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Equation 1 · Part 4 · Typed Tools: Protocols as an Agent's Action Alphabet

Symbol R_t

t: At×Σ  ⇀  Rt×Σt:\ \mathcal{A}_t \times \Sigma \;\rightharpoonup\; \mathcal{R}_t \times \Sigma
Rt\mathcal{R}_t

What this part means

the result type : what the caller is told.

Its job in the formula

RtR_t is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

Rt\mathcal{R}_t is the result type : what the caller is told.

The passage around this formula

Start with the smallest honest model. A tool is not a function in the mathematical sense, because it touches the world. Write it as a partial map from arguments and world-state to results and world-state: t: At×Σ  ⇀  Rt×Σt:\ \mathcal{A}_t \times \Sigma \;\rightharpoonup\; \mathcal{R}_t \times \Sigma. Four things are named there, and each corresponds to a design decision that is usually made by accident.

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the article section

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