FP programming language Guide, Meaning , Facts, Information and Description
FP (short for Function Programming) is a programming language created by John Backus to support the Function-level programming paradigm.
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2 Functionals 3 Equational functions 4 See also |
The values that FP programs map into one another comprise a set which is closed under sequence formation:
Overview
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:
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 = xcomposition 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 ≡ Efwhere Ef is an expression built from primitives, other defined functions, and the function symbol f' itself, using functionals.
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
See also
- FL programming language (Backus' successor to FP)
- Function-level programming
- Programs as mathematical objects
- J and NGL programming languages
- John Backus
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