An overview of the Coq Formalization

For the Coq code, click on the file name of each part of the development.

Basic constructions on top of and extensions to Iris

• The future modalities: future.v
• Saved predicates: saved_pred.v
• IC predicates: IC.v
• IC triples: ICTriple.v

STLang

• The language is defined in lang.v, where it is also registered as an Iris language.
• The type system is formalized in typing.v

Logical relations

• logrel_shared.v contains the part of the definitions of logical relation that are shared between the two logical relations.
• The main logical relation
• The logical relation is defined in logrel.v.
• The fundamental theorem is proven in fundamental.v.
• The fact that logical relatedness is closed under well-typed contexts logrel_ctx_closure.v.
• Soundness with regard to contextual equivalence is proven in soundness.v.
• The NN-logical relation
• The NN-logical relation is defined in logrelNN.v.
• The fundamental theorem is proven in fundamentalNN.v.
• The fact that NN-logical relatedness is closed under well-typed contexts logrelNN_ctx_closure.v.
• Soundness with regard to contextual equivalence is proven in soundnessNN.v.

The Theorems

• The State Independence Theorem is proved in state_independance.v.
• Neutrality, Idempotency and Commutativity are proven in basic_equations.v.
• Rec Hoisting is proven in rec_hoisting/rec_hoisting.v.
• Λ Hoisting is proven in tlam_hoisting.v.
• η-Expansion for Rec rec_eta.v.
• η-Expansion for Λ tlam_eta.v.
• β-Reduction for λ lam_beta.v.
• Rec-Unfolding rec_unfolding.v.
• β-Reduction for Rec rec_beta.v.
• β-Reduction for Λ tlam_beta.v.
• Left identity, Right identity and associativity for the ST monad are proven in effectful_equations.v.

Misc.

• reduction.v contains general auxiliary lemmas about reductions for Iris languages in general.
• ST_Lang_reduction.v contains lemmas about the operational semantics of STLang.