diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index bdb535f0a4..52b83a507e 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -2,9 +2,6 @@ on: [pull_request]
 
 name: CI
 
-variables:
-  RUSTC_WRAPPER: "./ci/sccache"
-
 jobs:
   test:
     name: fmt, clippy, test, test --release
@@ -31,6 +28,24 @@ jobs:
 
       - run: rustup component add rustfmt
 
+      - name: Cache cargo registry
+        uses: actions/cache@v1
+        with:
+          path: ~/.cargo/registry
+          key: ${{ runner.os }}-cargo-registry-${{ hashFiles('**/Cargo.lock') }}
+
+      - name: Cache cargo index
+        uses: actions/cache@v1
+        with:
+          path: ~/.cargo/git
+          key: ${{ runner.os }}-cargo-index-${{ hashFiles('**/Cargo.lock') }}
+
+      - name: Cache compiled valgrind
+        uses: actions/cache@v1
+        with:
+          path: ~/valgrind-3.6.1/
+          key: ${{ runner.os }}-cargo-registry-${{ hashFiles('**/Cargo.lock') }}
+
       - uses: actions-rs/cargo@v1
         name: rustfmt version
         with:
@@ -69,5 +84,3 @@ jobs:
         with:
           command: test
           args: --release
-
-      - run: ./ci/sccache --show-stats
diff --git a/ci/sccache b/ci/sccache
deleted file mode 100755
index 57ecbea0db..0000000000
Binary files a/ci/sccache and /dev/null differ
diff --git a/compiler/builtins/src/unique.rs b/compiler/builtins/src/unique.rs
index 1b1f9c7510..ce7a5e75c8 100644
--- a/compiler/builtins/src/unique.rs
+++ b/compiler/builtins/src/unique.rs
@@ -1242,36 +1242,34 @@ fn lift(u: VarId, a: SolvedType) -> SolvedType {
 
 #[inline(always)]
 fn float_type(u: VarId) -> SolvedType {
+    let b_64 = builtin_aliases::binary64_type();
+    let attr_b_64 = lift(u, b_64);
+    let fp = builtin_aliases::floatingpoint_type(attr_b_64);
+    let attr_fb = lift(u, fp);
+    let num = builtin_aliases::num_type(attr_fb);
+
     SolvedType::Apply(
         Symbol::ATTR_ATTR,
         vec![
             flex(u),
-            SolvedType::Alias(
-                Symbol::NUM_F64,
-                Vec::new(),
-                Box::new(builtin_aliases::num_type(SolvedType::Apply(
-                    Symbol::ATTR_ATTR,
-                    vec![flex(u), builtin_aliases::floatingpoint_type()],
-                ))),
-            ),
+            SolvedType::Alias(Symbol::NUM_F64, Vec::new(), Box::new(num)),
         ],
     )
 }
 
 #[inline(always)]
 fn int_type(u: VarId) -> SolvedType {
+    let signed_64 = builtin_aliases::signed64_type();
+    let attr_signed_64 = lift(u, signed_64);
+    let integer = builtin_aliases::integer_type(attr_signed_64);
+    let attr_fb = lift(u, integer);
+    let num = builtin_aliases::num_type(attr_fb);
+
     SolvedType::Apply(
         Symbol::ATTR_ATTR,
         vec![
             flex(u),
-            SolvedType::Alias(
-                Symbol::NUM_I64,
-                Vec::new(),
-                Box::new(builtin_aliases::num_type(SolvedType::Apply(
-                    Symbol::ATTR_ATTR,
-                    vec![flex(u), builtin_aliases::integer_type()],
-                ))),
-            ),
+            SolvedType::Alias(Symbol::NUM_I64, Vec::new(), Box::new(num)),
         ],
     )
 }
diff --git a/compiler/constrain/src/builtins.rs b/compiler/constrain/src/builtins.rs
index 9b57b9934a..1df15d5aef 100644
--- a/compiler/constrain/src/builtins.rs
+++ b/compiler/constrain/src/builtins.rs
@@ -76,33 +76,71 @@ pub fn num_float() -> Type {
     Type::Alias(
         Symbol::NUM_F64,
         vec![],
-        Box::new(num_num(num_floatingpoint())),
+        Box::new(num_num(num_floatingpoint(num_binary64()))),
     )
 }
 
 #[inline(always)]
-pub fn num_floatingpoint() -> Type {
+pub fn num_floatingpoint(range: Type) -> Type {
     let alias_content = Type::TagUnion(
-        vec![(TagName::Private(Symbol::NUM_AT_FLOATINGPOINT), vec![])],
+        vec![(
+            TagName::Private(Symbol::NUM_AT_FLOATINGPOINT),
+            vec![range.clone()],
+        )],
         Box::new(Type::EmptyTagUnion),
     );
 
-    Type::Alias(Symbol::NUM_FLOATINGPOINT, vec![], Box::new(alias_content))
+    Type::Alias(
+        Symbol::NUM_FLOATINGPOINT,
+        vec![("range".into(), range)],
+        Box::new(alias_content),
+    )
+}
+
+#[inline(always)]
+pub fn num_binary64() -> Type {
+    let alias_content = Type::TagUnion(
+        vec![(TagName::Private(Symbol::NUM_AT_BINARY64), vec![])],
+        Box::new(Type::EmptyTagUnion),
+    );
+
+    Type::Alias(Symbol::NUM_BINARY64, vec![], Box::new(alias_content))
 }
 
 #[inline(always)]
 pub fn num_int() -> Type {
-    Type::Alias(Symbol::NUM_I64, vec![], Box::new(num_num(num_integer())))
+    Type::Alias(
+        Symbol::NUM_I64,
+        vec![],
+        Box::new(num_num(num_integer(num_signed64()))),
+    )
 }
 
 #[inline(always)]
-pub fn num_integer() -> Type {
+pub fn num_signed64() -> Type {
     let alias_content = Type::TagUnion(
-        vec![(TagName::Private(Symbol::NUM_AT_INTEGER), vec![])],
+        vec![(TagName::Private(Symbol::NUM_AT_SIGNED64), vec![])],
         Box::new(Type::EmptyTagUnion),
     );
 
-    Type::Alias(Symbol::NUM_INTEGER, vec![], Box::new(alias_content))
+    Type::Alias(Symbol::NUM_SIGNED64, vec![], Box::new(alias_content))
+}
+
+#[inline(always)]
+pub fn num_integer(range: Type) -> Type {
+    let alias_content = Type::TagUnion(
+        vec![(
+            TagName::Private(Symbol::NUM_AT_INTEGER),
+            vec![range.clone()],
+        )],
+        Box::new(Type::EmptyTagUnion),
+    );
+
+    Type::Alias(
+        Symbol::NUM_INTEGER,
+        vec![("range".into(), range)],
+        Box::new(alias_content),
+    )
 }
 
 #[inline(always)]
diff --git a/compiler/constrain/src/pattern.rs b/compiler/constrain/src/pattern.rs
index 7258dfe6ad..164df10b34 100644
--- a/compiler/constrain/src/pattern.rs
+++ b/compiler/constrain/src/pattern.rs
@@ -157,7 +157,7 @@ pub fn constrain_pattern(
         IntLiteral(_) => {
             state.constraints.push(Constraint::Pattern(
                 region,
-                PatternCategory::Float,
+                PatternCategory::Int,
                 builtins::num_int(),
                 expected,
             ));
diff --git a/compiler/constrain/src/uniq.rs b/compiler/constrain/src/uniq.rs
index 25352f73e0..c3ce919dd3 100644
--- a/compiler/constrain/src/uniq.rs
+++ b/compiler/constrain/src/uniq.rs
@@ -1,4 +1,4 @@
-use crate::builtins::{num_floatingpoint, num_integer, num_num};
+use crate::builtins::{num_binary64, num_floatingpoint, num_integer, num_num, num_signed64};
 use crate::expr::{exists, Info};
 use roc_can::annotation::IntroducedVariables;
 use roc_can::constraint::Constraint::{self, *};
@@ -166,24 +166,25 @@ fn constrain_pattern(
         }
 
         NumLiteral(inner_var, _) => {
-            let (num_uvar, val_uvar, num_type, num_var) = unique_unbound_num(*inner_var, var_store);
+            let (inner_uvar, num_var, num_type) = unique_unbound_num(*inner_var, var_store);
             state.constraints.push(exists(
-                vec![val_uvar, num_uvar, num_var, *inner_var],
+                vec![num_var, inner_uvar, *inner_var],
                 Constraint::Pattern(pattern.region, PatternCategory::Num, num_type, expected),
             ));
         }
 
         IntLiteral(_) => {
-            let (num_uvar, int_uvar, num_type) = unique_int(var_store);
+            let (a, b, c, num_type) = unique_int(var_store);
             state.constraints.push(exists(
-                vec![num_uvar, int_uvar],
+                vec![a, b, c],
                 Constraint::Pattern(pattern.region, PatternCategory::Int, num_type, expected),
             ));
         }
         FloatLiteral(_) => {
-            let (num_uvar, float_uvar, num_type) = unique_float(var_store);
+            let (a, b, c, num_type) = unique_float(var_store);
+
             state.constraints.push(exists(
-                vec![num_uvar, float_uvar],
+                vec![a, b, c],
                 Constraint::Pattern(pattern.region, PatternCategory::Float, num_type, expected),
             ));
         }
@@ -405,41 +406,47 @@ fn constrain_pattern(
     }
 }
 
-fn unique_unbound_num(
-    inner_var: Variable,
-    var_store: &mut VarStore,
-) -> (Variable, Variable, Type, Variable) {
-    let num_var = var_store.fresh();
+fn unique_unbound_num(inner_var: Variable, var_store: &mut VarStore) -> (Variable, Variable, Type) {
     let num_uvar = var_store.fresh();
-    let val_uvar = var_store.fresh();
+    let inner_uvar = var_store.fresh();
 
     let val_type = Type::Variable(inner_var);
-    let val_utype = attr_type(Bool::variable(val_uvar), val_type);
+    let val_utype = attr_type(Bool::variable(inner_uvar), val_type);
 
     let num_utype = num_num(val_utype);
     let num_type = attr_type(Bool::variable(num_uvar), num_utype);
 
-    (num_uvar, val_uvar, num_type, num_var)
+    (inner_uvar, num_uvar, num_type)
 }
 
-fn unique_num(var_store: &mut VarStore, val_type: Type) -> (Variable, Variable, Type) {
-    let num_uvar = var_store.fresh();
-    let val_uvar = var_store.fresh();
+fn unique_int(var_store: &mut VarStore) -> (Variable, Variable, Variable, Type) {
+    let num_uvar1 = var_store.fresh();
+    let num_uvar2 = var_store.fresh();
+    let num_uvar3 = var_store.fresh();
 
-    let val_utype = attr_type(Bool::variable(val_uvar), val_type);
+    let signed_64 = num_signed64();
+    let attr_signed_64 = attr_type(Bool::variable(num_uvar1), signed_64);
+    let integer = num_integer(attr_signed_64);
+    let attr_int = attr_type(Bool::variable(num_uvar2), integer);
+    let num = num_num(attr_int);
+    let attr_num = attr_type(Bool::variable(num_uvar3), num);
 
-    let num_utype = num_num(val_utype);
-    let num_type = attr_type(Bool::variable(num_uvar), num_utype);
-
-    (num_uvar, val_uvar, num_type)
+    (num_uvar1, num_uvar2, num_uvar3, attr_num)
 }
 
-fn unique_int(var_store: &mut VarStore) -> (Variable, Variable, Type) {
-    unique_num(var_store, num_integer())
-}
+fn unique_float(var_store: &mut VarStore) -> (Variable, Variable, Variable, Type) {
+    let num_uvar1 = var_store.fresh();
+    let num_uvar2 = var_store.fresh();
+    let num_uvar3 = var_store.fresh();
 
-fn unique_float(var_store: &mut VarStore) -> (Variable, Variable, Type) {
-    unique_num(var_store, num_floatingpoint())
+    let binary_64 = num_binary64();
+    let attr_binary_64 = attr_type(Bool::variable(num_uvar1), binary_64);
+    let fp = num_floatingpoint(attr_binary_64);
+    let attr_fp = attr_type(Bool::variable(num_uvar2), fp);
+    let num = num_num(attr_fp);
+    let attr_num = attr_type(Bool::variable(num_uvar3), num);
+
+    (num_uvar1, num_uvar2, num_uvar3, attr_num)
 }
 
 pub fn constrain_expr(
@@ -456,10 +463,10 @@ pub fn constrain_expr(
     match expr {
         Num(inner_var, _) => {
             let var = var_store.fresh();
-            let (num_uvar, val_uvar, num_type, num_var) = unique_unbound_num(*inner_var, var_store);
+            let (inner_uvar, num_var, num_type) = unique_unbound_num(*inner_var, var_store);
 
             exists(
-                vec![var, *inner_var, val_uvar, num_uvar, num_var],
+                vec![var, *inner_var, inner_uvar, num_var],
                 And(vec![
                     Eq(
                         Type::Variable(var),
@@ -472,10 +479,10 @@ pub fn constrain_expr(
             )
         }
         Int(var, _) => {
-            let (num_uvar, int_uvar, num_type) = unique_int(var_store);
+            let (a, b, c, num_type) = unique_int(var_store);
 
             exists(
-                vec![*var, num_uvar, int_uvar],
+                vec![*var, a, b, c],
                 And(vec![
                     Eq(
                         Type::Variable(*var),
@@ -488,10 +495,10 @@ pub fn constrain_expr(
             )
         }
         Float(var, _) => {
-            let (num_uvar, float_uvar, num_type) = unique_float(var_store);
+            let (a, b, c, num_type) = unique_float(var_store);
 
             exists(
-                vec![*var, num_uvar, float_uvar],
+                vec![*var, a, b, c],
                 And(vec![
                     Eq(
                         Type::Variable(*var),
diff --git a/compiler/gen/tests/gen_num.rs b/compiler/gen/tests/gen_num.rs
index f3a5da674a..ba2117ff73 100644
--- a/compiler/gen/tests/gen_num.rs
+++ b/compiler/gen/tests/gen_num.rs
@@ -555,7 +555,7 @@ mod gen_num {
         assert_evals_to!(
             indoc!(
                 r#"
-                    always42 : Num.Num Num.Integer -> Num.Num Num.Integer
+                    always42 : Num.Num (Num.Integer Num.Signed64) -> Num.Num (Num.Integer Num.Signed64)
                     always42 = \_ -> 42
 
                     always42 5
diff --git a/compiler/module/src/symbol.rs b/compiler/module/src/symbol.rs
index 951aaeb3e7..efa7f13cc1 100644
--- a/compiler/module/src/symbol.rs
+++ b/compiler/module/src/symbol.rs
@@ -797,11 +797,35 @@ define_builtins! {
         54 NUM_ATAN: "atan"
         55 NUM_ACOS: "acos"
         56 NUM_ASIN: "asin"
-        57 NUM_BITWISE_AND: "bitwiseAnd"
-        58 NUM_SUB_WRAP: "subWrap"
-        59 NUM_SUB_CHECKED: "subChecked"
-        60 NUM_MUL_WRAP: "mulWrap"
-        61 NUM_MUL_CHECKED: "mulChecked"
+        57 NUM_AT_SIGNED128: "@Signed128"
+        58 NUM_SIGNED128: "Signed128" imported
+        59 NUM_AT_SIGNED64: "@Signed64"
+        60 NUM_SIGNED64: "Signed64" imported
+        61 NUM_AT_SIGNED32: "@Signed32"
+        62 NUM_SIGNED32: "Signed32" imported
+        63 NUM_AT_SIGNED16: "@Signed16"
+        64 NUM_SIGNED16: "Signed16" imported
+        65 NUM_AT_SIGNED8: "@Signed8"
+        66 NUM_SIGNED8: "Signed8" imported
+        67 NUM_AT_UNSIGNED128: "@Unsigned128"
+        68 NUM_UNSIGNED128: "Unsigned128" imported
+        69 NUM_AT_UNSIGNED64: "@Unsigned64"
+        70 NUM_UNSIGNED64: "Unsigned64" imported
+        71 NUM_AT_UNSIGNED32: "@Unsigned32"
+        72 NUM_UNSIGNED32: "Unsigned32" imported
+        73 NUM_AT_UNSIGNED16: "@Unsigned16"
+        74 NUM_UNSIGNED16: "Unsigned16" imported
+        75 NUM_AT_UNSIGNED8: "@Unsigned8"
+        76 NUM_UNSIGNED8: "Unsigned8" imported
+        77 NUM_AT_BINARY64: "@Binary64"
+        78 NUM_BINARY64: "Binary64" imported
+        79 NUM_AT_BINARY32: "@Binary32"
+        80 NUM_BINARY32: "Binary32" imported
+        81 NUM_BITWISE_AND: "bitwiseAnd"
+        82 NUM_SUB_WRAP: "subWrap"
+        83 NUM_SUB_CHECKED: "subChecked"
+        84 NUM_MUL_WRAP: "mulWrap"
+        85 NUM_MUL_CHECKED: "mulChecked"
     }
     2 BOOL: "Bool" => {
         0 BOOL_BOOL: "Bool" imported // the Bool.Bool type alias
diff --git a/compiler/mono/src/ir.rs b/compiler/mono/src/ir.rs
index 5ccfd4ee64..dc08c98176 100644
--- a/compiler/mono/src/ir.rs
+++ b/compiler/mono/src/ir.rs
@@ -5832,7 +5832,9 @@ pub enum IntOrFloat {
 pub fn num_argument_to_int_or_float(subs: &Subs, var: Variable) -> IntOrFloat {
     match subs.get_without_compacting(var).content {
         Content::Alias(Symbol::NUM_INTEGER, args, _) => {
-            debug_assert!(args.is_empty());
+            debug_assert!(args.len() == 1);
+
+            // TODO: we probably need to match on the type of the arg
             IntOrFloat::IntType
         }
         Content::FlexVar(_) => {
@@ -5840,7 +5842,9 @@ pub fn num_argument_to_int_or_float(subs: &Subs, var: Variable) -> IntOrFloat {
             IntOrFloat::IntType
         }
         Content::Alias(Symbol::NUM_FLOATINGPOINT, args, _) => {
-            debug_assert!(args.is_empty());
+            debug_assert!(args.len() == 1);
+
+            // TODO: we probably need to match on the type of the arg
             IntOrFloat::FloatType
         }
         Content::Structure(FlatType::Apply(Symbol::ATTR_ATTR, attr_args)) => {
@@ -5849,6 +5853,11 @@ pub fn num_argument_to_int_or_float(subs: &Subs, var: Variable) -> IntOrFloat {
             // Recurse on the second argument
             num_argument_to_int_or_float(subs, attr_args[1])
         }
+        Content::Alias(Symbol::NUM_F64, args, _) | Content::Alias(Symbol::NUM_F32, args, _) => {
+            debug_assert!(args.is_empty());
+
+            IntOrFloat::FloatType
+        }
         other => {
             panic!(
                 "Unrecognized Num type argument for var {:?} with Content: {:?}",
diff --git a/compiler/mono/src/layout.rs b/compiler/mono/src/layout.rs
index 4b74489946..aa9cb3be17 100644
--- a/compiler/mono/src/layout.rs
+++ b/compiler/mono/src/layout.rs
@@ -1296,11 +1296,17 @@ fn unwrap_num_tag<'a>(subs: &Subs, var: Variable) -> Result<Layout<'a>, LayoutPr
             }
         },
         Content::Alias(Symbol::NUM_INTEGER, args, _) => {
-            debug_assert!(args.is_empty());
+            debug_assert!(args.len() == 1);
+
+            // TODO: we probably need to match on the type of the arg
+            // and return the correct builtin ex: Builtin::{Int32, Int16}
             Ok(Layout::Builtin(Builtin::Int64))
         }
         Content::Alias(Symbol::NUM_FLOATINGPOINT, args, _) => {
-            debug_assert!(args.is_empty());
+            debug_assert!(args.len() == 1);
+
+            // TODO: we probably need to match on the type of the arg
+            // and return the correct builtin ex: Builtin::Float32
             Ok(Layout::Builtin(Builtin::Float64))
         }
         Content::FlexVar(_) | Content::RigidVar(_) => {
diff --git a/compiler/reporting/src/error/type.rs b/compiler/reporting/src/error/type.rs
index 1decdf059d..c5beb5dfc3 100644
--- a/compiler/reporting/src/error/type.rs
+++ b/compiler/reporting/src/error/type.rs
@@ -1643,6 +1643,17 @@ fn to_diff<'b>(
                 ErrorType::Type(Symbol::NUM_F64, _) => true,
                 ErrorType::Alias(Symbol::NUM_F64, _, _) => true,
 
+                ErrorType::Type(Symbol::NUM_NUM, args) => match &args.get(0) {
+                    Some(ErrorType::Type(Symbol::NUM_FLOATINGPOINT, _)) => true,
+                    Some(ErrorType::Alias(Symbol::NUM_FLOATINGPOINT, _, _)) => true,
+                    _ => false,
+                },
+                ErrorType::Alias(Symbol::NUM_NUM, args, _) => match &args.get(0) {
+                    Some((_, ErrorType::Type(Symbol::NUM_FLOATINGPOINT, _))) => true,
+                    Some((_, ErrorType::Alias(Symbol::NUM_FLOATINGPOINT, _, _))) => true,
+                    _ => false,
+                },
+
                 _ => false,
             };
 
diff --git a/compiler/reporting/tests/test_reporting.rs b/compiler/reporting/tests/test_reporting.rs
index 0f3b3dfc56..8903fe25dc 100644
--- a/compiler/reporting/tests/test_reporting.rs
+++ b/compiler/reporting/tests/test_reporting.rs
@@ -448,8 +448,8 @@ mod test_reporting {
 
                     baz
                     Str
-                    main
                     U8
+                    F64
                 "#
             ),
         )
@@ -620,9 +620,9 @@ mod test_reporting {
 
                 these names seem close though:
 
+                    Result
                     Num
                     Set
-                    Result
                     U8
                 "#
             ),
@@ -1374,7 +1374,7 @@ mod test_reporting {
                     Bool
                     U8
                     F64
-                    Num
+                    Str
                 "#
             ),
         )
@@ -2094,7 +2094,7 @@ mod test_reporting {
 
                 But `add` needs the 2nd argument to be:
 
-                    Num Integer
+                    Num (Integer Signed64)
                 "#
             ),
         )
@@ -2123,7 +2123,7 @@ mod test_reporting {
 
                 But `add` needs the 2nd argument to be:
 
-                    Num Integer
+                    Num (Integer Signed64)
 
                 Tip: You can convert between Int and Float using functions like
                 `Num.toFloat` and `Num.round`.
diff --git a/compiler/solve/tests/solve_expr.rs b/compiler/solve/tests/solve_expr.rs
index 835473f518..c1fbb2dba9 100644
--- a/compiler/solve/tests/solve_expr.rs
+++ b/compiler/solve/tests/solve_expr.rs
@@ -1326,7 +1326,7 @@ mod solve_expr {
         infer_eq(
             indoc!(
                 r#"
-                   int : Num.Num Num.Integer
+                   int : Num.Num (Num.Integer Num.Signed64)
 
                    int
                 "#
@@ -1339,7 +1339,7 @@ mod solve_expr {
         infer_eq(
             indoc!(
                 r#"
-                   int : Num.Num Num.Integer
+                   int : Num.Num (Num.Integer Num.Signed64)
                    int = 5
 
                    int
@@ -1353,7 +1353,7 @@ mod solve_expr {
         infer_eq(
             indoc!(
                 r#"
-                   int : Num Integer
+                   int : Num (Integer Signed64)
 
                    int
                 "#
@@ -1366,7 +1366,7 @@ mod solve_expr {
         infer_eq(
             indoc!(
                 r#"
-                   int : Num Integer
+                   int : Num (Integer Signed64)
                    int = 5
 
                    int
@@ -1931,7 +1931,7 @@ mod solve_expr {
         infer_eq(
             indoc!(
                 r#"
-                   float : Num.Num Num.FloatingPoint
+                   float : Num.Num (Num.FloatingPoint Num.Binary64)
 
                    float
                 "#
@@ -1944,7 +1944,7 @@ mod solve_expr {
         infer_eq(
             indoc!(
                 r#"
-                   float : Num.Num Num.FloatingPoint
+                   float : Num.Num (Num.FloatingPoint Num.Binary64)
                    float = 5.5
 
                    float
@@ -1958,7 +1958,7 @@ mod solve_expr {
         infer_eq(
             indoc!(
                 r#"
-                   float : Num FloatingPoint
+                   float : Num (FloatingPoint Binary64)
 
                    float
                 "#
@@ -1971,7 +1971,7 @@ mod solve_expr {
         infer_eq(
             indoc!(
                 r#"
-                   float : Num FloatingPoint
+                   float : Num (FloatingPoint Binary64)
                    float = 5.5
 
                    float
@@ -2216,7 +2216,7 @@ mod solve_expr {
         infer_eq_without_problem(
             indoc!(
                 r#"
-                    x : Num.Num Num.Integer
+                    x : Num.Num (Num.Integer Num.Signed64)
                     x =
                         when 2 is
                             3 -> 4
@@ -2428,7 +2428,7 @@ mod solve_expr {
                 r#"
                 Foo a : { foo : a }
 
-                v : Foo (Num.Num Num.Integer)
+                v : Foo (Num.Num (Num.Integer Num.Signed64))
                 v = { foo: 42 }
 
                 v
@@ -2492,7 +2492,7 @@ mod solve_expr {
                 r#"
                     Peano : [ S Peano, Z ]
 
-                    length : Peano -> Num.Num Num.Integer
+                    length : Peano -> Num.Num (Num.Integer Num.Signed64)
                     length = \peano ->
                         when peano is
                             Z -> 0
@@ -2592,10 +2592,10 @@ mod solve_expr {
         infer_eq(
             indoc!(
                 r#"
-                r : { x : (Num.Num Num.Integer) }
+                r : { x : (Num.Num (Num.Integer Signed64)) }
                 r = { x : 1 }
 
-                s : { left : { x : Num.Num Num.FloatingPoint } }
+                s : { left : { x : Num.Num (Num.FloatingPoint Num.Binary64) } }
                 s = { left: { x : 3.14 } }
 
                 when 0 is
@@ -2757,7 +2757,7 @@ mod solve_expr {
         infer_eq_without_problem(
             indoc!(
                 r#"
-                    { x, y } : { x : Str.Str, y : Num.Num Num.FloatingPoint }
+                    { x, y } : { x : Str.Str, y : Num.Num (Num.FloatingPoint Num.Binary64) }
                     { x, y } = { x : "foo", y : 3.14 }
 
                     x
@@ -2772,7 +2772,7 @@ mod solve_expr {
         infer_eq(
             indoc!(
                 r#"
-                    Foo : { x : Str.Str, y : Num.Num Num.FloatingPoint }
+                    Foo : { x : Str.Str, y : Num.Num (Num.FloatingPoint Num.Binary64) }
 
                     { x, y } : Foo
                     { x, y } = { x : "foo", y : 3.14 }
@@ -2830,7 +2830,7 @@ mod solve_expr {
         infer_eq_without_problem(
             indoc!(
                 r#"
-                    Foo : { x : Str.Str, y : Num.Num Num.FloatingPoint }
+                    Foo : { x : Str.Str, y : Num.Num (Num.FloatingPoint Num.Binary64) }
 
                     { x, y } : Foo
                     { x, y } = { x : "foo", y : 3.14 }
diff --git a/compiler/solve/tests/solve_uniq_expr.rs b/compiler/solve/tests/solve_uniq_expr.rs
index adf9f098bf..6f943c8bbe 100644
--- a/compiler/solve/tests/solve_uniq_expr.rs
+++ b/compiler/solve/tests/solve_uniq_expr.rs
@@ -1118,7 +1118,7 @@ mod solve_uniq_expr {
         infer_eq(
             indoc!(
                 r#"
-                    x : Num.Num Num.Integer
+                    x : Num.Num (Num.Integer Num.Signed64)
                     x = 4
 
                     x
@@ -1368,7 +1368,7 @@ mod solve_uniq_expr {
         infer_eq(
             indoc!(
                 r#"
-                    x : Num.Num Num.Integer
+                    x : I64
                     x =
                         when 2 is
                             3 -> 4
@@ -1816,7 +1816,7 @@ mod solve_uniq_expr {
         infer_eq(
             indoc!(
                 r#"
-                    { x, y } : { x : Str.Str, y : Num.Num Num.FloatingPoint }
+                    { x, y } : { x : Str.Str, y : F64 }
                     { x, y } = { x : "foo", y : 3.14 }
 
                     x
@@ -2662,7 +2662,7 @@ mod solve_uniq_expr {
                 f
                 "#
             ),
-            "Attr * (Attr a I64, Attr b I64 -> Attr c I64)",
+            "Attr * (Attr b I64, Attr c I64 -> Attr d I64)",
         );
     }
 
@@ -3150,7 +3150,7 @@ mod solve_uniq_expr {
             indoc!(
                 r#"
                 empty : List I64
-                empty = 
+                empty =
                     []
 
                 List.walkBackwards empty (\a, b -> a + b) 0
@@ -3159,4 +3159,55 @@ mod solve_uniq_expr {
             "Attr a I64",
         );
     }
+
+    #[test]
+    fn list_set_out_of_bounds_num() {
+        infer_eq(
+            indoc!(
+                r#"
+                List.set [2] 1337 0
+                "#
+            ),
+            "Attr * (List (Attr * (Num (Attr * *))))",
+        );
+    }
+
+    #[test]
+    fn list_set_out_of_bounds_int() {
+        infer_eq(
+            indoc!(
+                r#"
+                List.set [0x2] 1337 0
+                "#
+            ),
+            "Attr * (List (Attr * I64))",
+        );
+    }
+
+    #[test]
+    fn list_set_out_of_bounds_float() {
+        infer_eq(
+            indoc!(
+                r#"
+                List.set [0.2] 1337 0
+                "#
+            ),
+            "Attr * (List (Attr * F64))",
+        );
+    }
+
+    #[test]
+    #[ignore]
+    fn list_set_out_of_bounds_int_int() {
+        // the unification of an integer list with a new integer element is a problem
+        // same for floats, but it's fine with the unspecified Num
+        infer_eq(
+            indoc!(
+                r#"
+                List.set [0x2] 1337 0x1
+                "#
+            ),
+            "Attr * (List (Attr a I64))",
+        );
+    }
 }
diff --git a/compiler/types/src/builtin_aliases.rs b/compiler/types/src/builtin_aliases.rs
index 885d9fa395..8e734fe99a 100644
--- a/compiler/types/src/builtin_aliases.rs
+++ b/compiler/types/src/builtin_aliases.rs
@@ -38,143 +38,213 @@ pub fn aliases() -> MutMap<Symbol, BuiltinAlias> {
         },
     );
 
-    // Integer : [ @Integer ]
+    // Integer range : [ @Integer range ]
     add_alias(
         Symbol::NUM_INTEGER,
         BuiltinAlias {
             region: Region::zero(),
-            vars: Vec::new(),
-            typ: integer_alias_content(),
+            vars: vec![Located::at(Region::zero(), "range".into())],
+            typ: integer_alias_content(flex(TVAR1)),
         },
     );
 
-    // I128 Num Integer
+    // Signed128 : [ @Signed128 ]
+    add_alias(
+        Symbol::NUM_SIGNED128,
+        BuiltinAlias {
+            region: Region::zero(),
+            vars: vec![],
+            typ: signed128_alias_content(),
+        },
+    );
+
+    // I128 : Num (Integer Signed128)
     add_alias(
         Symbol::NUM_I128,
         BuiltinAlias {
             region: Region::zero(),
             vars: Vec::new(),
-            typ: int_alias_content(),
+            typ: int_alias_content(signed128_type()),
         },
     );
 
-    // U128 : Num Integer
+    // U128 : Num (Integer Unsigned128)
     add_alias(
         Symbol::NUM_U128,
         BuiltinAlias {
             region: Region::zero(),
             vars: Vec::new(),
-            typ: int_alias_content(),
+            typ: int_alias_content(unsigned128_type()),
         },
     );
 
-    // I64 Num Integer
+    // Signed64 : [ @Signed64 ]
+    add_alias(
+        Symbol::NUM_SIGNED64,
+        BuiltinAlias {
+            region: Region::zero(),
+            vars: vec![],
+            typ: signed64_alias_content(),
+        },
+    );
+
+    // I64 : Num (Integer Signed64)
     add_alias(
         Symbol::NUM_I64,
         BuiltinAlias {
             region: Region::zero(),
             vars: Vec::new(),
-            typ: int_alias_content(),
+            typ: int_alias_content(signed64_type()),
         },
     );
 
-    // U64 : Num Integer
+    // U64 : Num (Integer Unsigned64)
     add_alias(
         Symbol::NUM_U64,
         BuiltinAlias {
             region: Region::zero(),
             vars: Vec::new(),
-            typ: int_alias_content(),
+            typ: int_alias_content(unsigned64_type()),
         },
     );
 
-    // I32 Num Integer
+    // Signed32 : [ @Signed32 ]
+    add_alias(
+        Symbol::NUM_SIGNED32,
+        BuiltinAlias {
+            region: Region::zero(),
+            vars: vec![],
+            typ: signed32_alias_content(),
+        },
+    );
+
+    // I32 : Num (Integer Signed32)
     add_alias(
         Symbol::NUM_I32,
         BuiltinAlias {
             region: Region::zero(),
             vars: Vec::new(),
-            typ: int_alias_content(),
+            typ: int_alias_content(signed32_type()),
         },
     );
 
-    // U32 : Num Integer
+    // U32 : Num (Integer Unsigned32)
     add_alias(
         Symbol::NUM_U32,
         BuiltinAlias {
             region: Region::zero(),
             vars: Vec::new(),
-            typ: int_alias_content(),
+            typ: int_alias_content(unsigned32_type()),
         },
     );
 
-    // I16 Num Integer
+    // Signed16 : [ @Signed16 ]
+    add_alias(
+        Symbol::NUM_SIGNED16,
+        BuiltinAlias {
+            region: Region::zero(),
+            vars: vec![],
+            typ: signed16_alias_content(),
+        },
+    );
+
+    // I16 : Num (Integer Signed16)
     add_alias(
         Symbol::NUM_I16,
         BuiltinAlias {
             region: Region::zero(),
             vars: Vec::new(),
-            typ: int_alias_content(),
+            typ: int_alias_content(signed16_type()),
         },
     );
 
-    // U16 : Num Integer
+    // U16 : Num (Integer Unsigned16)
     add_alias(
         Symbol::NUM_U16,
         BuiltinAlias {
             region: Region::zero(),
             vars: Vec::new(),
-            typ: int_alias_content(),
+            typ: int_alias_content(unsigned16_type()),
         },
     );
 
-    // I8 Num Integer
+    // Signed8 : [ @Signed8 ]
+    add_alias(
+        Symbol::NUM_SIGNED8,
+        BuiltinAlias {
+            region: Region::zero(),
+            vars: vec![],
+            typ: signed8_alias_content(),
+        },
+    );
+
+    // I8 : Num (Integer Signed8)
     add_alias(
         Symbol::NUM_I8,
         BuiltinAlias {
             region: Region::zero(),
             vars: Vec::new(),
-            typ: int_alias_content(),
+            typ: int_alias_content(signed8_type()),
         },
     );
 
-    // U8 : Num Integer
+    // U8 : Num (Integer Unsigned8)
     add_alias(
         Symbol::NUM_U8,
         BuiltinAlias {
             region: Region::zero(),
             vars: Vec::new(),
-            typ: int_alias_content(),
+            typ: int_alias_content(unsigned8_type()),
         },
     );
 
-    // FloatingPoint : [ @FloatingPoint ]
+    // Binary64 : [ @Binary64 ]
+    add_alias(
+        Symbol::NUM_BINARY64,
+        BuiltinAlias {
+            region: Region::zero(),
+            vars: vec![],
+            typ: binary64_alias_content(),
+        },
+    );
+
+    // Binary32 : [ @Binary32 ]
+    add_alias(
+        Symbol::NUM_BINARY32,
+        BuiltinAlias {
+            region: Region::zero(),
+            vars: vec![],
+            typ: binary32_alias_content(),
+        },
+    );
+
+    // FloatingPoint range : [ @FloatingPoint range ]
     add_alias(
         Symbol::NUM_FLOATINGPOINT,
         BuiltinAlias {
             region: Region::zero(),
-            vars: Vec::new(),
-            typ: floatingpoint_alias_content(),
+            vars: vec![Located::at(Region::zero(), "range".into())],
+            typ: floatingpoint_alias_content(flex(TVAR1)),
         },
     );
 
-    // F64 : Num FloatingPoint
+    // F64 : Num (FloatingPoint Binary64)
     add_alias(
         Symbol::NUM_F64,
         BuiltinAlias {
             region: Region::zero(),
             vars: Vec::new(),
-            typ: float_alias_content(),
+            typ: float_alias_content(binary64_type()),
         },
     );
 
-    // F32 : Num FloatingPoint
+    // F32 : Num (FloatingPoint Binary32)
     add_alias(
         Symbol::NUM_F32,
         BuiltinAlias {
             region: Region::zero(),
             vars: Vec::new(),
-            typ: float_alias_content(),
+            typ: float_alias_content(binary32_type()),
         },
     );
 
@@ -226,57 +296,233 @@ fn num_alias_content(range: SolvedType) -> SolvedType {
 // FLOATING POINT
 
 #[inline(always)]
-pub fn floatingpoint_type() -> SolvedType {
+pub fn floatingpoint_type(range: SolvedType) -> SolvedType {
     SolvedType::Alias(
         Symbol::NUM_FLOATINGPOINT,
-        Vec::new(),
-        Box::new(floatingpoint_alias_content()),
+        vec![("range".into(), range.clone())],
+        Box::new(floatingpoint_alias_content(range)),
     )
 }
 
 #[inline(always)]
-fn floatingpoint_alias_content() -> SolvedType {
-    single_private_tag(Symbol::NUM_AT_FLOATINGPOINT, Vec::new())
+fn floatingpoint_alias_content(range: SolvedType) -> SolvedType {
+    single_private_tag(Symbol::NUM_AT_FLOATINGPOINT, vec![range])
 }
 
 // FLOAT
 
 #[inline(always)]
 pub fn float_type() -> SolvedType {
-    SolvedType::Alias(Symbol::NUM_F64, Vec::new(), Box::new(float_alias_content()))
+    SolvedType::Alias(
+        Symbol::NUM_F64,
+        Vec::new(),
+        Box::new(float_alias_content(binary64_type())),
+    )
 }
 
 #[inline(always)]
-fn float_alias_content() -> SolvedType {
-    num_type(floatingpoint_type())
+fn float_alias_content(typ: SolvedType) -> SolvedType {
+    num_type(floatingpoint_type(typ))
 }
 
 // INT
 
 #[inline(always)]
 pub fn int_type() -> SolvedType {
-    SolvedType::Alias(Symbol::NUM_I64, Vec::new(), Box::new(int_alias_content()))
+    SolvedType::Alias(
+        Symbol::NUM_I64,
+        Vec::new(),
+        Box::new(int_alias_content(signed64_type())),
+    )
 }
 
 #[inline(always)]
-fn int_alias_content() -> SolvedType {
-    num_type(integer_type())
+fn int_alias_content(range: SolvedType) -> SolvedType {
+    num_type(integer_type(range))
 }
 
 // INTEGER
 
 #[inline(always)]
-pub fn integer_type() -> SolvedType {
+pub fn integer_type(range: SolvedType) -> SolvedType {
     SolvedType::Alias(
         Symbol::NUM_INTEGER,
-        Vec::new(),
-        Box::new(integer_alias_content()),
+        vec![("range".into(), range.clone())],
+        Box::new(integer_alias_content(range)),
     )
 }
 
 #[inline(always)]
-fn integer_alias_content() -> SolvedType {
-    single_private_tag(Symbol::NUM_AT_INTEGER, Vec::new())
+fn integer_alias_content(range: SolvedType) -> SolvedType {
+    single_private_tag(Symbol::NUM_AT_INTEGER, vec![range])
+}
+
+#[inline(always)]
+pub fn binary64_type() -> SolvedType {
+    SolvedType::Alias(
+        Symbol::NUM_BINARY64,
+        vec![],
+        Box::new(binary64_alias_content()),
+    )
+}
+
+#[inline(always)]
+pub fn binary64_alias_content() -> SolvedType {
+    single_private_tag(Symbol::NUM_AT_BINARY64, vec![])
+}
+
+#[inline(always)]
+pub fn binary32_type() -> SolvedType {
+    SolvedType::Alias(
+        Symbol::NUM_BINARY32,
+        vec![],
+        Box::new(binary32_alias_content()),
+    )
+}
+
+#[inline(always)]
+fn binary32_alias_content() -> SolvedType {
+    single_private_tag(Symbol::NUM_AT_BINARY32, vec![])
+}
+
+#[inline(always)]
+pub fn signed128_type() -> SolvedType {
+    SolvedType::Alias(
+        Symbol::NUM_SIGNED128,
+        vec![],
+        Box::new(signed128_alias_content()),
+    )
+}
+
+#[inline(always)]
+fn signed128_alias_content() -> SolvedType {
+    single_private_tag(Symbol::NUM_AT_SIGNED128, vec![])
+}
+
+#[inline(always)]
+pub fn signed64_type() -> SolvedType {
+    SolvedType::Alias(
+        Symbol::NUM_SIGNED64,
+        vec![],
+        Box::new(signed64_alias_content()),
+    )
+}
+
+#[inline(always)]
+fn signed64_alias_content() -> SolvedType {
+    single_private_tag(Symbol::NUM_AT_SIGNED64, vec![])
+}
+
+#[inline(always)]
+pub fn signed32_type() -> SolvedType {
+    SolvedType::Alias(
+        Symbol::NUM_SIGNED32,
+        vec![],
+        Box::new(signed32_alias_content()),
+    )
+}
+
+#[inline(always)]
+fn signed32_alias_content() -> SolvedType {
+    single_private_tag(Symbol::NUM_AT_SIGNED32, vec![])
+}
+
+#[inline(always)]
+pub fn signed16_type() -> SolvedType {
+    SolvedType::Alias(
+        Symbol::NUM_SIGNED16,
+        vec![],
+        Box::new(signed16_alias_content()),
+    )
+}
+
+#[inline(always)]
+fn signed16_alias_content() -> SolvedType {
+    single_private_tag(Symbol::NUM_AT_SIGNED16, vec![])
+}
+
+#[inline(always)]
+pub fn signed8_type() -> SolvedType {
+    SolvedType::Alias(
+        Symbol::NUM_SIGNED8,
+        vec![],
+        Box::new(signed8_alias_content()),
+    )
+}
+
+#[inline(always)]
+fn signed8_alias_content() -> SolvedType {
+    single_private_tag(Symbol::NUM_AT_SIGNED8, vec![])
+}
+
+#[inline(always)]
+pub fn unsigned128_type() -> SolvedType {
+    SolvedType::Alias(
+        Symbol::NUM_UNSIGNED128,
+        vec![],
+        Box::new(unsigned128_alias_content()),
+    )
+}
+
+#[inline(always)]
+fn unsigned128_alias_content() -> SolvedType {
+    single_private_tag(Symbol::NUM_AT_UNSIGNED128, vec![])
+}
+
+#[inline(always)]
+pub fn unsigned64_type() -> SolvedType {
+    SolvedType::Alias(
+        Symbol::NUM_UNSIGNED64,
+        vec![],
+        Box::new(unsigned64_alias_content()),
+    )
+}
+
+#[inline(always)]
+fn unsigned64_alias_content() -> SolvedType {
+    single_private_tag(Symbol::NUM_AT_UNSIGNED64, vec![])
+}
+
+#[inline(always)]
+pub fn unsigned32_type() -> SolvedType {
+    SolvedType::Alias(
+        Symbol::NUM_UNSIGNED32,
+        vec![],
+        Box::new(unsigned32_alias_content()),
+    )
+}
+
+#[inline(always)]
+fn unsigned32_alias_content() -> SolvedType {
+    single_private_tag(Symbol::NUM_AT_UNSIGNED32, vec![])
+}
+
+#[inline(always)]
+pub fn unsigned16_type() -> SolvedType {
+    SolvedType::Alias(
+        Symbol::NUM_UNSIGNED16,
+        vec![],
+        Box::new(unsigned16_alias_content()),
+    )
+}
+
+#[inline(always)]
+fn unsigned16_alias_content() -> SolvedType {
+    single_private_tag(Symbol::NUM_AT_UNSIGNED16, vec![])
+}
+
+#[inline(always)]
+pub fn unsigned8_type() -> SolvedType {
+    SolvedType::Alias(
+        Symbol::NUM_UNSIGNED8,
+        vec![],
+        Box::new(unsigned8_alias_content()),
+    )
+}
+
+#[inline(always)]
+fn unsigned8_alias_content() -> SolvedType {
+    single_private_tag(Symbol::NUM_AT_UNSIGNED8, vec![])
 }
 
 #[inline(always)]
@@ -351,7 +597,7 @@ pub fn dict_type(key: SolvedType, value: SolvedType) -> SolvedType {
     SolvedType::Apply(Symbol::DICT_DICT, vec![key, value])
 }
 
-fn single_private_tag(symbol: Symbol, type_arguments: Vec<SolvedType>) -> SolvedType {
+pub fn single_private_tag(symbol: Symbol, type_arguments: Vec<SolvedType>) -> SolvedType {
     SolvedType::TagUnion(
         vec![(TagName::Private(symbol), type_arguments)],
         Box::new(SolvedType::EmptyTagUnion),
diff --git a/compiler/types/src/pretty_print.rs b/compiler/types/src/pretty_print.rs
index d2dd43db1c..b4891ce080 100644
--- a/compiler/types/src/pretty_print.rs
+++ b/compiler/types/src/pretty_print.rs
@@ -753,10 +753,10 @@ fn write_apply(
 
             match &arg_content {
                 Content::Structure(FlatType::Apply(symbol, nested_args)) => match *symbol {
-                    Symbol::NUM_INTEGER if nested_args.is_empty() => {
+                    Symbol::NUM_INTEGER if nested_args.len() == 1 => {
                         buf.push_str("I64");
                     }
-                    Symbol::NUM_FLOATINGPOINT if nested_args.is_empty() => {
+                    Symbol::NUM_FLOATINGPOINT if nested_args.len() == 1 => {
                         buf.push_str("F64");
                     }
                     Symbol::ATTR_ATTR => match nested_args
@@ -767,10 +767,10 @@ fn write_apply(
                             double_nested_symbol,
                             double_nested_args,
                         ))) => match double_nested_symbol {
-                            Symbol::NUM_INTEGER if double_nested_args.is_empty() => {
+                            Symbol::NUM_INTEGER if double_nested_args.len() == 1 => {
                                 buf.push_str("I64");
                             }
-                            Symbol::NUM_FLOATINGPOINT if double_nested_args.is_empty() => {
+                            Symbol::NUM_FLOATINGPOINT if double_nested_args.len() == 1 => {
                                 buf.push_str("F64");
                             }
                             _ => default_case(subs, arg_content),
diff --git a/compiler/unify/src/unify.rs b/compiler/unify/src/unify.rs
index c3767540ad..96935b1e90 100644
--- a/compiler/unify/src/unify.rs
+++ b/compiler/unify/src/unify.rs
@@ -198,7 +198,7 @@ fn unify_alias(
 
                     problems
                 } else {
-                    mismatch!()
+                    mismatch!("{}", symbol)
                 }
             } else {
                 unify_pool(subs, pool, real_var, *other_real_var)