CoCaml: Functional Programming with Regular Coinductive Types

@article{Jeannin2017CoCamlFP,
  title={CoCaml: Functional Programming with Regular Coinductive Types},
  author={Jean-Baptiste Jeannin and Dexter Kozen and Alexandra Silva},
  journal={Fundam. Informaticae},
  year={2017},
  volume={150},
  pages={347-377}
}
Functional languages offer a high level of abstraction, which results in programs that are elegant and easy to understand. Central to the development of functional programming are inductive and coinductive types and associated programming constructs, such as pattern-matching. Whereas inductive types have a long tradition and are well supported in most languages, coinductive types are subject of more recent research and are less mainstream. We present CoCaml, a functional programming language… 

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References

SHOWING 1-10 OF 81 REFERENCES
Language Constructs for Non-Well-Founded Computation
TLDR
This paper proposes programming language constructs that would allow the specification of alternative solutions and methods to compute them, and gives numerous examples in which it would be useful to do so: free variables, α-conversion, and substitution in infinitary λ-terms; halting probabilities and expected running times of probabilistic protocols; abstract interpretation; and constructions involving finite automata.
Wellfounded recursion with copatterns: a unified approach to termination and productivity
TLDR
A type-based approach to strong normalization of a core language based on System F-omega by tracking size information about finite and infinite data in the type which guarantees compositionality.
Copatterns: programming infinite structures by observations
TLDR
This paper presents a core language for programming with infinite structures by observations together with its operational semantics based on (co)pattern matching, and develops the concept of copattern matching, which allows us to synthesize infinite data.
Co-Logic Programming: Extending Logic Programming with Coinduction
TLDR
The theory and practice of co-logic programming is presented, a paradigm that combines both inductive and coinductive logic programming that has applications to rational trees, verifying infinitary properties, lazy evaluation, concurrent LP, model checking, bisimilarity proofs, etc.
Cycle therapy: a prescription for fold and unfold on regular trees
TLDR
This paper shows how to implement the unfold (anamorphism) operator in both eager and lazy languages so as to create cyclic structures when the result is a regular tree as opposed to merely infinite lazy structures.
Well-founded coalgebras, revisited
TLDR
Some theoretical results characterizing well-founded coalgebras are proved, along with several examples for which this extension is useful, and several examples that are not well founded but still have a desired solution that can be specified and computed with the programming language constructs proposed.
Initializing Mutually Referential Abstract Objects: The Value Recursion Challenge
  • Don Syme
  • Computer Science
    Electron. Notes Theor. Comput. Sci.
  • 2006
...
...