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Published March 9, 2023 | Version v1
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Behavioral up/down casting for statically typed languages (Coq artifact)

Authors/Creators

  • 1. ROR icon University of Bologna
  • 2. ROR icon University of Oxford
  • 3. ROR icon 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 /proofs folder);
  • HTML documentation (in the /proofs/docs folder).

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

  1. Import the image provided into docker:
  • docker load -i behavioral-casting-coq.tar
  1. Run the docker image:
  • docker run -it behavioral-casting-coq:latest
  1. 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