## Initial algebra semantics is enough (2007)

Venue: | Proceedings, Typed Lambda Calculus and Applications |

Citations: | 10 - 5 self |

### BibTeX

@INPROCEEDINGS{Johann07initialalgebra,

author = {Patricia Johann and Neil Ghani},

title = {Initial algebra semantics is enough},

booktitle = {Proceedings, Typed Lambda Calculus and Applications},

year = {2007},

pages = {207--222}

}

### OpenURL

### Abstract

Abstract. Initial algebra semantics is a cornerstone of the theory of modern functional programming languages. For each inductive data type, it provides a fold combinator encapsulating structured recursion over data of that type, a Church encoding, a build combinator which constructs data of that type, and a fold/build rule which optimises modular programs by eliminating intermediate data of that type. It has long been thought that initial algebra semantics is not expressive enough to provide a similar foundation for programming with nested types. Specifically, the folds have been considered too weak to capture commonly occurring patterns of recursion, and no Church encodings, build combinators, or fold/build rules have been given for nested types. This paper overturns this conventional wisdom by solving all of these problems. 1

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