The examples subcollection contains several small languages 
to demonstrate various different uses of PLT Redex:

  arithmetic.rkt: an arithmetic language with every
  possible order of evaluation

  beginner.rkt: a PLT Redex implementation of (much of) the
  beginning student teaching language.

  church.rkt: Church numerals with call by name
  normal order evaluation

  combinators.rkt: fills in the gaps in a proof in
  Barendregt that i and j (defined in the file) are
  a combinator basis

  compatible-closure.rkt: an example use of compatible
  closure. Also, one of the first examples from Matthias
  Felleisen and Matthew Flatt's monograph

  cont-mark-transform: the continuation mark transformation from
  McCarthy's ICFP '09 paper “Automatically RESTful Web Applications
  Or, Marking Modular Serializable Continuations" 

  contracts.rkt: A core contract calculus, including blame, 
  with function contracts, (eager) pair contracts, 
  and a few numeric predicates

  delim-cont: The model from Flatt, Yu, Findler, and Felleisen's ICFP
  '07 paper "Adding Delimited and Composable Control to a Production
  Programming Environment"

  letrec.rkt: shows how to model letrec with a store and
  some infinite looping terms

  omega.rkt: the call by value lambda calculus with call/cc.
  Includes omega and two call/cc-based infinite loops, one of
  which has an ever-expanding term size and one of which has
  a bounded term size.

  pi-calculus.rkt: a formulation of the pi calculus, following
  Milner's 1990 paper, "Functions as Processes"

  racket-machine: an operational semantics for (much of) Racket 
  bytecode

  r6rs: an implementation of the R6RS Scheme formal semantics

  semaphores.rkt: a simple threaded language with semaphores

  subject-reduction.rkt: demos traces/pred that type checks
  the term.

  threads.rkt: shows how non-deterministic choice can be
  modeled in a reduction semantics. Contains an example use
  of a simple alternative pretty printer.

  types.rkt: shows how the simply-typed lambda calculus's
  type system can be written as a rewritten system (see
  Kuan, MacQueen, Findler in ESOP 2007 for more).