Published March 9, 2023
| Version v1
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Behavioral up/down casting for statically typed languages (Coq artifact)
-
1.
University of Bologna
-
2.
University of Oxford
-
3.
Universidade Nova de Lisboa
Description
Artifact Submission
Title of the submitted paper: Behavioral up/down casting for statically typed languages
What does the artifact comprise?
The Docker image contains:
- Coq source code (in the
/proofsfolder); - HTML documentation (in the
/proofs/docsfolder).
Following is a mapping from definitions in the paper to the corresponding Coq ones:
| Definition | Paper | Coq file | Name of formalization | Notation |
|---|---|---|---|---|
| States | Definition 1 | Protocols.v | state | |
| Typestate name definitions | Definition 2 | Protocols.v | unfold | |
| State simulation | Definition 3 | Subtyping.v | state_sim | |
| Subtyping on states | Definition 4 | Subtyping.v | state_sub | a <s b |
| Algorithmic state subtyping | Definition 7 | Subtyping.v | state_sub_alg | |
| Types | Definition 10 | Types.v | ttype | |
| Subtyping on types | Definition 11 | Subtyping.v | type_sub | a <: b |
| Super relation on classes | Definition 14 | Classes.v | super | |
| Subtyping relation on classes | Definition 15 | Classes.v | class_sub | a <c b |
| Protocol input states | Definition 17 | Classes.v | prot_input_states | |
| Upcast on types | Definition 19 | Casting.v | upcast | |
| Downcast on types | Definition 24 | Casting.v | downcast | |
| Evolve on types | Definition 31 | Evolve.v | evolve | |
| Typestate Trees | Definition 36 | TypestateTrees.v | TT | |
| Well-formedness Of Typestate Trees | Definition 38 | TypestateTrees.v | well_formed_tt | |- tt |
| Upcast on typestate trees | Definition 39 | TypestateTrees.v | upcast_tt | |
| Closest subtree | Definition 41 | TypestateTrees.v | closest | |
| Downcast on typestate trees | Definition 43 | TypestateTrees.v | downcast_tt | |
| Evolve on typestate trees | Definition 45 | TypestateTrees.v | evolve_tt | |
| Typestate Tree Height | Definition 47 | TypestateTrees.v | height | |
| Classes in typestate tree set | Definition 48 | TypestateTrees.v | classes | |
| Find in typestate tree set | Definition 49 | TypestateTrees.v | find | |
| Merge on typestate trees | Definition 50 | TypestateTrees.v | merge_tt | |
| Sequence of upcasts on types | Definition 52 | Casting.v | upcast_many | |
| Soundness Of Typestate Trees | Definition 53 | Soundness.v | sound_tt |
Regarding some definitions in the paper that differ from the Coq formalization:
| Definition | Paper | Explanation |
|---|---|---|
| Reachable states | Definition 16 | Excluding unreachable states is an optimization, and since our results do not depend on it, we do not formalize it in Coq. |
| Typestates in type | Definition 18 | The purpose of this function is to contrain the typestates occuring in a type. In the paper, it is always used in the form typestates(t) ⊆ ProtInputStates(c). Because of that, in Coq, we define the relation all_typestates_in t c (defined in the Classes.v file with the notation t \in c) which states that all typestates in t belong to the protocol of class c. |
| No duplicate classes | Definition 37 | Defined directly with List.NoDup (classes tts), so no auxiliary definition is required. |
Following is a mapping from the main theorems and lemmas in the paper to the corresponding Coq ones:
| Theorem/Lemma | Paper | Coq file | Name of formalization |
|---|---|---|---|
| Reflexivity (of states subtyping) | Lemma 5 | Subtyping.v | state_sub_reflex |
| Transitivity (of states subtyping) | Lemma 6 | Subtyping.v | state_sub_trans |
| Algorithm soundness and completeness | Theorems 8 and 9 | Subtyping.v | state_sub_alg_sound_complete |
| Reflexivity (of types subtyping) | Lemma 12 | Subtyping.v | type_sub_reflex |
| Transitivity (of types subtyping) | Lemma 13 | Subtyping.v | type_sub_trans |
| Upcast preserves protocol membership | Lemma 20 | Casting.v | upcast_preserves_prot |
| Upcast Consistency | Theorem 21 | Casting.v | upcast_consistency |
| Upcast Least Upper Bound | Theorem 22 | Casting.v | upcast_least_upper_bound |
| Upcast Preserves Subtyping | Theorem 23 | Casting.v | upcast_preserves_subtyping |
| Downcast preserves protocol membership | Lemma 25 | Casting.v | downcast_preserves_prot |
| Downcast Consistency | Theorem 26 | Casting.v | downcast_consistency |
| Downcast Greatest Lower Bound | Theorem 27 | Casting.v | downcast_greatest_lower_bound |
| Downcast Preserves Subtyping | Theorem 28 | Casting.v | downcast_preserves_subtyping |
| Downcast reverses upcast | Corollary 29 | Casting.v | downcast_reverses_upcast |
| Upcast reverses downcast | Corollary 30 | Casting.v | upcast_reverses_downcast |
| Evolve preserves protocol membership | Lemma 32 | Evolve.v | evolve_preserves_prot |
| Evolve Preserves Subtyping | Theorem 33 | Evolve.v | evolve_preserves_subtyping |
| Evolve and upcast | Theorem 34 | Evolve.v | evolve_upcast |
| Evolve and downcast | Theorem 35 | Evolve.v | evolve_downcast |
| Typestate Trees Well-formedness Preserved By Upcast | Theorem 40 | TypestateTrees.v | wf_preserved_by_upcast |
| Closest correctness | Lemma 42 | TypestateTrees.v | closest_correct |
| Typestate Trees Well-formedness Preserved By Downcast | Theorem 44 | TypestateTrees.v | wf_preserved_by_downcast |
| Typestate Trees Well-formedness Preserved By Evolve | Theorem 46 | TypestateTrees.v | wf_preserved_by_evolve |
| Typestate Trees Well-formedness Preserved By Merge | Theorem 51 | TypestateTrees.v | wf_preserved_by_merge |
| Typestate Trees Soundness Preservation | Theorem 54 | Soundness.v | soundness_preserved_by_upcast, soundness_preserved_by_downcast, soundness_preserved_by_evolve, soundness_preserved_by_merge |
Software requirements
- Docker
- GNU Bash
Getting Started
- Open Docker Desktop with your GUI: this will launch the daemon.
- Open a shell.
Shell instructions
- Import the image provided into docker:
docker load -i behavioral-casting-coq.tar
- Run the docker image:
docker run -it behavioral-casting-coq:latest
- A prompt of the form
coq@f09e365aabf8:/proofs$should be opened. Now run:
make
Output
A successful compilation (make) indicates all the results hold.
Files
Files
(3.2 GB)
| Name | Size | Download all |
|---|---|---|
|
md5:5493f3f16b2fca57bed992b37757d318
|
3.2 GB | Download |