echo "Hello World" > index.html Pop 'n' Fresh

Pop 'n' Fresh

Welcome to the Pop 'n' Fresh language specification!

This page provides a detailed overview of the language's syntax, semantics, and supported data types.

If you're new to the language, start with the Syntax section to understand the basic structure and rules.

For more information on the language, check out the Semantics section, which covers the operations and commands supported by the language.

The Data Types section provides an overview of the supported data types and structures in the language.

If you're ready to dive into the language, check out the Built-in Functions section, which lists the built-in functions available in the language.

Syntax Semantics Data Types Built-in Functions

Syntax

The syntax of Pop 'n' Fresh follows a clear structure defined by strict formatting and rule sets. Each statement in the language adheres to the following general format:

// Single-line comment   
                {
                operation: "add"; // Block start
                num1: 3;
                num2: 5;
                result: 0;
                // Call operation
                result = add(num1, num2);
                }

Semantics

Operations in Pop 'n' Fresh are built on a functional paradigm with state transformations being explicit. All operations consist of a source, a command, and an optional result. The language ensures that side effects are minimized by default, making state changes explicit within blocks.

{
                                    input: 4;
                                    factor: 3;
                                    output: 0;
                                    output = multiply(input, factor); // Semantically pure operation
                                }

Arithmetic Operations such as add(), subtract(), multiply(), and divide() follow traditional semantics.
Assignment Operations such as x = y; assign the value of y to x.

Data Types

The language supports the following primitive data types and composite structures:

Primitives:
- int: Represents integer numbers.
- float: Represents floating-point numbers.
- string: A sequence of characters.
- bool: Represents boolean values (true or false).
Composite Types:
- Array: Denoted by square brackets, [ ], and can hold multiple values of any type.
- Object: Denoted by curly braces {}, these are key-value pairs where the key is a string and the value can be any type.

{
                                    arr: [1, 2, 3, 4];
                                    obj: {
                                        "key1": "value1",
                                        "key2": true,
                                        "key3": 3.14
                                    };
                                }

Built-in Functions

The language provides a set of built-in functions that can be used to perform common operations. These functions are:

Arithmetic Operations:
- add(int, int): Adds two integers.
- subtract(int, int): Subtracts two integers.
- multiply(int, int): Multiplies two integers.
- divide(int, int): Divides two integers.
String Operations:
- concat(string, string): Concatenates two strings.
- length(string): Returns the length of a string.
- substring(string, int, int): Extracts a substring from a string.

{
                                    arr: [1, 2, 3, 4];
                                    obj: {
                                        "key1": "value1",
                                        "key2": true,
                                        "key3": 3.14
                                    };
                                }

PopN'Fresh: ".pnf"

1. Syntax and Structure

The syntax of Pop 'n' Fresh follows a clear structure defined by strict formatting and rule sets. Each statement in the language adheres to the following general format:

Statements: Must end with a semicolon (;).
Blocks: Blocks are enclosed by curly braces {}.
Indentation: Indentation is not mandatory but strongly recommended for clarity.
Comments: Single-line comments start with //, while multi-line comments are enclosed in /* */.

Syntax Example:

// Single-line comment
{
  operation: "add"; // Block start
  num1: 3;
  num2: 5;
  result: 0;
  // Call operation
  result = add(num1, num2);
}

2. Semantics of Operations and Commands

Operations in toaster.Json are built on a functional paradigm with state transformations being explicit. All operations consist of a source, a command, and an optional result. The language ensures that side effects are minimized by default, making state changes explicit within blocks.

Example of Operation Semantics:

{
  input: 4;
  factor: 3;
  output: 0;
  output = multiply(input, factor); // Semantically pure operation
}

Arithmetic Operations such as add(), subtract(), multiply(), and divide() follow traditional semantics.
Assignment Operations such as x = y; assign the value of y to x.

3. Supported Data Types and Structures

The language supports the following primitive data types and composite structures:

Primitives:
- int: Represents integer numbers.
- float: Represents floating-point numbers.
- string: A sequence of characters.
- bool: Represents boolean values (true or false).
Composite Types:
- Arrays are denoted by square brackets [] and can hold elements of the same type.
- Objects are denoted by curly braces {} and consist of key-value pairs, where the key is a string and the value can be of any type.

Interaction Example:

{
  arr: [1, 2, 3, 4];
  obj: {
    "key1": "value1",
    "key2": true,
    "key3": 3.14
  };
}

4. Built-in Functions

The language provides a set of built-in functions that can be used to perform common operations. These functions are:

Arithmetic Operations:

Language Specification for microwave.Json

1. Syntax Rules

The syntax of microwave.Json follows a clear structure defined by strict formatting and rule sets. Each statement in the language adheres to the following general format:

Statements: Must end with a semicolon (;).
Blocks: Blocks are enclosed by curly braces {}.
Indentation: Indentation is not mandatory but strongly recommended for clarity.
Comments: Single-line comments start with //, while multi-line comments are enclosed in /* */.

Syntax Example:

// Single-line comment
{
  operation: "add"; // Block start
  num1: 3;
  num2: 5;
  result: 0;
  // Call operation
  result = add(num1, num2);
}

2. Semantics of Operations and Commands

Example of Operation Semantics:

{
  input: 4;
  factor: 3;
  output: 0;
  output = multiply(input, factor); // Semantically pure operation
}

1. Syntax and Structure

The syntax of Pop 'n' Fresh follows a clear structure defined by strict formatting and rule sets. Each statement in the language adheres to the following general format:

Statements: Must end with a semicolon (;).
Blocks: Blocks are enclosed by curly braces {}.
Indentation: Indentation is not mandatory but strongly recommended for clarity.
Comments: Single-line comments start with //, while multi-line comments are enclosed in /* */.

Syntax Example:

// Single-line comment    
    {
      operation: "add"; // Block start
      num1: 3;
      num2: 5;
      result: 0;
      // Call operation
      result = add(num1, num2);
    }

2. Semantics of Operations and Commands

Example of Operation Semantics:

{
      input: 4;
      factor: 3;
      output: 0;
      output = multiply(input, factor); // Semantically pure operation
    }

1. Syntax Rules

The syntax of toaster.Json follows a clear structure defined by strict formatting and rule sets. Each statement in the language adheres to the following general format:

Statements: Must end with a semicolon (;).
Blocks: Blocks are enclosed by curly braces {}.
Indentation: Indentation is not mandatory but strongly recommended for clarity.
Comments: Single-line comments start with //, while multi-line comments are enclosed in /* */.

Syntax Example:

// Single-line comment
{
  operation: "add"; // Block start
  num1: 3;
  num2: 5;
  result: 0;
  // Call operation
  result = add(num1, num2);
}

2. Semantics of Operations and Commands

Example of Operation Semantics:

{
  input: 4;
  factor: 3;
  output: 0;
  output = multiply(input, factor); // Semantically pure operation
}

Arithmetic Operations such as add(), subtract(), multiply(), and divide() follow traditional semantics.
Assignment Operations such as x = y; assign the value of y to x.

3. Supported Data Types and Structures

The language supports the following primitive data types and composite structures:

Primitives:
- int: Represents integer numbers.
- float: Represents floating-point numbers.
- string: A sequence of characters.
- bool: Represents boolean values (true or false).
Composite Types:
- Array: Denoted by square brackets, [ ], and can hold multiple values of any type.
- Object: Denoted by curly braces {}, these are key-value pairs where the key is a string and the value can be of any type.

Interaction Example:

{
  arr: [1, 2, 3, 4];
  obj: { name: "Bob", age: 25 };
  x: 5;
  y: "Alice";
  boolFlag: true;
}

4. Operations, Functions, Constants, Modifiers, Categories, and Variables

Operations:

Operations are predefined commands that manipulate data and return results.

add(x, y): Adds two numbers.
subtract(x, y): Subtracts y from x.
multiply(x, y): Multiplies two numbers.
divide(x, y): Divides x by y (raises an error if y is 0).

Functions:

Functions are user-defined commands that take input parameters, perform operations, and return results. Functions must be explicitly defined and invoked.

function addTwoNumbers(a, b) {
  return add(a, b);
}

result = addTwoNumbers(2, 3);

Constants:

Constants are fixed values that cannot be altered once declared. They are denoted by the const keyword.

const PI = 3.14159;

Modifiers:

Modifiers alter the behavior or scope of variables and operations. toaster.Json includes the following modifiers:

mutable: Indicates that a variable can be changed.
immutable: Forces a variable to remain constant after its initial assignment.

Categories:

Variables in toaster.Json are categorized based on scope:

Global: Accessible throughout the program.
Local: Only accessible within a block or function.

global x = 10;
function example() {
  local y = 5;
  return add(x, y);
}

5. Error Handling

Errors in toaster.Json are managed using the try-catch mechanism. Whenever a potential error might occur, the try block is used to attempt execution, and any errors are caught in the catch block.

try {
  result = divide(10, 0);
} catch (error) {
  log("Error occurred: ", error);
}

6. Grammar and Formal Rules for Combining Elements

Function Calls: Functions must be invoked with parentheses () containing arguments.
Assignment: Variable assignment is done using = and the type is inferred from the value.
Control Flow: Conditional statements (if, else) and loops (while, for) follow the traditional C-like grammar.

Formal Example:

{
  x: 5;
  y: 10;
  
  if (x < y) {
    z = add(x, y);
  } else {
    z = subtract(y, x);
  }
}

7. Language-Specific Utilities and Standard Libraries

toaster.Json comes with a set of standard utilities and libraries to perform common tasks, such as math operations, string manipulations, and array operations.

Standard Library Functions:

Math: sqrt(x), pow(base, exponent)
String: length(string), concat(string1, string2)
Array: push(array, element), pop(array)

8. Compiler-Specific Behavior for toaster.Json

The toaster.Json compiler interprets and translates source code into executable bytecode. The compiler includes the following steps:

Lexical Analysis: Tokenizes the source code.
Syntax Analysis: Ensures code follows syntax rules.
Semantic Analysis: Ensures operations are semantically valid.
Optimization: Optimizes the code for performance.
Bytecode Generation: Translates the code into machine-readable bytecode.

The toaster.Json compiler automatically manages memory and handles garbage collection.

9. List of Functions, Operations, and Modifiers

Functions:

add(x, y)
subtract(x, y)
multiply(x, y)
divide(x, y)
sqrt(x)
pow(base, exponent)

Operations:

Arithmetic: +, -, *, /
Logical: &&, ||, !
Comparison: ==, !=, >, <, >=, <=

Modifiers:

mutable
immutable
global
local

Bob and Alice Example:

{
  // Bob calculates his total balance
  bobBalance: 100;
  addAmount: 50;
  bobBalance = add(bobBalance, addAmount);

  // Alice checks if her balance is enough
  aliceBalance: 75;
  if (aliceBalance >= 100) {
    log("Alice has enough balance.");
  } else {
    log("Alice needs more funds.");
  }
}

Proof Example Using Pop 'n' Fresh Commands:

Arithmetic Proof:
- A + B = C can be formally represented as Pop A B add -> C.

Pop 'n' Fresh Language Specification (Version 1.0)

1. Syntax and Structure

1.1 Basic Elements

IDENTIFIER: [a-zA-Z_][a-zA-Z0-9_]*
NUMBER: [0-9]+(\.[0-9]+)?
STRING: "[^"]*"

1.2 Operators

Arithmetic: +, -, *, /, %, ^
Comparison: ==, !=, <, >, <=, >=
Logical: &&, ||, !
Assignment: :=

1.3 Delimiters

Parentheses: ()
Braces: {}
Brackets: []
Angle Brackets: <>

1.4 Keywords

DEF, IF, ELSE, LOOP, BREAK, CONTINUE, RETURN, TRY, CATCH, THROW, ASSERT

1.5 Comments

Single-line: // comment
Multi-line: /* comment */

2. Data Types

2.1 Primitive Types

INT: Integer
FLD: Field element
BOOL: Boolean
STR: String

2.2 Cryptographic Types

H256: 256-bit hash
PK: Public key
SK: Secret key
SIG: Signature
COMM: Commitment

2.3 Complex Types

VEC: Vector of type T
MAP: Map with key type K and value type V
OPT: Optional value of type T

2.4 Circuit-Specific Types

GATE: Circuit gate
WIRE: Circuit wire
CONSTRAINT: Circuit constraint

3. Functions and Control Flow

3.1 Function Definition

FUNC_NAME(param1:TYPE, param2:TYPE) -> RETURN_TYPE {
  // function body
}

3.2 Control Structures

If-Else:

IF (condition) {
  // code
} ELSE {
  // code
}

Loops:

LOOP {
  // code
  IF (condition) BREAK
}

Try-Catch:

TRY {
  // code
} CATCH (error_type) {
  // error handling
}

4. Cryptographic Operations

4.1 Hashing

HASH(data:VEC<INT>) -> H256

4.2 Signatures

SIGN(sk:SK, msg:VEC<INT>) -> SIG
VERIFY(pk:PK, msg:VEC<INT>, sig:SIG) -> BOOL

4.3 Encryption

ENC(pk:PK, msg:VEC<INT>) -> VEC<INT>
DEC(sk:SK, cipher:VEC<INT>) -> VEC<INT>

4.4 Zero-Knowledge Proofs

ZKP_GEN(circuit:VEC<CONSTRAINT>, witness:VEC<FLD>) -> PROOF
ZKP_VERIFY(circuit:VEC<CONSTRAINT>, proof:PROOF, public_input:VEC<FLD>) -> BOOL

4.5 Commitments

COMM_GEN(value:FLD, randomness:FLD) -> COMM
COMM_OPEN(comm:COMM, value:FLD, randomness:FLD) -> BOOL

4.6 Lattice-Based Cryptography

LWE_SAMPLE(s:VEC<FLD>, e:VEC<FLD>) -> VEC<FLD>
LWE_DECODE(c:VEC<FLD>, s:VEC<FLD>) -> FLD

4.7 Witness Encryption

WE_ENC(stmt:STR, msg:VEC<INT>) -> VEC<INT>
WE_DEC(ct:VEC<INT>, witness:VEC<FLD>) -> OPT<VEC<INT>>

4.8 Verifiable Delay Functions

VDF_SETUP(security_parameter:INT) -> VDF_PP
VDF_EVAL(pp:VDF_PP, input:VEC<INT>, time:INT) -> (VEC<INT>, PROOF)
VDF_VERIFY(pp:VDF_PP, input:VEC<INT>, output:VEC<INT>, proof:PROOF) -> BOOL

5. Circuit Operations

5.1 Circuit Construction

CIRCUIT_NEW() -> CIRCUIT
CIRCUIT_ADD_GATE(circuit:CIRCUIT, gate:GATE) -> CIRCUIT
CIRCUIT_CONNECT(circuit:CIRCUIT, wire1:WIRE, wire2:WIRE) -> CIRCUIT

5.2 Constraint Systems

CS_NEW() -> CS
CS_ADD_CONSTRAINT(cs:CS, constraint:CONSTRAINT) -> CS

5.3 Proof Systems

GROTH16_SETUP(cs:CS) -> GROTH16_PP
GROTH16_PROVE(pp:GROTH16_PP, witness:VEC<FLD>) -> PROOF
GROTH16_VERIFY(pp:GROTH16_PP, proof:PROOF, public_input:VEC<FLD>) -> BOOL

PLONK_SETUP(cs:CS) -> PLONK_PP
PLONK_PROVE(pp:PLONK_PP, witness:VEC<FLD>) -> PROOF
PLONK_VERIFY(pp:PLONK_PP, proof:PROOF, public_input:VEC<FLD>) -> BOOL

6. Advanced Cryptographic Constructs

6.1 Multi-Party Computation

MPC_INIT(parties:VEC<PK>) -> MPC_SESSION
MPC_CONTRIBUTE(session:MPC_SESSION, input:VEC<FLD>) -> MPC_STATE
MPC_COMPUTE(session:MPC_SESSION, function:FUNC) -> VEC<FLD>

6.2 Threshold Cryptography

TSS_KEYGEN(t:INT, n:INT) -> (VEC<SK>, PK)
TSS_SIGN(keys:VEC<SK>, msg:VEC<INT>) -> SIG
TSS_COMBINE(sigs:VEC<SIG>) -> SIG

6.3 Post-Quantum Cryptography

PQ_KEYGEN(security_parameter:INT) -> (PK, SK)
PQ_ENC(pk:PK, msg:VEC<INT>) -> VEC<INT>
PQ_DEC(sk:SK, cipher:VEC<INT>) -> VEC<INT>

7. Privacy-Preserving Protocols

7.1 Ring Signatures

RING_SIGN(sk:SK, msg:VEC<INT>, ring:VEC<PK>) -> RING_SIG
RING_VERIFY(msg:VEC<INT>, sig:RING_SIG, ring:VEC<PK>) -> BOOL

7.2 Blind Signatures

BLIND_SIGN(sk:SK, blinded_msg:VEC<INT>) -> BLIND_SIG
BLIND_VERIFY(pk:PK, msg:VEC<INT>, sig:BLIND_SIG) -> BOOL

7.3 Homomorphic Encryption

HE_KEYGEN(security_parameter:INT) -> (HE_PK, HE_SK)
HE_ENC(pk:HE_PK, msg:FLD) -> HE_CIPHER
HE_ADD(pk:HE_PK, c1:HE_CIPHER, c2:HE_CIPHER) -> HE_CIPHER
HE_MULT(pk:HE_PK, c1:HE_CIPHER, c2:HE_CIPHER) -> HE_CIPHER
HE_DEC(sk:HE_SK, c:HE_CIPHER) -> FLD

8. Blockchain-Specific Operations

8.1 Merkle Trees

MT_NEW() -> MT
MT_INSERT(mt:MT, leaf:H256) -> MT
MT_PROOF(mt:MT, leaf:H256) -> MT_PROOF
MT_VERIFY(root:H256, leaf:H256, proof:MT_PROOF) -> BOOL

8.2 State Channels

SC_OPEN(participants:VEC<PK>, initial_state:VEC<INT>) -> SC
SC_UPDATE(sc:SC, new_state:VEC<INT>, sigs:VEC<SIG>) -> SC
SC_CLOSE(sc:SC, final_state:VEC<INT>, sigs:VEC<SIG>) -> BOOL

8.3 zk-SNARKs

SNARK_SETUP(circuit:

CS) -> SNARK_PP
SNARK_PROVE(pp:SNARK_PP, witness:VEC<FLD>) -> SNARK_PROOF
SNARK_VERIFY(pp:SNARK_PP, proof:SNARK_PROOF, public_input:VEC<FLD>) -> BOOL

9. Performance Optimizations

9.1 Parallel Execution

PAR_EXEC(tasks:VEC<FUNC>) -> VEC<RESULT>

9.2 Lazy Evaluation

LAZY(expr:EXPR) -> LAZY_EXPR
FORCE(expr:LAZY_EXPR) -> RESULT

9.3 Memoization

MEMO(func:FUNC) -> MEMO_FUNC

10. Safety and Formal Verification

10.1 Invariant Checking

INVARIANT(condition:BOOL, msg:STR)

10.2 Pre and Post Conditions

PRE(condition:BOOL, msg:STR)
POST(condition:BOOL, msg:STR)

10.3 Formal Proof Generation

PROVE(theorem:EXPR) -> PROOF
CHECK_PROOF(theorem:EXPR, proof:PROOF) -> BOOL

11. Interoperability

11.1 Foreign Function Interface

FFI_IMPORT(language:STR, func:STR) -> FUNC
FFI_EXPORT(func:FUNC, language:STR) -> STR

11.2 Serialization

SERIALIZE(obj:T) -> VEC<INT>
DESERIALIZE(data:VEC<INT>, type:TYPE) -> T

12. Error Handling and Debugging

12.1 Custom Error Types

ERROR_TYPE(name:STR, fields:VEC<(STR, TYPE)>)

12.2 Debugging

DEBUG_PRINT(expr:EXPR)
STACK_TRACE() -> STR

12.2 Debugging (continued)

DEBUG_PRINT(expr:EXPR)

Description: Outputs the value of an expression or variable for debugging purposes.
Example:

DEBUG_PRINT(x) // Outputs the value of x

STACK_TRACE() -> STR

Description: Returns the current call stack as a string, which is useful for tracing the sequence of function calls leading to an error.
Example:

STR trace = STACK_TRACE();
DEBUG_PRINT(trace);

12.3 Error Handling

TRY {
  // Block of code that might throw an error
} CATCH (error_type) {
  // Code to handle the error
}

Description: TRY block executes the enclosed code. If an error occurs, control is transferred to the CATCH block, where the error is handled based on the error type.
Example:

TRY {
  x := divide(10, 0); // May cause a divide-by-zero error
} CATCH (DivideByZeroError) {
  DEBUG_PRINT("Error: Division by zero");
}

THROW(error_type)

Description: Raises an error of the specified type, allowing control to pass to the nearest CATCH block.
Example:

THROW(FileNotFoundError);

ASSERT(condition:BOOL, msg:STR)

Description: Checks if a condition is true. If the condition is false, the program throws an error with the provided message.
Example:

ASSERT(x > 0, "x must be greater than 0");

13. Interoperability

13.1 Foreign Function Interface (FFI)

FFI_IMPORT(language:STR, func:STR) -> FUNC

Description: Imports a function from an external language, making it callable from within Pop 'n' Fresh.
Example:

FUNC sqrt = FFI_IMPORT("C", "sqrt");

FFI_EXPORT(func:FUNC, language:STR) -> STR

Description: Exports a function to be used in an external language.
Example:

FFI_EXPORT(myFunc, "Python");

13.2 Serialization/Deserialization

SERIALIZE(obj:T) -> VEC<INT>

Description: Converts an object of any type T into a serialized vector of integers.
Example:

VEC<INT> serialized_obj = SERIALIZE(myObject);

DESERIALIZE(data:VEC<INT>, type:TYPE) -> T

Description: Converts a serialized vector of integers back into an object of type T.
Example:

MyType obj = DESERIALIZE(serialized_data, MyType);

14. Concurrency and Parallelism

14.1 Concurrency

ASYNC(func:FUNC) -> FUTURE<T>

Description: Executes a function asynchronously, returning a future that will hold the result when the operation completes.
Example:

FUTURE<INT> result = ASYNC(myAsyncFunction);

AWAIT(fut:FUTURE<T>) -> T

Description: Waits for the result of an asynchronous function and retrieves the value from the future.
Example:

INT value = AWAIT(result);

14.2 Parallel Execution

PAR_EXEC(tasks:VEC<FUNC>) -> VEC<RESULT>

Description: Executes a vector of tasks in parallel and returns a vector of results.
Example:

VEC<FUNC> tasks = [task1, task2, task3];
VEC<RESULT> results = PAR_EXEC(tasks);

15. Performance Optimizations

15.1 Lazy Evaluation

LAZY(expr:EXPR) -> LAZY_EXPR

Description: Delays the evaluation of an expression until its value is actually needed, improving performance when certain operations may not need to be computed immediately.
Example:

LAZY_EXPR delayed_expr = LAZY(expensive_computation());

FORCE(expr:LAZY_EXPR) -> RESULT

Description: Forces the evaluation of a lazy expression and returns the result.
Example:

RESULT computed_value = FORCE(delayed_expr);

15.2 Memoization

MEMO(func:FUNC) -> MEMO_FUNC

Description: Caches the results of function calls to avoid redundant computations, particularly for expensive operations.
Example:

MEMO_FUNC memoized_function = MEMO(expensive_function);

16. Formal Verification and Proofs

16.1 Invariant Checking

INVARIANT(condition:BOOL, msg:STR)

Description: Ensures that a certain condition remains true during program execution. If violated, the program will throw an error with the given message.
Example:

INVARIANT(balance >= 0, "Balance must not be negative");

16.2 Pre and Post Conditions

PRE(condition:BOOL, msg:STR)

Description: Defines a condition that must be true before a function is executed.
Example:

PRE(x > 0, "x must be positive");

POST(condition:BOOL, msg:STR)

Description: Defines a condition that must be true after a function has executed.
Example:

POST(result != NULL, "Result cannot be null");

16.3 Formal Proof Generation

PROVE(theorem:EXPR) -> PROOF

Description: Generates a formal proof for a given theorem or expression.
Example:

PROOF proof = PROVE(x + y == y + x);

CHECK_PROOF(theorem:EXPR, proof:PROOF) -> BOOL

Description: Verifies the validity of a provided proof against the theorem.
Example:

BOOL valid = CHECK_PROOF(theorem, proof);

17. Energy and Computation Symbols

17.1 Fast Computation

⚡:BUILD

Description: Represents fast computation or circuit building in a visual flow.

17.2 Heavy Computation

⚙:COMPUTE

Description: Represents computationally intensive operations, often used to highlight expensive tasks in visual output.

17.3 Parallel Computation

⧉:PARALLEL

Description: Indicates that an operation is executed in parallel with others. Used to visually represent parallel execution paths in the system.

17.4 Conditional Computation

⧫:CONDITIONAL

Description: Represents conditional computation that depends on specific branching logic (e.g., IF-ELSE). This symbol highlights sections of code where different paths may be taken based on evaluation results.

17.5 Looping Computation

↻:LOOP

Description: Signifies operations within a loop structure. This symbol is used to visualize repeated operations in graphical representations, often indicating iterative processes.

17.6 Delayed Computation

🕒:DELAYED

Description: Marks computations that are delayed or lazily evaluated. This symbol is typically used in conjunction with lazy evaluation structures where certain expressions are not immediately computed.

18. Advanced Proof Systems

18.1 Recursive SNARKs

REC_SNARK(circuit:CS) -> PROOF

Description: Generates a recursive SNARK proof for a given circuit, allowing the combination of multiple SNARKs into a single proof.
Example:

PROOF recursive_proof = REC_SNARK(circuit);

18.2 Bulletproofs

BP_PROVE(v:FLD, gamma:FLD) -> PROOF

Description: Generates a Bulletproof for a confidential transaction or statement.
Example:

PROOF bp_proof = BP_PROVE(v, gamma);

BP_VERIFY(proof:PROOF, comm:COMM) -> BOOL

Description: Verifies the correctness of a Bulletproof against a commitment.
Example:

BOOL valid = BP_VERIFY(bp_proof, commitment);

19. Multi-Party Computation

19.1 Secure Multi-Party Computation

MPC_PROTOCOL(parties:VEC<PK>, inputs:VEC<FLD>) -> VEC<FLD>

Description: Executes a secure multi-party computation protocol where multiple parties contribute inputs and receive results without revealing their individual inputs.
Example:

VEC<FLD> result = MPC_PROTOCOL([party1, party2], [input1, input2]);

19.2 Oblivious Transfer

OT_SEND(m0:VEC<INT>, m1:VEC<INT>) -> OT_MESSAGE

Description: Sends two messages in an oblivious transfer protocol.
Example:

OT_MESSAGE message = OT_SEND(msg0, msg1);

OT_RECEIVE(b:BOOL) -> VEC<INT>

Description: Receives one of the two messages in an oblivious transfer based on a secret bit b.
Example:

VEC<INT> received_message = OT_RECEIVE(true);

20. Quantum-Resistant Cryptography

20.1 Lattice-Based Encryption

LWE_ENC(pk:PK, msg:FLD) -> CIPHER

Description: Encrypts a message using lattice-based encryption (Learning With Errors).
Example:

CIPHER cipher = LWE_ENC(public_key, message);

LWE_DEC(sk:SK, cipher:CIPHER) -> FLD

Description: Decrypts a message using lattice-based encryption.
Example:

FLD message = LWE_DEC(secret_key, cipher);

20.2 Hash-Based Signatures

SPHINCS_SIGN(sk:SK, msg:VEC<INT>) -> SIG

Description: Signs a message using SPHINCS+ hash-based signature scheme.
Example:

SIG signature = SPHINCS_SIGN(secret_key, message);

SPHINCS_VERIFY(pk:PK, msg:VEC<INT>, sig:SIG) -> BOOL

Description: Verifies a SPHINCS+ signature.
Example:

BOOL valid = SPHINCS_VERIFY(public_key, message, signature);

21. Privacy-Enhancing Technologies

21.1 Mix Networks

MIX_NET(participants:VEC<PK>, msgs:VEC<INT>) -> VEC<INT>

Description: Implements a mix network for message obfuscation, ensuring that the output messages are anonymized.
Example:

VEC<INT> mixed_msgs = MIX_NET([pk1, pk2, pk3], [msg1, msg2, msg3]);

21.2 Garbled Circuits

GARBLED_CIRCUIT(input_labels:VEC<INT>, gates:VEC<GATE>) -> CIRCUIT

Description: Constructs a garbled circuit for secure multi-party computation.
Example:

CIRCUIT gc = GARBLED_CIRCUIT(input_labels, circuit_gates);

EVALUATE_GARBLED(circuit:CIRCUIT, input:VEC<INT>) -> VEC<INT>

Description: Evaluates a garbled circuit and returns the output.
Example:

VEC<INT> output = EVALUATE_GARBLED(gc, inputs);

22. Blockchain-Specific Operations

22.1 Smart Contract Interaction

SC_CALL(contract:SC, method:STR, args:VEC<INT>) -> RESULT

Description: Calls a method on a smart contract with the specified arguments and returns the result.
Example:

RESULT res = SC_CALL(my_contract, "transfer", [amount, recipient]);

SC_DEPLOY(code:VEC<INT>, init_state:VEC<INT>) -> SC

Description: Deploys a smart contract with the provided code and initial state.
Example:

SC contract = SC_DEPLOY(contract_code, initial_state);

22.2 Layer 2 Scaling

L2_BATCH(txns:VEC<INT>) -> BATCH

Description: Bundles multiple transactions into a batch for Layer 2 scalability.
Example:

BATCH batch = L2_BATCH([txn1, txn2, txn3]);

L2_COMMIT(batch:BATCH) -> RESULT

Description: Commits a batch of Layer 2 transactions to the Layer 1 blockchain.
Example:

RESULT commit_result = L2_COMMIT(batch);

22.3 zk-SNARK-Based Smart Contract Verification

SC_ZK_VERIFY(proof:SNARK_PROOF, public_input:VEC<FLD>, contract:SC) -> BOOL

Description: Verifies a zk-SNARK proof on-chain using the smart contract, ensuring that the proof is valid for the provided public inputs.
Example:

BOOL verified = SC_ZK_VERIFY(proof, public_input, my_contract);

22.4 Merkle Tree Operations in Smart Contracts

SC_MT_INSERT(contract:SC, leaf:H256) -> SC

Description: Inserts a leaf into a Merkle tree within a smart contract and updates the contract’s state.
Example:

SC updated_contract = SC_MT_INSERT(my_contract, new_leaf);

SC_MT_VERIFY(contract:SC, root:H256, leaf:H256, proof:MT_PROOF) -> BOOL

Description: Verifies that a leaf belongs to a Merkle tree with the given root, using a proof inside the smart contract.
Example:

BOOL valid = SC_MT_VERIFY(my_contract, root_hash, leaf_hash, proof);

23. Advanced Cryptographic Protocols

23.1 Oblivious Transfer in Secure Computation

OT_PROTOCOL(participants:VEC<PK>, choices:VEC<BOOL>, msgs:VEC<VEC<INT>>) -> VEC<INT>

Description: Implements an oblivious transfer protocol between participants, where each party receives a message based on their secret choices.
Example:

VEC<INT> received_msgs = OT_PROTOCOL([pk1, pk2], [true, false], [[msg1a, msg1b], [msg2a, msg2b]]);

23.2 Secure Multiparty Computation with Garbled Circuits

MPC_GARBLED_CIRCUIT(inputs:VEC<INT>, circuit:CIRCUIT) -> VEC<INT>

Description: Executes a secure multiparty computation using garbled circuits, with each party providing inputs and the circuit computing the result securely.
Example:

VEC<INT> result = MPC_GARBLED_CIRCUIT([input1, input2], secure_circuit);

24. Formal Verification and Model Checking

24.1 Formal Proof Steps

FORMAL_PROOF(steps:VEC<EXPR>) -> PROOF

Description: Constructs a formal proof by evaluating a series of logical steps or expressions.
Example:

PROOF proof = FORMAL_PROOF([step1, step2, step3]);

24.2 Model Checking

MODEL_CHECK(model:EXPR, property:EXPR) -> BOOL

Description: Verifies that a model satisfies a given property, ensuring correctness in a formal system.
Example:

BOOL result = MODEL_CHECK(system_model, safety_property);

25. Quantum-Safe Key Exchange

25.1 Lattice-Based Key Exchange

LWE_KEY_EXCHANGE(participant1:PK, participant2:PK) -> (SK, PK)

Description: Generates shared keys using a lattice-based key exchange protocol, which is quantum-resistant.
Example:

(SK, PK) keys = LWE_KEY_EXCHANGE(pk1, pk2);

25.2 Hash-Based Key Derivation

HKDF(input_key:FLD, salt:FLD, info:STR) -> FLD

Description: Derives a key from input material using a hash-based key derivation function (HKDF).
Example:

FLD derived_key = HKDF(input_key, salt, "key derivation info");

25.3 Post-Quantum Digital Signatures

PQ_SIGN(sk:SK, msg:VEC<INT>) -> SIG

Description: Generates a quantum-resistant digital signature for a message using a post-quantum signature algorithm.
Example:

SIG pq_signature = PQ_SIGN(secret_key, message);

PQ_VERIFY(pk:PK, msg:VEC<INT>, sig:SIG) -> BOOL

Description: Verifies the quantum-resistant digital signature against the message and public key.
Example:

BOOL is_valid = PQ_VERIFY(public_key, message, pq_signature);

26. Error Handling in Cryptographic Operations

26.1 Error Types in Cryptography

ERROR_TYPE(CryptoError, [(message:STR), (code:INT)])

Description: Defines a custom error type for cryptographic failures, including a descriptive message and error code.
Example:

THROW(CryptoError("Invalid key length", 1001));

26.2 Error Propagation in Secure Functions

FUNC safe_decrypt(sk:SK, cipher:VEC<INT>) -> OPT<VEC<INT>> {
  TRY {
    RETURN DEC(sk, cipher);
  } CATCH (CryptoError) {
    RETURN OPT<>; // Return empty if decryption fails
  }
}

Description: Uses a TRY-CATCH block to handle cryptographic errors during decryption. If decryption fails, the function returns an empty optional value.
Example:

OPT<VEC<INT>> plaintext = safe_decrypt(secret_key, ciphertext);

27. Cross-Platform Cryptographic Support

27.1 FFI for Cryptographic Libraries

FFI_IMPORT("C", "openssl_encrypt") -> FUNC

Description: Imports a cryptographic function from an external C library (e.g., OpenSSL) into Pop 'n' Fresh for encryption.
Example:

FUNC encrypt = FFI_IMPORT("C", "openssl_encrypt");
VEC<INT> cipher = encrypt(message, key);

27.2 Exporting Functions to External Cryptographic Systems

FFI_EXPORT(hash_function, "Rust")

Description: Exports a Pop 'n' Fresh cryptographic function for use in an external Rust-based cryptographic system.
Example:

FFI_EXPORT(PQ_HASH, "Rust");

28. Security Auditing and Verification

28.1 Static Security Analysis

SEC_ANALYZE(code:STR) -> REPORT

Description: Performs static analysis on a block of code to detect potential security vulnerabilities or unsafe cryptographic practices.
Example:

REPORT security_report = SEC_ANALYZE(contract_code);

28.2 Formal Security Proofs

SEC_PROVE(theorem:EXPR) -> PROOF

Description: Generates a formal proof to verify the security properties of a given cryptographic protocol or algorithm.
Example:

PROOF security_proof = SEC_PROVE(security_theorem);

29. Energy-Efficient Cryptographic Primitives

29.1 Optimized Elliptic Curve Cryptography (ECC)

ECC_MUL(k:FLD, P:POINT) -> POINT

Description: Computes the elliptic curve multiplication of a point P by a scalar k using an energy-optimized algorithm.
Example:

POINT result = ECC_MUL(scalar, base_point);

29.2 Low-Power Cryptographic Hashing

LP_HASH(data:VEC<INT>) -> H256

Description: Computes a cryptographic hash using a low-power hashing algorithm optimized for energy-constrained environments.
Example:

H256 hash_result = LP_HASH(sensor_data);

30. Formal Verification for Energy Optimization

30.1 Proof of Energy Efficiency

ENERGY_PROVE(func:FUNC) -> PROOF

Description: Proves that a given function meets specific energy efficiency constraints, ensuring that its cryptographic operations are optimized for low energy consumption.
Example:

PROOF energy_proof = ENERGY_PROVE(ECC_MUL);

30.2 Energy-Aware Function Profiling

ENERGY_PROFILE(func:FUNC) -> REPORT

Description: Profiles the energy consumption of a function, generating a detailed report on its energy usage during execution. This is particularly useful for optimizing cryptographic operations in constrained environments.
Example:

REPORT energy_report = ENERGY_PROFILE(LP_HASH);

30.3 Energy Constraints Enforcement

SET_ENERGY_LIMIT(func:FUNC, limit:INT)

Description: Sets an upper limit on the energy consumption for a function. If the function exceeds the specified energy limit during execution, an error will be thrown.
Example:

SET_ENERGY_LIMIT(ECC_MUL, 1000); // Sets a maximum energy usage of 1000 units

31. Quantum-Resistant Primitives with Energy Optimization

31.1 Energy-Efficient Lattice-Based Encryption

LWE_ENC_EFFICIENT(pk:PK, msg:FLD) -> CIPHER

Description: Performs lattice-based encryption optimized for low energy consumption, while maintaining post-quantum security.
Example:

CIPHER cipher = LWE_ENC_EFFICIENT(public_key, message);

31.2 Energy-Constrained Post-Quantum Signatures

PQ_SIGN_EFFICIENT(sk:SK, msg:VEC<INT>) -> SIG

Description: Generates a post-quantum digital signature optimized for low energy usage.
Example:

SIG pq_signature = PQ_SIGN_EFFICIENT(secret_key, message);

31.3 Energy-Optimized zk-SNARK Verification

ZK_VERIFY_EFFICIENT(proof:SNARK_PROOF, public_input:VEC<FLD>) -> BOOL

Description: Verifies a zk-SNARK proof using an energy-efficient verification algorithm. Useful for lightweight, on-chain proof verification.
Example:

BOOL verified = ZK_VERIFY_EFFICIENT(proof, public_input);

32. Advanced Blockchain Energy Management

32.1 Energy-Limited Smart Contract Execution

SC_SET_ENERGY_LIMIT(contract:SC, limit:INT)

Description: Sets an energy usage limit for smart contract execution. If the contract exceeds this limit during operation, it will revert to its previous state.
Example:

SC_SET_ENERGY_LIMIT(my_contract, 5000);

32.2 Energy Tracking for Transactions

TX_TRACK_ENERGY(tx:TX) -> REPORT

Description: Tracks and reports the energy consumption of a blockchain transaction, providing insights into how energy is used during execution.
Example:

REPORT energy_usage = TX_TRACK_ENERGY(my_transaction);

33. Energy Auditing and Optimization

33.1 Static Energy Analysis

ENERGY_ANALYZE(code:STR) -> REPORT

Description: Analyzes the energy consumption of a block of code, highlighting potential areas for optimization.
Example:

REPORT energy_analysis = ENERGY_ANALYZE(contract_code);

33.2 Dynamic Energy Profiling

DYNAMIC_ENERGY_PROFILE(func:FUNC) -> REPORT

Description: Profiles the energy consumption of a function at runtime, providing real-time feedback on its energy usage.
Example:

REPORT dynamic_profile = DYNAMIC_ENERGY_PROFILE(PQ_SIGN_EFFICIENT);

33.3 Energy Consumption Audits

AUDIT_ENERGY_USAGE(contract:SC) -> REPORT

Description: Audits the energy usage of a smart contract over a defined period, generating a comprehensive report that can be used for optimizing future executions.
Example:

REPORT audit = AUDIT_ENERGY_USAGE(my_contract);

33.4 Energy Efficiency Recommendations

ENERGY_OPTIMIZE_REPORT(report:REPORT) -> VEC<RECOMMENDATION>

Description: Analyzes the results of an energy consumption audit or profile and provides a set of recommendations for improving the energy efficiency of the code or smart contract.
Example:

VEC<RECOMMENDATION> optimizations = ENERGY_OPTIMIZE_REPORT(audit);

33.5 Real-Time Energy Monitoring

REALTIME_ENERGY_MONITOR(contract:SC) -> REPORT

Description: Continuously monitors the energy consumption of a smart contract in real-time, producing ongoing reports that can be used for immediate adjustments to execution or optimization strategies.
Example:

REPORT real_time_monitor = REALTIME_ENERGY_MONITOR(my_contract);

33.6 Energy-Based Contract Throttling

SC_THROTTLE_ON_ENERGY(contract:SC, threshold:INT)

Description: Automatically throttles the execution speed of a smart contract if its energy consumption exceeds a specified threshold. This can help prevent contracts from depleting resources too quickly.
Example:

SC_THROTTLE_ON_ENERGY(my_contract, 10000);

34. Energy Efficient zk-SNARK Circuits

34.1 Low-Energy zk-SNARK Circuit Generation

ZK_CIRCUIT_GEN_EFFICIENT(constraints:VEC<CONSTRAINT>, inputs:VEC<FLD>) -> CIRCUIT

Description: Generates a zk-SNARK circuit optimized for minimal energy consumption, ideal for use in resource-constrained environments such as mobile devices or lightweight nodes.
Example:

CIRCUIT energy_efficient_circuit = ZK_CIRCUIT_GEN_EFFICIENT(constraints, public_inputs);

34.2 Optimized zk-SNARK Proof Generation

ZK_PROOF_GEN_EFFICIENT(circuit:CIRCUIT, witness:VEC<FLD>) -> PROOF

Description: Generates a zk-SNARK proof using energy-optimized algorithms, reducing the computational overhead typically associated with proof generation.
Example:

PROOF optimized_proof = ZK_PROOF_GEN_EFFICIENT(energy_efficient_circuit, witness);

35. Energy-Constrained Blockchain Protocols

35.1 Proof of Work with Energy Constraints

POW_ENERGY_LIMIT(mining_func:FUNC, max_energy:INT) -> BLOCK

Description: Limits the energy consumption of a proof-of-work mining function. If the energy limit is exceeded, the function terminates without completing the block.
Example:

BLOCK new_block = POW_ENERGY_LIMIT(mine_block, 5000);

35.2 Energy-Aware Consensus Mechanisms

CONSENSUS_ENERGY_AWARE(nodes:VEC<NODE>, energy_limits:VEC<INT>) -> NODE

Description: Implements a consensus mechanism that takes into account the energy constraints of participating nodes, selecting the node that can perform the consensus action within its energy budget.
Example:

NODE leader = CONSENSUS_ENERGY_AWARE(node_list, energy_limits);

35.3 Energy-Efficient Proof of Stake

POS_ENERGY_AWARE(stakeholders:VEC<NODE>, energy_threshold:INT) -> NODE

Description: Selects a validator for a proof-of-stake system, optimizing for nodes that meet energy efficiency requirements. Validators are chosen not only based on their stake but also on their ability to operate within the specified energy threshold.
Example:

NODE validator = POS_ENERGY_AWARE(stakeholder_list, 3000);

35.4 Energy-Optimized Block Validation

BLOCK_VALIDATE_ENERGY(block:BLOCK, energy_limit:INT) -> BOOL

Description: Validates a block while ensuring the total energy consumption during validation does not exceed the given limit. If the process exceeds the limit, validation halts and returns false.
Example:

BOOL is_valid = BLOCK_VALIDATE_ENERGY(new_block, 5000);

35.5 Energy-Aware Transaction Processing

TX_PROCESS_ENERGY_AWARE(tx:TX, max_energy:INT) -> RESULT

Description: Processes a transaction within a smart contract or blockchain environment, enforcing a maximum energy consumption limit during execution.
Example:

RESULT tx_result = TX_PROCESS_ENERGY_AWARE(my_transaction, 2000);

36. Energy-Constrained Blockchain Governance

36.1 Energy-Limited Voting Mechanisms

VOTE_ENERGY_AWARE(voters:VEC<NODE>, proposals:VEC<STR>, max_energy:INT) -> STR

Description: Conducts a voting process among blockchain nodes, ensuring that each voter remains within an energy usage limit during the voting process.
Example:

STR winning_proposal = VOTE_ENERGY_AWARE(node_list, proposal_list, 1000);

36.2 Governance Proposal Energy Analysis

ANALYZE_PROPOSAL_ENERGY(proposal:STR) -> REPORT

Description: Analyzes the energy implications of a governance proposal, generating a detailed report on its potential energy consumption and recommending optimizations if necessary.
Example:

REPORT proposal_analysis = ANALYZE_PROPOSAL_ENERGY("Upgrade block size");

37. Energy-Efficient Layer 2 Solutions

37.1 Layer 2 Transaction Batching with Energy Constraints

L2_BATCH_ENERGY(txns:VEC<TX>, energy_limit:INT) -> BATCH

Description: Batches transactions into a Layer 2 block, ensuring the total energy consumption for processing the batch remains within the specified limit.
Example:

BATCH tx_batch = L2_BATCH_ENERGY(transaction_list, 3000);

37.2 Optimized Rollup Execution

ROLLUP_EXEC_ENERGY(rollup:ROLLUP, energy_limit:INT) -> RESULT

Description: Executes a Layer 2 rollup while enforcing a maximum energy limit. Ensures that the rollup process is energy-efficient while maintaining security and correctness.
Example:

RESULT rollup_result = ROLLUP_EXEC_ENERGY(layer2_rollup, 4000);

37.3 Layer 2 Energy-Aware State Channels

SC_UPDATE_ENERGY_AWARE(sc:SC, new_state:VEC<INT>, sigs:VEC<SIG>, energy_limit:INT) -> SC

Description: Updates the state of a Layer 2 state channel with an energy consumption limit, preventing resource exhaustion during the update process.
Example:

SC updated_channel = SC_UPDATE_ENERGY_AWARE(my_state_channel, new_state, signatures, 2500);

38. Advanced Blockchain Energy Auditing

38.1 Comprehensive Blockchain Energy Audit

BLOCKCHAIN_ENERGY_AUDIT(blockchain:BC, time_period:INT) -> REPORT

Description: Conducts an in-depth energy audit of a blockchain over a specified time period, generating a detailed report on overall energy consumption, efficiency improvements, and recommendations.
Example:

REPORT energy_audit = BLOCKCHAIN_ENERGY_AUDIT(my_blockchain, 30); // Audit over 30 days

38.2 Energy Cost Prediction for Transactions

TX_ENERGY_COST_PREDICT(tx:TX) -> INT

Description: Predicts the energy cost of processing a given transaction before execution, providing insight into whether the transaction will meet predefined energy limits.
Example:

INT predicted_cost = TX_ENERGY_COST_PREDICT(my_transaction);

38.3 Energy Efficiency Comparison for Consensus Algorithms

CONSENSUS_ENERGY_COMPARE(algo1:FUNC, algo2:FUNC) -> REPORT

Description: Compares the energy efficiency of two different consensus algorithms, producing a report that details their relative energy consumption, scalability, and impact on network resources.
Example:

REPORT energy_comparison = CONSENSUS_ENERGY_COMPARE(ProofOfWork, ProofOfStake);

38.4 Real-Time Energy Usage Alerts

ENERGY_ALERT(contract:SC, threshold:INT) -> BOOL

Description: Monitors the real-time energy consumption of a smart contract and triggers an alert if it exceeds the specified energy threshold.
Example:

BOOL alert_triggered = ENERGY_ALERT(my_contract, 5000);

38.5 Energy-Aware Transaction Fees

TX_FEE_ENERGY_AWARE(tx:TX, energy_usage:INT) -> INT

Description: Calculates the transaction fee based on the energy usage of the transaction. This incentivizes energy-efficient transactions and penalizes those that consume excessive resources.
Example:

INT tx_fee = TX_FEE_ENERGY_AWARE(my_transaction, predicted_energy_usage);

39. Optimizing Smart Contract Performance

39.1 Gas and Energy Correlation Analysis

GAS_ENERGY_ANALYZE(contract:SC) -> REPORT

Description: Analyzes the relationship between gas consumption and energy usage for a given smart contract, providing insights for optimizing both costs and energy efficiency.
Example:

REPORT gas_energy_report = GAS_ENERGY_ANALYZE(my_contract);

39.2 Contract Rewriting for Energy Optimization

CONTRACT_OPTIMIZE_ENERGY(code:STR) -> STR

Description: Automatically rewrites a smart contract to improve its energy efficiency, applying a series of optimization techniques to reduce computational overhead.
Example:

STR optimized_code = CONTRACT_OPTIMIZE_ENERGY(original_contract_code);

39.3 Energy Consumption Benchmarks for Smart Contracts

SC_BENCHMARK_ENERGY(contract:SC) -> REPORT

Description: Benchmarks the energy consumption of a smart contract across multiple test scenarios, producing a comprehensive report that details the contract's performance and energy profile.
Example:

REPORT benchmark_report = SC_BENCHMARK_ENERGY(my_contract);

39.4 Energy-Optimized Smart Contract Deployment

SC_DEPLOY_ENERGY_AWARE(code:STR, init_state:VEC<INT>, max_energy:INT) -> SC

Description: Deploys a smart contract with an energy usage cap, ensuring that both the deployment process and the contract’s initial state setup remain within a defined energy budget.
Example:

SC new_contract = SC_DEPLOY_ENERGY_AWARE(optimized_code, initial_state, 5000);

39.5 Energy-Constrained Contract Execution

SC_EXECUTE_ENERGY_AWARE(contract:SC, method:STR, args:VEC<INT>, max_energy:INT) -> RESULT

Description: Executes a method on a smart contract, enforcing a limit on the energy consumed during the operation. If the energy limit is exceeded, the execution is halted.
Example:

RESULT execution_result = SC_EXECUTE_ENERGY_AWARE(my_contract, "transfer", [recipient, amount], 3000);

39.6 Energy-Efficient Contract Upgrades

SC_UPGRADE_ENERGY_AWARE(contract:SC, new_code:STR, max_energy:INT) -> SC

Description: Upgrades an existing smart contract to a new version, ensuring that the upgrade process consumes energy within the specified limits.
Example:

SC upgraded_contract = SC_UPGRADE_ENERGY_AWARE(my_contract, updated_code, 4000);

40. Blockchain Network-Wide Energy Optimization

40.1 Network-Wide Energy Monitoring

NETWORK_ENERGY_MONITOR(nodes:VEC<NODE>) -> REPORT

Description: Monitors the energy consumption of all nodes in a blockchain network, generating a report that details network-wide energy usage and highlights areas for optimization.
Example:

REPORT network_energy_report = NETWORK_ENERGY_MONITOR(blockchain_nodes);

40.2 Energy-Efficient Node Selection for Block Validation

NODE_SELECT_ENERGY_AWARE(nodes:VEC<NODE>, energy_threshold:INT) -> NODE

Description: Selects a node for block validation based on its energy consumption profile, ensuring that the chosen node can complete the task within the specified energy threshold.
Example:

NODE selected_node = NODE_SELECT_ENERGY_AWARE(network_nodes, 2000);

40.3 Consensus Protocol Energy Optimization

CONSENSUS_OPTIMIZE_ENERGY(protocol:STR, max_energy:INT) -> STR

Description: Optimizes a consensus protocol to operate within a specified energy limit, reducing unnecessary energy consumption while maintaining network security and performance.
Example:

STR optimized_protocol = CONSENSUS_OPTIMIZE_ENERGY("ProofOfStake", 10000);

41. Advanced Functionality for Core Programming Commands

41.1 Function Overloading

FUNC_NAME(param1:TYPE) -> RETURN_TYPE
FUNC_NAME(param1:TYPE, param2:TYPE) -> RETURN_TYPE

Description: Supports function overloading, where multiple functions with the same name can be defined with different parameters.
Example:

FUNC add(x:INT) -> INT {
  RETURN x + 1;
}
FUNC add(x:INT, y:INT) -> INT {
  RETURN x + y;
}

41.2 Variable Scope

local_var := value; // Local scope
global_var := value; // Global scope

Description: Defines variable scoping rules. Local variables exist within the function or block, while global variables are accessible throughout the program.
Example:

global x := 5;

FUNC example() {
  local y := 10;
  RETURN x + y;
}

41.3 Default Parameters

FUNC_NAME(param1:TYPE, param2:TYPE = default_value) -> RETURN_TYPE

Description: Allows functions to have default parameters, providing flexibility when calling functions without needing to pass every argument.
Example:

FUNC greet(name:STR, message:STR = "Hello") -> STR {
  RETURN message + " " + name;
}

41.4 Optional Parameters

FUNC_NAME(param1:TYPE, param2:OPT<INT>) -> RETURN_TYPE

Description: Defines optional parameters, allowing certain arguments to be passed or omitted in function calls.
Example:

FUNC multiply(x:INT, y:OPT<INT>) -> INT {
  RETURN IF y != NULL THEN x * y ELSE x;
}

42. Intermediate Programming Features

42.1 Lambda Functions

lambda := (param1:TYPE, param2:TYPE) -> RETURN_TYPE {
  // Body
}

Description: Defines anonymous functions (lambdas) that can be passed around as first-class citizens.
Example:

lambda := (x:INT, y:INT) -> INT {
  RETURN x + y;
};

result := lambda(3, 4); // Outputs 7

42.2 Closures

closure := FUNC_NAME(param1:TYPE) -> FUNC

Description: Supports closures, where a function can capture variables from its outer scope and retain access to them after the outer scope has finished execution.
Example:

FUNC make_multiplier(factor:INT) -> FUNC {
  RETURN (x:INT) -> INT {
    RETURN x * factor;
  };
}

double := make_multiplier(2);
result := double(5); // Outputs 10

42.3 Pattern Matching

MATCH expression {
  CASE pattern1: // code
  CASE pattern2: // code
  DEFAULT: // code
}

Description: Implements pattern matching, allowing the programmer to perform conditional actions based on the structure of data.
Example:

FUNC process(value:VEC<INT>) -> STR {
  MATCH value {
    CASE [1, 2, 3]: RETURN "Sequence matched!";
    CASE [_, _, _]: RETURN "Three elements!";
    DEFAULT: RETURN "No match!";
  }
}

43. Advanced Programming Constructs

43.1 Meta-Programming

macro MACRO_NAME(params) {
  // Body
}

Description: Introduces macros that allow the programmer to write code that generates other code, providing flexibility and reducing redundancy.
Example:

macro LOG(expr:EXPR) {
  DEBUG_PRINT(expr);
  RETURN expr;
}

result := LOG(x + y); // Prints x + y, then returns the result

43.2 Type Inference

var_name := value;

Description: Allows the language to infer the type of a variable based on its initial value.
Example:

x := 42; // Inferred as INT
name := "Alice"; // Inferred as STR

43.3 Coroutines

COROUTINE func_name() -> YIELD_TYPE {
  // Body
}

Description: Supports coroutines, which are functions that can yield execution and be resumed later, enabling non-blocking asynchronous behavior.
Example:

COROUTINE producer() -> INT {
  FOR i := 0 TO 10 {
    YIELD i;
  }
}

result := producer(); // Yields values 0 to 10 incrementally

44. Error Handling Mechanisms

44.1 Custom Error Types

ERROR_TYPE(name:STR, fields:VEC<(STR, TYPE)>)

Description: Allows the creation of custom error types with specific fields to represent different error conditions.
Example:

ERROR_TYPE(InvalidInputError, [(message:STR), (code:INT)]);

THROW(InvalidInputError("Invalid input provided", 101));

44.2 Chained Error Handling

TRY {
  // Code
} CATCH (error1:ErrorType1) {
  // Handle error1
} CATCH (error2:ErrorType2) {
  // Handle error2
}

Description: Enables multiple CATCH blocks to handle different types of errors, chaining error handling mechanisms for robustness.
Example:

TRY {
  result := divide(10, 0);
} CATCH (DivideByZeroError) {
  DEBUG_PRINT("Cannot divide by zero!");
} CATCH (InvalidInputError) {
  DEBUG_PRINT("Invalid input!");
}

45. Data Structures and Complex Types

45.1 Enumerations (Enums)

enum ENUM_NAME {
  VALUE1,
  VALUE2,
  VALUE3
}

Description: Defines enumerations to represent a set of named constant values, which can improve readability and reduce errors in handling predefined choices.
Example:

enum Color {
  RED,
  GREEN,
  BLUE
}

color := Color.RED;

45.2 Tuples

tuple_name := (value1, value2, value3);

Description: Supports tuples, which are ordered collections of heterogeneous values that can be used for returning multiple values from functions or packing related data together.
Example:

tuple := (42, "Alice", true);
x, name, flag := tuple;

45.3 Records

record RECORD_NAME {
  field1: TYPE;
  field2: TYPE;
  // More fields
}

Description: Allows the creation of records (similar to structs), which group multiple fields together, providing a way to define custom types.
Example:

record Person {
  name: STR;
  age: INT;
}

p := Person {name: "Bob", age: 30};

46. Concurrency and Parallelism

46.1 Parallel Task Execution

PAR_EXEC(tasks:VEC<FUNC>) -> VEC<RESULT>

Description: Executes multiple tasks in parallel, returning the results once all tasks have completed.
Example:

tasks := [task1, task2, task3];
results := PAR_EXEC(tasks);

46.2 Synchronization Primitives

LOCK(mutex:MUTEX) {
  // Critical section
}

Description: Provides basic synchronization mechanisms like locks and mutexes to control access to shared resources in concurrent programming.
Example:

LOCK(resource_mutex) {
  shared_resource := shared_resource + 1;
}

46.3 Thread Management

THREAD_START(func:FUNC) -> THREAD
THREAD_JOIN(thread:THREAD) -> RESULT

Description: Supports thread creation and management, allowing functions to run in separate threads and be joined later for result retrieval.
Example:

thread := THREAD_START(worker_function);
result := THREAD_JOIN(thread);

Visual Output Specification to Match the Programming Logic

1. Syntax and Structure

1.1 Component Box Representation

Visual representation of programming components such as functions, variables, and expressions:

╔═════════════════════════════════════╗
║ Component Name                      ║
╚═════════════════════════════════════╝

Purpose: This box visually encloses any logical operation or function.
Example: Representing a function call visually.

╔══════════════════════╗
║ add(5, 10)           ║
╚══════════════════════╝

1.2 Data Flow Indicator

The visual representation of how data flows between components.

──▶

Purpose: Indicates data movement from one part of the system to another.
Example:

╔══════════════════════╗   ──▶   ╔══════════════════════╗
║ add(5, 10)           ║         ║ result: 15           ║
╚══════════════════════╝         ╚══════════════════════╝

1.3 Assignment Representation

A visual output for assignment operations.

:=

Purpose: Represents the assignment of a value to a variable.
Example:

╔════════════════════════╗
║ x := 5                 ║
╚════════════════════════╝

2. Data Types and Structures

2.1 Primitive Types Box

Each data type will be encapsulated in a separate box:

╔══════════════════════╗
║ INT                  ║
╚══════════════════════╝
╔══════════════════════╗
║ STR                  ║
╚══════════════════════╝

Example:

╔═════════════╗        ╔═════════════╗
║ x: INT      ║  ──▶   ║ y: STR      ║
╚═════════════╝        ╚═════════════╝

2.2 Complex Types Visualization

Visual output for structures like VEC and MAP.

╔════════════════════════════╗
║ VEC<INT>                   ║
║ ────────────               ║
║ [1, 2, 3]                  ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ MAP<STR, INT>              ║         ║ VEC<INT>                   ║
║ ────────────               ║         ║ ────────────               ║
║ { "age" : 30 }             ║         ║ [1, 2, 3]                  ║
╚════════════════════════════╝         ╚════════════════════════════╝

3. Functions and Control Flow

3.1 Function Definition

Each function is represented visually with input/output flows.

╔══════════════════════╗
║ FUNC add(x, y)       ║
║ ───────────────      ║
║ RETURN x + y         ║
╚══════════════════════╝

Example:

╔══════════════════════╗   ──▶   ╔══════════════════════╗
║ FUNC add(x, y)       ║         ║ RETURN x + y         ║
║ ───────────────      ║         ║ result := 15         ║
╚══════════════════════╝         ╚══════════════════════╝

3.2 If-Else Control Flow

Visual output for IF-ELSE structures.

╔══════════════════════╗
║ IF condition         ║
╚══════════════════════╝
        │
   ┌────┴────┐
   ▼         ▼
╔══════════╗  ╔══════════╗
║ True     ║  ║ False    ║
╚══════════╝  ╚══════════╝

Example:

╔══════════════════════╗
║ IF x > 10            ║
╚══════════════════════╝
        │
   ┌────┴────┐
   ▼         ▼
╔════════════╗   ╔════════════╗
║ x := x + 1 ║   ║ x := x - 1 ║
╚════════════╝   ╚════════════╝

3.3 Loop Structures

Loops such as FOR, WHILE, and LOOP visualized as recurring operations.

╔══════════════════════╗
║ LOOP                 ║
║ ───────────────      ║
║ (i := 0 TO n)        ║
╚══════════════════════╝
        │
        ▼
╔══════════════════════╗
║ body of loop         ║
╚══════════════════════╝
        │
        └──▶ back to condition

Example:

╔══════════════════════╗
║ LOOP (i := 0 TO 5)   ║
╚══════════════════════╝
        │
        ▼
╔══════════════════════╗
║ x := x + i           ║
╚══════════════════════╝
        │
        └──▶ Repeat

4. Cryptographic Operations

4.1 Hashing

Visualizing cryptographic operations like hashing.

╔══════════════════════╗
║ HASH(input)          ║
╚══════════════════════╝
        │
        ▼
╔══════════════════════╗
║ H256: hash_output    ║
╚══════════════════════╝

Example:

╔══════════════════════╗   ──▶   ╔══════════════════════╗
║ HASH("message")      ║         ║ H256: 123abc         ║
╚══════════════════════╝         ╚══════════════════════╝

4.2 Signatures and Encryption

╔══════════════════════╗
║ SIGN(sk, msg)        ║
╚══════════════════════╝
        │
        ▼
╔══════════════════════╗
║ SIG: signature       ║
╚══════════════════════╝

Example:

╔══════════════════════╗   ──▶   ╔══════════════════════╗
║ SIGN(sk, "data")     ║         ║ SIG: abc123          ║
╚══════════════════════╝         ╚══════════════════════╝

5. Error Handling

5.1 Error Flow Representation

Error handling is shown with catch paths and error outputs.

╔══════════════════════╗
║ TRY {                ║
║   operation          ║
╚══════════════════════╝
        │
        ▼
╔══════════════════════╗
║ CATCH error_type     ║
╚══════════════════════╝

Example:

╔══════════════════════╗
║ TRY { x / 0 }        ║
╚══════════════════════╝
        │
        ▼
╔══════════════════════╗
║ CATCH(DivideByZero)  ║
╚══════════════════════╝

6. Concurrency and Parallelism

6.1 Parallel Task Execution

Visualizing parallel task execution with task flows.

╔══════════════════════╗
║ PAR_EXEC(task_list)  ║
╚══════════════════════╝
        │
        ▼
╔══════════════════════╗
║ [task1, task2, task3]║
╚══════════════════════╝

Example:

╔══════════════════════╗   ──▶   ╔══════════════════════╗
║ PAR_EXEC([t1, t2])   ║         ║ results: [r1, r2]    ║
╚══════════════════════╝         ╚══════════════════════╝

6.2 Synchronization and Locking

╔══════════════════════╗
║ LOCK(mutex)          ║
╚══════════════════════╝
        │
        ▼
╔══════════════════════╗
║ critical_section     ║
╚══════════════════════╝

Example:

╔══════════════════════╗   ──▶   ╔══════════════════════╗
║ LOCK(mutex)          ║         ║ shared_resource += 1 ║
╚══════════════════════╝         ╚══════════════════════╝

7. Data Types and Structures (Continued)

7.1 Enumerations (Enums)

Visual representation of enumerations (enums), showing the options available:

╔══════════════════════╗
║ ENUM Color           ║
║ ───────────────      ║
║ RED                  ║
║ GREEN                ║
║ BLUE                 ║
╚══════════════════════╝

Example:

╔══════════════════════╗   ──▶   ╔══════════════════════╗
║ ENUM Color           ║         ║ current_color := RED ║
╚══════════════════════╝         ╚══════════════════════╝

7.2 Tuples

Tuples visualized as structured collections:

╔══════════════════════╗
║ TUPLE                ║
║ ───────────────      ║
║ (INT, STR, BOOL)     ║
╚══════════════════════╝

Example:

╔═════════════════════════╗   ──▶   ╔═════════════════════════╗
║ TUPLE (42, "Alice", T)  ║         ║ x := (42, "Alice", true)║
╚═════════════════════════╝         ╚═════════════════════════╝

7.3 Records

Records (similar to structs) visually represented with fields and their values:

╔══════════════════════╗
║ RECORD Person        ║
║ ───────────────      ║
║ name: STR            ║
║ age: INT             ║
╚══════════════════════╝

Example:

╔══════════════════════╗   ──▶   ╔══════════════════════╗
║ Person {             ║         ║ p := { "Bob", 30 }   ║
║ name: "Bob",         ║         ║ name := "Bob", age := 30 ║
║ age: 30              ║         ║                      ║
╚══════════════════════╝         ╚══════════════════════╝

8. Function Handling and Advanced Operations

8.1 Function Overloading

Visualizing multiple functions with the same name but different parameters.

╔══════════════════════╗
║ FUNC add(x:INT)      ║
╚══════════════════════╝
╔══════════════════════╗
║ FUNC add(x:INT, y:INT)║
╚══════════════════════╝

Example:

╔══════════════════════╗   ──▶   ╔══════════════════════╗
║ add(5)               ║         ║ result := 6          ║
╚══════════════════════╝         ╚══════════════════════╝

╔══════════════════════╗   ──▶   ╔══════════════════════╗
║ add(5, 3)            ║         ║ result := 8          ║
╚══════════════════════╝         ╚══════════════════════╝

8.2 Closures and Lambdas

Visualizing anonymous and closure functions:

╔══════════════════════╗
║ CLOSURE make_adder   ║
║ ───────────────      ║
║ factor: INT          ║
║ RETURN FUNC          ║
╚══════════════════════╝

Example:

╔════════════════════════╗   ──▶   ╔════════════════════════╗
║ CLOSURE multiplier(2)  ║         ║ double := FUNC (x) {x*2}║
╚════════════════════════╝         ╚════════════════════════╝

8.3 Pattern Matching

Flow for MATCH statements represented visually:

╔══════════════════════╗
║ MATCH expr           ║
╚══════════════════════╝
        │
   ┌────┴────┐
   ▼         ▼
╔══════════╗  ╔══════════╗
║ CASE 1   ║  ║ CASE 2   ║
╚══════════╝  ╚══════════╝
        │
   └────┴────┐
        ▼
╔══════════════════════╗
║ DEFAULT              ║
╚══════════════════════╝

Example:

╔══════════════════════╗
║ MATCH [1, 2, 3]      ║
╚══════════════════════╝
        │
   ┌────┴────┐
   ▼         ▼
╔══════════╗  ╔══════════╗
║ CASE [1,2,3] MATCHED!  ║
╚══════════╝

9. Error Handling

9.1 Chained Error Handling

Flow for catching multiple error types:

╔══════════════════════╗
║ TRY { operation }    ║
╚══════════════════════╝
        │
   ┌────┴─────┐
   ▼          ▼
╔════════════╗   ╔════════════╗
║ CATCH 1    ║   ║ CATCH 2    ║
╚════════════╝   ╚════════════╝

Example:

╔══════════════════════╗
║ TRY { divide(10, 0) }║
╚══════════════════════╝
        │
   ┌────┴─────┐
   ▼          ▼
╔════════════╗   ╔════════════╗
║ CATCH(DivBy0)  ║ DEBUG PRINT ║
╚════════════╝

10. Concurrency and Synchronization

10.1 Thread Management

Flow for threads:

╔══════════════════════╗
║ THREAD_START(func)   ║
╚══════════════════════╝
        │
        ▼
╔══════════════════════╗
║ THREAD: thread_id    ║
╚══════════════════════╝

Example:

╔══════════════════════╗   ──▶   ╔══════════════════════╗
║ THREAD_START(worker) ║         ║ THREAD_ID: 1001      ║
╚══════════════════════╝         ╚══════════════════════╝

10.2 Synchronization Primitives

Visual flow for using locks:

╔══════════════════════╗
║ LOCK(mutex)          ║
╚══════════════════════╝
        │
        ▼
╔══════════════════════╗
║ Critical Section     ║
╚══════════════════════╝

Example:

╔══════════════════════╗   ──▶   ╔══════════════════════╗
║ LOCK(resource_mutex) ║         ║ shared += 1          ║
╚══════════════════════╝         ╚══════════════════════╝

11. Coroutines and Asynchronous Handling

11.1 Coroutine Execution Flow

Flow for coroutine yield and resumption:

╔══════════════════════╗
║ COROUTINE(func)      ║
╚══════════════════════╝
        │
        ▼
╔══════════════════════╗
║ YIELD value          ║
╚══════════════════════╝
        │
        └──▶ Resume

Example:

╔══════════════════════╗
║ COROUTINE producer() ║
╚══════════════════════╝
        │
        ▼
╔══════════════════════╗   ──▶   ╔══════════════════════╗
║ YIELD i (i:=0 to 5)  ║         ║ resumption returns 2 ║
╚══════════════════════╝         ╚══════════════════════╝

Continuing the Visual Output Specification

12. Data Structures and Complex Types (Continued)

12.1 Vectors

Vectors are visualized as ordered collections.

╔════════════════════════════╗
║ VEC<INT>                   ║
║ ────────────               ║
║ [1, 2, 3, 4]               ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ VEC<STR>                   ║         ║ VEC: ["apple", "banana"]   ║
║ ────────────               ║         ║                           ║
║ ["apple", "banana"]        ║         ╚════════════════════════════╝
╚════════════════════════════╝

12.2 Maps

Maps show key-value pairs with keys pointing to their corresponding values.

╔════════════════════════════╗
║ MAP<STR, INT>              ║
║ ────────────               ║
║ {"age": 30, "year": 2024}  ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ MAP<STR, INT>              ║         ║ MAP: {"age": 30, "year": 24}║
║ ────────────               ║         ║                           ║
║ {"age": 30, "year": 24}    ║         ╚════════════════════════════╝
╚════════════════════════════╝

12.3 Optional Values

Optionals are displayed visually as boxed values that can be present or absent (null).

╔════════════════════════════╗
║ OPT<INT>                   ║
║ ────────────               ║
║ Present: 5                 ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ OPT<INT>                   ║         ║ OPT<INT>: None             ║
║ ────────────               ║         ╚════════════════════════════╝
║ Value: 5                   ║
╚════════════════════════════╝

13. Cryptographic Operations (Continued)

13.1 Hashing Functions

Hashing operations visually demonstrate the transformation of data to hash.

╔════════════════════════════╗
║ HASH(data)                 ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ H256: 0xabc123             ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ HASH("message")            ║         ║ H256: 123abc               ║
╚════════════════════════════╝         ╚════════════════════════════╝

13.2 Signatures

Visualizing cryptographic signatures.

╔════════════════════════════╗
║ SIGN(sk, msg)              ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ SIG: abc123                ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ SIGN(private_key, "data")  ║         ║ SIG: 0x45abc               ║
╚════════════════════════════╝         ╚════════════════════════════╝

13.3 Encryption and Decryption

Visualizing encryption and decryption flows.

╔════════════════════════════╗
║ ENC(pk, msg)               ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ CIPHER: 0xdef456           ║
╚════════════════════════════╝

╔════════════════════════════╗
║ DEC(sk, cipher)            ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ PLAINTEXT: "message"       ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ ENC(public_key, "secret")  ║         ║ CIPHER: 0x789xyz           ║
╚════════════════════════════╝         ╚════════════════════════════╝

13.4 Zero-Knowledge Proofs

Zero-knowledge proofs visually demonstrate the verification of a proof without revealing details.

╔════════════════════════════╗
║ ZKP_GEN(circuit, witness)  ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ PROOF: zk_snark_proof      ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ ZKP_GEN(circuit, inputs)   ║         ║ PROOF: zk_abc123           ║
╚════════════════════════════╝         ╚════════════════════════════╝

14. Control Flow and Logic (Continued)

14.1 Try-Catch Blocks

Visualizing error handling using TRY and CATCH.

╔════════════════════════════╗
║ TRY { operation }          ║
╚════════════════════════════╝
        │
   ┌────┴─────┐
   ▼          ▼
╔════════════╗   ╔════════════╗
║ Success    ║   ║ CATCH error║
╚════════════╝   ╚════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ TRY { x := divide(10, 0) } ║         ║ CATCH(DivByZero)            ║
╚════════════════════════════╝         ╚════════════════════════════╝

14.2 Assertions

Assertions are visually represented as checks that must hold true.

╔════════════════════════════╗
║ ASSERT(condition, msg)     ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ If true: Continue          ║
║ If false: Error            ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ ASSERT(x > 0, "x must > 0")║         ║ TRUE: Continue execution   ║
╚════════════════════════════╝         ╚════════════════════════════╝

15. Parallelism and Concurrency (Continued)

15.1 Parallel Execution

Parallel execution flows show tasks running simultaneously and collecting results.

╔════════════════════════════╗
║ PAR_EXEC(task_list)        ║
╚════════════════════════════╝
        │
   ┌────┴─────┐
   ▼          ▼
╔════════════╗   ╔════════════╗
║ Task 1     ║   ║ Task 2     ║
╚════════════╝   ╚════════════╝
        │          │
        ▼          ▼
╔════════════════════════════╗
║ Results: [res1, res2]      ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ PAR_EXEC([t1, t2])         ║         ║ Results: [output1, output2]║
╚════════════════════════════╝         ╚════════════════════════════╝

15.2 Thread Management

Threads are visualized with a start and join process.

╔════════════════════════════╗
║ THREAD_START(func)         ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ THREAD: thread_id          ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ THREAD_JOIN(thread_id)     ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Result: output             ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ THREAD_START(worker)       ║         ║ THREAD_ID: 1001            ║
╚════════════════════════════╝         ╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ THREAD_JOIN(1001)          ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Result: output_value       ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ THREAD_START(task_worker)  ║         ║ THREAD_ID: 1012            ║
╚════════════════════════════╝         ╚════════════════════════════╝
        │                                    │
        ▼                                    ▼
╔════════════════════════════╗         ╔════════════════════════════╗
║ THREAD_JOIN(1012)          ║         ║ Result: completed_task     ║
╚════════════════════════════╝         ╚════════════════════════════╝

16. Synchronization and Locking

16.1 Mutex Lock and Unlock

Visualizing a mutex locking mechanism to control concurrent access.

╔════════════════════════════╗
║ LOCK(mutex)                ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Critical Section           ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ UNLOCK(mutex)              ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ LOCK(resource_mutex)        ║         ║ shared_resource += 1       ║
╚════════════════════════════╝         ╚════════════════════════════╝
        │                                    │
        ▼                                    ▼
╔════════════════════════════╗         ╔════════════════════════════╗
║ UNLOCK(resource_mutex)     ║         ║ Continue execution         ║
╚════════════════════════════╝         ╚════════════════════════════╝

17. Coroutines and Asynchronous Handling (Continued)

17.1 Coroutine Yielding

Visual representation of a coroutine yielding and resuming.

╔════════════════════════════╗
║ COROUTINE(func)            ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ YIELD value                ║
╚════════════════════════════╝
        │
        └──▶ Resume

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ COROUTINE producer()       ║         ║ YIELD i (i:=0 to 5)        ║
╚════════════════════════════╝         ╚════════════════════════════╝
        │                                    │
        ▼                                    ▼
╔════════════════════════════╗         ╔════════════════════════════╗
║ Resume coroutine           ║         ║ YIELD next value: i=3      ║
╚════════════════════════════╝         ╚════════════════════════════╝

17.2 Awaiting Future Results

Visualizing asynchronous function calls and awaiting results.

╔════════════════════════════╗
║ ASYNC(func) -> FUTURE<T>   ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ AWAIT(future) -> RESULT    ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ ASYNC(fetch_data)          ║         ║ FUTURE<INT>: pending       ║
╚════════════════════════════╝         ╚════════════════════════════╝
        │                                    │
        ▼                                    ▼
╔════════════════════════════╗         ╔════════════════════════════╗
║ AWAIT(fetch_future)        ║         ║ RESULT: 100                ║
╚════════════════════════════╝         ╚════════════════════════════╝

18. Pattern Matching and Control Flow

18.1 Pattern Matching

Visual output for MATCH statements with multiple cases.

╔════════════════════════════╗
║ MATCH expression           ║
╚════════════════════════════╝
        │
   ┌────┴────┐
   ▼         ▼
╔════════════╗  ╔════════════╗
║ CASE 1     ║  ║ CASE 2     ║
╚════════════╝  ╚════════════╝
        │
   └────┴────┐
        ▼
╔══════════════════════╗
║ DEFAULT              ║
╚══════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ MATCH value                ║         ║ CASE [1, 2, 3]: Matched!   ║
╚════════════════════════════╝         ╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ DEFAULT: No match found!   ║
╚════════════════════════════╝

18.2 Conditional Expressions

IF-ELSE statements visually demonstrate conditional branching.

╔════════════════════════════╗
║ IF condition               ║
╚════════════════════════════╝
        │
   ┌────┴────┐
   ▼         ▼
╔════════════╗  ╔════════════╗
║ True       ║  ║ False      ║
╚════════════╝  ╚════════════╝
        │
   └────┴────┐
        ▼
╔══════════════════════╗
║ CONTINUE execution   ║
╚══════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ IF (x > 10)                ║         ║ x := x + 1                 ║
╚════════════════════════════╝         ╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ ELSE x := x - 1            ║         ║ Result: x = 9              ║
╚════════════════════════════╝         ╚════════════════════════════╝

19. Function Handling

19.1 Default Parameters and Function Overloading

Visually representing function calls with optional or default parameters.

╔════════════════════════════╗
║ FUNC greet(name, msg="Hi") ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ CALL: greet("Alice")       ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Result: "Hi Alice"         ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ FUNC add(x, y=10)          ║         ║ CALL: add(5)               ║
╚════════════════════════════╝         ╚════════════════════════════╝
        │                                    │
        ▼                                    ▼
╔════════════════════════════╗         ╔════════════════════════════╗
║ Result: 15                 ║         ║ x + y = 15                 ║
╚════════════════════════════╝         ╚════════════════════════════╝

19.2 Lambda Functions and Closures

Visually representing lambdas and closures.

╔════════════════════════════╗
║ LAMBDA (x, y) -> x + y     ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ CALL: lambda(3, 4)         ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Result: 7                  ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ LAMBDA (x) -> x * factor   ║         ║ Result of closure: 20      ║
╚════════════════════════════╝         ╚════════════════════════════╝

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ LAMBDA (x) -> x * factor   ║         ║ CALL: closure(10)          ║
╚════════════════════════════╝         ╚════════════════════════════╝
        │                                    │
        ▼                                    ▼
╔════════════════════════════╗         ╔════════════════════════════╗
║ factor := 2                ║         ║ Result of closure: 20      ║
╚════════════════════════════╝         ╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ FUNC make_multiplier(f)    ║         ║ Result: LAMBDA (x) -> x * f║
╚════════════════════════════╝         ╚════════════════════════════╝
        │                                    │
        ▼                                    ▼
╔════════════════════════════╗         ╔════════════════════════════╗
║ LAMBDA := make_multiplier(2)         ║ CALL: LAMBDA(10)           ║
╚════════════════════════════╝         ╚════════════════════════════╝
        │                                    │
        ▼                                    ▼
╔════════════════════════════╗         ╔════════════════════════════╗
║ LAMBDA (x) -> x * 2        ║         ║ Result: 20                 ║
╚════════════════════════════╝         ╚════════════════════════════╝

This matches the lambda and closure concept by showing how the closure captures the factor from the outer scope, and then it visually demonstrates how calling the lambda works with captured values. The flow proceeds through the creation of the lambda, calling it, and returning the computed result.

20.1 Custom Error Types

Visual representation of defining and throwing custom errors.

╔════════════════════════════╗
║ ERROR_TYPE(name, fields)   ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ THROW(ErrorType)           ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ ERROR_TYPE(InvalidInput,   ║         ║ THROW(InvalidInput("Wrong")║
║ [(msg: STR)])              ║         ╚════════════════════════════╝
╚════════════════════════════╝

20.2 Chained Error Handling

Handling multiple error types with chained TRY-CATCH.

╔════════════════════════════╗
║ TRY { operation }          ║
╚════════════════════════════╝
        │
   ┌────┴─────┐
   ▼          ▼
╔════════════╗   ╔════════════╗
║ CATCH 1    ║   ║ CATCH 2    ║
╚════════════╝   ╚════════════╝
        │
   └────┴────┐
        ▼
╔══════════════════════╗
║ FINAL: Continue      ║
╚══════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ TRY { operation() }        ║         ║ CATCH(DivideByZero)        ║
╚════════════════════════════╝         ╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ CATCH(InvalidInput)        ║         ║ FINAL: Handle gracefully   ║
╚════════════════════════════╝         ╚════════════════════════════╝

21. Advanced Programming Constructs (Continued)

21.1 Meta-Programming with Macros

Macros visually generate code, simplifying repeated operations.

╔════════════════════════════╗
║ macro MACRO_NAME(params)   ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Code generated by macro    ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ macro LOG(expr)            ║         ║ LOG(x + y) expands to:     ║
╚════════════════════════════╝         ║ DEBUG_PRINT(x + y)         ║
                                        ║ RETURN (x + y)             ║
                                        ╚════════════════════════════╝

21.2 Type Inference

Visual output showing how type inference works.

╔════════════════════════════╗
║ var_name := value          ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Type inferred: INT         ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ x := 42                    ║         ║ Type inferred: INT         ║
╚════════════════════════════╝         ╚════════════════════════════╝

22. Concurrency and Parallelism (Continued)

22.1 Parallel Task Execution

Visual representation of parallel task execution and result aggregation.

╔════════════════════════════╗
║ PAR_EXEC(tasks)            ║
╚════════════════════════════╝
        │
   ┌────┴─────┐
   ▼          ▼
╔════════════╗   ╔════════════╗
║ Task 1     ║   ║ Task 2     ║
╚════════════╝   ╚════════════╝
        │          │
        ▼          ▼
╔════════════════════════════╗
║ Aggregated Results         ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ PAR_EXEC([download1,       ║         ║ Results: [file1, file2]     ║
║ download2])                ║         ╚════════════════════════════╝
╚════════════════════════════╝

22.2 Mutex Locks

Visualizing the locking and unlocking of shared resources.

╔════════════════════════════╗
║ LOCK(mutex)                ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Critical Section           ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ UNLOCK(mutex)              ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ LOCK(shared_mutex)         ║         ║ Critical Section           ║
╚════════════════════════════╝         ╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ UNLOCK(shared_mutex)       ║         ║ Continue execution         ║
╚════════════════════════════╝         ╚════════════════════════════╝

23. Data Structures (Continued)

23.1 Enumerations (Enums)

Enums visually represent the predefined choices.

╔════════════════════════════╗
║ ENUM Color                 ║
╚════════════════════════════╝
        │
   ┌────┴─────┐
   ▼          ▼
╔════════════╗  ╔════════════╗
║ RED        ║  ║ BLUE       ║
╚════════════╝  ╚════════════╝
        │
        ▼
╔══════════════════════╗
║ Enum Value: GREEN    ║
╚══════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ ENUM Color: RED, GREEN,    ║         ║ Enum Value: GREEN          ║
║ BLUE                      ║         ╚════════════════════════════╝
╚════════════════════════════╝

23.2 Tuples

Visualizing tuples as a collection of multiple data types.

╔════════════════════════════╗
║ TUPLE (INT, STR, BOOL)     ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ (42, "Alice", true)        ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ TUPLE (42, "Alice", true)  ║         ║ Elements: INT, STR, BOOL   ║
╚════════════════════════════╝         ╚════════════════════════════╝

23.3 Records (Structs)

Visual representation of record (struct) fields and values.

╔════════════════════════════╗
║ RECORD Person              ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ name: "Alice"              ║
║ age: 30                    ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ RECORD {name: "Alice",     ║         ║ Person {name: "Alice", age:30}║
║ age: 30}                  ║         ╚════════════════════════════╝
╚════════════════════════════╝

24. Advanced Cryptographic Operations

24.1 Lattice-Based Cryptography

Visual representation of Lattice-based operations such as sampling and decoding.

╔════════════════════════════╗
║ LWE_SAMPLE(s, e)           ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ VEC<FLD>: Sample Output    ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ LWE_SAMPLE(secret, error)  ║         ║ VEC: [0x32, 0x45, 0x78]    ║
╚════════════════════════════╝         ╚════════════════════════════╝

24.2 Witness Encryption

Visualizing witness encryption and decryption.

╔════════════════════════════╗
║ WE_ENC(stmt, msg)          ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ CIPHER: Encrypted Data     ║
╚════════════════════════════╝

╔════════════════════════════╗
║ WE_DEC(cipher, witness)    ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ RESULT: Decrypted Message  ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ WE_ENC("statement", msg)   ║         ║ CIPHER: 0xabc456           ║
╚════════════════════════════╝         ╚════════════════════════════╝

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ WE_DEC(cipher, witness)    ║         ║ RESULT: "Decrypted Data"   ║
╚════════════════════════════╝         ╚════════════════════════════╝

25. Blockchain-Specific Operations

25.1 Merkle Trees

Visualizing Merkle Tree creation, insertion, and proof verification.

╔════════════════════════════╗
║ MT_NEW()                   ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Merkle Tree Created        ║
╚════════════════════════════╝

╔════════════════════════════╗
║ MT_INSERT(mt, leaf)        ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ New Leaf Added: 0x123abc   ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ MT_INSERT(mt, 0x123abc)    ║         ║ Leaf Added: 0x123abc       ║
╚════════════════════════════╝         ╚════════════════════════════╝

25.2 State Channels

State channel operations, including opening, updating, and closing a channel.

╔════════════════════════════╗
║ SC_OPEN(participants, state)║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ State Channel Opened       ║
╚════════════════════════════╝

╔════════════════════════════╗
║ SC_UPDATE(sc, new_state, sigs)║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ State Updated              ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ SC_OPEN([pk1, pk2], state) ║         ║ Channel Opened             ║
╚════════════════════════════╝         ╚════════════════════════════╝

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ SC_UPDATE(channel, new_state, sigs)  ║ State Updated Successfully ║
╚════════════════════════════╝         ╚════════════════════════════╝

25.3 zk-SNARKs

Visual representation of zk-SNARK setup, proof generation, and verification.

╔════════════════════════════╗
║ SNARK_SETUP(circuit)       ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Proving Parameters: Setup  ║
╚════════════════════════════╝

╔════════════════════════════╗
║ SNARK_PROVE(pp, witness)   ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ PROOF: zk_snark_proof      ║
╚════════════════════════════╝

╔════════════════════════════╗
║ SNARK_VERIFY(pp, proof)    ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ VERIFICATION: SUCCESSFUL   ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ SNARK_SETUP(circuit)       ║         ║ Setup Completed            ║
╚════════════════════════════╝         ╚════════════════════════════╝

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ SNARK_PROVE(pp, witness)   ║         ║ PROOF: zk_abc123           ║
╚════════════════════════════╝         ╚════════════════════════════╝

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ SNARK_VERIFY(pp, proof)    ║         ║ VERIFICATION: SUCCESSFUL   ║
╚════════════════════════════╝         ╚════════════════════════════╝

26. Privacy-Preserving Protocols

26.1 Ring Signatures

Visual representation of ring signature generation and verification.

╔════════════════════════════╗
║ RING_SIGN(sk, msg, ring)   ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ RING_SIG: signature_output ║
╚════════════════════════════╝

╔════════════════════════════╗
║ RING_VERIFY(msg, sig, ring)║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ VERIFICATION: SUCCESS      ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ RING_SIGN(sk, msg, [pk1, pk2])║      ║ RING_SIG: ring_sig_123     ║
╚════════════════════════════╝         ╚════════════════════════════╝

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ RING_VERIFY(msg, sig, [pk1, pk2])║   ║ VERIFICATION: SUCCESS      ║
╚════════════════════════════╝         ╚════════════════════════════╝

26.2 Blind Signatures

Visual representation of blind signature creation and verification.

╔════════════════════════════╗
║ BLIND_SIGN(sk, blinded_msg)║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ BLIND_SIG: blind_signature ║
╚════════════════════════════╝

╔════════════════════════════╗
║ BLIND_VERIFY(pk, msg, sig) ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ VERIFICATION: SUCCESS      ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ BLIND_SIGN(sk, blinded_msg)║         ║ BLIND_SIG: blind_sig_456   ║
╚════════════════════════════╝         ╚════════════════════════════╝

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ BLIND_VERIFY(pk, msg, sig) ║         ║ VERIFICATION: SUCCESS      ║
╚════════════════════════════╝         ╚════════════════════════════╝

27. Post-Quantum Cryptography

27.1 Key Generation for Post-Quantum Cryptography

Visualizing the generation of post-quantum keys.

╔════════════════════════════╗
║ PQ_KEYGEN(security_param)  ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ PK: public_key             ║
║ SK: secret_key             ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ PQ_KEYGEN(256)             ║         ║ PK: pq_public_key          ║
║                            ║         ║ SK: pq_secret_key          ║
╚════════════════════════════╝         ╚════════════════════════════╝

27.2 Post-Quantum Encryption and Decryption

Visualizing post-quantum encryption and decryption processes.

╔════════════════════════════╗
║ PQ_ENC(pk, msg)            ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ CIPHER: Encrypted PQ Data  ║
╚════════════════════════════╝

╔════════════════════════════╗
║ PQ_DEC(sk, cipher)         ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ PLAINTEXT: Decrypted PQ Msg║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ PQ_ENC(pq_public_key, msg) ║         ║ CIPHER: pq_encrypted_data   ║
╚════════════════════════════╝         ╚════════════════════════════╝

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ PQ_DEC(pq_secret_key, cipher)║       ║ PLAINTEXT: decrypted_msg    ║
╚════════════════════════════╝         ╚════════════════════════════╝

28. Verifiable Delay Functions

28.1 Setup of Verifiable Delay Function

Visualizing the setup phase for VDF.

╔════════════════════════════╗
║ VDF_SETUP(security_param)  ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ VDF_PP: Setup Parameters   ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ VDF_SETUP(256)             ║         ║ VDF_PP: vdf_params_256     ║
╚════════════════════════════╝         ╚════════════════════════════╝

28.2 Evaluation of Verifiable Delay Function

Visualizing VDF evaluation.

╔════════════════════════════╗
║ VDF_EVAL(pp, input, time)  ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Output: Evaluated Result   ║
║ Proof: VDF Proof           ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ VDF_EVAL(vdf_params, input, 5)║      ║ Output: 12345, Proof: vdf_p1║
╚════════════════════════════╝         ╚════════════════════════════╝

28.3 Verification of Verifiable Delay Function

Visualizing the verification of the result of a VDF.

╔════════════════════════════╗
║ VDF_VERIFY(pp, input, output, proof)║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ VERIFICATION: SUCCESSFUL   ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ VDF_VERIFY(vdf_params, input, output, proof)║  ║ VERIFICATION: SUCCESS  ║
╚════════════════════════════╝         ╚════════════════════════════╝

29. Homomorphic Encryption

29.1 Key Generation for Homomorphic Encryption

Visualizing key generation for homomorphic encryption.

╔════════════════════════════╗
║ HE_KEYGEN(security_param)  ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ HE_PK: Public Key          ║
║ HE_SK: Secret Key          ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ HE_KEYGEN(128)             ║         ║ HE_PK: he_public_key       ║
║                            ║         ║ HE_SK: he_secret_key       ║
╚════════════════════════════╝         ╚════════════════════════════╝

29.2 Homomorphic Encryption and Decryption

Visualizing the encryption and decryption processes.

╔════════════════════════════╗
║ HE_ENC(pk, msg)            ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ CIPHER: Homomorphic Cipher ║
╚════════════════════════════╝

╔════════════════════════════╗
║ HE_DEC(sk, cipher)         ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ PLAINTEXT: Decrypted Result║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ HE_ENC(he_public_key, msg) ║         ║ CIPHER: he_ciphertext      ║
╚════════════════════════════╝         ╚════════════════════════════╝

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ HE_DEC(he_secret_key, cipher)║       ║ PLAINTEXT: decrypted_result║
╚════════════════════════════╝         ╚════════════════════════════╝

29.3 Homomorphic Operations (Addition and Multiplication)

Visualizing homomorphic addition and multiplication operations.

╔════════════════════════════╗
║ HE_ADD(pk, cipher1, cipher2)║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Result: Homomorphic Sum    ║
╚════════════════════════════╝

╔════════════════════════════╗
║ HE_MULT(pk, cipher1, cipher2)║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Result: Homomorphic Product║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ HE_ADD(he_public_key, c1, c2)║       ║ Result: homomorphic_sum     ║
╚════════════════════════════╝         ╚════════════════════════════╝

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ HE_MULT(he_public_key, c1, c2)║      ║ Result: homomorphic_product ║
╚════════════════════════════╝         ╚════════════════════════════╝

30. Formal Verification and Safety

30.1 Invariant Checking

Visual representation of invariant checks in code execution.

╔════════════════════════════╗
║ INVARIANT(condition, msg)  ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ ASSERTION: Condition True  ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ INVARIANT(x > 0, "x must > 0")║     ║ ASSERTION: TRUE             ║
╚════════════════════════════╝         ╚════════════════════════════╝

30.2 Formal Proof Generation

Visualizing proof generation and verification.

╔════════════════════════════╗
║ PROVE(theorem)             ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ PROOF: Formal Proof        ║
╚════════════════════════════╝

╔════════════════════════════╗
║ CHECK_PROOF(theorem, proof)║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ VERIFICATION: SUCCESS      ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ PROVE("x + y = y + x")     ║         ║ PROOF: formal_proof_123     ║
╚════════════════════════════╝         ╚════════════════════════════╝

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ CHECK_PROOF("x + y = y + x", proof) ║  ║ VERIFICATION: SUCCESS     ║
╚════════════════════════════╝         ╚════════════════════════════╝

31. Error Handling and Debugging (Continued)

31.1 Detailed Error Message Structure

Visualizing detailed error messages and stack traces for easier debugging.

╔════════════════════════════╗
║ ERROR: <error_message>     ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Location: <file>:<line>    ║
║ Callstack: [Function1,     ║
║             Function2,     ║
║             Function3]     ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ ERROR: Divide by zero      ║         ║ Location: main.rs:20        ║
╚════════════════════════════╝         ║ Callstack: [divide, main]   ║
                                        ╚════════════════════════════╝

##### 31.2 **Debugging Information**
Visual representation of debug print statements and stack traces.
╔════════════════════════════╗
║ DEBUG_PRINT(expr)          ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Output: Value of expr      ║
╚════════════════════════════╝

╔════════════════════════════╗
║ STACK_TRACE()              ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Callstack: [Function1,     ║
║             Function2,     ║
║             Function3]     ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ DEBUG_PRINT(x + y)         ║         ║ Output: 10                 ║
╚════════════════════════════╝         ╚════════════════════════════╝

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ STACK_TRACE()              ║         ║ Callstack: [func1, func2]  ║
╚════════════════════════════╝         ╚════════════════════════════╝

32. Interoperability

32.1 Foreign Function Interface (FFI) Import

Visualizing the process of importing functions from other languages using FFI.

╔════════════════════════════╗
║ FFI_IMPORT(language, func) ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Imported Function: func    ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ FFI_IMPORT("C", "math_func")║        ║ Imported Function: math_func║
╚════════════════════════════╝         ╚════════════════════════════╝

32.2 Foreign Function Interface (FFI) Export

Visualizing the process of exporting functions to other languages using FFI.

╔════════════════════════════╗
║ FFI_EXPORT(func, language) ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Exported to: language      ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ FFI_EXPORT(my_func, "Python")║       ║ Exported to Python: my_func ║
╚════════════════════════════╝         ╚════════════════════════════╝

33. Serialization

33.1 Serialization of Data Structures

Visualizing the serialization process where data structures are converted into byte arrays.

╔════════════════════════════╗
║ SERIALIZE(object)          ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Byte Stream: [0x45, 0x23]  ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ SERIALIZE(my_obj)          ║         ║ Byte Stream: [0x12, 0x34]  ║
╚════════════════════════════╝         ╚════════════════════════════╝

33.2 Deserialization of Data Structures

Visualizing the deserialization process where byte streams are converted back into data structures.

╔════════════════════════════╗
║ DESERIALIZE(data, type)    ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Deserialized Object        ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ DESERIALIZE([0x12, 0x34], T)║       ║ Deserialized: my_object     ║
╚════════════════════════════╝         ╚════════════════════════════╝

34. Safety and Formal Verification (Continued)

34.1 Preconditions

Visualizing precondition checks before function execution.

╔════════════════════════════╗
║ PRE(condition, msg)        ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Check Passed: Continue     ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ PRE(x > 0, "x must be > 0")║        ║ Check Passed: TRUE          ║
╚════════════════════════════╝         ╚════════════════════════════╝

34.2 Postconditions

Visualizing postcondition checks after function execution.

╔════════════════════════════╗
║ POST(condition, msg)       ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Check Passed: Continue     ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ POST(result != NULL, "result valid") ║  ║ Check Passed: TRUE        ║
╚════════════════════════════╝         ╚════════════════════════════╝

34.3 Invariant Checking

Visualizing invariant checks to maintain consistency throughout the program execution.

╔════════════════════════════╗
║ INVARIANT(condition, msg)  ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Invariant Held: Continue   ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ INVARIANT(balance >= 0,    ║         ║ Invariant Held: TRUE       ║
║ "Balance cannot be negative") ║       ╚════════════════════════════╝
╚════════════════════════════╝

35. Parallel Execution and Lazy Evaluation

35.1 Parallel Task Execution

Visualizing the execution of multiple tasks in parallel.

╔════════════════════════════╗
║ PAR_EXEC(tasks)            ║
╚════════════════════════════╝
        │
   ┌────┴─────┐
   ▼          ▼
╔════════════╗  ╔════════════╗
║ Task 1     ║  ║ Task 2     ║
╚════════════╝  ╚════════════╝
        │          │
        ▼          ▼
╔════════════════════════════╗
║ Aggregated Results         ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ PAR_EXEC([task1, task2])   ║         ║ Aggregated Results: [r1, r2]║
╚════════════════════════════╝         ╚════════════════════════════╝

35.2 Lazy Evaluation

Visualizing how expressions are lazily evaluated only when needed.

╔════════════════════════════╗
║ LAZY(expr)                 ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Lazy Expression Created    ║
╚════════════════════════════╝

╔════════════════════════════╗
║ FORCE(expr)                ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Evaluated: Result          ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ LAZY(x + y)                ║         ║ Lazy Expression Created    ║
╚════════════════════════════╝         ╚════════════════════════════╝

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ FORCE(x + y)               ║         ║ Evaluated: Result: 10      ║
╚════════════════════════════╝         ╚════════════════════════════╝

36. Memoization

36.1 Memoized Function Call

Visual representation of memoization where the result of function calls is cached for future use.


╔════════════════════════════╗
║ MEMO(func)                 ║
╚════════════════════════════╝
        │
        ▼
╔════════════════════════════╗
║ Cache Created              ║
╚════════════════════════════╝

╔════════════════════════════╗
║ Call with Cached Result    ║
╚════════════════════════════╝

Example:

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ MEMO(expensive_computation)║        ║ Cache Created for Future Use║
╚════════════════════════════╝         ╚════════════════════════════╝

╔════════════════════════════╗   ──▶   ╔════════════════════════════╗
║ Call(expensive_computation)║         ║ Cached Result: 100          ║
╚════════════════════════════╝         ╚════════════════════════════╝

With these sections done, we are nearing the end of the core visual outputs that match the programming logic we've mapped out so far. Let me know if you'd like to continue or focus on specific remaining areas. We're ensuring every input is thoroughly matched with a visual counterpart!