15-317 Constructive Logic
Recitation 5: Common Mistakes and Classical Computation

Today in recitation we went over selected solutions to problems from Assignment 2. We highlighted some common mistakes and misconceptions to watch out for:

  • Don't name two parameters the same: if a derivation uses two rules that introduce a parameter, make sure they're different.
  • Don't let parameters escape their scope: closed-scope elims like OrE and ExistsE introduce hypotheses only in certain premises, and they shouldn't leak into the conclusion. (Closed-scope elims sort of turn your proof on its side: instead of deriving downward, you gain a new assumption in a new line of reasoning.)
  • Don't confuse terms and parameters. Metavariables like t, s, and r represent general terms with arbitrary structure, while metavariables like a, b, and c represent parameters that can be substituted for. (We sometimes also use x, y, and z to be parameters.)
  • Do make sure metavariables don't overlap. In particular, when showing a local reduction, name all of the subderivations and subterms differently, so as to ensure that the derivation you are reducing is as general as possible.
Check the Homework 2 Solutions for details.

We also talked intuitively about classical computation, going over the multiplication early-exit example from class. Call/cc or let/cc is a primitive that lets you capture the current continuation, or "rest of the program", in such a way that it can be restored later by throw'ing a value to it. That value replaces the entire call/cc expression.


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Frank Pfenning