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Discussion of the connection between normalization and logical consistency. One approach is to prove normalization and type preservation, to show (in proof-theoretic terms) that all detours can be eliminated from proofs (this is normalization) and that the resulting proof still proves the same theorem (this is type preservation). I mention an alternative I use for Cedille, which is to use a realizability semantics (often used for normalization proofs) directly to prove consistency.
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TÌM KIẾM CÁC TẬP TRƯỚC
Tìm kiếm các tập trước của Iowa Type Theory Commute.
CÁC TẬP KHÁC TRONG PODCAST NÀY
In this episode, I talk about the control operator callcc, and how it is implemented during compilation using continuation-passing style (CPS). I sketch how CPS conversion (transforming a program with callcc into one in CPS that does not need callcc any more) corresponds to double-negation transla…
In this episode, I talk about a somewhat more advanced case of the Curry-Howard isomorphism (the connection between logic and programming languages where formulas in logic are identified with types, and proofs with programs). This is the identification of double-negation translations in logic, whi…
I discuss a nice paper I quite enjoyed reading, called The Calculated Typer, by Garby, Bahr, and Hutton. The authors take a very nice general look at the specification of a type checker, for a very simple expression language. They then manually derive the actual code for the type checker by effec…
I am currently on a frolic into the literature on Control Flow Analysis (CFA), and discuss what this is, for pure lambda calculus. A wonderful reference for this is this paper by Palsberg.
Commuting conversions are transformations on proofs in natural deduction, that move certain stuck inferences out of the way, so that the normal detour reductions (which correspond to beta-reduction under Curry-Howard) are enabled. The stuck inferences are uses of disjunction elimination. In progr…
Tuyên bố miễn trừ trách nhiệm: Podcast và tác phẩm nghệ thuật được nhúng trên trang này là của Aaron Stump, là tài sản của chủ sở hữu và không được liên kết hoặc xác nhận bởi Listen Notes, Inc.
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