This repository holds formalizations of a variety of programming language topics in the style of Software Foundations.

To use, you'll need a copy of the latest version of Software Foundations. Once that is installed, you'll need to update the _CoqProject file to point LF and PLF to the locations of Volumes 1 + 2 of Software Foundations. With that done, running make in the top-level directory will build everything.

Church Encodings (ChurchEncodings)

A deeply embedded formalization of the untyped lambda calculus with natural numbers, as well as a number of examples of church-encoded datatypes (namely booleans, pairs, natural numbers, and lists).

• LCNat.v: a formalization of the untyped lambda calculus with natural numbers
• Church.v: several church encoding examples

Denotational Semantics (DenotationalSemantics)

The denotational semantics of a simple imperative language.

• Fixpoints.v: basics of fixpoints of monotone functions
• Denotational.v: denotational semantics of Imp from Software Foundations