What was the original intent for the creation of Lambda calculus?
I’ve read that initially Church proposed the $lambda$-calculus as part of his Postulates of Logic paper (which is a dense read). But Kleene proved his “system” inconsistent after which, Church...
View ArticleScott's stochastic lambda calculi
Recently, Dana Scott proposed stochastic lambda calculus, an attempt to introduce probabilistic elements into (untyped) lambda calculus based on a semantics called graph model. You can find his slides...
View ArticleConcepts related to higher order functions [on hold]
I am trying to understand higher order functions. I know that they are functions that can take functions as parameters and return functions as results. But I feel there is more to it, for example, I...
View ArticleWhat is the benefit of Krivine's notation?
I saw some people uses Krivine’s notation for function application when presenting the syntax for the $lambda$-calculus. For example, the $lambda$-term $lambda f . lambda x . lambda y . f x y$ (with...
View ArticleCommutativity of addition in polymorphic lambda calculus
In the article “Extensional models of polymorphism” by Breazu-Tannen and Coquand, natural numbers are presented using a Church-like encoding: $polyint = forall t . (t to t) to t to t$ Addition for this...
View ArticleResources for Church's paper “An Unsolvable Problem of Elementary Number...
I’m trying to understand and breakdown into simple English Church’s paper for “An Unsolvable Problem of Elementary Number Theory” but I’m not finding anything useful online, only citations and links to...
View ArticleA function is lambda-2-definable iff it is HG computable and provably type...
I’m having a problem regarding Theorem 5.4.40.3 of Barendregt’s Lambda calculi with types (1992), a chapter in Handbook in logic in computer science. (I’m referring to the PostScript version available...
View ArticleWeakly normalizing + confluent = strongly normalizing?
I was reading this abstract and saw that they prove weak normalization and confluence. My limited understanding suggests that those two properties should provide strong normalization, which then leaves...
View ArticleWhy do constructivists not seem to care too much about call/cc
So a little while back I first had someone tell me that call/cc could allow proof objects for classical proofs by implementing Peirce’s law. I did some thinking about the topic recently and I can’t...
View ArticleIs there any known CCC closed under a probabilistic powerdomain operation?
Equivalently, is there a known denotational semantics for probabilistic higher-order functional programming languages? Specifically, is there a domain model of pure untyped $lambda$-calculus extended...
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