Advanced TypeScript Function Type Utilities

This challenge focuses on building powerful utility types in TypeScript to manipulate function signatures. You will create types that can infer, transform, and augment function parameters and return types, enabling more flexible and robust code. Mastering these utilities is crucial for advanced type-level programming in TypeScript.

Problem Description

Your task is to implement a set of TypeScript utility types that operate on function types. These utilities should allow developers to inspect and modify function signatures at compile time, leading to more maintainable and type-safe codebases, especially in scenarios involving higher-order functions, decorators, or complex API definitions.

Key Requirements:

1. Parameters<T>: Create a type that extracts the parameter types of a function type T.
2. ReturnType<T>: Create a type that extracts the return type of a function type T.
3. ArgumentTypes<T>: Create a type that extracts the argument types of a function type T. This is equivalent to Parameters<T> for regular functions, but should handle potential differences for arrow functions or methods if applicable (though for this challenge, treat it as a synonym for Parameters<T>).
4. OmitParameters<T, K>: Create a type that takes a function type T and omits a specified parameter type K from its parameter list. K can be a single type or a union of types to omit.
5. PrependParameters<T, P>: Create a type that takes a function type T and prepends a specified parameter list P to its existing parameters. P should be a tuple type.
6. AppendParameters<T, P>: Create a type that takes a function type T and appends a specified parameter list P to its existing parameters. P should be a tuple type.
7. ReplaceParameters<T, NewP>: Create a type that takes a function type T and replaces its entire parameter list with a new tuple type NewP.

Expected Behavior:

• All utility types should work correctly for arrow functions, regular function declarations, and methods within object types.
• The types should be purely declarative and operate solely at the type level.

Edge Cases to Consider:

• Functions with no parameters.
• Functions with a single parameter.
• Functions with variadic parameters (using ...args).
• OmitParameters should handle cases where the parameter to omit is not present or when omitting from a union of parameter types.
• PrependParameters and AppendParameters should correctly merge tuple types.

Examples

Example 1: Parameters<T>

type MyFunc = (a: string, b: number) => boolean;
type Params = Parameters<MyFunc>; // Expected: [string, number]

Example 2: ReturnType<T>

type AnotherFunc = (x: number) => string;
type Result = ReturnType<AnotherFunc>; // Expected: string

Example 3: OmitParameters<T, K>

type WithIdFunc = (id: number, name: string, age: number) => void;
type WithoutId = OmitParameters<WithIdFunc, number>; // Expected: (name: string, age: number) => void

type ComplexFunc = (a: string | number, b: boolean, c: string) => void;
type WithoutStringOrNumber = OmitParameters<ComplexFunc, string | number>; // Expected: (b: boolean) => void

Example 4: PrependParameters<T, P>

type BaseFunc = (b: number, c: boolean) => string;
type PrependingParams = [a: string, x: object];
type PrependingResult = PrependParameters<BaseFunc, PrependingParams>;
// Expected: (a: string, x: object, b: number, c: boolean) => string

Example 5: AppendParameters<T, P>

type BaseFunc2 = (a: string, b: number) => void;
type AppendingParams = [c: boolean, d: string];
type AppendingResult = AppendParameters<BaseFunc2, AppendingParams>;
// Expected: (a: string, b: number, c: boolean, d: string) => void

Example 6: ReplaceParameters<T, NewP>

type OriginalFunc = (a: string, b: number) => boolean;
type NewParamsTuple = [x: number, y: string, z: object];
type ReplacedFunc = ReplaceParameters<OriginalFunc, NewParamsTuple>;
// Expected: (x: number, y: string, z: object) => boolean

Example 7: Edge Case - No Parameters

type NoParamsFunc = () => void;
type NoParamsResult = Parameters<NoParamsFunc>; // Expected: []
type AppendedNoParams = AppendParameters<NoParamsFunc, [string]>; // Expected: (arg: string) => void

Example 8: Edge Case - Variadic Parameters

type VariadicFunc = (...args: any[]) => number;
type VariadicParams = Parameters<VariadicFunc>; // Expected: any[]

Constraints

• Your solutions must be implemented using TypeScript's advanced type features (infer, conditional types, mapped types, etc.).
• You should not use any runtime JavaScript code; all logic must be at the type level.
• The provided examples should pass type checking with your implemented utility types.
• Aim for clear and readable type definitions.

Notes

• Remember that infer is your best friend when extracting type information from a generic type.
• Conditional types (T extends U ? X : Y) will be essential for pattern matching and type extraction.
• Consider how to handle the never type and empty tuples appropriately.
• For OmitParameters, think about how to effectively filter types from a tuple. You might need to build an intermediate type that can filter tuple elements.
• For PrependParameters and AppendParameters, tuple concatenation will be key.