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This artifact comprises the Coq implementation of supporting proofs of the material in the ICFP'18 paper titled 'Static Interpretation of Higher-Order Modules in Futhark'.


These files have been tested with the The Coq Proof Assistant, version 8.6 (March 2018) under Mac and under Linux.

Compiling the files

To compile the files, run make.

To clean-up, run make clean

Step-by-Step Guide

In this section, we give a short description of the development of the module system formalisation. We outline the file structure of the project and describe the content of the source files with the references to the paper text.

Throughout our development, we assume axioms of functional extensionality and proof-irrelevance. The main development is fully formalised and does not contain admitted theorems. Parts of the material in the Experimental folder contain admitted lemmas, but these parts serve as direction for further improvement.

Main development

Basics.v : Definitions and notations for identifiers.  Properties
  of equality for the proofs involving dependent types.

Syntax.v : Syntax for the source language (core language and
modules) --- Section 2.

Target.v : Target language syntax and semantics --- Section 5.1.

SemObjects.v : Semantic objects definition (Section 4, Figure 4),
  enrichment relation (Section 4.1).

ElabCore.v : Elaboration rules for core-level types, expressions
  and declarations; examples --- Section 4.4, Figure 6.

MiniElab.v : Elaboration rules for modules --- Section 4.5,
  Figures 7 and 8.

CompCore.v : Compilation rules for core-level expressions and
  declarations --- Section 5.4, Figure 10.

IntObjects.v : Interpretation objects, interpretation erasure,
  environment filtering --- Sections 5.2, 5.3 and 5.5.

MiniInt.v : Static interpretation relation (Section 5.6,
  Figure 12), type consistency logical relation (Section 6,
  Figure 13), and the proof of termination (Section 6,
  normalisation part of Proposition 6.1).

Finite maps and sets

SetExt.v : Finite sets with extensionality.

EnvExt.v : Environments (finite maps) with
  extensionality. Includes an isomorphic (to the one form the Coq
  standard library) and a representation of environments used to
  overcome some issues with the strict-positivity checker --- see
  Section 9.

Nominal techniques

NomEnv.v : Nominal set of semantic objects and interpretation

Nom.v : Basic definitions of nominal sets and a nominal set of
  finite sets of atoms. This part of the development is generic
  and can be used in different contexts.

CpdtTactics.v : Some tactics from CPDT.

CustomTactics.v : Selected tactics from Pierce et al.; some custom

Supplementary examples

stlc.v : Proof of termination of simply-typed lambda calculus.

Example.v : Examples showing that Coq can reject certain strictly
  positive inductive definitions. We provide workarounds for this
  issue for simple examples.  In our development, we use similar
  techniques to define semantic objects.

Experimental development (future work)

Experimental/MiniElab1.v : Elaboration rules with
  alpha-equivalence. An example, showing when alpha-equivalence is
  important for the elaboration.


Public artifact for ICFP'18 paper on Futhark modules




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