Class 18: Scheme Semantics (3)

Held Friday, March 5

Summary

• Assignment 3 due.

Contents

Notes

• Start reading Backus's paper before next week.
• I note that a number of you are still using my office as a hallway.
  • Given the current state of the office, I'm not sure that's a good idea.
  • It's okay in many cases, but if either door is closed, you should not walk through my office.
• Are there any final questions on assignment 3?

Notation

A web page can't do everything they can do.

• Concatenation: &
• Kth element: @
• Drop first k elements: !
• Is an element of: is in

Semantic Functions

The meaning of a variable

E[[I]] = \u k . hold (lookup u I) (single (\ e . e = undefined -> wrong ``undefined variable'', send e k))

• What's going on with the \e . e
  • Hint: that's a misparse
• What does single do?
  single : (E -> C) -> K
  single = \f e* . #e* = 1 -> f (e* @ 1), wrong ``wrong number of return values''
• What does lookup do? Does it really need to be there?
  lookup : U -> Ide -> L
  lookup = \u I . u I
• What does hold do?
  hold : L -> K -> C
  hold = \l k s . send (s l @ 1) k s
  • Why does it have three arguments in the definition, but only two in the type?
  • Why does it call send with three arguments, when send only expects two?

The meaning of function application

E[[(E E*)]] = \ u k . E* (permute(<E> & E*)) u (\e₁* . ((\e₂* . applicate (e₂* @ 1) (e₂* ! 1) k) (unpermute e₁*)))

• Why are there two \e* expressions?
• What do we know about permute and unpermute?
• What do we know about applicate?
  applicate : E -> E* -> K -> C
  applicate = \e e* k . e is in F -> (e | F @ 2) e* k, wrong ``bad procedure''
• What do we note about E*?

The meaning of lambda abstraction

You're foolish if you think that I'm going to retype the meaning of a lambda abstraction.

• Why are we using injection?
• What does tievals do?
• ...

History

• Created Tuesday, January 19, 1999 as a blank outline.
• Filled in the details on Friday, March 5, 1999. Some were taken from a previous outline.