🔀 Type-Level Boolean Logic: Conditional Operations

🎯 Introduction

Welcome to the logical reasoning center of TypeScript’s type system! 🔀 This tutorial explores the fascinating world of boolean logic and conditional operations at the type level, where you’ll learn to build sophisticated decision-making algorithms using only TypeScript’s type features.

You’ll discover how to implement boolean algebra, create complex conditional logic trees, and build type-safe decision systems that can reason about program states at compile time. Whether you’re building permission systems 🔐, creating complex validators 📋, or implementing state machines with intricate logic 🎰, type-level boolean operations provide the foundation for intelligent type systems.

By the end of this tutorial, you’ll be crafting logical reasoning systems that execute during compilation and building decision trees that guarantee correctness at the type level! Let’s think logically! 🧠

📚 Boolean Logic Fundamentals

🤔 Boolean Types and Operations

TypeScript’s boolean logic operates on true, false, and complex conditional expressions. Let’s explore the foundational patterns:

// 🌟 Basic boolean types
type True = true;
type False = false;
type Boolean = true | false;

// 🎯 Boolean literals and type guards
type IsTrue<T> = T extends true ? true : false;
type IsFalse<T> = T extends false ? true : false;
type IsBoolean<T> = T extends boolean ? true : false;

// ✨ Boolean extraction from complex types
type ExtractBoolean<T> = T extends { value: infer B }
  ? B extends boolean
    ? B
    : never
  : never;

// 🧪 Boolean type examples
type TrueTest = IsTrue<true>;     // true
type FalseTest = IsFalse<false>;  // true
type BoolTest = IsBoolean<boolean>; // true
type ExtractTest = ExtractBoolean<{ value: true }>; // true

🏗️ Logical Operators Implementation

// 🎯 AND operation (conjunction)
type And<A extends boolean, B extends boolean> = 
  A extends true 
    ? B extends true 
      ? true 
      : false
    : false;

// 🔄 OR operation (disjunction)
type Or<A extends boolean, B extends boolean> = 
  A extends true 
    ? true 
    : B extends true 
      ? true 
      : false;

// ❌ NOT operation (negation)
type Not<A extends boolean> = 
  A extends true ? false : true;

// ⚡ XOR operation (exclusive or)
type Xor<A extends boolean, B extends boolean> = 
  A extends true
    ? B extends true
      ? false
      : true
    : B extends true
      ? true
      : false;

// 🔗 NAND operation (not and)
type Nand<A extends boolean, B extends boolean> = Not<And<A, B>>;

// 🔄 NOR operation (not or)
type Nor<A extends boolean, B extends boolean> = Not<Or<A, B>>;

// ✅ Logical operation examples
type AndTest = And<true, false>;   // false
type OrTest = Or<true, false>;     // true
type NotTest = Not<true>;          // false
type XorTest = Xor<true, true>;    // false
type NandTest = Nand<true, true>;  // false
type NorTest = Nor<false, false>;  // true

🧮 Multi-Operand Logic Operations

// 🎯 AND with multiple operands
type AndAll<T extends readonly boolean[]> = 
  T extends readonly [infer First, ...infer Rest]
    ? First extends boolean
      ? Rest extends readonly boolean[]
        ? First extends true
          ? AndAll<Rest>
          : false
        : First
      : false
    : true; // Empty array is true (identity for AND)

// 🔄 OR with multiple operands
type OrAny<T extends readonly boolean[]> = 
  T extends readonly [infer First, ...infer Rest]
    ? First extends boolean
      ? Rest extends readonly boolean[]
        ? First extends true
          ? true
          : OrAny<Rest>
        : First
      : false
    : false; // Empty array is false (identity for OR)

// 📊 Counting true values
type CountTrue<T extends readonly boolean[], Count extends unknown[] = []> = 
  T extends readonly [infer First, ...infer Rest]
    ? First extends boolean
      ? Rest extends readonly boolean[]
        ? First extends true
          ? CountTrue<Rest, [...Count, unknown]>
          : CountTrue<Rest, Count>
        : Count['length']
      : Count['length']
    : Count['length'];

// 🎯 Majority vote logic
type Majority<T extends readonly boolean[]> = 
  T['length'] extends infer Length
    ? Length extends number
      ? CountTrue<T> extends infer TrueCount
        ? TrueCount extends number
          ? Length extends number
            ? TrueCount extends 0 ? false :
              TrueCount extends 1 ? Length extends 1 ? true : false :
              TrueCount extends 2 ? Length extends 2 | 3 ? true : false :
              TrueCount extends 3 ? Length extends 3 | 4 | 5 ? true : false :
              boolean
            : boolean
          : boolean
        : boolean
      : boolean
    : boolean;

// ✅ Multi-operand examples
type AllTrue = AndAll<[true, true, true]>;     // true
type AllFalse = AndAll<[true, false, true]>;   // false
type AnyTrue = OrAny<[false, false, true]>;    // true
type NonTrue = OrAny<[false, false, false]>;   // false
type TrueCount = CountTrue<[true, false, true, true]>; // 3
type MajorityTest = Majority<[true, true, false]>; // true

🌳 Conditional Logic Trees

🎯 If-Then-Else Constructs

// 🌟 Basic conditional type
type If<Condition extends boolean, Then, Else> = 
  Condition extends true ? Then : Else;

// 🔄 Nested conditional logic
type IfElseIf<
  Condition1 extends boolean,
  Then1,
  Condition2 extends boolean,
  Then2,
  Else> = Condition1 extends true
  ? Then1
  : Condition2 extends true
    ? Then2
    : Else;

// 🎨 Switch-case pattern
type Switch<
  Value,
  Cases extends Record<PropertyKey, any>,
  Default = never> = Value extends keyof Cases ? Cases[Value] : Default;

// 🧪 Conditional examples
type CondTest1 = If<true, "yes", "no">;       // "yes"
type CondTest2 = If<false, "yes", "no">;      // "no"

type ElseIfTest = IfElseIf<false, "first", true, "second", "third">; // "second"

type SwitchTest = Switch<"red", {
  red: "stop";
  yellow: "caution";
  green: "go";
}, "unknown">; // "stop"

// 🎯 Complex conditional patterns
type ComplexCondition<
  A extends boolean,
  B extends boolean,
  C extends boolean> = And<A, B> extends true
  ? "A and B"
  : Or<A, C> extends true
    ? "A or C"
    : "neither";

type ComplexTest = ComplexCondition<true, false, true>; // "A or C"

🏗️ Decision Trees and Pattern Matching

// 🌳 Binary decision tree
type BinaryDecision<
  Value extends string | number,
  LeftCondition extends boolean,
  LeftResult,
  RightResult> = LeftCondition extends true ? LeftResult : RightResult;

// 🎯 Multi-level decision tree
type DecisionTree<
  Input,
  Rules extends {
    condition: boolean;
    result: any;
    children?: DecisionTree<Input, any>[];
  }[]
> = Rules extends readonly [infer First, ...infer Rest]
  ? First extends { condition: boolean; result: any }
    ? First['condition'] extends true
      ? First['result']
      : Rest extends DecisionTree<Input, any>[]
        ? DecisionTree<Input, Rest>
        : never
    : never
  : never;

// 🎨 Pattern matching with guards
type PatternMatch<
  Value,
  Patterns extends readonly { 
    guard: boolean; 
    value: any; 
    result: any; 
  }[]
> = Patterns extends readonly [infer First, ...infer Rest]
  ? First extends { guard: boolean; value: any; result: any }
    ? First['guard'] extends true
      ? Value extends First['value']
        ? First['result']
        : Rest extends readonly { guard: boolean; value: any; result: any }[]
          ? PatternMatch<Value, Rest>
          : never
      : Rest extends readonly { guard: boolean; value: any; result: any }[]
        ? PatternMatch<Value, Rest>
        : never
    : never
  : never;

// ✅ Decision tree examples
type SimpleDecision = BinaryDecision<"test", true, "left path", "right path">; // "left path"

type PatternResult = PatternMatch<
  5,
  [
    { guard: false; value: 1; result: "one" },
    { guard: true; value: 5; result: "five" },
    { guard: true; value: 10; result: "ten" }
  ]
>; // "five"

🔄 State Machine Logic

// 🎰 State machine with boolean conditions
type StateMachine<
  CurrentState extends string,
  Event extends string,
  Transitions extends Record<string, Record<string, { 
    condition: boolean; 
    nextState: string; 
  }>>
> = CurrentState extends keyof Transitions
  ? Event extends keyof Transitions[CurrentState]
    ? Transitions[CurrentState][Event]['condition'] extends true
      ? Transitions[CurrentState][Event]['nextState']
      : CurrentState
    : CurrentState
  : CurrentState;

// 🚦 Traffic light state machine
type TrafficLightTransitions = {
  red: {
    timer: { condition: true; nextState: "green" };
    emergency: { condition: true; nextState: "flashing" };
  };
  green: {
    timer: { condition: true; nextState: "yellow" };
    emergency: { condition: true; nextState: "flashing" };
  };
  yellow: {
    timer: { condition: true; nextState: "red" };
    emergency: { condition: true; nextState: "flashing" };
  };
  flashing: {
    reset: { condition: true; nextState: "red" };
  };
};

// 🔐 Authentication state machine
type AuthTransitions = {
  unauthenticated: {
    login: { condition: true; nextState: "authenticating" };
  };
  authenticating: {
    success: { condition: true; nextState: "authenticated" };
    failure: { condition: true; nextState: "unauthenticated" };
    timeout: { condition: true; nextState: "unauthenticated" };
  };
  authenticated: {
    logout: { condition: true; nextState: "unauthenticated" };
    expire: { condition: true; nextState: "unauthenticated" };
    refresh: { condition: true; nextState: "authenticated" };
  };
};

// ✅ State machine examples
type NextTrafficState = StateMachine<"red", "timer", TrafficLightTransitions>; // "green"
type NextAuthState = StateMachine<"authenticating", "success", AuthTransitions>; // "authenticated"

// 🎯 Complex state transitions with conditions
type ConditionalStateMachine<
  State extends string,
  Event extends string,
  Context extends Record<string, boolean>,
  Transitions extends Record<string, Record<string, {
    condition: keyof Context;
    nextState: string;
  }>>
> = State extends keyof Transitions
  ? Event extends keyof Transitions[State]
    ? Transitions[State][Event]['condition'] extends keyof Context
      ? Context[Transitions[State][Event]['condition']] extends true
        ? Transitions[State][Event]['nextState']
        : State
      : State
    : State
  : State;

type ContextualTransition = ConditionalStateMachine<
  "pending",
  "approve",
  { hasPermission: true; isValid: true },
  {
    pending: {
      approve: { condition: "hasPermission"; nextState: "approved" };
      reject: { condition: "hasPermission"; nextState: "rejected" };
    };
  }
>; // "approved"

🧮 Advanced Boolean Algorithms

🔍 Truth Table Generation

// 🎯 Truth table for binary operations
type TruthTable2<Op extends string> = {
  [A in boolean]: {
    [B in boolean]: Op extends "AND"
      ? And<A, B>
      : Op extends "OR"
        ? Or<A, B>
        : Op extends "XOR"
          ? Xor<A, B>
          : Op extends "NAND"
            ? Nand<A, B>
            : Op extends "NOR"
              ? Nor<A, B>
              : never;
  };
};

// 📊 Truth tables for common operations
type AndTruthTable = TruthTable2<"AND">;
type OrTruthTable = TruthTable2<"OR">;
type XorTruthTable = TruthTable2<"XOR">;

// 🎯 Custom boolean function evaluation
type EvaluateBoolean<
  Expr extends string,
  Variables extends Record<string, boolean>
> = Expr extends `${infer Left} AND ${infer Right}`
  ? And<
      EvaluateBoolean<Left, Variables>,
      EvaluateBoolean<Right, Variables>
    >
  : Expr extends `${infer Left} OR ${infer Right}`
    ? Or<
        EvaluateBoolean<Left, Variables>,
        EvaluateBoolean<Right, Variables>
      >
    : Expr extends `NOT ${infer Operand}`
      ? Not<EvaluateBoolean<Operand, Variables>>
      : Expr extends keyof Variables
        ? Variables[Expr]
        : Expr extends "true"
          ? true
          : Expr extends "false"
            ? false
            : never;

// ✅ Boolean evaluation examples
type BooleanResult1 = EvaluateBoolean<"A AND B", { A: true; B: false }>; // false
type BooleanResult2 = EvaluateBoolean<"A OR B", { A: true; B: false }>; // true
type BooleanResult3 = EvaluateBoolean<"NOT A", { A: true }>; // false

🎨 Boolean Circuit Simulation

// 🔌 Logic gate definitions
type LogicGate<Type extends string, Inputs extends readonly boolean[]> = 
  Type extends "AND"
    ? AndAll<Inputs>
    : Type extends "OR"
      ? OrAny<Inputs>
      : Type extends "NOT"
        ? Inputs extends readonly [infer Input]
          ? Input extends boolean
            ? Not<Input>
            : never
          : never
        : Type extends "XOR"
          ? Inputs extends readonly [infer A, infer B]
            ? A extends boolean
              ? B extends boolean
                ? Xor<A, B>
                : never
              : never
            : never
          : never;

// 🏗️ Circuit composition
type Circuit<
  Gates extends Record<string, { type: string; inputs: readonly any[] }>,
  Inputs extends Record<string, boolean>
> = {
  [K in keyof Gates]: Gates[K]['type'] extends string
    ? Gates[K]['inputs'] extends readonly any[]
      ? LogicGate<Gates[K]['type'], Gates[K]['inputs']>
      : never
    : never;
};

// 🎯 Half adder circuit
type HalfAdder<A extends boolean, B extends boolean> = {
  sum: Xor<A, B>;
  carry: And<A, B>;
};

// 🧮 Full adder circuit
type FullAdder<A extends boolean, B extends boolean, CarryIn extends boolean> = {
  sum: Xor<Xor<A, B>, CarryIn>;
  carry: Or<And<A, B>, And<CarryIn, Xor<A, B>>>;
};

// ✅ Circuit examples
type HalfAdderTest = HalfAdder<true, false>; // { sum: true; carry: false }
type FullAdderTest = FullAdder<true, true, false>; // { sum: false; carry: true }

// 🎨 Multiplexer implementation
type Mux2to1<
  Input0 extends boolean,
  Input1 extends boolean,
  Select extends boolean> = Select extends true ? Input1 : Input0;

type Mux4to1<
  Inputs extends readonly [boolean, boolean, boolean, boolean],
  Select extends readonly [boolean, boolean]
> = Select extends readonly [infer S1, infer S0]
  ? S1 extends boolean
    ? S0 extends boolean
      ? S1 extends true
        ? S0 extends true
          ? Inputs[3]
          : Inputs[2]
        : S0 extends true
          ? Inputs[1]
          : Inputs[0]
      : never
    : never
  : never;

type MuxTest = Mux4to1<[false, true, false, true], [true, false]>; // false (selects input 2)

🔄 Boolean Satisfiability (SAT)

// 🎯 Clause representation (disjunctive normal form)
type Literal<Variable extends string, Negated extends boolean = false> = {
  variable: Variable;
  negated: Negated;
};

type Clause<Literals extends readonly Literal<string, boolean>[]> = Literals;

type CNF<Clauses extends readonly Clause<readonly Literal<string, boolean>[]>[]> = Clauses;

// 🔍 SAT solver (simplified for small cases)
type EvaluateLiteral<
  Lit extends Literal<string, boolean>,
  Assignment extends Record<string, boolean>
> = Lit['variable'] extends keyof Assignment
  ? Lit['negated'] extends true
    ? Not<Assignment[Lit['variable']]>
    : Assignment[Lit['variable']]
  : never;

type EvaluateClause<
  Clause extends readonly Literal<string, boolean>[],
  Assignment extends Record<string, boolean>
> = Clause extends readonly [infer First, ...infer Rest]
  ? First extends Literal<string, boolean>
    ? Rest extends readonly Literal<string, boolean>[]
      ? Or<
          EvaluateLiteral<First, Assignment>,
          EvaluateClause<Rest, Assignment>
        >
      : EvaluateLiteral<First, Assignment>
    : never
  : false;

// ✅ SAT solver example
type SATExample = EvaluateClause<
  [
    { variable: "A"; negated: false },
    { variable: "B"; negated: true }
  ],
  { A: false; B: false }
>; // true (false OR NOT false = false OR true = true)

🛡️ Type-Safe Permission and Access Control

🔐 Permission System

// 🎯 Permission definitions
type Permission = 
  | "read"
  | "write" 
  | "delete"
  | "admin"
  | "create"
  | "update"
  | "execute";

type Role = "user" | "moderator" | "admin" | "guest";

// 🏗️ Role-based permissions
type RolePermissions = {
  guest: ["read"];
  user: ["read", "create", "update"];
  moderator: ["read", "create", "update", "delete"];
  admin: ["read", "create", "update", "delete", "admin", "execute"];
};

// 🔍 Permission checking
type HasPermission<
  UserRole extends Role,
  RequiredPermission extends Permission> = UserRole extends keyof RolePermissions
  ? RequiredPermission extends RolePermissions[UserRole][number]
    ? true
    : false
  : false;

// 🎯 Multi-permission requirements
type HasAllPermissions<
  UserRole extends Role,
  RequiredPermissions extends readonly Permission[]
> = RequiredPermissions extends readonly [infer First, ...infer Rest]
  ? First extends Permission
    ? Rest extends readonly Permission[]
      ? And<
          HasPermission<UserRole, First>,
          HasAllPermissions<UserRole, Rest>
        >
      : HasPermission<UserRole, First>
    : false
  : true;

type HasAnyPermission<
  UserRole extends Role,
  RequiredPermissions extends readonly Permission[]
> = RequiredPermissions extends readonly [infer First, ...infer Rest]
  ? First extends Permission
    ? Rest extends readonly Permission[]
      ? Or<
          HasPermission<UserRole, First>,
          HasAnyPermission<UserRole, Rest>
        >
      : HasPermission<UserRole, First>
    : false
  : false;

// ✅ Permission examples
type CanRead = HasPermission<"user", "read">;        // true
type CanDelete = HasPermission<"user", "delete">;    // false
type CanAdmin = HasPermission<"admin", "admin">;     // true

type CanReadWrite = HasAllPermissions<"user", ["read", "write"]>; // false
type CanReadOrDelete = HasAnyPermission<"user", ["read", "delete"]>; // true

// 🔒 Conditional access control
type SecureOperation<
  UserRole extends Role,
  RequiredPermission extends Permission,
  SuccessResult,
  FailureResult = "Access Denied"> = HasPermission<UserRole, RequiredPermission> extends true
  ? SuccessResult
  : FailureResult;

type DeleteResult = SecureOperation<"user", "delete", "File deleted", "Insufficient permissions">; 
// "Insufficient permissions"

type ReadResult = SecureOperation<"user", "read", "Data retrieved">; 
// "Data retrieved"

🌐 Feature Flag System

// 🎯 Feature flag definitions
type FeatureFlag = {
  enabled: boolean;
  rolloutPercentage?: number;
  userGroups?: readonly string[];
  requirements?: readonly string[];
};

type FeatureFlags = {
  darkMode: { enabled: true };
  betaFeatures: { enabled: false };
  premiumFeatures: { enabled: true; userGroups: ["premium", "admin"] };
  experimentalUI: { enabled: true; rolloutPercentage: 50 };
  advancedAnalytics: { 
    enabled: true; 
    requirements: ["authenticated", "consented"] 
  };
};

// 🔍 Feature flag evaluation
type IsFeatureEnabled<
  FlagName extends keyof FeatureFlags,
  UserContext extends {
    group?: string;
    authenticated?: boolean;
    consented?: boolean;
  } = {}
> = FeatureFlags[FlagName] extends { enabled: infer Enabled }
  ? Enabled extends true
    ? FeatureFlags[FlagName] extends { userGroups: readonly string[] }
      ? UserContext extends { group: infer Group }
        ? Group extends FeatureFlags[FlagName]['userGroups'][number]
          ? true
          : false
        : false
      : FeatureFlags[FlagName] extends { requirements: readonly string[] }
        ? FeatureFlags[FlagName]['requirements'] extends readonly ["authenticated", "consented"]
          ? And<
              UserContext extends { authenticated: true } ? true : false,
              UserContext extends { consented: true } ? true : false>
          : boolean
        : true
    : false
  : false;

// ✅ Feature flag examples
type DarkModeEnabled = IsFeatureEnabled<"darkMode">; // true
type BetaEnabled = IsFeatureEnabled<"betaFeatures">; // false
type PremiumForAdmin = IsFeatureEnabled<"premiumFeatures", { group: "admin" }>; // true
type PremiumForUser = IsFeatureEnabled<"premiumFeatures", { group: "user" }>; // false
type AnalyticsForUser = IsFeatureEnabled<
  "advancedAnalytics", 
  { authenticated: true; consented: true }
>; // true

🎮 Complex Boolean Applications

🎰 Game Logic System

// 🎮 Game state conditions
type GameConditions = {
  playerAlive: boolean;
  hasKey: boolean;
  doorUnlocked: boolean;
  bossDefeated: boolean;
  allItemsCollected: boolean;
  timeRemaining: boolean;
};

// 🏆 Win/lose conditions
type CanWin<Conditions extends GameConditions> = 
  And<
    Conditions['playerAlive'],
    And<
      Conditions['bossDefeated'],
      Conditions['allItemsCollected']
    >
  >;

type HasLost<Conditions extends GameConditions> = 
  Or<
    Not<Conditions['playerAlive']>,
    Not<Conditions['timeRemaining']>
  >;

type CanProgress<Conditions extends GameConditions> = 
  And<
    Conditions['playerAlive'],
    Or<
      Conditions['hasKey'],
      Conditions['doorUnlocked']
    >
  >;

// 🎯 Quest completion logic
type QuestComplete<
  Requirements extends Record<string, boolean>,
  CompletedTasks extends Record<string, boolean>
> = {
  [K in keyof Requirements]: K extends keyof CompletedTasks
    ? Requirements[K] extends true
      ? CompletedTasks[K] extends true
        ? true
        : false
      : true
    : false;
}[keyof Requirements] extends false ? false : true;

// ✅ Game logic examples
type WinCondition = CanWin<{
  playerAlive: true;
  hasKey: true;
  doorUnlocked: true;
  bossDefeated: true;
  allItemsCollected: true;
  timeRemaining: true;
}>; // true

type LoseCondition = HasLost<{
  playerAlive: false;
  hasKey: true;
  doorUnlocked: true;
  bossDefeated: false;
  allItemsCollected: false;
  timeRemaining: true;
}>; // true

type QuestStatus = QuestComplete<
  { killBoss: true; findTreasure: true; rescueNPC: false },
  { killBoss: true; findTreasure: false; rescueNPC: true }
>; // false

📊 Data Validation Pipeline

// 🔍 Validation rule definitions
type ValidationRule<T> = {
  required: boolean;
  minLength?: number;
  maxLength?: number;
  pattern?: string;
  customValidator?: (value: T) => boolean;
};

type FormValidation = {
  email: { required: true; pattern: "email" };
  password: { required: true; minLength: 8 };
  age: { required: false; minLength: 1; maxLength: 3 };
  terms: { required: true };
};

// 🎯 Field validation logic
type ValidateField<
  FieldName extends keyof FormValidation,
  Value extends string | boolean,
  Rules extends ValidationRule<any> = FormValidation[FieldName]
> = Rules extends { required: true }
  ? Value extends ""
    ? false
    : Rules extends { minLength: infer MinLen }
      ? MinLen extends number
        ? Value extends string
          ? /* would need string length check */ true
          : true
        : true
      : true
  : true;

// 🔄 Form validation aggregation
type ValidateForm<
  FormData extends Record<keyof FormValidation, string | boolean>
> = {
  [K in keyof FormValidation]: ValidateField<K, FormData[K]>
};

type FormValidationResult<
  ValidationResults extends Record<keyof FormValidation, boolean>
> = AndAll<[
  ValidationResults['email'],
  ValidationResults['password'],
  ValidationResults['age'],
  ValidationResults['terms']
]>;

// ✅ Validation examples
type ValidForm = FormValidationResult<{
  email: true;
  password: true;
  age: true;
  terms: true;
}>; // true

type InvalidForm = FormValidationResult<{
  email: false;
  password: true;
  age: true;
  terms: true;
}>; // false

🔄 Workflow Engine

// 🏭 Workflow step definition
type WorkflowStep = {
  id: string;
  condition: boolean;
  dependencies: readonly string[];
  parallel: boolean;
};

type Workflow = Record<string, WorkflowStep>;

// 🎯 Step execution eligibility
type CanExecuteStep<
  StepId extends string,
  WorkflowDef extends Workflow,
  CompletedSteps extends readonly string[]
> = StepId extends keyof WorkflowDef
  ? WorkflowDef[StepId]['condition'] extends true
    ? WorkflowDef[StepId]['dependencies'] extends readonly string[]
      ? AndAll<{
          [K in keyof WorkflowDef[StepId]['dependencies']]: 
            WorkflowDef[StepId]['dependencies'][K] extends CompletedSteps[number]
              ? true
              : false
        }[keyof WorkflowDef[StepId]['dependencies']][]>
      : true
    : false
  : false;

// 🔄 Workflow completion checking
type IsWorkflowComplete<
  WorkflowDef extends Workflow,
  CompletedSteps extends readonly string[]
> = AndAll<{
  [K in keyof WorkflowDef]: K extends CompletedSteps[number] ? true : false
}[keyof WorkflowDef][]>;

// ✅ Workflow examples
type SampleWorkflow = {
  init: { id: "init"; condition: true; dependencies: []; parallel: false };
  validate: { id: "validate"; condition: true; dependencies: ["init"]; parallel: false };
  process: { id: "process"; condition: true; dependencies: ["validate"]; parallel: true };
  notify: { id: "notify"; condition: true; dependencies: ["process"]; parallel: true };
  cleanup: { id: "cleanup"; condition: true; dependencies: ["process", "notify"]; parallel: false };
};

type CanProcess = CanExecuteStep<"process", SampleWorkflow, ["init", "validate"]>; // true
type CanCleanup = CanExecuteStep<"cleanup", SampleWorkflow, ["init", "validate", "process"]>; // false
type WorkflowDone = IsWorkflowComplete<SampleWorkflow, ["init", "validate", "process", "notify", "cleanup"]>; // true

🎓 Key Takeaways

You’ve mastered the logical reasoning capabilities of TypeScript’s type system! Here’s what you now command:

✅ Boolean algebra operations including AND, OR, NOT, XOR, and complex logic 💪
✅ Conditional logic trees and sophisticated decision-making patterns 🛡️
✅ State machine logic with boolean conditions and transitions 🎯
✅ Truth table generation and boolean circuit simulation 🐛
✅ Permission systems and access control with type-level logic 🚀
✅ Feature flags and complex validation pipelines ✨
✅ Real-world applications in gaming, workflows, and business logic 🔄

Remember: Type-level boolean logic enables you to build intelligent reasoning systems that execute at compile time! 🤝

🤝 Next Steps

Congratulations! 🎉 You’ve become a master of logical reasoning in TypeScript’s type system!

Here’s what to do next:

💻 Build permission systems and access control with compile-time validation
🏗️ Create complex state machines and workflow engines using boolean logic
📚 Move on to our next tutorial: Type-Level Arrays - Tuple Manipulations
🌟 Implement feature flag systems and conditional compilation patterns
🔍 Explore formal verification and theorem proving in type systems
🎯 Build intelligent validation pipelines and decision support systems
🚀 Push the boundaries of logical reasoning at the type level

Remember: You now possess the power to encode logical reasoning directly into TypeScript’s type system! Use this knowledge to build incredibly intelligent and safe systems. 🚀

Happy logical reasoning mastering! 🎉🔀✨

Prerequisites

What you'll learn