# Questions tagged [pl.programming-languages]

Programming languages, in particular, focussing on their semantics.

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### Generalizing limit-colimit coincidence to Scott-continuous adjunctions: any uses?

In Abramsky and Jung's 1994 handbook chapter on denotational semantics, after proving that the limit and colimit of expanding sequences exist and coincide, they have the following to say about ...
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### Typed Lambda Calculus models and denotations

I'm trying to draw a general mental picture about the models and the denotational semantics of the typed lambda calculus, in its different variants. I'm particularly interested in how the semantics ...
283 views

### A bijection between ordered lambda terms and rooted planar maps?

Consider the following recurrence in two parameters $n$ and $k$: \begin{aligned} NF(0,k) &= 0 \\ NF(n,k) &= Neu(n,k) + NF(n-1,k+1) \\ Neu(n,k) &= [n=1 \wedge k=1] + \sum_{l=1}^{n-1}\sum_{...
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### What is known about reduction by “$P_1$ interprets $P_2$” for generalized programming languages?

Inspired by this answer, let's say that a programming language is given by the data $L=(P,ev)$ where $P$ (the set of "valid programs") is a computable subset of $\Sigma^*$ and $ev$ (the "evaluator") ...
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### Complete combinator basis for System F-omega

The S and K combinators form a complete (and Turing complete) basis when untyped. Within the Hindley-Milner type-system, and I believe within system $F$ as well, S and K can encode any well-typed ...
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### Type inference with subtype constraints and polymorphism using Trifonov and Smith's constraint maps

Trifonov and Smith's Subtyping Constrained Types (1996) introduces constraint maps to represent consistent closed constraint sets (such maps providing sets of lower and upper bounds to each variable ...
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### Is there a programming language where any arbitrary recursive function can be fused?

Compilers like GHC for Haskell use inlining as one of its most important optimising tools. Doing that is not possible for recursive functions, in general. A few techniques have been developed to amend ...
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### Relationship between Pataraia's theorem and inductive-recursive definitions?

Pataraia's fixed point theorem gives a constructive proof of the fact that if you have a monotone function $f$ on a DCPO, then it has a least fixed point. I've frequently used this fixed point theorem ...
239 views

N.B. I asked the same question on Stack Overflow but it was suggested that it is too theoretical for this forum. It is great that Haskell allows us to walk around in the category $Hask$. But ...
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### Notions of Computability at Higher Type III

I've recently found a very nice survey paper called "Notions of Computability at Higher Type" by John R. Longley. The paper says it is part of a 3-part series, with the 3rd concerning non-extensional ...
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### How can unification be applied to interaction combinators?

The problem of unifying interaction combinators is probably undecidable since those are turing complete. As opposed to the lambda calculus, there is nothing like a simple type theory for interaction ...
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### conceptual tools for illustrating types of computation?

From time to time I come across concepts in programming that take a certain number of exposures to grasp. Things like: tail calls, futures, monads, coroutines, closures, call/cc. The common theme is ...
256 views

### Commonalities and differences between canonical structures and the implicit calculus

There is a paper on The Implicit Calculus as a generalization of type classes. Coq's canonical structures are also a generalization of type classes. The paper does not mention canonical structures ...
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### Proof that CIC or Dybjer-style eliminators are strongly-normalizing?

Related to this question I'm wondering, what is the standard technique for showing that dependent types with eliminators are strongly normalizing? I'm thinking something like the Calculus of ...
136 views

### Hereditary Substitution with Inductives and Eliminators?

I'm wondering, is there any existing work on hereditary substitution with inductive type families and dependent eliminators? In particular, normalizing the application of an eliminator to an ...
133 views

### What are the parts of consistency model playing in hardware, operating system, and programming language?

In multiprocessor programming, consistency model is the key concept to express the correctness of concurrent objects ranging from simple read/write shared variable to concurrent data structures like ...
118 views

### Set:Set or Negative Inductives in a Total Language?

In total dependently typed languages, general recursion is forbidden, since this can allow for non-terimination. However, dependently typed language can still describe Turing-complete computations (...
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### Busy Beaver Equivalent for the Untyped Lambda Calculus

In the same way that the Busy Beaver function is defined for Turing Machines, we could define a similar function for the untyped lambda calculus: Over all terms in the ULC composed of ...
166 views

### How useful is program search in the field of programming-language theory?

I've been thinking: computing systems such as the Lambda Calculus and its variations are usually very simple and can be implemented in as few as ~80 lines of Haskell code. There is a self-interpreter ...
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### Is there any system where function equality (extensionality) is decidable?

Is there any programming language or system where function equality (extensionality) is decidable?
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### Understanding the goals you can reach with different programming models and languages

I come to ask this question here, because Meta told me this place was probably best for it. Reference: https://meta.stackexchange.com/questions/114043/ I've read this article many a times and ran in ...
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### Confusion about the visibility and arbitration relations in a formal framework for distributed consistency models

In the POPL'14 paper "Replicated Data Types: Specification, Verification, Optimality" and the book "Principles of Eventual Consistency", the authors propose a formal framework for specifying ...
110 views

### Object-Oriented Programming Languages based on assignment

Is it correct to claim that an object-oriented programming language based on assignment (e.g., Java and Smalltalk) introduces mutability and hence complexity in concurrent applications ? In other ...
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### Sample Terms in System Omega

I've been implementing mini languages that fall into each corner of the Lambda Cube. My main reference for this has been Types and Programming Languages. The latest one I finished is System Omega. I ...
59 views

### Proposition terms vs types in Coq

Consider the following div function written in Coq. It takes in a proof that the divider is non-zero. Definition div (n d:nat) (pf: ~(d = 0)) := n/d. Focus on <...