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Can application in untyped lambda calculus be seen as the uncurried unit of some monad?

Simply typed lambda calculus in one type variable in a Cartesian closed category $\mathbf{C}$ can be interpreted as a family of Cartesian closed functors (described below, do they have a name?) from ...
7 votes
1 answer
183 views

Is lambda calculus polymorphism a type of generalized monad?

Let $\mathbf{C}$ be a Cartesian closed category. Then simply typed lambda calculus in $\mathbf{C}$ in one type variable can be interpreted as a category $\mathbf{STLC}_{\mathbf C}$ where the objects ...
0 votes
0 answers
110 views

Expressing a model transformation by using monads in the simply-typed lambda calculus

In https://link.springer.com/content/pdf/10.1007/s10670-019-00128-z.pdf , page 16, the following clause is given for a modal operator $\langle R_k \rangle$ (see definition 4.2 for the definition of a ...
23 votes
1 answer
1k views

What, mathematically speaking, does it mean to say that the continuation monad can simulate all monads?

In various places it is stated that the continuation monad can simulate all monads in some sense (see for example http://lambda1.jimpryor.net/manipulating_trees_with_monads/)) In particular, in http://...
9 votes
0 answers
539 views

The Curry Howard Isomorphism and models for an intuitionistic modal logic and its bimodal translation

My question regards the Curry Howard Isomorphism and how it constrains models in the case of a particular logic. Consider quantified Lax Logic $QLL$. https://pdfs.semanticscholar.org/468e/...