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The functional model of computation

A computation

Takes a set of inputs

Information encoded in some representation(s)

Does some stuff (computes)
Generates an output

Again, information encoded in some representation

Stops

input(s)

output

COMPUTE

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Programming is a psychological discipline

Reasoning about the actual physical layout of data as binary text is an unnecessary burden on programmers

Most people don’t think well in binary

So we design programming languages to match how we think about our data so much as possible
Your programming language’s compiler and run-time system manage storage for you so you can think in terms of objects instead of bits

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Objects

A computer’s memory is ultimately implemented as binary text

In other words, a series of 0s and 1s.

In practice, that text is really a bunch of separate representations of different pieces of data
Each of those representations of a piece of data is known as an object

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Everything is an object

So from now on, everything in your computer’s memory is an object

Primitive (indivisible) data objects

Numbers (1, 7, -3.5)
Text strings ("bla bla bla")
functions

Compound data objects

Tables of data
Lists of objects
Bitmaps (contain many little color objects, one per pixel)
Sounds (contain 1 number per sound sample)

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Objects and computation

When we do computation, we traffic in objects

Objects are the inputs to functions
Objects are the outputs of functions

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Types of Objects (aka Data Types)

Computers have a taxonomy of types of data objects
Every object has a type

The object’s type determines what functions it can be used with
Example: Can add numbers, but not pictures or functions

object

number

integer

float

function

point

color

picture

string

boolean

exception

contract-violation

arity-mismatch

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Calls and data flow

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Function calls

When we run a function/program, we

Specify one data object for each of its inputs
Receive one data object as its output

Calls are so important, they have many synonyms

Run: execute, call, apply, invoke
Input: argument, parameter

Or: pass (as in “pass the function 2 as an argument”)

Output: result, return value

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Data flow diagrams

Most programming languages use textual notations
We will start with a graphical notation called a data flow diagram

Easy to understand what is an input to what and what’s the output
Doesn’t scale well to complicated programs

We’re using this as an informal learning tool: don’t get hung up on trying to memorize the details of it

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Changing the inputs changes the output

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Except when it doesn’t

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Chaining calls

In functional programming, programs/functions are built up by chaining together calls of existing functions

The output of one becomes the input of another

Data flows through the chain, from left to right

Hence the name data flow diagram

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Chaining chains

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A single object can be used as input to many functions

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Order of inputs (usually) matters

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Different diagrams can produce the same result

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Computers are literal-minded

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What versus how

Over time, you’ll want to learn how to look past the code to understand what a function is trying to do

What it computes
Versus how it computes it

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