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Andrej Bauer
Andrej Bauer
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Say we have an arbitrary domain $D$ with a countable basis $B$. Now, how do i build a "language" whose "denotation" lives in the domain?

My understanding is that DansDana Scott initially built domains to get a model of untypedtyped lambda calculus. Then, people bgan studing domains in their own right. So if I know that something forms a domain, can I "extract computation" / "extract a language" out of it?

Perhaps said differently, does every domain $D$ [with more conditions as necessary] always come equipped with the structure of a closed cartesian category?

Say we have an arbitrary domain $D$ with a countable basis $B$. Now, how do i build a "language" whose "denotation" lives in the domain?

My understanding is that Dans Scott initially built domains to get a model of untyped lambda calculus. Then, people bgan studing domains in their own right. So if I know that something forms a domain, can I "extract computation" / "extract a language" out of it?

Perhaps said differently, does every domain $D$ [with more conditions as necessary] always come equipped with the structure of a closed cartesian category?

Say we have an arbitrary domain $D$ with a countable basis $B$. Now, how do i build a "language" whose "denotation" lives in the domain?

My understanding is that Dana Scott initially built domains to get a model of typed lambda calculus. Then, people bgan studing domains in their own right. So if I know that something forms a domain, can I "extract computation" / "extract a language" out of it?

Perhaps said differently, does every domain $D$ [with more conditions as necessary] always come equipped with the structure of a closed cartesian category?

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Siddharth Bhat
Siddharth Bhat
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Given a domain, how do we build a language whose denotation is the domain?

Say we have an arbitrary domain $D$ with a countable basis $B$. Now, how do i build a "language" whose "denotation" lives in the domain?

My understanding is that Dans Scott initially built domains to get a model of untyped lambda calculus. Then, people bgan studing domains in their own right. So if I know that something forms a domain, can I "extract computation" / "extract a language" out of it?

Perhaps said differently, does every domain $D$ [with more conditions as necessary] always come equipped with the structure of a closed cartesian category?