FP (short for functional programming) is a programming language created by John Backus to support the function-level programming paradigm. It allows building programs from a set of generally useful primitives and avoiding named variables (a style also called tacit programming or "point free"). It was heavily influenced by APL which was developed by Kenneth E. Iverson in the early 1960s. The FP language was introduced in Backus's 1977 Turing Award paper, "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, eventually leading to modern functional languages, which are largely founded on the lambda calculus paradigm, and not the function-level paradigm Backus had hoped. In his Turing award paper, Backus described how the FP style is different: FP itself never found much use outside of academia. In the 1980s Backus created a successor language, FL, which was an internal project at IBM Research. Overview The values that FP programs map into one another comprise a set which is closed under sequence formation: if x1,...,xn are values, then the sequence 〈x1,...,xn〉 is also a value These values can be built from any set of atoms: booleans, integers, reals, characters, etc.: boolean : {T, F} integer : {0,1,2,...,∞} character : {'a','b','c',...} symbol : {x,y,...} ⊥ is the undefined value, or bottom. Sequences are bottom-preserving: 〈x1,...,⊥,...,xn〉 = ⊥ FP programs are functions f that each map a single value x into another: f:x represents the value that results from applying the function f to the value x 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: f:⊥ = ⊥ Another example of a primitive function is the selector function family, denoted by 1,2,... where: i:〈x1,...,xn〉 = xi if 1 ≤ i ≤ n = ⊥ otherwise 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: unit + = 0 unit × = 1 unit foo = ⊥ These are the core functionals of FP: composition f∘g where f∘g:x =