Reverse Polish Notation (RPN)

Reverse Polish Notation (RPN), also known as postfix notation, is a mathematical notation in which operators follow their operands. In relation to Haskell, RPN is not a core language feature but is relevant when implementing or understanding stack-based computations or evaluating expressions using a stack. It is often encountered in the context of parsing, expression evaluation, or custom interpreters written in Haskell.

And while it may not directly relate to Cardano as a core blockchain concept, it is relevant to Plutus, Cardano’s smart contract programming framework, because RPN is used in the implementation of Uplc (Untyped Plutus Core), which is part of the Cardano smart contract stack.

What is Reverse Polish Notation?

In RPN:

• Operators appear after their operands, eliminating the need for parentheses to define operation order.
• For example:
  • Infix Notation (standard): (3 + 4) * 5
  • RPN: 3 4 + 5 *

The RPN expression is evaluated from left to right using a stack-based approach:

1. Push operands onto the stack.
2. Apply operators to the top elements of the stack.

Result for RPN example:

Push 3 → Push 4 → Apply + → Result 7 → Push 5 → Apply * → Final Result: 35.

How Does RPN Relate to Cardano?

1. Plutus Core and RPN

Plutus Core, the intermediate language for Cardano smart contracts, is designed to be simple, expressive, and efficient for blockchain execution. Untyped Plutus Core (Uplc), which is closer to the underlying computational model, employs a stack-based execution model similar to RPN.

• Why RPN? RPN aligns well with stack-based virtual machines used in smart contracts. It eliminates the need for parentheses and precedence rules, making computation simpler and more deterministic—crucial for blockchain environments.

2. Efficient Evaluation

Using RPN in Uplc helps:

• Reduce ambiguity in evaluating smart contract expressions.
• Simplify the implementation of the Plutus interpreter.
• Optimize contract execution on the Cardano blockchain by minimizing computational overhead.

Advantages of RPN in Cardano’s Context

1. Deterministic Execution:
   • Smart contracts must execute deterministically across all nodes to maintain consensus. RPN simplifies this by ensuring a straightforward evaluation order.
2. Efficient for Blockchain:
   • Blockchain environments benefit from lightweight, stack-based processing. RPN’s alignment with stack operations makes it well-suited for such tasks.
3. Lower Gas Costs:
   • Simplified computation reduces execution complexity, potentially lowering transaction fees (gas) for running Plutus smart contracts.

Example of RPN in Smart Contracts

Suppose a Plutus smart contract involves this expression:

(x + y) * z

In Untyped Plutus Core (or RPN):

x y + z *

Evaluation:

1. Push x and y onto the stack.
2. Apply + to get x + y.
3. Push z onto the stack.
4. Apply * to get (x + y) * z.

Conclusion

Reverse Polish Notation is not directly visible to end-users of Cardano, but it is an integral part of the Plutus Core language that powers smart contracts on the blockchain. By leveraging RPN for efficient and deterministic computation, Cardano ensures secure and scalable execution of its smart contracts, contributing to its mission of creating a robust and efficient blockchain platform.