Analogy-Based Notional Machines

Analogy

imperative / any Language:

Builds from the notion of a 'Variable as a Parking Space' and leverages the notion that spaces in larger parking lots are often numbered.

The use of indices in arrays as ell as the array's construction from contiguous adjacent variables in memory.

PL	NM
array	row of spaces in a parking lot
array element	car
element index	space number in lot
element value	specific car in a specific value

Collected by Jan Pearce

Analogy

imperative / any Language:

Makes arrays tangible, embodied activity.

Lists as compound data type

PL	NM
array	stack of boxes
array element	box
element index	number on each box
element value	post-it in box

Collected by Felienne Hermans

Analogy

imperative / any Language:

Creates memorable live demonstration of indexed list elements in order to distinguish between index and value. Also useful to demonstrate out-of-bound errors.

Array/list indices and the values at those locations.

PL	NM
array	row of students
array element	student (standing in a row)
element index	relative position of the student, start with 0
element value	nationality of student

Collected by Craig S. Miller

Analogy

imperative / any Language:

Makes concrete the workings of a call 'stack' (push/pop stack frames), and the notion of a 'stack frame'.

The call stack.

PL	NM
call stack	stack of papers
stack frame	sheet of paper
local variable	line of text on a sheet
call	push a sheet on top of the stack
return	pop the top sheet off the stack

Collected by Matthias Hauswirth

Analogy

imperative or functional / any Language:

Makes explicit that functions have inputs (parameters) and outputs (return value).

Parameter passing and return value.

PL	NM
function	black box
parameters	arrow into the box
return value	arrow out of the box

Collected by Jan Pearce

Analogy

imperative or functional / any Language:

Makes explicit that functions have inputs (parameters) and outputs (return value).

Parameter passing and return value.

PL	NM
function	tank
parameters	hoppers on top of tank
return value	output pipe on bottom of tank

Collected by Matthias Hauswirth

Analogy

declarative / BNF / EBNF Language:

Pushing a train engine through the track makes visible the process of interpretation (generation or parsing) of the grammar (that is the track).

The process of parsing or generating driven by a grammar.

PL	NM
grammar rule	a train track with a start and an end
parsing or generating	pushing a train engine through the train track
terminal symbol (in a grammar rule)	tunnel representing a terminal symbol, generating or recognizing the text with which it is labeled
non-terminal symbol (in a grammar rule)	tunnel representing a non-terminal symbol, invoking the rule mentioned on its label
sequence	track segment going from one tunnel to the next
selection	two switches to split and join the track, requiring the train engine to decide which track to take
repetition	two switches allowing the train engine to go back and repeat a part of the grammar multiple times

Collected by Matthias Hauswirth

Analogy

imperative / Java Language:

Explains need for hashCode() and equals() methods when using HashSet

Need for .hashCode() and .equals(Object o) methods

PL	NM
HashSet	Box of hanging folders
bucket	Single file folder
key	Piece of paper in a file folder
value	N/A (HashSet, not HashMap)
add(key) method	Find correct folder, check if the folder already contains the key by comparing the key to all contents of the folder

Collected by Colleen Lewis

Analogy

imperative / any Language:

Emphasises that only the head of list (top box) or the whole list (the stack on the pallet) is directly accessible, and that new items can be added on top of a list but not into the middle of it.

First-in, first-out property of a stack.

PL	NM
list	stack of boxes on a pallet
list element	box on the stack
[	top of the stack
]	pallet

Collected by Benedict du Boulay

Analogy

any / any Language:

See inside logic gates/operations. Construct/invent them from atomic components, and observe/analyze their full workings.

The inner workings of a Boolean logic operation (and, or, xor).

PL	NM
Boolean value	domino piece (standing, or fallen)
or operation	two joining lines of dominos
xor operation	two lines of dominos like in left image
and operation	two lines of dominos like in right image
function argument	first domino piece in a line
function return value	last domino piece in a line

Collected by Matthias Hauswirth

Analogy

imperative / Java / C# / any Language:

To illustrate method calls, the teacher dances to another location, performs some actions there (changing the memory), and then returns to the previous location through the return address, where he continues with performing actions

It illustrates that you `go elsewhere in the memory' when you call a method, and that you need to remember where you came from (return address) when you go elsewhere. A dancing teacher helps students to remember the concept.

PL	NM
method call	dance to another location
return address	dance back to the previous location

Collected by Johan Jeuring

Analogy

object-oriented / any Language:

Makes explicit that an object is an identifiable thing that answers to calls.

Objects, method calls, and returns.

PL	NM
class	natural language description of methods and their behaviors (on sheet of paper)
object	student
method call	verbal request made to student
actual argument	stated as part of verbal request
return value	verbal response from student

Collected by Matthias Hauswirth

Analogy

imperative / assembly Language:

Provides tangible focus for discussing addresses, offsets, and even byte ordering and segments.

Relationships between items in memory, whether they are elements of an array, bytes in a single value, or different methods for allocating space.

PL	NM
memory cell	seat
value	student or number given to student
address	established by counting off
offset	number of seats between two targets
segment	front, middle, or back of the room

Collected by Andrew Petersen

Analogy

imperative / any Language:

Provides a way to visualise input and action, and later the difference between action and output. The same visualisation extended to cover user defined procedures, parameters and later to explain sub-procedure calls including recursion.

PL	NM
procedure	worker who knows how to do a particular job
procedure call	calling the name of the worker, so that he starts doing his particular job
procedure input	giving information to the worker (telling them in their right ear)
procedure implementation	instructions for the worker on how to do their job
procedure effect	how the worker affects the world
procedure result	what the worker speaks to the worker on their left

Collected by Benedict du Boulay

Analogy

imperative / any Language:

Makes explicit the difference between data and instructions, shows how little a single instruction really can achieve. Can be stretched to explain all kinds of concepts (although eventually becomes a bit of a stretch).

Data an instruction operates on, 'mechanistic' workings of instructions.

PL	NM
processor	file clerk
instruction	action taken by file clerk (e.g., read info off a card)

Collected by Matthias Hauswirth

Analogy

imperative / any Language:

Makes explicit recursive calls as a form to 'delegate' parts of work, base case as a situation where delegation stops. Allows unpacking many aspects of recursive computation (pairing of call/return, passing info down through params, up through return values, tail recursion).

Recursive calls and returns, base case & recursive case, tail recursion

PL	NM
object	person
method call	verbal request to next person in line
return value	verbal response from next person in line
base case	(action of) last person in line
recursive case	(action of) all but last persons in line
linked list	line of persons (e.g., waiting in amusement park, or row in classroom)

Collected by Matthias Hauswirth

Analogy

imperative / staticaly-typed Language:

Helps understanding of why types matter both in parking spaces and in statically-typed languages

The idea of a statement, a condition, and how they are used to build sequence, selection, and repetition constructs of structured programming

PL	NM
variable	parking space
value	vehicle
type of variable	vehicle size/shape/constraint on parking space
type of value	type of vehicle

Collected by Jan Pearce

Analogy

imperative / any Language:

Makes variable tangible, embodied activity

Variables, access, initialization

PL	NM
Variable	Box
access	opening box, accessing topmost post-it
rename variable	new name on box
assign (list)	new name also on box
assign simple value	second box with same post-it

Collected by Felienne Hermans

Analogy

imperative / BASIC Language:

Makes variable tangible, gives impression of memory as a bunch of variables

Variables contain values

PL	NM
variable	pigeon hole in shelf
variable name	label attached to the pigeon hole
value	note inside the pigeon hole

Collected by Matthias Hauswirth

Analogy-Based Notional Machines

What is an analogy-based notional machine?

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Forms of NMs

What is a Notional Machine?

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