v-- / lcpt

Some exercises from a lambda calculus course

Lambda calculus and proof theory

This repository contains some of the exercises for an introductory course for lambda calculus with elements of proof theory.

Most of the exercises are propositions for proving and so this repository contains only the fraction of exercises that require implementations.

All exercises are verified with unit tests that can be ran using make test=exercises/2.1.hs or, in order to run all the tests, simply make test.

Terms

The term implementation in the types/term directory contains a parser and a serializer for terms. Haskell's read and show functions can also be used. Here are some specificities of the representation:

• All valid Char value are valid variable names. Even read "λ" :: Var creates a variable named λ.
• Variables are ordered and enumerable, so comparison and succ are valid operations on variables. This is useful for creating new variables for use in substitution.
• Term types are sum types of VarTerm, Combination or Abstraction types. The string representations are:
  • Variable names for VerTerm values.
  • Concatenated terms in parentheses for Combination values (e.g. (xy))
  • A λ character concatenated with a variable name and a term, put in parentheses for Abstraction values (e.g. (λxy) or even (λλλ))