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https://github.com/DeepSpec/InteractionTrees
A Library for Representing Recursive and Impure Programs in Coq
https://github.com/DeepSpec/InteractionTrees
Last synced: 3 months ago
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A Library for Representing Recursive and Impure Programs in Coq
- Host: GitHub
- URL: https://github.com/DeepSpec/InteractionTrees
- Owner: DeepSpec
- License: mit
- Created: 2018-06-21T18:53:18.000Z (over 6 years ago)
- Default Branch: master
- Last Pushed: 2024-04-19T15:04:00.000Z (9 months ago)
- Last Synced: 2024-08-01T03:42:19.620Z (5 months ago)
- Language: Coq
- Homepage:
- Size: 5.22 MB
- Stars: 195
- Watchers: 17
- Forks: 49
- Open Issues: 28
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: LICENSE
Awesome Lists containing this project
- awesome-coq - Interaction Trees - Library for representing recursive and impure programs. (Projects / Libraries)
README
# Interaction Trees [](https://travis-ci.com/DeepSpec/InteractionTrees)
A Library for Representing Recursive and Impure Programs in Coq
## Introduction
For a quick overview of the core features of the library, see
[`examples/ReadmeExample.v`](./examples/ReadmeExample.v).
See also [the tutorial](./tutorial/README.md).
[The coqdoc documentation for this library is available here.](https://deepspec.github.io/InteractionTrees/)
### Top-level modules
- `ITree.ITree`: Definitions to program with interaction trees.
- `ITree.ITreeFacts`: Theorems to reason about interaction trees.
- `ITree.Events`: Some standard event types.
## Installation
### Via opam
```
opam install coq-itree
```
### Dependencies
- [coq](https://coq.inria.fr/)
- [coq-paco](https://github.com/snu-sf/paco)
- [coq-ext-lib](https://github.com/coq-community/coq-ext-lib)
See [`coq-itree.opam`](./coq-itree.opam) for version details.
## Axioms
This library currently depends on UIP, functional extensionality, excluded middle,
and choice; see also [`theories/Axioms.v`](./theories/Axioms.v).
### UIP
This library depends on UIP for the inversion lemma:
```coq
Lemma eqit_inv_Vis
: eutt eq (Vis e k1) (Vis e k2) ->
forall x, eutt eq (k1 x) (k2 x).
```
There are a few more lemmas that depend on it, but you might not actually need
it. For example, the compiler proof in `tutorial` doesn't need it and is
axiom-free.
That lemma also has a weaker, but axiom-free version using heterogeneous
equality: `eqit_inv_Vis_weak`.
The axiom that's technically used here is `eq_rect_eq` (and also `JMeq_eq` in
old versions of Coq), which is equivalent to UIP.
### Functional extensionality
The closed category of functions assumes `functional_extensionality`,
in [`Basics.FunctionFacts.CartesianClosed_Fun`](./theories/Basics/FunctionFacts.v).
### Excluded middle and choice
The theory of traces (`theories/ITrace/`)—which Dijkstra monads for ITree
depend on (`theories/Dijkstra`)—assumes excluded middle, to decide whether an
itree diverges, and a type-theoretic axiom of choice, which provides a strong
excluded middle in propositional contexts:
```
Theorem classicT_inhabited : inhabited (forall T : Type, T + (T -> False)).
```
Remark: excluded middle implies UIP, but we still consider UIP as a separate
dependency because it's used in a more central part of the library.
### Exported: strong bisimulation is propositional equality
The library exports the following axiom for convenience, though it's unlikely
you'll need it, and the rest of the library does not depend on it:
```coq
Axiom bisimulation_is_eq : t1 ≅ t2 -> t1 = t2.
```
## Contributions welcome
Feel free to open an issue or a pull request!
See also [`DEV.md`](./DEV.md) for working on this library.