CS578 Spring 2024 Midterm Guide

The midterm is in-class (75 minutes) on Thursday, May 2.  

The exam will be closed book, using paper and pencil.

Any language definitions, transition rules, and typing rules that you might need
will be provided with the exam, so there is no need to memorize these.

There will be no OCaml code to read or write on the exam.

Broadly, the exam will cover:
  - Pierce Chapters 1-11, and the Contextual Semantics handout
  - Homeworks 1-4
  - Lectures through Apr. 25.

More specifically, here is a list of topics:

  Basic Concepts:
    Syntax of terms and types
    Small-step semantic evaluation rules
    Contextual semantic rules
    Big-step semantic evaluation rules
    Typing rules  

  Induction proof techniques:
    Structural induction on terms
    Induction on derivations
    Induction on the length of a derivation sequence

  Languages:
    Arithmetic+Boolean expressions (untyped and typed)
    Untyped lambda calculus (pure and applied)
       (Note: You do NOT need to memorize encodings such as the Church numerals.)
    Simply-typed lambda calculus (STLC)
    STLC with extensions: Booleans, Arithmetic, Unit, Ascription, Sequencing, Let, Pairs, Sums, Recursion

  Definitions of metaproperties:
    Determinism (one-step and multi-step)
    Termination (= normalization)
    Uniqueness of normal forms  
    Uniqueness of typing
    Progress
    Preservation
    Type Safety

  Proofs that metaproperties hold (or counterexamples showing that they don't) for specific languages.

Some typical questions:

  - Apply evaluation and/or typing rules to specific examples.
  - Given a modification to one of the standard languages we've studied, determine what
    metaproperties hold.
  - Given an outline proof of some metaproperty on some language, fill in the missing cases.
  - Prove from scratch a simple result requiring structural induction on terms.