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Then ๐›ฟ โŠข ๐‘„ =โ‡’ ๐‘„โ€ฒ with ๐‚ห˜๐‘ (๐‘ƒ2{๐‘/๐‘ฅ}) โ‰ˆ ๐›ฟ,e๐‘Žโˆ—e๐‘Žโ€ฒ ๐‘„โ€ฒ It also holds๐›ฟ โŠข ๐‚e๐‘ฅ ๐‘„๐œŽ =โ‡’ ๐‚e๐‘ฅ ๐‘„ โ€ฒ๐œŽ and we are done, as ๐‘ƒโ˜… = ๐‚e๐‘ฅ (( ๐‚ห˜๐‘ ๐‘ƒ2{๐‘/๐‘ฅ})๐œŽ) R ๐›ฟ ๐‚e๐‘ฅ (๐‘„โ€ฒ๐œŽ) K

If ๐‘ƒ ๐‘Žโ€ฒ (๐‘) โˆ’ โˆ’ โˆ’ โˆ’ โ†’๐‘ƒ1 ๐‘Ž ( ๐‘ฅ ) โˆ’ โˆ’ โˆ’ โˆ’ โ†’๐‘ƒ2, since ๐‘Žโˆ—๐‘Žโ€ฒ โˆˆ ๐›ฟ, we also have๐›ฟ โŠข ๐‘ƒ ๐œ โˆ’ โ†’๐‚ห˜๐‘ (๐‘ƒ2{๐‘/๐‘ฅ})

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Wiring the Pi-calculus to Denotational Semantics

cs.LO ยท 2026-05-18 ยท unverdicted ยท novelty 6.0

AWpi dialect equips the pi-calculus with single-ownership and uni-capability rules so that wires act as identity morphisms, yielding a relative Seely category that supports denotational semantics for higher-order concurrent languages.

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  • Wiring the Pi-calculus to Denotational Semantics cs.LO ยท 2026-05-18 ยท unverdicted ยท none ยท ref 22

    AWpi dialect equips the pi-calculus with single-ownership and uni-capability rules so that wires act as identity morphisms, yielding a relative Seely category that supports denotational semantics for higher-order concurrent languages.