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Escrows are optics

Fabrizio Genovese, Fosco Loregian, Daniele Palombi

Abstract

We provide a categorical interpretation for escrows, i.e. trading protocols in trustless environment, where the exchange between two agents is mediated by a third party where the buyer locks the money until they receive the goods they want from the seller. A simplified escrow system can be modeled as a certain kind of morphism in the category of optics on a monoidal category. When objects in the base category have monoid and comonoid structures, more involved kinds of escrows `with intermediaries' can be modelled as morphisms with action-like properties.

Escrows are optics

Abstract

We provide a categorical interpretation for escrows, i.e. trading protocols in trustless environment, where the exchange between two agents is mediated by a third party where the buyer locks the money until they receive the goods they want from the seller. A simplified escrow system can be modeled as a certain kind of morphism in the category of optics on a monoidal category. When objects in the base category have monoid and comonoid structures, more involved kinds of escrows `with intermediaries' can be modelled as morphisms with action-like properties.

Paper Structure

This paper contains 7 sections, 4 theorems, 27 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Related work on optics, and conventions
  3. Escrows are optics
  4. Composing escrows
  5. Using agents as intermediaries
  6. Information and resources
  7. Conclusion and future work

Key Result

Proposition 3.3

The rule above is associative and unital: this means that the diagrams commute for a choice of 'unit' $\nu_X : 1 \to \langle X,X\rangle$.

Figures (3)

  • Figure 1: A simple trade.
  • Figure 2: An escrow trade.
  • Figure 3: An escrow trade with a greedy intermediary.

Theorems & Definitions (21)

  • Remark 2.1
  • Definition 2.2: The category of optics
  • Remark 2.3
  • Definition 2.4
  • Definition 2.5
  • Remark 2.6
  • Definition 3.1: The building blocks of escrow composition
  • Remark 3.2
  • Proposition 3.3
  • proof
  • ...and 11 more