Clutch Project

This repository contains the formal development of multiple higher-order probabilistic separation logics for proving properties of higher-order probabilistic programs. All of the logics are built using the Iris program logic framework and mechanized in the Coq proof assistant.

Publications

Error Credits: Resourceful Reasoning about Error Bounds for Higher-Order Probabilistic Programs
Alejandro Aguirre, Philipp G. Haselwarter, Markus de Medeiros, Kwing Hei Li, Simon Oddershede Gregersen, Joseph Tassarotti, Lars Birkedal
arXiv:2404.14223

Almost-Sure Termination by Guarded Refinement
Simon Oddershede Gregersen, Alejandro Aguirre, Philipp G. Haselwarter, Joseph Tassarotti, Lars Birkedal
arXiv:2404.08494

Asynchronous Probabilistic Couplings in Higher-Order Separation Logic
Simon Oddershede Gregersen, Alejandro Aguirre, Philipp G. Haselwarter, Joseph Tassarotti, Lars Birkedal
In POPL 2024: ACM SIGPLAN Symposium on Principles of Programming Languages

Building the development

The project is known to compile with

• Coq 8.19.1
• std++ 1.10.0
• Iris 4.2.0
• Coquelicot 3.4.1
• Autosubst 1.8
• Mathcomp-solvable 2.2.0

The recommended way to install the dependencies is through opam.

1. Install opam if not already installed (a version greater than 2.0 is required).
2. Install a new switch and link it to the project.

opam switch create clutch 4.14.1
opam switch link clutch .

3. Add the Coq and Iris opam repositories.

opam repo add coq-released https://coq.inria.fr/opam/released
opam repo add iris-dev https://gitlab.mpi-sws.org/iris/opam.git
opam update

4. Install the right version of the dependencies as specified in the clutch.opam file.

opam install . --deps-only

You should now be able to build the development by using make -j N where N is the number of cores available on your machine.

Axioms

The development relies on axioms for classical reasoning and an axiomatization of the reals numbers, both found in Coq's standard library. For example, the following list is produced when executing the command Print Assumptions eager_lazy_equiv. in theories/clutch/examples/lazy_eager_coin.v:

ClassicalDedekindReals.sig_not_dec : ∀ P : Prop, {¬ ¬ P} + {¬ P}
ClassicalDedekindReals.sig_forall_dec : ∀ P : nat → Prop, (∀ n : nat, {P n} + {¬ P n}) → {n : nat | ¬ P n} + {∀ n : nat, P n}
functional_extensionality_dep : ∀ (A : Type) (B : A → Type) (f g : ∀ x : A, B x), (∀ x : A, f x = g x) → f = g
constructive_indefinite_description : ∀ (A : Type) (P : A → Prop), (∃ x : A, P x) → {x : A | P x}
classic : ∀ P : Prop, P ∨ ¬ P