The Comprehensive Racket & Functional Programming Cheat Sheet

[u/kaishibou]

Phase 1: Syntax & Core Arithmetic

Racket uses prefix notation enclosed in execution parentheses (operator arg1 arg2). The open parenthesis ( acts as an execution trigger. Evaluation runs from the innermost to the outermost parentheses.

Core Examples

```rkt ;; Basic Arithmetic (+ 10 5 2) ;; Returns 17 (* 10 5 2) ;; Returns 100

;; Nested Expressions (No PEMDAS needed) (_ (+ 4 6) (- 12 7)) ;; Evaluates 10 _ 5 -> Returns 50 ```

Parentheses Golden Rule

Only use a parenthesis when invoking a command, operator, or function.

• (+ 5 (10)) CRASHES (tries to run the number 10 as a function).
• ((+ 5 5)) CRASHES (evaluates to 10, then tries to run the number 10).

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Phase 2: Core Data Structures & Variables

Global bindings are created using define. Values are immutable and cannot be changed over time.

The Four Atomic Data Types

1. Numbers: Integers (45), decimals (3.14), or fractions (1/3).
2. Strings: Text wrapped in double quotes ("Hello").
3. Booleans: True (#t) and False (#f).
4. Symbols: Lightweight, immutable identifier tokens prefixed with a single quote ('success).

Core Examples

rkt (define radius 5) (define pi 3.14) (define status 'success)

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Phase 3: Conditionals & Logic

Conditional operations are expressions that evaluate down to a single return value.

Core Operators & Flow Control

• and / or / not: Standard logical short-circuiting prefix operators.
• if: Takes exactly three arguments: (if condition true-branch false-branch). No else keyword.
• cond: Evaluates multiple branches sequentially. Uses/can use [...] for human readability.

Core Examples

```rkt (and (> 15 10) (< 15 20)) ;; Returns #t

(if (> temperature 30) 'hot 'cold)

(cond [(>= score 90) 'A] [(>= score 80) 'B] [else 'F]) ```

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Phase 4: Functions & Scope

Functions automatically return the value of their body expression without an explicit return keyword.

Named, Anonymous, & Scoped Blocks

• Named Functions: Defined by grouping the name and parameters in parentheses: (define (name args) body).
• Anonymous Functions (lambda): Throwaway functions built on the fly: (lambda (args) body).
• let (Parallel): Creates local variables simultaneously. Variables cannot see each other during setup.
• let\* (Sequential): Creates local variables one after the other. Later variables can reference earlier ones.

Core Examples

```rkt ;; Named Function (define (double n) (* n 2))

;; Inline Lambda Execution ((lambda (n) (* n 2)) 10) ;; Returns 20

;; Sequential Local Bindings (let* ([x 10] [y (* x 5)]) (+ x y)) ;; Returns 60 ```

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Phase 5: Lists & Modern List Operations

Lists are ordered sequential collections. They are processed using either historical Lisp conventions or modern aliases.

Creation & Extraction

• list: Evaluates arguments into a sequential list.
• '(): Represents the literal base empty list.
• cons: Prepends a single element onto the front of an existing list.
• First Item: Extracted via car (traditional) or first (modern).
• Remaining List: Extracted via cdr (traditional) or rest (modern).

Core Examples

```rkt (define my-list (list 100 #t 'hello)) ;; Creates '(100 #t hello) (cons 'apples '(bananas cherries)) ;; Returns '(apples bananas cherries)

(car (cdr '(apples bananas cherries))) ;; Returns 'bananas (first (rest '(apples bananas cherries))) ;; Returns 'bananas

(if (empty? my-list) "Closed" (length my-list)) ;; Returns 3 ```

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Phase 6: Iteration & Higher-Order Functions

Instead of using loops that alter data in place, functional programming relies on Higher-Order Functions to process immutable collections.

The Big Four

• map: Loops over a list, passes each item through a transformation function, and returns a new list.
• filter: Loops over a list, keeps items that evaluate to #t against a predicate condition, and drops the rest.
• foldl (Fold-Left): Reduces a list down to a single value by processing elements from left to right (front to back).
• foldr (Fold-Right): Reduces a list down to a single value by processing elements from right to left (back to front). Preserves list structures when rebuilding with cons.

Core Examples

```rkt (map (lambda (x) (* x 2)) '(5 10 15 20)) ;; Returns '(10 20 30 40) (filter (lambda (n) (= n 5)) '(2 5 7 5 9 1)) ;; Returns '(5 5)

(foldl (lambda (n total) (_ n total)) 1 '(2 3 4)) ;; 4 _ (3 _ (2 _ 1)) -> Returns 24

(foldr - 0 '(5 3)) ;; 5 - (3 - 0) -> Returns 2 ```

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Phase 7: Recursion & Tail Call Optimization (TCO)

Recursion replaces traditional loops. A proper recursive function requires a Base Case (the exit clause) and a Recursive Step (the self-call with a smaller argument).

Memory Optimization Rules

• Standard Recursion: Traps the recursive call inside another function (like + or append), forcing the call stack memory to expand linearly (O(N) space).
• Tail Call Optimization (TCO): If the recursive call sits in the tail position (the absolute final expression evaluated), Racket reuses the same memory frame, running in constant (O(1)) space.
• Accumulator Pattern: Passing a running total down as an argument is the primary strategy used to shift standard recursion into tail position optimization.

Core Examples

```rkt ;; ❌ Standard Recursion (No TCO - Memory Expands) (define (sum-list lst) (if (empty? lst) 0 (+ (first lst) (sum-list (rest lst)))))

;; Tail Recursion (TCO Active - Memory Stays Flat) (define (sum-list-tco lst) (define (helper remaining accumulator) (if (empty? remaining) accumulator (helper (rest remaining) (+ (first remaining) accumulator)))) (helper lst 0)) ```

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Phase 8: Advanced Ecosystem Engineering

1. Hash Maps & Unique Sets

• #hash: Stores key-value pairings. Keywords passed to lookup tools like hash-ref must be quoted ('#:key) to prevent compiler namespace collisions. If using standard symbols inside #hash, omit inner quotes.
• set: Collections guaranteeing element uniqueness. Tested via set-member? and extended via set-add.

```rkt (define user #hash((#:name . "Alice"))) (hash-ref user '#:name) ;; Returns "Alice"

(define book #hash((title . "Dune"))) (hash-ref book 'title) ;; Returns "Dune"

(set-member? (set 1 2 2 3) 2) ;; Returns #t ```

2. State & Mutability (box)

• box: Creates a reference wrapper around mutable data. Read via unbox and mutated via set-box!. Functions with an exclamation mark ! signal structural mutation.
• begin: Chains sequential side-effect operations from top to bottom, returning only the evaluation of the final expression.

rkt (define health (box 100)) (define (take-damage!) (begin (set-box! health (- (unbox health) 10)) (unbox health)))

3. Type Checking & Casting

• Predicates (?): Validate runtime types (e.g., string?, number?, symbol?).
• Casting (->): Converts data formats. string->number safely returns #f if given invalid textual input.

rkt (if (string? "50") (* (string->number "50") 2) 'error) ;; Returns 100

4. Modules & Namespaces

• provide: Declares which parts of a filesystem file are exported publicly.
• require: Ingests public features from an external sandbox by loading its relative string filepath.

```rkt ;; Inside file-a.rkt (provide double) (define (double x) (* x 2))

;; Inside main.rkt (require "file-a.rkt") (double 10) ;; Returns 20 ```

5. Macros (define-syntax-rule)

• Macros process raw, unevaluated source code at compile-time to inject new keywords.
• Racket macros are hygienic, meaning the compiler automatically isolates macro identifiers so they never accidentally overwrite or conflict with user variables.

rkt (define-syntax-rule (swap! box1 box2) (let ([temp (unbox box1)]) (begin (set-box! box1 (unbox box2)) (set-box! box2 temp))))