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Now, given their encoding, it's possible to add a catch-all case to their lambda datatype that isn't a tag, but which contains a higher-order function. This means that it should be possible to use …

"Resumable exceptions" are indeed a well-known idea in some programming language circles. In particular, Common Lisp has had resumable exceptions for a long time (so they are really not confined to re …

Let fill be the Turing machine that writes 1 on all positions of its output tape (it doesn't terminate, but that's not an issue). Let now syra be the machine that computes the Syracuse/Collatz sequenc …

I thought a bit about this and I am afraid that it is harder than it looks -- as you suspected! In the spirit of encouraging discussion, I'll write my chain of thoughts. The subtyping rules are often …

This is the notation for Harper's "abstract binding structures": x.t represents the binding site of a variable x and the term t the variable scopes over. Apparently you are in the parts that define va …

The "Reduction strategy" wikipedia article is entirely extracted out of a particular edit made by an anonymous IP to the "Evaluation strategy" article. The view that it represents is not consensual, …

(I'm familiar with the lambda-calculus, less so with its categorical models.) It is well-known that cartesian-closed categories are in tight correspondence to the simply-typed lambda-calculus with fun …

No, to my knowledge there has been no work on formalizing TeX of the kind you are interested in. (What follows is a subjective and personal commentary). I think it is an intriguing and well-posed ide …

My answer is not intented to be formal, precise and absolutely in-topic. I think Marc Hamman's answer is rock solid, but your question made me think of a related topic. Grammars may be considered spe …

One vision of the limits of strongly normalizing calculi I like is the computability angle. In a strongly normalizing typed calculus, such as the core simply-typed lambda calculus, System F, or Calcul …

There has been interesting work recently on making the relation between proof net and focused calculi tighter, using "multi-focused" variants where you may have several simultaneous left holes, and st …

You should have a look at Uniform Proofs as a Foudation for Logic Programming by Dale Miller, Gopalan Nadathur, Frank Pfenning and Andre Scedrov, 1991. The idea of this work and the rich area that has …

Two remarks first: I have used the "randomly generate terms and check that they are well-typed" approach (you mention that "untyped" terms are generated, you can also randomly generate terms in a Ch …

Let's look at a simple example of a toy programming language with unary natural numbers and a "predecessor" operation. $$t ::= 0 \mid S~t \mid p~t$$ whose semantics is given by the following rewrite r …

There are no metrics, but an excellent discussion of many concurrency models, in Tony Garnock-Jones PhD thesis. See the (HTML version of the) chapter "Approaches to coordination". This studies concurr …