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This is a personal recollection on the Move fire on May 13, 1985
 | This article may contain original research. (April 2018) |
In computer science, function-level programming is 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.
In his 1977 Turing Award lecture, Backus set forth what he considered to be the need to switch to a different philosophy in programming language design:[1]
Programming languages appear to be in trouble. Each successive language incorporates, with a little cleaning up, all the features of its predecessors plus a few more. [...] Each new language claims new and fashionable features... but the plain fact is that few languages make programming sufficiently cheaper or more reliable to justify the cost of producing and learning to use them.
He designed FP to be the first programming language to specifically support the function-level programming style.
A function-level program is variable-free (cf. point-free programming), since program variables, which are essential in value-level definitions, are not needed in function-level programs.
In the function-level style of programming, a program is built directly from programs that are given at the outset, by combining them with program-forming operations or functionals. Thus, in contrast with the value-level approach that applies the given programs to values to form a succession of values culminating in the desired result value, the function-level approach applies program-forming operations to the given programs to form a succession of programs culminating in the desired result program.
As a result, the function-level approach to programming invites study of the space of programs under program-forming operations, looking to derive useful algebraic properties of these program-forming operations. The function-level approach offers the possibility of making the set of programs a mathematical space by emphasizing the algebraic properties of the program-forming operations over the space of programs.
Another potential advantage of the function-level view is the ability to use only strict functions and thereby have bottom-up semantics, which are the simplest kind of all. Yet another is the existence of function-level definitions that are not the lifted (that is, lifted from a lower value-level to a higher function-level) image of any existing value-level one: these (often terse) function-level definitions represent a more powerful style of programming not available at the value-level.
When Backus studied and publicized his function-level style of programming, his message was mostly misunderstood[2] as supporting the traditional functional programming style languages instead of his own FP and its successor FL.
Backus calls functional programming applicative programming;[clarification needed] his function-level programming is a particular, constrained type.
A key distinction from functional languages is that Backus' language has the following hierarchy of types:
...and the only way to generate new functions is to use one of the functional forms, which are fixed: you cannot build your own functional form (at least not within FP; you can within FFP (Formal FP)).
This restriction means that functions in FP are a module (generated by the built-in functions) over the algebra of functional forms, and are thus algebraically tractable. For instance, the general question of equality of two functions is equivalent to the halting problem, and is undecidable, but equality of two functions in FP is just equality in the algebra, and thus (Backus imagines) easier.
Even today, many users of lambda style languages often misinterpret Backus' function-level approach as a restrictive variant of the lambda style, which is a de facto value-level style. In fact, Backus would not have disagreed with the 'restrictive' accusation: he argued that it was precisely due to such restrictions that a well-formed mathematical space could arise, in a manner analogous to the way structured programming limits programming to a restricted version of all the control-flow possibilities available in plain, unrestricted unstructured programs.
The value-free style of FP is closely related to the equational logic of a cartesian-closed category.
The canonical function-level programming language is FP. Others include FL, and J.
Source: Wikipedia. Article content is retrieved live through the MediaWiki API.
In computer science, function-level programming is 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. In his 1977 Turing Award lecture, Backus set forth what he considered to be the need to switch to a different philosophy in programming language design: Programming languages appear to be in trouble. Each successive language incorporates, with a little cleaning up, all the features of its predecessors plus a few more. [...] Each new language claims new and fashionable features... but the plain fact is that few languages make programming sufficiently cheaper or more reliable to justify the cost of producing and learning to use them. He designed FP to be the first programming language to specifically support the function-level programming style. A function-level program is variable-free (cf. point-free programming), since program variables, which are essential in value-level definitions, are not needed in function-level programs.
In computer programming, a function (also procedure, method, subroutine, routine, or subprogram) is a callable unit of software logic that has a well-formed interface and behavior and can be invoked multiple times. Callable units provide a powerful programming tool. The primary purpose is to enable the decomposition of a large and/or complicated problem into chunks that have relatively low cognitive load. These smaller, less complicated chunks (callable units) can become conceptually independent of the larger problem, taking on meaningful names of their own and potentially becoming useful to other unrelated problems through reusability. Judicious application can reduce the cost of developing and maintaining software through modularity and reusability, while increasing quality and reliability. Callable units are present at multiple levels of abstraction in the programming environment. For example, a programmer may write a function in source code that is compiled to machine code that implements similar semantics. There is a callable unit in the source code and an associated one in the machine code, but they are different kinds of callable units—with different implications and features.
In computer programming, a nested function (or nested procedure or subroutine) is a named function that is defined within another (enclosing) block and is lexically scoped within the enclosing block – meaning it is only callable by name within the body of the enclosing block and can use identifiers declared in outer blocks, including outer functions. The enclosing block is typically, but not always, another function. Programming language support for nested functions varies. With respect to structured programming languages, it is supported in some outdated languages such as ALGOL, Simula 67 and Pascal and in the commonly used JavaScript. It is commonly supported in dynamic and functional languages. However, it is not supported in some commonly used languages including standard C and C++. Other programming technologies provide similar benefit. For example, a lambda function also allows for a function to be defined inside of a function (as well as elsewhere) and allows for similar data hiding and encapsulation. Notably, a lambda function has no name (is anonymous) and therefore cannot be called by name and has no visibility aspect.
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality. Its objective function is a real-valued affine (linear) function defined on this polytope. A linear programming algorithm finds a point in the polytope where this function has the largest (or smallest) value if such a point exists. Linear programs are problems that can be expressed in standard form as: Find a vector x that maximizes c T x subject to A x ≤ b and x ≥ 0 . {\displaystyle {\begin{aligned}&{\text{Find a vector}}&&\mathbf {x} \\&{\text{that maximizes}}&&\mathbf {c} ^{\mathsf {T}}\mathbf {x} \\&{\text{subject to}}&&A\mathbf {x} \leq \mathbf {b} \\&{\text{and}}&&\mathbf {x} \geq \mathbf {0} .\end{aligned}}} Here the components of x {\displaystyle \mathbf {x} } are the variables to be determined, c {\displaystyle \mathbf {c} } and b {\displaystyle \mathbf {b} } are given vectors, and A {\displaystyle A} is a given matrix. The function whose value is to be maximized ( x ↦ c T x {\displaystyle \mathbf {x} \mapsto \mathbf {c} ^{\mathsf {T}}\mathbf {x} } in this case) is called the objective function. The constraints A x ≤ b {\displaystyle A\mathbf {x} \leq \mathbf {b} } and x ≥ 0 {\displaystyle \mathbf {x} \geq \mathbf {0} } specify a convex polytope over which the objective function is to be optimized. Linear programming can be applied to various fields of study. It is widely used in mathematics and, to a lesser extent, in business, economics, and some engineering problems. There is a close connection between linear programs, eigenequations, John von Neumann's general equilibrium model, and structural equilibrium models (see dual linear program for details). Industries that use linear programming models include transportation, energy, telecommunications, and manufacturing. It has proven useful in modeling diverse types of problems in planning, routing, scheduling, assignment, and design.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Mae Jemison, aboard Space Shuttle Endeavour in 1992.