# FP (programming language)

# FP (programming language)

Paradigm | function-level |
---|---|

Designed by | John Backus |

First appeared | 1977 |

Dialects | |

FP84 | |

Influenced by | |

APL^{[1]} | |

Influenced | |

FL, Haskell, J |

**FP** (short for *function programming*) is a programming language created by John Backus to support the function-level programming^{[2]} paradigm. This allows eliminating named variables. The language was introduced in Backus's 1977 Turing Award lecture, "Can Programming Be Liberated from the von Neumann Style?", subtitled "a functional style and its algebra of programs." The paper sparked interest in functional programming research,^{[3]} eventually leading to modern functional languages, and not the function-level paradigm Backus had hoped. FP itself never found much use outside of academia.^{[4]} In the 1980s Backus created a successor language, FL, which remained a research project.

Paradigm | function-level |
---|---|

Designed by | John Backus |

First appeared | 1977 |

Dialects | |

FP84 | |

Influenced by | |

APL^{[1]} | |

Influenced | |

FL, Haskell, J |

Overview

The **values** that FP programs map into one another comprise a set which is closed under **sequence formation**:

These values can be built from any set of atoms: booleans, integers, reals, characters, etc.:

**⊥** is the **undefined** value, or **bottom**. Sequences are *bottom-preserving*:

FP programs are *functions* **f** that each map a single *value* **x** into another:

Functions are either primitive (i.e., provided with the FP environment) or are built from the primitives by **program-forming operations** (also called **functionals**).

An example of primitive function is **constant**, which transforms a value **x** into the constant-valued function **x̄**. Functions are strict:

Another example of a primitive function is the **selector** function family, denoted by **1**,**2**,... where:

Functionals

In contrast to primitive functions, functionals operate on other functions. For example, some functions have a *unit* value, such as 0 for *addition* and 1 for *multiplication*. The functional **unit** produces such a **value** when applied to a **function f** that has one:

These are the core functionals of FP:

Equational functions

In addition to being constructed from primitives by functionals, a function may be defined recursively by an equation, the simplest kind being:

where *E***f** is an expression built from primitives, other defined functions, and the function symbol **f** itself, using functionals.

FP84

**FP84** is an extension of FP to include infinite sequences, programmer-defined combining forms (analogous to those that Backus himself added to FL, his successor to FP), and lazy evaluation. Unlike FFP, another one of Backus' own variations on FP, FP84 makes a clear distinction between objects and functions: i.e., the latter are no longer represented by sequences of the former. FP84's extensions are accomplished by removing the FP restriction that sequence construction be applied only to *non*-⊥ objects: in FP84 the entire universe of expressions (including those whose meaning is ⊥) is closed under sequence construction.

FP84's semantics are embodied in an underlying algebra of programs, a set of function-level equalities that may be used to manipulate and reason about programs.

See also

FL, Backus's FP successor

PLaSM, FL Dialect

## References

*Communications of the ACM*.

**21**(8): 613. doi:10.1145/359576.359579. Backus' 1977 Turing Award lecture

*People of Programming Languages*.

*Programming in the Twenty-First Century*.