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FP (short for Function Programming) is a programming language created by John Backus to support the Function-level programming paradigm. This allows for the elimination of named variables. A programming language or computer language is a standardized communication technique for expressing instructions to a computer. ...
John Backus (born December 3, 1924) is an American computer scientist, notable as the inventor of the first high-level programming language (FORTRAN), the Backus-Naur form (BNF, the almost universally used notation to define formal language syntax), and the concept of Function-level programming. ...
Function-level programming refers to one of the two contrasting programming paradigms identified by John Backus in his work on Programs as mathematical objects, the other being Value-level programming. ...
Overview
The values that FP programs map into one another comprise a set which is closed under sequence formation: SET may refer to: Secure electronic transaction, a protocol used for credit card processing, Simulated Emergency Test, an Amateur radio training exercise, Society for the Eradication of Television, Stock Exchange of Thailand, a national stock exchange of Thailand, SET Index, an index for Stock Exchange of Thailand This is a...
In topology and related branches of mathematics, a closed set is a set whose complement is open. ...
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 one such operation is constant, which transforms a value x into the constant-valued function x̄. Functions are strict: In the denotational semantics of programming languages, a function f is said to be strict if . ...
f:⊥ = ⊥ 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 = ⊥
Functionals These are the core functionals of FP: constant x̄ where x̄:y = x composition f&#x°g where f&#x°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 f
Equational functions In addition to being constructed from primitives by functionals, a function may be defined recursively by an equation, the simplest kind being: f ≡ Ef where E'f is an expression built from primitives, other defined functions, and the function symbol f itself, using functionals. An expression in a programming language is a combination of values and functions or procedures, interpreted according to the particular rules of precedence and of association for a particular programming language, which computes and then returns another value. ...
An example of a primitive function is the selector function family, denoted by 1,2,... where:
1:〈x1,...,xn〉 = x1 i:〈x1,...,xn〉 = xi if 0 < i ≤ n = ⊥ otherwise
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