FP (programming Language) - Overview

Overview

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

if x₁,...,x_n are values, then the sequence 〈x₁,...,x_n〉 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,...,⊥,...,x_n〉 = ⊥

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:

1:〈x₁,...,x_n〉 = x₁ i:〈x₁,...,x_n〉 = x_i if 0 < i ≤ n = ⊥ otherwise