Related papers: Structural Induction Principles for Functional Pro…

The functional programming paradigm has a long and storied history, with its beginnings in the Lambda Calculus. In recent decades, pure functional languages such as Haskell have been shown to be highly effective in producing robust software…

Throughout the history of functional programming, recursion has emerged as a natural method for describing loops in programs. However, there does often exist a substantial cognitive distance between the recursive definition and the simplest…

We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…

A circular program creates a data structure whose computation depends upon itself or refers to itself. The technique is used to implement the classic data structures circular and doubly-linked lists, threaded trees and queues, in a…

Programming physicists use, as all programmers, arrays, lists, tuples, records, etc., and this requires some change in their thought patterns while converting their formulae into some code, since the "data structures" operated upon, while…

A circular program contains a data structure whose definition is self-referential or recursive. The use of such a definition allows efficient functional programs to be written and can avoid repeated evaluations and the creation of…

Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind:…

In this paper we present a new static data type inference algorithm for logic programming. Without the need of declaring types for predicates, our algorithm is able to automatically assign types to predicates which, in most cases,…

Inductive datatypes in programming languages allow users to define useful data structures such as natural numbers, lists, trees, and others. In this paper we show how inductive datatypes may be added to the quantum programming language QPL.…

Structured recursion schemes have been widely used in constructing, optimising, and reasoning about programs over inductive and coinductive datatypes. Their plain forms, catamorphisms and anamorphisms, are restricted in expressiveness. Thus…

Learning functional programming requires learning a substitution-based computational model. While substitution should be a familiar concept from high-school algebra, students often have difficulty applying it to new settings, such as…

Type classes in Haskell are used to implement ad-hoc polymorphism, i.e. a way to ensure both to the programmer and the compiler that a set of functions are defined for a specific data type. All instances of such type classes are expected to…

In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…

We describe a method for utilizing the known structure of input data to make learning more efficient. Our work is in the domain of programming languages, and we use deep neural networks to do program analysis. Computer programs include a…

In functional logic programs, rules are applicable independently of textual order, i.e., any rule can potentially be used to evaluate an expression. This is similar to logic languages and contrary to functional languages, e.g., Haskell…

We describe a method for deepening a student's understanding of basic physics by asking the student to express physical ideas in a functional programming language. The method is implemented in a second-year course in computational physics…

Neural networks are typically represented as data structures that are traversed either through iteration or by manual chaining of method calls. However, a deeper analysis reveals that structured recursion can be used instead, so that…

Structural recursion is a common technique used by programmers in modern languages and is taught to introductory computer science students. But what about its dual, structural corecursion? Structural corecursion is an elegant technique,…

In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof…

Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful…