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Lightweight higher-kinded polymorphism
Jeremy Yallop, Leo White

“Higher-kinded polymorphism — i.e. abstraction over type constructors — is an essential component of many functional programming techniques such as monads, folds, and embedded DSLs. ML-family languages typically support a form of abstraction over type constructors using functors, but the separation between the core language and the module language leads to awkwardness as functors proliferate.

We show how to express higher-kinded polymorphism in OCaml without functors, using an abstract type `app` to represent type application, and opaque brands to denote abstractable type constructors. We demonstrate the flexibility of our approach by using it to translate a variety of standard higher-kinded programs into functor-free OCaml code.”

Referenced *everywhere*; but notably:

- (reference impl, OCaml)
- (for JavaScript)

paper  PLT  programming  type-systems  higher-kinded-types  type-inference  OCaml  Haskell  to-read 
22 hours ago by elliottcable
Predicate Exchange: Inference with Declarative Knowledge
To support a broader class of predicates, we develop an inference procedure called predicate exchange, which softens predicates. A soft predicate quantifies the extent to which values of model variables are consistent with its hard counterpart.
via marco c.
probability  to-read 
2 days ago by jar
Ludus-Opuscula RMM
We investigate a type of a Sudoku variant called Sudo-Kurve, which allows bent rows and columns, and develop a new, yet equivalent, variant we call a Sudo-Cube. We examine the total number of distinct solution grids for this type with or without symmetry. We study other mathematical aspects of this puzzle along with the minimum number of clues needed and the number of ways to place individual symbols.
mathematical-recreations  puzzles  sudoku  out-of-the-box  to-write-about  to-read 
5 days ago by Vaguery - The "What Is...?" column
I very much enjoy reading the "What Is...?" column in the Notices of the AMS. Unfortunately, there seemed to be no index to this column. I have therefore created this one in the hope that it might be helpful to others as well.
mathematics  explanation  mathematical-recreations  to-read  via:arthegall 
7 days ago by Vaguery

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