Consider:

we can consider this as two parts

• the computation of x = e1
• and the continuation e2

it essentially create statement labels:

such that:

• \(k_0 = \lambda w . k_1 e\)
• \(k_1 = \lambda x . k_2 e’\)
• \(k_2 = \lambda y . k_3 (x+y)\)
• \(k_3 = \lambda z . z\)

why

• we can make the order of evaluatinos explicit
• we give a name to each intermediate value
• we name every step of the computation

it is important in language implementation (where ever intermediate result is named); but we can also make continuation available as program value.

Because we want to including rounding during continuity correction to account for things discretized to certain values.

basically “less than

This is a continuous distribution for which the probability can be quantified as:

\begin{equation} p(x) \dd{x} \end{equation}

You will note that, at any given exact point, the probability is \(\lim_{\dd{x} \to 0} p(x)\dd{x} = 0\). However, to get the actual probability, we take an integral over some range:

\begin{equation} \int_{-\infty}^{\infty} p(x) \dd{x} = 1 \end{equation}

See also cumulative distribution function which represents the chance of something happening up to a threshold.

a controller is a that maintains its own state.

constituents

• \(X\): a set of nodes (hidden, internal states)
• \(\Psi(a|x)\): probability of taking an action
• \(\eta(x’|x,a,o)\) : transition probability between hidden states

requirements

Controllers are nice because we:

1. don’t have to maintain a belief over time: we need an initial belief, and then we can create beliefs as we’d like without much worry
2. controllers can be made shorter than conditional plans

additional information

finite state controller

A finite state controller has a finite amount of hidden internal state.