Paradigm function-level First appeared 1977 | Designed by John Backus | |
FP (short for Function Programming) is a programming language created by John Backus to support the function-level programming 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."
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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 valueThese 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 xFunctions 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 = ⊥ otherwiseFunctionals
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 = f:(g:x) construction [f1,...fn] where [f1,...fn]:x = 〈f1:x,...,fn:x〉 condition (h ⇒ f;g) where (h ⇒ f;g):x = f:x if h:x = T = g:x if h:x = F = ⊥ otherwise apply-to-all αf where αf:〈x1,...,xn〉 = 〈f:x1,...,f:xn〉 insert-right /f where /f:〈x〉 = x and /f:〈x1,x2,...,xn〉 = f:〈x1,/f:〈x2,...,xn〉〉 and /f:〈 〉 = unit f insert-left f where f:〈x〉 = x and f:〈x1,x2,...,xn〉 = f:〈f:〈x1,...,xn-1〉,xn〉 and f:〈 〉 = unit fEquational functions
In addition to being constructed from primitives by functionals, a function may be defined recursively by an equation, the simplest kind being:
f ≡ Efwhere Ef is an expression built from primitives, other defined functions, and the function symbol f itself, using functionals.