Midterm Review

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Midterm Review
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Problem 1

• Q1 Tail-recursive factorial
• Assignment 2
• Q2 Factorial with mutable references
• similar example in Section 6.1
• Q3 Functional representation of sets
• last year's midterm

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Problem 2

• Q1 A derivable rule is admissible.
• Section 2.3"A derivable rule is certainly
  admissible, but ..."
• Q3 ?-conversion in Exercise 3.1
• Q4 Definition of fixed points
• if f(v) v, then (f o f o ... o f)(v) v.
• Q6 Type inhabitation
• Section 5.5

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Problem 2

• Q7 Soundness vs. Completeness
• Section 7.1"... an algorithmic typing judgment
  covers all possible cases of well-typed
  expressions and is thus complete."
• Q8 Static type system for a safe language
• TPL page 6"Language safety is not the same
  thing as static type safety."

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Problem 3

• Q1 Call-by-name reduction
• example in Section 3.2
• Q3 Encoding bool
• Section 5.3
• Q4 Fixed point construct
• Section 5.4

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Problem 3

• Q5 Reduction of mutable references
• more complicated example in Section 6.2
• Q6 Store typing judgment
• a rule in Section 6.3

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Problem 3

• Q7 Environment semantics
• definition and rules in Section 9.2
• Q8 Templates in C
• A Critical Look at Programming Languages"Unfortu
  nately, the C language bastardizes this concept
  in its support for templates ..."

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Problem 4

• Inductive definition
• Inductive function

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Problem 5 Logarithm

• Q1 Fixed point combinator
• ¼ Can you write an SML function for log?
• fun log n if n 1 then 0 else 1 (log (n /
  2))
• Q2 log without the fixed point combinator
• Idea
• (8, 0) ! (4, 1) ! (2, 2) ! (1, 3) ! (1, 3) ! (1,
  3) ! (1, 3) ! (1, 3) ! (1, 3)
• an error in the sample solution

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Problem 6 Complete CBN

• Answer to Q1
• A typical wrong answer in Q1

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Problem 7

• Q1 Substitution
• Q2 Type preservation
• good job!
• Significant upgrade from PL 2006!
• Quizzes are good!
• We will have two more quizzes!

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Score Distribution
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CSE-321 Programming LanguagesAbstract Machine E
???

• POSTECH
• April 30, 2007

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Operational Semantics of ?-Calculus
no substitution
explicit analysis of an expression
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Key Ideas in Environment Semantics

• No substitution
• Delay the substitution v / x e as much as
  possible.
• store v / x in the environment.
• proceed to evaluate e.
• replace x by v only if necessary.
• A closure stores the values of all free variables
  in a given ?-abstraction.

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Environment Semantics
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Abstract Machine E
explicit analysis of an expression and no
substitution
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Outline

• Overview V
• Abstract machine E
• Fixed point construct

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Abstract Machine C Environment Semantics
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States of the Abstract Machine E
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Definition
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State Transition
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State Transition
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State Transition
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Example
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Outline

• Overview V
• Abstract machine E V
• Fixed point construct

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Reduction Rule
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fix for creating recursive functions
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Abstract Syntax and Typing
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Reduction