GPLC is a gradual source probabilistic lambda calculus formalized with probabilistic couplings for static relations, elaborated to a distribution-based target language TPLC, and proven type-safe with conservative extension and gradual guarantee properties.
IfΓ⊢v≈𝑣 ′ : Bool,Γ⊢m 1 ≈𝑚 ′ 1 : 𝑇 ,Γ⊢m 2 ≈𝑚 ′ 2 : 𝑇 , 𝜀⊢Bool∼BoolthenΓ⊢if v then m 1 else m2 ≈let𝑥=𝜀𝑣 ′ :: Bool in if𝑥then m 1 else m2 : 𝑇
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A Gradual Probabilistic Lambda Calculus
GPLC is a gradual source probabilistic lambda calculus formalized with probabilistic couplings for static relations, elaborated to a distribution-based target language TPLC, and proven type-safe with conservative extension and gradual guarantee properties.