EPISODE · Mar 9, 2020 · 14 MIN
Normalization and logical consistency
from Iowa Type Theory Commute · host Aaron Stump
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.
What this episode covers
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.
NOW PLAYING
Normalization and logical consistency
No transcript for this episode yet
Similar Episodes
Mar 4, 2026 ·7m
Feb 22, 2026 ·9m
Feb 8, 2026 ·11m
Feb 2, 2026 ·12m
Jan 30, 2026 ·31m
Jan 29, 2026 ·39m