Synthetic Topology in Homotopy Type Theory for probabilstic programming
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Cpo.v
D_op.v
Dominance.v
Flip.v
Functions.v
Giry.v
Interp.v
LICENSE.txt
LowerIntegrals.v
Makefile
OpenFun.v
Opens.v
README.md
Random.v
RandomWalk.v
Riesz1.v
Rlow.v
S_compute_tac.v
U01.v
Valuations.v
wCpo_compl.v

README.md

Synthetic Topology in Homotopy Type Theory for probabilstic programming

Florian Faissole - Bas Spitters

This work is based on HoTT and HoTTClasses.

Build

You need the following dependencies:

Install the dependencies and run the following commands:

  • cd Valuations/
  • make

Organization

The project is organized as it follows:

  • Dominance.v: proof that the Sierpinski space is a dominance.
  • Cpo.v: formalization of w-cpo.
  • wCpo_compl.v: proof of the w-Cpo completion.
  • Rlow.v: formalization of the lower reals.
  • Opens.v: open subspaces in synthetic topology.
  • Functions.v: integrable functions.
  • Valuations.v: theory of valuations.
  • LowerIntegrals.v: theory of lower integrals.
  • D_op.v: operator which takes a function and a rational and gives the open in which the function is bigger than the rational.
  • OpenFun.v: characteristic functions of open subspaces.
  • Riesz1.v: embedding of lower integrals into valuations.
  • Giry.v: Giry monad on lower integrals.
  • Interp.v: Interpretation of probabilistic languages.
  • Flip.v: flip coin program.
  • Random.v: random number generator.
  • RandomWalk.v: random walk programm.
  • S_compute_tac.v: tactic for partial values.
  • U01.v: valuation on [0,1] from an axiomatic integral.