diff --git a/src/basis/Basis.ts b/src/basis/Basis.ts
index b49712ee8..dbd372cc3 100644
--- a/src/basis/Basis.ts
+++ b/src/basis/Basis.ts
@@ -34,6 +34,10 @@ import bootstrapStructure from './StructureBasis';
 import { toTokens } from '../parser/toTokens';
 import parseType from '../parser/paresType';
 import type Locales from '../locale/Locales';
+import AnyType from '../nodes/AnyType';
+import BooleanType from '../nodes/BooleanType';
+import ValueException from '../values/ValueException';
+import BoolValue from '../values/BoolValue';
 
 export class Basis {
     readonly locales: Locales;
@@ -177,6 +181,30 @@ export function createBasisFunction(
     );
 }
 
+export function createEqualsFunction(
+    locales: Locales,
+    text: (locale: Locale) => FunctionText<NameAndDoc[]>,
+    equal: boolean
+) {
+    return createBasisFunction(
+        locales,
+        text,
+        undefined,
+        [new AnyType()],
+        BooleanType.make(),
+        (requestor, evaluation) => {
+            const left: Value | Evaluation | undefined =
+                evaluation.getClosure();
+            const right = evaluation.getInput(0);
+            if (!(left instanceof Value))
+                return new ValueException(evaluation.getEvaluator(), requestor);
+            if (!(right instanceof Value))
+                return new ValueException(evaluation.getEvaluator(), requestor);
+            return new BoolValue(requestor, left.isEqualTo(right) === equal);
+        }
+    );
+}
+
 export function createBasisConversion<ValueType extends Value>(
     docs: Docs,
     input: Type | string,
diff --git a/src/basis/BoolBasis.ts b/src/basis/BoolBasis.ts
index b37f9caf6..4cef25e49 100644
--- a/src/basis/BoolBasis.ts
+++ b/src/basis/BoolBasis.ts
@@ -3,7 +3,11 @@ import BooleanType from '@nodes/BooleanType';
 import StructureDefinition from '@nodes/StructureDefinition';
 import BoolValue from '@values/BoolValue';
 import TextValue from '@values/TextValue';
-import { createBasisConversion, createBasisFunction } from './Basis';
+import {
+    createBasisConversion,
+    createBasisFunction,
+    createEqualsFunction,
+} from './Basis';
 import type Value from '@values/Value';
 import { getDocLocales } from '@locale/getDocLocales';
 import { getNameLocales } from '@locale/getNameLocales';
@@ -12,7 +16,6 @@ import type Expression from '../nodes/Expression';
 import type Locale from '../locale/Locale';
 import type { FunctionText, NameAndDoc } from '../locale/Locale';
 import type Type from '../nodes/Type';
-import AnyType from '../nodes/AnyType';
 import type Locales from '../locale/Locales';
 
 export default function bootstrapBool(locales: Locales) {
@@ -88,17 +91,15 @@ export default function bootstrapBool(locales: Locales) {
                         return left.not(requestor);
                     }
                 ),
-                createBooleanFunction(
+                createEqualsFunction(
+                    locales,
                     (locale) => locale.basis.Boolean.function.equals,
-                    [new AnyType()],
-                    (requestor, left, right) =>
-                        new BoolValue(requestor, left.isEqualTo(right))
+                    true
                 ),
-                createBooleanFunction(
+                createEqualsFunction(
+                    locales,
                     (locale) => locale.basis.Boolean.function.notequal,
-                    [new AnyType()],
-                    (requestor, left, right) =>
-                        new BoolValue(requestor, !left.isEqualTo(right))
+                    false
                 ),
                 createBasisConversion(
                     getDocLocales(
diff --git a/src/basis/MapBasis.test.ts b/src/basis/MapBasis.test.ts
index 93a8e9604..95ca1de75 100644
--- a/src/basis/MapBasis.test.ts
+++ b/src/basis/MapBasis.test.ts
@@ -11,6 +11,8 @@ test.each([
         "{'cat':1 'dog':2 'mouse':3}.translate(ƒ(k v) -v)",
         '{"cat":-1 "dog":-2 "mouse":-3}',
     ],
+    ['{1:1 2:2} = ø', '⊥'],
+    ['{1:1 2:2} ≠ ø', '⊤'],
 ])('Expect %s to be %s map functions', (code, value) => {
     expect(evaluateCode(code)?.toString()).toBe(value);
 });
diff --git a/src/basis/MapBasis.ts b/src/basis/MapBasis.ts
index 7a346248f..6085a7c13 100644
--- a/src/basis/MapBasis.ts
+++ b/src/basis/MapBasis.ts
@@ -7,7 +7,11 @@ import ListValue from '@values/ListValue';
 import TextValue from '@values/TextValue';
 import MapValue from '@values/MapValue';
 import SetValue from '@values/SetValue';
-import { createBasisConversion, createBasisFunction } from './Basis';
+import {
+    createBasisConversion,
+    createBasisFunction,
+    createEqualsFunction,
+} from './Basis';
 import BoolValue from '@values/BoolValue';
 import TypeVariables from '@nodes/TypeVariables';
 import { getDocLocales } from '@locale/getDocLocales';
@@ -23,7 +27,6 @@ import NumberValue from '@values/NumberValue';
 import TextType from '../nodes/TextType';
 import SetType from '../nodes/SetType';
 import ListType from '../nodes/ListType';
-import AnyType from '../nodes/AnyType';
 import type Locales from '../locale/Locales';
 
 export default function bootstrapMap(locales: Locales) {
@@ -74,45 +77,15 @@ export default function bootstrapMap(locales: Locales) {
                               );
                     }
                 ),
-                createBasisFunction(
+                createEqualsFunction(
                     locales,
                     (locale) => locale.basis.Map.function.equals,
-                    undefined,
-                    [new AnyType()],
-                    BooleanType.make(),
-                    (requestor, evaluation) => {
-                        const map = evaluation?.getClosure();
-                        const other = evaluation.getInput(0);
-                        return !(
-                            map instanceof MapValue && other instanceof MapValue
-                        )
-                            ? evaluation.getValueOrTypeException(
-                                  requestor,
-                                  MapType.make(),
-                                  other
-                              )
-                            : new BoolValue(requestor, map.isEqualTo(other));
-                    }
+                    true
                 ),
-                createBasisFunction(
+                createEqualsFunction(
                     locales,
                     (locale) => locale.basis.Map.function.notequals,
-                    undefined,
-                    [new AnyType()],
-                    BooleanType.make(),
-                    (requestor, evaluation) => {
-                        const map = evaluation?.getClosure();
-                        const other = evaluation.getInput(0);
-                        return !(
-                            map instanceof MapValue && other instanceof MapValue
-                        )
-                            ? evaluation.getValueOrTypeException(
-                                  requestor,
-                                  MapType.make(),
-                                  other
-                              )
-                            : new BoolValue(requestor, !map.isEqualTo(other));
-                    }
+                    false
                 ),
                 createBasisFunction(
                     locales,
diff --git a/src/basis/NumberBasis.ts b/src/basis/NumberBasis.ts
index 5df1d32fd..cbbfb47ea 100644
--- a/src/basis/NumberBasis.ts
+++ b/src/basis/NumberBasis.ts
@@ -14,7 +14,11 @@ import NumberValue from '@values/NumberValue';
 import TextValue from '@values/TextValue';
 import TypeException from '@values/TypeException';
 import type Value from '@values/Value';
-import { createBasisConversion, createBasisFunction } from './Basis';
+import {
+    createBasisConversion,
+    createBasisFunction,
+    createEqualsFunction,
+} from './Basis';
 import InternalExpression from './InternalExpression';
 import type Evaluation from '@runtime/Evaluation';
 import ListValue from '@values/ListValue';
@@ -368,21 +372,16 @@ export default function bootstrapNumber(locales: Locales) {
                                 left.isEqualTo(right)
                         )
                 ),
-                createBinaryOp(
+                createEqualsFunction(
+                    locales,
                     (locale) => locale.basis.Number.function.equal,
-                    NumberType.make((unit) => unit),
-                    BooleanType.make(),
-                    (requestor, left, right) =>
-                        new BoolValue(requestor, left.isEqualTo(right))
+                    true
                 ),
-                createBinaryOp(
+                createEqualsFunction(
+                    locales,
                     (locale) => locale.basis.Number.function.notequal,
-                    NumberType.make((unit) => unit),
-                    BooleanType.make(),
-                    (requestor, left, right) =>
-                        new BoolValue(requestor, !left.isEqualTo(right))
+                    false
                 ),
-
                 // Trigonometry
                 createUnaryOp(
                     (locale) => locale.basis.Number.function.cos,
diff --git a/src/basis/SetBasis.test.ts b/src/basis/SetBasis.test.ts
index 8eafec4d9..aaa992f26 100644
--- a/src/basis/SetBasis.test.ts
+++ b/src/basis/SetBasis.test.ts
@@ -10,6 +10,8 @@ test.each([
     ['{1 2 3}.difference({3 4 5})', '{1 2}'],
     ['{1 2 3}.filter(ƒ(v) v % 2 = 1)', '{1 3}'],
     ['{1 2 3}.translate(ƒ(v) v + 2)', '{3 4 5}'],
+    ['{1 2 3} = ø', '⊥'],
+    ['{1 2 3} ≠ ø', '⊤'],
 ])('Expect %s to be %s', (code, value) => {
     expect(evaluateCode(code)?.toString()).toBe(value);
 });
diff --git a/src/basis/SetBasis.ts b/src/basis/SetBasis.ts
index fb22bb246..2a9ec3c7e 100644
--- a/src/basis/SetBasis.ts
+++ b/src/basis/SetBasis.ts
@@ -6,7 +6,11 @@ import StructureDefinition from '@nodes/StructureDefinition';
 import ListValue from '@values/ListValue';
 import TextValue from '@values/TextValue';
 import SetValue from '@values/SetValue';
-import { createBasisConversion, createBasisFunction } from './Basis';
+import {
+    createBasisConversion,
+    createBasisFunction,
+    createEqualsFunction,
+} from './Basis';
 import BoolValue from '@values/BoolValue';
 import type Value from '@values/Value';
 import type Evaluation from '@runtime/Evaluation';
@@ -21,7 +25,6 @@ import NumberType from '../nodes/NumberType';
 import NumberValue from '@values/NumberValue';
 import ListType from '../nodes/ListType';
 import TextType from '../nodes/TextType';
-import AnyType from '../nodes/AnyType';
 import type Locales from '../locale/Locales';
 
 export default function bootstrapSet(locales: Locales) {
@@ -67,45 +70,15 @@ export default function bootstrapSet(locales: Locales) {
                               );
                     }
                 ),
-                createBasisFunction(
+                createEqualsFunction(
                     locales,
                     (locale) => locale.basis.Set.function.equals,
-                    undefined,
-                    [new AnyType()],
-                    BooleanType.make(),
-                    (requestor, evaluation) => {
-                        const set = evaluation?.getClosure();
-                        const other = evaluation.getInput(0);
-                        return !(
-                            set instanceof SetValue && other instanceof SetValue
-                        )
-                            ? evaluation.getValueOrTypeException(
-                                  requestor,
-                                  SetType.make(),
-                                  other
-                              )
-                            : new BoolValue(requestor, set.isEqualTo(other));
-                    }
+                    true
                 ),
-                createBasisFunction(
+                createEqualsFunction(
                     locales,
                     (locale) => locale.basis.Set.function.notequals,
-                    undefined,
-                    [new AnyType()],
-                    BooleanType.make(),
-                    (requestor, evaluation) => {
-                        const set = evaluation?.getClosure();
-                        const other = evaluation.getInput(0);
-                        return !(
-                            set instanceof SetValue && other instanceof SetValue
-                        )
-                            ? evaluation.getValueOrTypeException(
-                                  requestor,
-                                  SetType.make(),
-                                  other
-                              )
-                            : new BoolValue(requestor, !set.isEqualTo(other));
-                    }
+                    false
                 ),
                 createBasisFunction(
                     locales,
diff --git a/src/basis/TableBasis.ts b/src/basis/TableBasis.ts
index 406c00561..f9c1a63df 100644
--- a/src/basis/TableBasis.ts
+++ b/src/basis/TableBasis.ts
@@ -1,29 +1,17 @@
-import Bind from '@nodes/Bind';
 import Block, { BlockKind } from '@nodes/Block';
-import BooleanType from '@nodes/BooleanType';
-import FunctionDefinition from '@nodes/FunctionDefinition';
 import StructureDefinition from '@nodes/StructureDefinition';
-import BoolValue from '@values/BoolValue';
-import InternalExpression from './InternalExpression';
-import type Docs from '@nodes/Docs';
-import type Names from '@nodes/Names';
-import { getInputLocales as getInputLocales } from '@locale/getInputLocales';
 import { getDocLocales } from '@locale/getDocLocales';
 import { getNameLocales } from '@locale/getNameLocales';
-import type Type from '../nodes/Type';
 import TableType from '../nodes/TableType';
-import TableValue from '../values/TableValue';
-import Evaluation from '@runtime/Evaluation';
+import type TableValue from '../values/TableValue';
 import type Expression from '../nodes/Expression';
-import type Value from '../values/Value';
-import { createBasisConversion } from './Basis';
+import { createBasisConversion, createEqualsFunction } from './Basis';
 import ListValue from '@values/ListValue';
 import ListType from '../nodes/ListType';
 import TextType from '../nodes/TextType';
 import TextValue from '../values/TextValue';
 import TypeVariables from '../nodes/TypeVariables';
 import TypeVariable from '../nodes/TypeVariable';
-import AnyType from '../nodes/AnyType';
 import type Locales from '../locale/Locales';
 
 export default function bootstrapTable(locales: Locales) {
@@ -32,25 +20,6 @@ export default function bootstrapTable(locales: Locales) {
         getNameLocales(locales, (locale) => locale.basis.Table.row)
     );
 
-    function createTableFunction(
-        docs: Docs,
-        names: Names,
-        inputs: { docs: Docs; names: Names }[],
-        types: Type[],
-        expression: InternalExpression
-    ) {
-        return FunctionDefinition.make(
-            docs,
-            names,
-            undefined,
-            inputs.map(({ docs, names }, index) =>
-                Bind.make(docs, names, types[index])
-            ),
-            expression,
-            expression.type
-        );
-    }
-
     return StructureDefinition.make(
         getDocLocales(locales, (locale) => locale.basis.Table.doc),
         getNameLocales(locales, (locale) => locale.basis.Table.name),
@@ -59,63 +28,15 @@ export default function bootstrapTable(locales: Locales) {
         [],
         new Block(
             [
-                createTableFunction(
-                    getDocLocales(
-                        locales,
-                        (locale) => locale.basis.Table.function.equals.doc
-                    ),
-                    getNameLocales(
-                        locales,
-                        (locale) => locale.basis.Table.function.equals.names
-                    ),
-                    getInputLocales(
-                        locales,
-                        (locale) => locale.basis.Table.function.equals.inputs
-                    ),
-                    [new AnyType()],
-                    new InternalExpression(
-                        BooleanType.make(),
-                        [],
-                        (requestor, evaluation) =>
-                            binaryOp(
-                                requestor,
-                                evaluation,
-                                (requestor, left, right) =>
-                                    new BoolValue(
-                                        requestor,
-                                        left.isEqualTo(right)
-                                    )
-                            )
-                    )
+                createEqualsFunction(
+                    locales,
+                    (locale) => locale.basis.Table.function.equals,
+                    true
                 ),
-                createTableFunction(
-                    getDocLocales(
-                        locales,
-                        (locale) => locale.basis.Table.function.notequal.doc
-                    ),
-                    getNameLocales(
-                        locales,
-                        (locale) => locale.basis.Table.function.notequal.names
-                    ),
-                    getInputLocales(
-                        locales,
-                        (locale) => locale.basis.Table.function.notequal.inputs
-                    ),
-                    [new AnyType()],
-                    new InternalExpression(
-                        BooleanType.make(),
-                        [],
-                        (requestor, evaluation) =>
-                            binaryOp(
-                                requestor,
-                                evaluation,
-                                (requestor, left, right) =>
-                                    new BoolValue(
-                                        requestor,
-                                        !left.isEqualTo(right)
-                                    )
-                            )
-                    )
+                createEqualsFunction(
+                    locales,
+                    (locale) => locale.basis.Table.function.notequal,
+                    false
                 ),
                 createBasisConversion(
                     getDocLocales(
@@ -142,32 +63,3 @@ export default function bootstrapTable(locales: Locales) {
         )
     );
 }
-
-function binaryOp(
-    requestor: Expression,
-    evaluation: Evaluation,
-    evaluate: (
-        requestor: Expression,
-        left: TableValue,
-        right: TableValue
-    ) => Value
-): Value {
-    const left = evaluation.getClosure();
-    const right = evaluation.resolve(
-        (evaluation.getDefinition() as FunctionDefinition).inputs[0].names
-    );
-    // This should be impossible, but the type system doesn't know it.
-    if (!(left instanceof TableValue))
-        return evaluation.getValueOrTypeException(
-            requestor,
-            TableType.make(),
-            left instanceof Evaluation ? undefined : left
-        );
-    if (!(right instanceof TableValue))
-        return evaluation.getValueOrTypeException(
-            requestor,
-            TableType.make(),
-            undefined
-        );
-    else return evaluate(requestor, left, right);
-}
diff --git a/src/basis/TextBasis.test.ts b/src/basis/TextBasis.test.ts
index 9d074a8a9..a7941fa59 100644
--- a/src/basis/TextBasis.test.ts
+++ b/src/basis/TextBasis.test.ts
@@ -3,4 +3,6 @@ import evaluateCode from '../runtime/evaluate';
 
 test('Test text functions', () => {
     expect(evaluateCode('"hello".length()')?.toString()).toBe('5');
+    expect(evaluateCode('"hello" = ø')?.toString()).toBe('⊥');
+    expect(evaluateCode('"hello" ≠ ø')?.toString()).toBe('⊤');
 });
diff --git a/src/basis/TextBasis.ts b/src/basis/TextBasis.ts
index 0f6cc0bfa..2e78b32e1 100644
--- a/src/basis/TextBasis.ts
+++ b/src/basis/TextBasis.ts
@@ -4,7 +4,11 @@ import TextType from '@nodes/TextType';
 import type Type from '@nodes/Type';
 import BoolValue from '@values/BoolValue';
 import type Value from '@values/Value';
-import { createBasisConversion, createBasisFunction } from './Basis';
+import {
+    createBasisConversion,
+    createBasisFunction,
+    createEqualsFunction,
+} from './Basis';
 import TextValue from '@values/TextValue';
 import StructureDefinition from '@nodes/StructureDefinition';
 import NumberValue from '@values/NumberValue';
@@ -16,7 +20,6 @@ import type Expression from '@nodes/Expression';
 import type Locale from '../locale/Locale';
 import type { FunctionText, NameAndDoc } from '../locale/Locale';
 import ListType from '../nodes/ListType';
-import AnyType from '../nodes/AnyType';
 import type Locales from '../locale/Locales';
 
 export default function bootstrapText(locales: Locales) {
@@ -96,41 +99,15 @@ export default function bootstrapText(locales: Locales) {
                         );
                     }
                 ),
-                createBasisFunction(
+                createEqualsFunction(
                     locales,
                     (locale) => locale.basis.Text.function.equals,
-                    undefined,
-                    [new AnyType()],
-                    BooleanType.make(),
-                    (requestor, evaluation) => {
-                        const text = evaluation.getClosure() as TextValue;
-                        const input = evaluation.getInput(0);
-                        if (input === undefined)
-                            return evaluation.getValueOrTypeException(
-                                requestor,
-                                TextType.make(),
-                                input
-                            );
-                        return new BoolValue(requestor, text.isEqualTo(input));
-                    }
+                    true
                 ),
-                createBasisFunction(
+                createEqualsFunction(
                     locales,
                     (locale) => locale.basis.Text.function.notequals,
-                    undefined,
-                    [new AnyType()],
-                    BooleanType.make(),
-                    (requestor, evaluation) => {
-                        const text = evaluation.getClosure() as TextValue;
-                        const input = evaluation.getInput(0);
-                        if (input === undefined)
-                            return evaluation.getValueOrTypeException(
-                                requestor,
-                                TextType.make(),
-                                input
-                            );
-                        return new BoolValue(requestor, !text.isEqualTo(input));
-                    }
+                    false
                 ),
                 createBinaryTextFunction(
                     (locale) => locale.basis.Text.function.notequals,
diff --git a/src/nodes/BooleanLiteral.test.ts b/src/nodes/BooleanLiteral.test.ts
index b12352d4a..8c4d2e734 100644
--- a/src/nodes/BooleanLiteral.test.ts
+++ b/src/nodes/BooleanLiteral.test.ts
@@ -1,5 +1,4 @@
-import { FALSE_SYMBOL, TRUE_SYMBOL } from '@parser/Symbols';
-import ExceptionValue from '@values/ExceptionValue';
+import { FALSE_SYMBOL, NONE_SYMBOL, TRUE_SYMBOL } from '@parser/Symbols';
 import { test, expect } from 'vitest';
 import evaluateCode from '../runtime/evaluate';
 
@@ -13,5 +12,10 @@ test('Test equality', () => {
     expect(evaluateCode(`${FALSE_SYMBOL} = ${FALSE_SYMBOL}`)?.toString()).toBe(
         TRUE_SYMBOL
     );
-    expect(evaluateCode(`${TRUE_SYMBOL} = 1`)).toBeInstanceOf(ExceptionValue);
+    expect(evaluateCode(`${FALSE_SYMBOL} = ${NONE_SYMBOL}`)?.toString()).toBe(
+        FALSE_SYMBOL
+    );
+    expect(evaluateCode(`${FALSE_SYMBOL} ≠ ${NONE_SYMBOL}`)?.toString()).toBe(
+        TRUE_SYMBOL
+    );
 });
diff --git a/src/nodes/Table.test.ts b/src/nodes/Table.test.ts
index c9f1a51d5..2a6e324d2 100644
--- a/src/nodes/Table.test.ts
+++ b/src/nodes/Table.test.ts
@@ -6,6 +6,8 @@ test.each([
     ['⎡a•# b•#⎦⎡1 2⎦ = ⎡a•# b•#⎦⎡1 2⎦', TRUE_SYMBOL],
     ['⎡a•# b•#⎦⎡1 2⎦ = ⎡a•# b•#⎦⎡1 3⎦', FALSE_SYMBOL],
     ['⎡a•# b•#⎦⎡1 2⎦ ≠ ⎡a•# b•#⎦⎡1 3⎦', TRUE_SYMBOL],
+    ['⎡a•# b•#⎦⎡1 2⎦ = ø', FALSE_SYMBOL],
+    ['⎡a•# b•#⎦⎡1 2⎦ ≠ ø', TRUE_SYMBOL],
 ])('%s = %s', (code: string, value: string) => {
     expect(evaluateCode(code)?.toString()).toBe(value);
 });
diff --git a/src/values/NumberValue.test.ts b/src/values/NumberValue.test.ts
index 7a145846a..535aee39e 100644
--- a/src/values/NumberValue.test.ts
+++ b/src/values/NumberValue.test.ts
@@ -46,8 +46,8 @@ test.each([
     [`1 = 1`, TRUE_SYMBOL],
     [`1 = 2`, FALSE_SYMBOL],
     [`1m = 1m`, TRUE_SYMBOL],
-    [`1m = 1`, '!TypeException'],
-    [`1 = ø`, '!TypeException'],
+    [`1m = 1`, FALSE_SYMBOL],
+    [`1 = ø`, FALSE_SYMBOL],
     ['5 < 3', FALSE_SYMBOL],
     ['5 < 10', TRUE_SYMBOL],
     ['100.1 < 100.2', TRUE_SYMBOL],
@@ -93,6 +93,8 @@ test.each([
     ['1.max(2 3)', '3'],
     ['1.max(0 -1)', '1'],
     ['1m.max()', '!ValueException'],
+    ['1 = ø', '⊥'],
+    ['1 ≠ ø', '⊤'],
 ])('Expect %s to be %s', (code, value) => {
     expect(evaluateCode(code)?.toString()).toBe(value);
 });