amintimany / iris-io

iris-io

Verifies with

• Coq 8.7.2
• Coq-std++
• Ssreflect
• Iris
• Autosubst

To verify, just type make.

Structure

• prelude/base.v - Streams
• lang.v - Syntax and instrumented small-step semantics of a programming language with incremental prophecy variables and IO specifications. Prophecy variable creation nondeterministically picks a stream of prophecy values; prophecy variable assignment loops if the assigned value does not match the first prophecy value of the stream, and otherwise replaces the stream by its tail in the prophecy heap.
• lang_proph_erased.v - An alternative small-step semantics for the same language, where the prophecy heap simply tracks the set of allocated prophecy variable identifiers. Creation does not branch; assignment does not loop.
• proph_erasure.v - Proves that if a program is safe under the prophecy instrumented semantics, then it is safe under after erasing prophecies.
• rules.v - Proves Hoare rules for the commands of the programming language against the instrumented semantics. These rules expose the prophecy variables as constrained incremental prophecy variables: an arbitrary (satisfiable) predicate on streams can be provided at prophecy variable creation time; the postcondition asserts that the prophecy value stream satisfies the predicate.
• adequacy.v Shows that proving a weakest precondition for the instrumented semantics (with both prophecies and IO specifications) implies safety of the fully erased program.
• abstract_petrinet.v Defines abstract Petri nets where places are Iris propositions.
• coin.v - Verifies the coin toss concurrent data structure.
• buffered_io.v Proves correctness of buffered output example.
• channel.v A simple in memory channel based on lists.
• chat_server.v A chat server example where the reading and writing over the network is abstracted.
• chat_server_concrete.v A concrete implementation of the chat server in chat_server.v which implements communication over the network as IO.
• full_erasure.v Erases the IO specifications from programs where prophecies are already erased.
• lang_fully_erased.v The programming language fully erased.
• petrinet.v Implements Petri nets in Iris.

Axioms used

Note that axioms below reported by coqchk starting with "iris." are not axioms; coqchk gets confused by the module system of Coq.

$ coqchk -o -R . iris_io -silent -admit stdpp.pretty iris_io.erasure iris_io.coin

CONTEXT SUMMARY
===============

* Theory: Set is predicative

* Axioms:
    Coq.Logic.FunctionalExtensionality.functional_extensionality_dep
    Coq.Logic.PropExtensionality.propositional_extensionality
    Coq.Logic.Classical_Prop.classic
    iris.base_logic.lib.iprop.iProp_solution.iPreProp
    iris.base_logic.lib.iprop.iProp_solution.iProp_fold
    iris.base_logic.lib.iprop.iProp_solution.iProp_fold_unfold
    iris.base_logic.lib.iprop.iProp_solution.iProp_unfold
    iris.base_logic.lib.iprop.iProp_solution.iProp_unfold_fold