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Type Theory

Discuss type-theoretic foundations and their applications to program analysis.
Topics include dependent types, gradual typing, refinement types, sized types, coinductive systems, and connections to abstract interpretation.
"Any static program analysis, such as the type checking algorithms in the semantic analysis phase of a compiler, has a connection to type theory."

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Dependent Types for Program Analysis
Can Π-types encode flow-sensitive properties? I've been thinking about how dependent types can express data-flow invariants...
Pinned Discussion 🔥 Hot
Started by AbstractKitty
AbstractKitty
83 replies
4.1k views
Today, 11:42
by FixpointFeline
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Gradual Typing is a Galois Connection?
AGT says gradual types are abstractions of sets of static types, formally captured via a Galois connection...
🔥 Hot Discussion
Started by GaloisCat
GaloisCat
61 replies
2.9k views
Today, 09:17
by MeownadTransformer
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Sized Types in Agda Deep Dive
Working through Abel's sized types in Agda. The ordinal annotations are making my head spin — anyone have good intuition pumps?
Agda Discussion
Started by CatamorphismCleo
CatamorphismCleo
34 replies
1.4k views
Yesterday, 22:05
by AbstractKitty
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Coinductive Type Systems and Productivity
How do productivity checks interact with abstract interpretation over infinite domains? The co-natural numbers lattice seems relevant here...
Coinduction Discussion
Started by FixpointFeline
FixpointFeline
27 replies
980 views
Mar 25, 18:44
by GaloisCat
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Refinement Types vs Abstract Interpretation
Both approaches aim to prove program properties statically. Are refinement types just abstract interpretation in disguise? Let's compare...
New Discussion
MeownadTransformer
19 replies
623 views
Mar 26, 14:30
by CatamorphismCleo
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Curry-Howard Correspondence for Program Analysis
If propositions-as-types holds, does proof-as-program give us verified analyses for free? Discussion on extracting certified analyzers...
Discussion
Started by FixpointFeline
FixpointFeline
45 replies
2.2k views
Mar 24, 10:01
by AbstractKitty
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HoTT and Program Analysis: Any Connection?
Homotopy type theory is an active research direction — does univalence or higher inductive types have any relevance to static analysis?
Discussion
Started by CatamorphismCleo
CatamorphismCleo
11 replies
441 views
Mar 22, 19:55
by GaloisCat
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Liquid Types Deep Dive (LiquidHaskell etc.)
Working through the Liquid Types paper. The SMT-backed refinement checking is slick but what are the fundamental limits?
Discussion New
MeownadTransformer
22 replies
799 views
Mar 23, 08:14
by AbstractKitty
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