run/let_shadowing.isle
index f25db3e2f61f..5db327b14103 100644
--- a/cranelift/isle/isle/isle_examples/run/let_shadowing.isle
+++ b/cranelift/isle/isle/isle_examples/run/let_shadowing.isle
@@ -1,6 +1,3 @@
-
-(type u64 (primitive u64))
-
 (decl foo (u64) u64)
 (rule (foo x) x)
 
diff --git a/cranelift/isle/isle/src/codegen.rs b/cranelift/isle/isle/src/codegen.rs
index 1535add2c160..769223d38368 100644
--- a/cranelift/isle/isle/src/codegen.rs
+++ b/cranelift/isle/isle/src/codegen.rs
@@ -1,7 +1,9 @@
 //! Generate Rust code from a series of Sequences.
 
 use crate::files::Files;
-use crate::sema::{ExternalSig, ReturnKind, Term, TermEnv, TermId, Type, TypeEnv, TypeId};
+use crate::sema::{
+    BuiltinType, ExternalSig, ReturnKind, Term, TermEnv, TermId, Type, TypeEnv, TypeId,
+};
 use crate::serialize::{Block, ControlFlow, EvalStep, MatchArm};
 use crate::stablemapset::StableSet;
 use crate::trie_again::{Binding, BindingId, Constraint, RuleSet};
@@ -915,18 +917,11 @@ impl<L: Length, C> Length for ContextIterWrapper<L, C> {{
         val: i128,
         ty: TypeId,
     ) -> Result<(), std::fmt::Error> {
-        // For the kinds of situations where we use ISLE, magic numbers are
-        // much more likely to be understandable if they're in hex rather than
-        // decimal.
-        // TODO: use better type info (https://github.com/bytecodealliance/wasmtime/issues/5431)
-        if val < 0
-            && self.typeenv.types[ty.index()]
-                .name(self.typeenv)
-                .starts_with('i')
-        {
-            write!(ctx.out, "-{:#X}", -val)
-        } else {
-            write!(ctx.out, "{val:#X}")
+        let ty_data = &self.typeenv.types[ty.index()];
+        match ty_data {
+            Type::Builtin(BuiltinType::Int(ty)) if ty.is_signed() => write!(ctx.out, "{val}_{ty}"),
+            Type::Builtin(BuiltinType::Int(ty)) => write!(ctx.out, "{val:#x}_{ty}"),
+            _ => write!(ctx.out, "{val:#x}"),
         }
     }
 }
diff --git a/cranelift/isle/isle/src/sema.rs b/cranelift/isle/isle/src/sema.rs
index 2ce75937d429..1b3d3aa1b5f5 100644
--- a/cranelift/isle/isle/src/sema.rs
+++ b/cranelift/isle/isle/src/sema.rs
@@ -22,6 +22,7 @@ use std::collections::hash_map::Entry;
 use std::collections::BTreeMap;
 use std::collections::BTreeSet;
 use std::collections::HashMap;
+use std::fmt;
 
 declare_id!(
     /// The id of an interned symbol.
@@ -82,26 +83,144 @@ pub struct TypeEnv {
 
 /// A built-in type.
 #[derive(Copy, Clone, Debug, PartialEq, Eq)]
+#[repr(u8)]
 pub enum BuiltinType {
     /// The type of booleans, with values `true` and `false`.
     Bool,
+    /// The types of fixed-width integers.
+    Int(IntType),
+}
+
+/// A built-in fixed-width integer type.
+#[derive(Copy, Clone, Debug, PartialEq, Eq)]
+pub enum IntType {
+    /// Unsigned, 8 bits.
+    U8,
+    /// Unsigned, 16 bits.
+    U16,
+    /// Unsigned, 32 bits.
+    U32,
+    /// Unsigned, 64 bits.
+    U64,
+    /// Unsigned, 128 bits.
+    U128,
+    /// Unsigned, enough bits to hold a pointer.
+    USize,
+    /// Signed, 8 bits.
+    I8,
+    /// Signed, 16 bits.
+    I16,
+    /// Signed, 32 bits.
+    I32,
+    /// Signed, 64 bits.
+    I64,
+    /// Signed, 128 bits.
+    I128,
+    /// Unsigned, enough bits to hold a pointer.
+    ISize,
+}
+
+impl IntType {
+    /// Get the integer type's name.
+    pub fn name(&self) -> &'static str {
+        match self {
+            IntType::U8 => "u8",
+            IntType::U16 => "u16",
+            IntType::U32 => "u32",
+            IntType::U64 => "u64",
+            IntType::U128 => "u128",
+            IntType::USize => "usize",
+            IntType::I8 => "i8",
+            IntType::I16 => "i16",
+            IntType::I32 => "i32",
+            IntType::I64 => "i64",
+            IntType::I128 => "i128",
+            IntType::ISize => "isize",
+        }
+    }
+
+    /// Is this integer type signed?
+    pub fn is_signed(&self) -> bool {
+        matches!(
+            self,
+            Self::I8 | Self::I16 | Self::I32 | Self::I64 | Self::I128 | Self::ISize
+        )
+    }
+}
+
+impl fmt::Display for IntType {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        write!(f, "{}", self.name())
+    }
 }
 
 impl BuiltinType {
     /// All the built-in types.
-    pub const ALL: &'static [Self] = &[Self::Bool];
+    pub const ALL: &'static [Self] = &[
+        Self::Bool,
+        Self::Int(IntType::U8),
+        Self::Int(IntType::U16),
+        Self::Int(IntType::U32),
+        Self::Int(IntType::U64),
+        Self::Int(IntType::U128),
+        Self::Int(IntType::USize),
+        Self::Int(IntType::I8),
+        Self::Int(IntType::I16),
+        Self::Int(IntType::I32),
+        Self::Int(IntType::I64),
+        Self::Int(IntType::I128),
+        Self::Int(IntType::ISize),
+    ];
 
     /// Get the built-in type's name.
     pub fn name(&self) -> &'static str {
         match self {
             BuiltinType::Bool => "bool",
+            BuiltinType::Int(it) => it.name(),
+        }
+    }
+
+    const fn to_usize(&self) -> usize {
+        match self {
+            Self::Bool => 0,
+            Self::Int(ty) => *ty as usize + 1,
         }
     }
 }
 
 impl TypeId {
+    const fn builtin(builtin: BuiltinType) -> Self {
+        Self(builtin.to_usize())
+    }
+
     /// TypeId for `bool`.
-    pub const BOOL: Self = Self(0);
+    pub const BOOL: Self = Self::builtin(BuiltinType::Bool);
+
+    /// TypeId for `u8`.
+    pub const U8: Self = Self::builtin(BuiltinType::Int(IntType::U8));
+    /// TypeId for `u16`.
+    pub const U16: Self = Self::builtin(BuiltinType::Int(IntType::U16));
+    /// TypeId for `u32`.
+    pub const U32: Self = Self::builtin(BuiltinType::Int(IntType::U32));
+    /// TypeId for `u64`.
+    pub const U64: Self = Self::builtin(BuiltinType::Int(IntType::U64));
+    /// TypeId for `u128`.
+    pub const U128: Self = Self::builtin(BuiltinType::Int(IntType::U128));
+    /// TypeId for `usize`.
+    pub const USIZE: Self = Self::builtin(BuiltinType::Int(IntType::USize));
+
+    /// TypeId for `i8`.
+    pub const I8: Self = Self::builtin(BuiltinType::Int(IntType::I8));
+    /// TypeId for `i16`.
+    pub const I16: Self = Self::builtin(BuiltinType::Int(IntType::I16));
+    /// TypeId for `i32`.
+    pub const I32: Self = Self::builtin(BuiltinType::Int(IntType::I32));
+    /// TypeId for `i64`.
+    pub const I64: Self = Self::builtin(BuiltinType::Int(IntType::I64));
+    /// TypeId for `i128`.
+    pub const I128: Self = Self::builtin(BuiltinType::Int(IntType::I128));
+    /// TypeId for `isize`.
+    pub const ISIZE: Self = Self::builtin(BuiltinType::Int(IntType::ISize));
 }
 
 /// A type.
@@ -161,6 +280,11 @@ impl Type {
     pub fn is_prim(&self) -> bool {
         matches!(self, Type::Primitive(..))
     }
+
+    /// Is this a built-in integer type?
+    pub fn is_int(&self) -> bool {
+        matches!(self, Self::Builtin(BuiltinType::Int(_)))
+    }
 }
 
 /// A variant of an enum.
@@ -467,7 +591,7 @@ impl Term {
             } => {
                 let (func_name, full_name) = match kind {
                     ConstructorKind::InternalConstructor => {
-                        let name = format!("constructor_{}", tyenv.syms[self.name.index()]);
+                        let name = format!("{}", tyenv.syms[self.name.index()]);
                         (name.clone(), name)
                     }
                     ConstructorKind::ExternalConstructor { name } => (
@@ -994,7 +1118,7 @@ impl TypeEnv {
             match def {
                 &ast::Def::Type(ref td) => {
                     let tid = TypeId(tyenv.type_map.len());
-                    let name = tyenv.intern_mut(&td.name);
+                    let name = tyenv.get_or_intern(&td.name);
 
                     if let Some(existing) = tyenv.type_map.get(&name).copied() {
                         tyenv.report_error(
@@ -1051,7 +1175,7 @@ impl TypeEnv {
                         continue;
                     }
                 };
-                let name = tyenv.intern_mut(name);
+                let name = tyenv.get_or_intern(name);
                 tyenv.const_types.insert(name, ty);
             }
         }
@@ -1081,7 +1205,7 @@ impl TypeEnv {
                     self.report_error(ty.pos, "primitive types cannot be marked `extern`");
                     return None;
                 }
-                Some(Type::Primitive(tid, self.intern_mut(id), ty.pos))
+                Some(Type::Primitive(tid, self.get_or_intern(id), ty.pos))
             }
             &ast::TypeValue::Enum(ref ty_variants, ..) => {
                 if ty.is_extern && ty.is_nodebug {
@@ -1093,8 +1217,8 @@ impl TypeEnv {
                 for variant in ty_variants {
                     let combined_ident =
                         ast::Ident(format!("{}.{}", ty.name.0, variant.name.0), variant.name.1);
-                    let fullname = self.intern_mut(&combined_ident);
-                    let name = self.intern_mut(&variant.name);
+                    let fullname = self.get_or_intern(&combined_ident);
+                    let name = self.get_or_intern(&variant.name);
                     let id = VariantId(variants.len());
                     if variants.iter().any(|v: &Variant| v.name == name) {
                         self.report_error(
@@ -1105,7 +1229,7 @@ impl TypeEnv {
                     }
                     let mut fields = vec![];
                     for field in &variant.fields {
-                        let field_name = self.intern_mut(&field.name);
+                        let field_name = self.get_or_intern(&field.name);
                         if fields.iter().any(|f: &Field| f.name == field_name) {
                             self.report_error(
                                 field.pos,
@@ -1166,7 +1290,7 @@ impl TypeEnv {
         self.errors.push(err);
     }
 
-    fn intern_mut(&mut self, ident: &ast::Ident) -> Sym {
+    fn get_or_intern(&mut self, ident: &ast::Ident) -> Sym {
         if let Some(s) = self.sym_map.get(&ident.0).copied() {
             s
         } else {
@@ -1277,7 +1401,7 @@ impl TermEnv {
         for def in defs {
             match def {
                 &ast::Def::Decl(ref decl) => {
-                    let name = tyenv.intern_mut(&decl.term);
+                    let name = tyenv.get_or_intern(&decl.term);
                     if let Some(tid) = self.term_map.get(&name) {
                         tyenv.report_error(
                             decl.pos,
@@ -1645,7 +1769,7 @@ impl TermEnv {
                     ref func,
                     pos,
                 }) => {
-                    let func_sym = tyenv.intern_mut(func);
+                    let func_sym = tyenv.get_or_intern(func);
                     let term_id = match self.get_term_by_name(tyenv, term) {
                         Some(term) => term,
                         None => {
@@ -1698,7 +1822,7 @@ impl TermEnv {
                     pos,
                     infallible,
                 }) => {
-                    let func_sym = tyenv.intern_mut(func);
+                    let func_sym = tyenv.get_or_intern(func);
                     let term_id = match self.get_term_by_name(tyenv, term) {
                         Some(term) => term,
                         None => {
@@ -1845,7 +1969,7 @@ impl TermEnv {
                         vars: bindings.seen,
                         prio,
                         pos,
-                        name: rule.name.as_ref().map(|i| tyenv.intern_mut(i)),
+                        name: rule.name.as_ref().map(|i| tyenv.get_or_intern(i)),
                     });
                 }
                 _ => {}
@@ -1941,11 +2065,11 @@ impl TermEnv {
             // TODO: flag on primitive type decl indicating it's an integer type?
             &ast::Pattern::ConstInt { val, pos } => {
                 let ty = &tyenv.types[expected_ty.index()];
-                if !ty.is_prim() {
+                if !ty.is_int() && !ty.is_prim() {
                     tyenv.report_error(
                         pos,
                         format!(
-                            "expected non-primitive type {}, but found integer literal '{}'",
+                            "expected non-integer type {}, but found integer literal '{}'",
                             ty.name(tyenv),
                             val,
                         ),
@@ -1967,7 +2091,7 @@ impl TermEnv {
                 Some(Pattern::ConstBool(TypeId::BOOL, val))
             }
             &ast::Pattern::ConstPrim { ref val, pos } => {
-                let val = tyenv.intern_mut(val);
+                let val = tyenv.get_or_intern(val);
                 let const_ty = match tyenv.const_types.get(&val) {
                     Some(ty) => *ty,
                     None => {
@@ -2006,7 +2130,7 @@ impl TermEnv {
                 // generate fewer follow-on error messages.
                 let ty = subpat.ty();
 
-                let name = tyenv.intern_mut(var);
+                let name = tyenv.get_or_intern(var);
                 if bindings.lookup(name).is_some() {
                     tyenv.report_error(
                         pos,
@@ -2023,7 +2147,7 @@ impl TermEnv {
                 // existing bound value), otherwise it becomes a
                 // `BindPattern` with a wildcard subpattern to capture
                 // at this location.
-                let name = tyenv.intern_mut(var);
+                let name = tyenv.get_or_intern(var);
                 match bindings.lookup(name) {
                     None => {
                         let id = bindings.add_var(name, expected_ty);
@@ -2198,7 +2322,7 @@ impl TermEnv {
                 pos,
             } => {
                 // Look up the term.
-                let name = tyenv.intern_mut(&sym);
+                let name = tyenv.get_or_intern(&sym);
                 let tid = match self.term_map.get(&name) {
                     Some(&t) => t,
                     None => {
@@ -2311,7 +2435,7 @@ impl TermEnv {
                 Some(Expr::Term(ty, tid, subexprs))
             }
             &ast::Expr::Var { ref name, pos } => {
-                let sym = tyenv.intern_mut(name);
+                let sym = tyenv.get_or_intern(name);
                 // Look through bindings, innermost (most recent) first.
                 let bv = match bindings.lookup(sym) {
                     None => {
@@ -2364,20 +2488,21 @@ impl TermEnv {
                 Some(Expr::ConstBool(TypeId::BOOL, val))
             }
             &ast::Expr::ConstInt { val, pos } => {
-                if ty.is_none() {
+                let Some(ty) = ty else {
                     tyenv.report_error(
                         pos,
                         "integer literal in a context that needs an explicit type".to_string(),
                     );
                     return None;
-                }
-                let ty = ty.unwrap();
+                };
+
+                let typ = &tyenv.types[ty.index()];
 
-                if !tyenv.types[ty.index()].is_prim() {
+                if !typ.is_int() && !typ.is_prim() {
                     tyenv.report_error(
                         pos,
                         format!(
-                            "expected non-primitive type {}, but found integer literal '{}'",
+                            "expected non-integer type {}, but found integer literal '{}'",
                             tyenv.types[ty.index()].name(tyenv),
                             val,
                         ),
@@ -2386,7 +2511,7 @@ impl TermEnv {
                 Some(Expr::ConstInt(ty, val))
             }
             &ast::Expr::ConstPrim { ref val, pos } => {
-                let val = tyenv.intern_mut(val);
+                let val = tyenv.get_or_intern(val);
                 let const_ty = match tyenv.const_types.get(&val) {
                     Some(ty) => *ty,
                     None => {
@@ -2419,7 +2544,7 @@ impl TermEnv {
                 let mut let_defs = vec![];
                 for def in defs {
                     // Check that the given variable name does not already exist.
-                    let name = tyenv.intern_mut(&def.var);
+                    let name = tyenv.get_or_intern(&def.var);
 
                     // Look up the type.
                     let tid = match tyenv.get_type_by_name(&def.ty) {
@@ -2497,7 +2622,7 @@ mod test {
     #[test]
     fn build_type_env() {
         let text = r"
-            (type u32 (primitive u32))
+            (type UImm8 (primitive UImm8))
             (type A extern (enum (B (f1 u32) (f2 u32)) (C (f1 u32))))
         ";
         let ast = parse(Lexer::new(0, text).unwrap()).expect("should parse");
@@ -2518,8 +2643,8 @@ mod test {
         let sym_a_c = tyenv
             .intern(&Ident("A.C".to_string(), Default::default()))
             .unwrap();
-        let sym_u32 = tyenv
-            .intern(&Ident("u32".to_string(), Default::default()))
+        let sym_uimm8 = tyenv
+            .intern(&Ident("UImm8".to_string(), Default::default()))
             .unwrap();
         let sym_f1 = tyenv
             .intern(&Ident("f1".to_string(), Default::default()))
@@ -2528,13 +2653,13 @@ mod test {
             .intern(&Ident("f2".to_string(), Default::default()))
             .unwrap();
 
-        assert_eq!(tyenv.type_map.get(&sym_u32).unwrap(), &TypeId(1));
-        assert_eq!(tyenv.type_map.get(&sym_a).unwrap(), &TypeId(2));
+        assert_eq!(tyenv.type_map.get(&sym_uimm8).unwrap(), &TypeId(13));
+        assert_eq!(tyenv.type_map.get(&sym_a).unwrap(), &TypeId(14));
 
         let expected_types = vec![
             Type::Primitive(
-                TypeId(1),
-                sym_u32,
+                TypeId(13),
+                sym_uimm8,
                 Pos {
                     file: 0,
                     offset: 19,
@@ -2542,7 +2667,7 @@ mod test {
             ),
             Type::Enum {
                 name: sym_a,
-                id: TypeId(2),
+                id: TypeId(14),
                 is_extern: true,
                 is_nodebug: false,
                 variants: vec![
@@ -2554,12 +2679,12 @@ mod test {
                             Field {
                                 name: sym_f1,
                                 id: FieldId(0),
-                                ty: TypeId(1),
+                                ty: TypeId::U32,
                             },
                             Field {
                                 name: sym_f2,
                                 id: FieldId(1),
-                                ty: TypeId(1),
+                                ty: TypeId::U32,
                             },
                         ],
                     },
@@ -2570,13 +2695,13 @@ mod test {
                         fields: vec![Field {
                             name: sym_f1,
                             id: FieldId(0),
-                            ty: TypeId(1),
+                            ty: TypeId::U32,
                         }],
                     },
                 ],
                 pos: Pos {
                     file: 0,
-                    offset: 58,
+                    offset: 62,
                 },
             },
         ];
diff --git a/cranelift/isle/veri/veri_engine/examples/mid-end/broken_bor_band_consts.isle b/cranelift/isle/veri/veri_engine/examples/mid-end/broken_bor_band_consts.isle
index cf55369a480d..c0363cf548c9 100644
--- a/cranelift/isle/veri/veri_engine/examples/mid-end/broken_bor_band_consts.isle
+++ b/cranelift/isle/veri/veri_engine/examples/mid-end/broken_bor_band_consts.isle
@@ -1,6 +1,5 @@
 (type Type (primitive Type))
 (type Value (primitive Value))
-(type u64 (primitive u64))
 (type Imm64 (primitive Imm64))
 (extern const true bool)
 
diff --git a/cranelift/isle/veri/veri_engine/examples/x86/amode_add_shl.isle b/cranelift/isle/veri/veri_engine/examples/x86/amode_add_shl.isle
index aec20bc42c81..94e56c767d2a 100644
--- a/cranelift/isle/veri/veri_engine/examples/x86/amode_add_shl.isle
+++ b/cranelift/isle/veri/veri_engine/examples/x86/amode_add_shl.isle
@@ -6,8 +6,6 @@
 (type MemFlags (primitive MemFlags))
 (type Gpr (primitive Gpr))
 (type Imm64 (primitive Imm64))
-(type u32 (primitive u32))
-(type u8 (primitive u8))
 
 (type MInst (enum))
 
diff --git a/cranelift/isle/veri/veri_engine/examples/x86/amode_add_uextend_shl.isle b/cranelift/isle/veri/veri_engine/examples/x86/amode_add_uextend_shl.isle
index f6675a3b2771..5e8aa8652bbf 100644
--- a/cranelift/isle/veri/veri_engine/examples/x86/amode_add_uextend_shl.isle
+++ b/cranelift/isle/veri/veri_engine/examples/x86/amode_add_uextend_shl.isle
@@ -8,8 +8,6 @@
 (type MemFlags (primitive MemFlags))
 (type Gpr (primitive Gpr))
 (type Imm64 (primitive Imm64))
-(type u32 (primitive u32))
-(type u8 (primitive u8))
 
 (type MInst (enum))