The Mechanized Semantic Library is a collection of mathematical techniques useful for developing semantic models of program logics and type systems. The library has a special emphasis on techniques which integrate smoothly into a mechanical theorem prover; at the moment the library is only available for use in Coq.
The Mechanized Semantic Library is made available under a BSD-style license.
|1.||Base||Axioms for computation; custom tactics; basic theorems|
|2.||Separation Algebras||Compositional semantic models for separation logic||, |
|4.||Shares||Share accounting to model fractional ownership in separation logic|||
|5.||Indirection Theory||Semantic models for approximating contravariant circularities|||
|6.||Logics||Definitions of substructural and modal logics||, , |
|||Multimodal Separation Logic
for Reasoning About Operational Semantics
|R. Dockins, A. W. Appel, A. Hobor||BibTeX|
|||A Fresh Look at Separation Algebras and Share Accounting||R. Dockins, A. Hobor, A. W. Appel||BibTeX|
|||A Theory of Indirection via Approximation||A. Hobor, R. Dockins, A. W. Appel||BibTeX|
List order is by publication date. For a mapping of files to papers please see the file list.
The goal of the Concurrent C Minor Project is to connect machine-verified source programs in sequential and concurrent programming languages to machine-verified optimizing compilers.
|#||File name||Component||Associated paper(s)|
|4.||sepalg_generators.v||Separation Algebras||, |
|16.||predicates_hered.v||Logics||, , |
This file contains the axiom base for the development. We assume the classical axiom, dependent unique choice, relational choice, functional extensionality and propositional extensionality. However, the proofs in this distribution use only the extensionality axioms.
This exports the parts of the Coq standard library used throughout the development as well as a few custom convenience tactics.
This file defines our relational form of separation algebras with the disjointness axiom. We also define the join_sub relation and the joins relation. Additionally, elementary lemmas about the definitions are proved.
We define SA operators in this file. All the operators mentioned in  and  appear here, along with a few others.
This file defines boolean algebras from an order-theoretic perspective. We also define axioms relating to properties we desire of share models, including relativization, splitting and token factory axioms.
Here we construct the boolean-labeled tree share model as discussed in . Note, however, that the proof of the token counting axioms follow a slightly different path than the proof in that paper. This is mostly because reasoning about sets in Coq is inconvenient.
This file simply repackages the construction from tree_shares.v into a nicer interface for downstream users. We also define the notion of a "positive" share; that is a nonunit share.
This file contains the central "knot" development used to model approximations to contravariant circularities. Included are both the axiomitization and the model construction. It follows section 8 of  quite closely.
An alternate, axiom-free, development of the knot. We avoid the need for the extensionality axiom by working explicitly up to equivalance relations and weakening the axioms of the theory accordingly.
Easy lemmas that follow from the theory of indirection.
The definition of a separation algebra on top of knots. In addition to the properties mentioned in , this development adds several properties (unage_join1 and unage_join2), which require the additional input axiom F_preserves_unmaps. These properties will be covered in an upcoming paper.
This file specializes the knot and knot_sa constructions to use "Prop" as truth values.
A technical development of "unmapping" needed to get the extra unage* properties in knot_sa.
The development of the uniqueness proof for knots. We prove that any two implementations of the theory of indirection are isomorphic.
We enhance the signature of separation algebras with a notion of aging. The "ASA" typeclass presents an interface sufficient to define the Kripke model below. The interface is straightforwardly implemented using the properties obtained from knot_sa.
Definition of the higher-order modal separation logic as discussed in sections 2, 4, 5, and 6 of ; section 4 of ; and sections 5, 6, and 7 of .
Copyright (c) 2009, Andrew Appel, Robert Dockins and Aquinas Hobor.
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