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.

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.

References:

• Mult example: mult.sml

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Frank Pfenning