Questions tagged [typed-lambda-calculus]

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Denotational semantics of System $F_\omega$ with recursive types and general recursion

Is there a denotational semantics for System $F_\omega$ in literature that supports both recursive types and general recursion? I'm looking for a model of Ralf Hinze's variant of System $F_\omega$ [4]...
5
votes
0answers
81 views

Characterisation of the BCIW definable functions

Given a full model of the simply typed lambda calculus, it's possible to characterise the lambda definable functions as those that are invariant under every "Kripke logical relation". (See here.) I ...
4
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0answers
72 views

Coherence spaces and full completeness for the implicative fragment of linear logic

Linear logic isn't complete for coherence space semantics since $1$ and $\top$ get identified. But it is, I believe, complete for the fragment of linear logic whose only connective is $\multimap$. I ...
3
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Is System-F with higher-kinded newtypes equivalent in computational power to System-F omega?

If we have System-F with higher-kinded types and newtypes, then we can express everything (I think) of System-F omega, except we have to manually (un)pack. For example: ...
3
votes
0answers
51 views

Functionality of a hierarchy of definable functions over $\mathbb{N}$

Let $T$ be the complete hierarchy of functions over $\mathbb{N}$. That is: $T$ = $\bigcup T_{\tau}$ for all simple types $\tau$ built up from the basic type $\mathbb{N}$, with $T_{\mathbb{N}} = \...
2
votes
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154 views

Heyting algebra in simply typed lambda calculus

The Emil Jeřábek's comment in Can boolean algebra be expressed in simply typed lambda caclulus? give rise to the following question: Can some non-trivial Heyting algebra be expressed in simply typed ...
-2
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Simply typed lambda calculus with single type Unit

I have a question that I can't solve: Given the simply typed lambda-calculus with call-by-value evaluation and the regular inference rules for abstraction, application and variables. If I just add ...