HW 10 – Type Checking and Evaluation
CS 421 – Spring 2008
Revision 1.0
Assigned April 10, 2008
Due April 17, 2008, submit in class
Extension due April 17, 5:00 pm, 20% penalty
Guideline:
•For problems 1 and 2, write your answers in the blanks right on page 1 and 2. For other problems, use the
templates provided starting on page 3.
•If you’re submitting late, hand in your homework either to Prof. Kamin in room 4237 or to Baris Aktemur in
room 4307, by 5:00pm on April 17, Thursday. Note that 20% penalty applies.
•Submit hard-copy only. No electronic submission.
Problem 1. We gave three versions of the dynamic semantics of OCaml in class:
(Env) Environment-based definition, 4/3, slides 10–11
(Rew) Rewriting version (β-value reduction), 4/3, slides 12-13
(Env-σ) Environment, with state, 4/8, slides 4-5. (Note that we have added a rule for sequencing (semicolon) that
wasn’t in the original notes.)
For each one, give a semantics for the pair operation and the fst and snd operations. Assume an expression
(e1, e2)produces a value that is written (v1, v2)(i.e. pairs are values).
(Env) e1,ρ⇓v1e2,ρ⇓v2
(e1,e2),ρ ⇓(v1,v2)
e,ρ⇓(v,v0)
fst e,ρ ⇓v
e,ρ⇓(v0,v)
snd e,ρ ⇓v
(Rew) e1⇓v1e2⇓v2
(e1,e2)⇓(v1,v2)
e⇓(v,v0)
fst e⇓v
e⇓(v0,v)
snd e⇓v
(Env-σ)ρ,σ`e1⇓v1,σ00 ρ,σ00`e2⇓v1,σ0
ρ,σ`(e1,e2)⇓(v1,v2),σ0
ρ,σ`e⇓(v,v0),σ0
ρ,σ`fst e⇓v,σ0
ρ,σ`e⇓(v0,v),σ0
ρ,σ`snd e⇓v,σ0
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