## How to name the inverse functions of constructors

I am working on the design of a language (Albatross) which allows for static verification. It has a strong functional core. One of the most important types in a functional language is the inductive or algebraic type. One of the most prominent examples is a list. E.g. a list type in Albatross is declared as follows.

A: ANY
class
LIST[A]
create
[]
(^) (head:A, tail:LIST[A])
end

It has the constructor [] to create an empty list and the constructor ^ to construct a new list by prefixing an already constructed list (tail) with a new element (head).

From a nonempty list we can extract the head and the tail with the following functions.

head(l:LIST[A]): A
require
l as _ ^ _
ensure
-> inspect
l
case h ^ _ then
h
end

tail(l:LIST[A]): LIST[A]
require
l as _ ^ _
ensure
-> inspect
l
case _ ^ t then
t
end

The functions head and tail reverse the effect of the constructor ^. I am looking for a name on how to describe these type of functions.

The most immediate ideas are _desctructors_ or _unconstructors_ which I don't find very appealing. A better name might be _inverse constructors_ which seem to precisely describe what they are, but sound a little bit clumsy.

Does anyone have a good idea on how to name these animals?

Some background information on why I need these type of functions:

Algebraic data types are a great tool, but they are not always the appropriate tool. E.g. in order to describe natural numbers their implementation is straighforward but awfully inefficient (this is one of the big problems when you want to extract source code from Coq). There are two ways to describe natural numbers with an efficient implementation. Either as machine numbers with modulo arithmetic or as arbitrary sized numbers where the components are machine numbers.

Machine numbers are not objects of algebraic type. But they are similar. The have constructors (zero and successor) and an induction law. Furthermore they have discriminator functions (n = 0) to decide how the number has been constructed and an inverse constructor (predecessor).

As soon as a type has an induction law (which implicitely defines the constructor functions), discriminator functions and inverse constructors the compiler can treat these types like inductive types in order to define recursive functions (which are guaranteed to terminate), do pattern matching etc. The discriminator functions and inverse constructors are necessary for the compiler in order to be able to compile pattern matching expressions into executable code.

In my opinion these pseudo algebraic/inductive types will be a great tool. Therefore I need good notions and names to express properties well.

Thanks for any help.

Language Description

## Best value for overloading?

There exist various approaches to overloading, including:

* type classes of various kinds
* traits
* implicits [2]
* multimethods
* other systems [1,3]

What seems to offer the best value for investment effort, expressiveness, and type safety?

For instance, multimethods are pretty flexible and uniformally allow a form of type-based and case-based overloading, but it seems quite difficult to capture accurate types with all the expressiveness we expect of ML functions, eg. first-class functions require intersection types and subtyping.

Type classes and traits seem more or less equivalent, but have problems with overlapping and named instances, a problem shared by [1] I believe. Implicits seem promising, and properly handle named and overlapping instances.

## List of POPL 2017 papers with crowd-sourced preprint links

https://github.com/gasche/popl2017-papers/ has a list of POPL 2017 papers with crowd-sourced links to the preprints. The deadline for camera-ready version (a version provided by the researchers that takes reviewers' comment into account) is only on November 7th, so one should expect more preprints to be available after that.

Feel free to mention any paper that catches your interest. If you are very curious in a particular work that does not have an online preprint, sending an email to the authors to ask them whether they plan to have a preprint accessible online can help a lot.

## Interesting use cases for universal quantifiers in rank 2?

Trevor Jim’s System P2 types the same terms as the second-rank System F2, but function arguments can only be typed as (finite) intersections of simple types. This restriction is reasonable and also seems to correspond neatly to the inner workings of a compiler which specializes polymorphic functions for every usage (such as Rust’s, IIRC). What do we lose, relative to F2? Here are the things that I can think of (in fact, they also apply to unrestricted System P, which prohibits universal quantifiers in negative positions):

• The ST monad of Peyton Jones et al. famously uses second-rank universal quantification to prevent imperative state from leaking outside, by defining runST :: forall a. (forall s. ST s a) -> a and threading the dummy parameter s through all related imperative things — e. g., imperative variables are accessed by readSTRef :: STRef s a -> ST s a and writeSTRef :: a -> STRef s a -> ST s (). Dynamic event switching in reactive-banana is guaranteed free of time leaks using a similar mechanism. (It sort of makes sense that we lose this: it is difficult to see how a universally quantified type could be inferred for any argument. Though…)
• Induction principles for non-regular datatypes have rank-2 types (always?). It seems to me that so do types defined using Haskell’s ExistentialQuantification extension.

Anything else?

Side note: What is then the class of all datatypes whose induction principles fit into P2? Is it interesting or any bigger than that for HM? I don’t understand what intersections could mean as eliminator arguments.

## How is structural typing checked?

If a language is decided to have structural type, how are the types checked?

With a nominal type system I can just have a table with the names, and lookup it. However with structural types is necessary to encode more info so I can know how do it.

How are this info encoded? How are the check performed?

## Implicit conversion (subtyping) vs Explicit conversion

In the design discussions for Zen, (see: http://lambda-the-ultimate.org/node/5376) we have hit an important decision point, and I wanted to get opinions from the PL community about what they think is the best approach. The choice is between:

- Implicit conversions with explicit invariance
- Implicit invariance with explicit conversions

By way of an example, given a type like this Set<Int>|Set<Float> we could implicitly convert it to Set<Int|Float> where required (so Set<Int>|Set<Float> <: Set<Int|Float>.

- Could this cause problems where the fact that all types in the collection must be the same is a property relied upon by an algorithm.
- How does this interact with mutability? Is it only sound to implicitly convert with immutable collections?

Then there is the question of boilerplate. With implicit conversion we need an annotation to say 'do not implicitly convert', in contrast by forcing explicit conversion we need an annotation (function call) to do the conversion.

- Which option results in the most boilerplate depends on how often the situations occur. Do people find they are wanting to convert types (subsumption/subtyping etc) more often than they are wanting types to remain fixed.

I would greatly appreciate views from the community on their experiences of designing languages with these features, or using languages with either approach.

## Parsing with derivatives - Elegant matching of regular languages in clojure

Parsing with derivatives - Elegant matching of regular languages in clojure is an interactive version of the first part of this paper: Parsing with derivatives - a Functional Pearl - the part that shows how to implement a regular expression matcher in a few lines of code using a concept from 1964 named Brzozowski’s derivative.

As David Nolen explains it in his talk about this paper at Papers We Love, clojure.spec implementation is based on this paper.

In this article, we are going to implement a regular expression matcher in clojure using Brzozowski’s derivative.

## Compile and Statically Verify

A new release of the Albatross compiler and a completely updated language description is available.

The new release has a complete coverage of induction with inductive datatypes and inductively defined sets and relations. The latter one adds great descriptive power to the language.

Furthermore proofs have been simplified by adding syntax support so that proofs written well are also well readable. Syntax support is available for proofs by induction, by contradiction, existential proofs, case split, transitivity proofs.

Download the compiler and the base library.

Read the language description as a gitbook.

Any comments on the language and any suggestions on expected language features are welcome.

## SPLASH'16 Amsterdam CFP: early registration ends Sept 30

#################################################
ACM Conference on Systems, Programming, Languages, and Applications:
Software for Humanity (SPLASH'16)
#################################################

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The dream of a lifetime: shaping how our children learn computing

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Fine-grained language composition without a common VM

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This is not a Type: Gradual typing in practice

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How to Design a Programming Language

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Snap! Scheme Disguised as Scratch

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Responsive Language Tooling For Cloud-based IDEs

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Simulating Cities: The Spacetime Framework

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Truffle and Graal: Fast Programming Languages With Modest Effort

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Designing and Debugging Surveys with SurveyMan

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How Domain Requirements Shape Languages

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## Bottom Types

I was having a discussion about typing with shelby3 regarding typing in our scripting language, and shelby3 made the following statement:

In an eager, CBV type system, then the type of Nil has to be subsumable to any instantiable type of List otherwise you will have unsoundness. Period.

I am reasonably sure, as I can have an eager language, which is call-by-value, and have strict typing, no sybtyping and no variance, and it will be sound.

Why do we both see this so differently?