Safe Haskell	None
Language	GHC2024

Circuit.Mat.Prob

Description

Prob carrier for Mat.

A Mat r i j is a linear map from input indices i to output indices j with weights in r. That is exactly the linear fragment of the double-dual probability arrow Prob. This module gives the embedding that lets a Mat construction flow through the Prob carrier with no rewrite.

Synopsis

matToProb :: forall r i j. (Additive r, Multiplicative r, Eq j, Finite i, Finite j) => Mat r i j -> Prob (->) r i j
runProbAt :: forall r i j. (Additive r, Multiplicative r, Eq j) => Prob (->) r i j -> i -> j -> r

Documentation

matToProb :: forall r i j. (Additive r, Multiplicative r, Eq j, Finite i, Finite j) => Mat r i j -> Prob (->) r i j Source #

Embed a semiring matrix into the Prob continuation carrier.

The resulting Prob (->) r i j is the expectation transformer:

  runProb (matToProb m) k (x, i) = Σⱼ m(i,j) · k(x,j)

runProbAt :: forall r i j. (Additive r, Multiplicative r, Eq j) => Prob (->) r i j -> i -> j -> r Source #

Run a Prob carrier at a single input/output pair.

This is the analogue of runMat for the Prob carrier: it selects one output index by feeding a continuation that is one at that index and zero elsewhere.