cs-4400-sp26

Lecture 5: Church Encodings

In this lecture, we introduce the following concepts:

• Compilers and what it means for them to be “correct”
  • the compiler correctness square

  •        compile
    source ~~~~~> target
    ||               ||  interpreters
    vv               vv
    v_s  ~~~~~~~~>  v_t
    

• Encoding data in untyped lambda calculus
  • Booleans
    • true = \x.\y.x
    • false = \x.\y.y
    • not, or, if-then-else
    • Plait implementation to test
  • Numbers
    • Peano numbers (unary natural numbers, zero and successor)
    • Church numerals
    • Encoding +1
    • Encoding addition
• Notion of “equals” for the concept of compiler correctness