Notional Machines

Representation

imperative / any Language:

Makes arrays tangible, embodied activity.

Arrays are compound data structures.

PL	NM
array	clothesline
array element	clothespin
element index	label on the pin
element value	paper sheet in the pin

Collected by Felienne Hermans

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

Representation

imperative / Processing Language:

Generates an idea of a dyamic program behavior.

How a program executes dynamically from a static program text.

PL	NM
processor	teacher
instruction	action taken by teacher, reported in list
canvas	drawing area on sheet of paper

Collected by Andreas Mühling

Representation

imperative / any Language:

Distinguishes between variable values in the main function and the parameters and local variables in a called function.

Each function call/frame has its own set of stored values.

PL	NM
local variable	box with label at bottom of a frame labeled with function name
parameter	box with label at the top of a frame labeled with function name
variable in main	box with label in a frame called main

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

Representation

object-oriented / any Language:

Make visible the flow of computation through method calls and returns, showing how calls relate to objects, and how calls and returns are paired.

The idea of a method calls being communication between two objects.

PL	NM
method call	solid arrow from caller activation to callee activation
method return	dashed arrow from callee activation to caller activation
activation	tall box along lifeline from call arrow to return arrow
object	box at top and lifeline down
thread	line through all calls and returns from start to finish of diagram

Collected by Matthias Hauswirth

Representation

imperative / Java Language:

See a method as a sequence of statements to execute, and make clear that that sequence starts when the method is called and ends when the method returns.

The idea of a 'sequence' in structured programming, where a sequence consists of statements to execute.

PL	NM
statement	rectangular node
control-flow between statements	arrow from node to node
method entry	round 'e' node at top
method exit	round 'x' node at bottom

Collected by Matthias Hauswirth

Representation

imperative / Java Language:

Understand concept of selection from structured programming (conditional statements like if, if-else), and make clear that a statement may or may not execute, based on a decision taken earlier in the control flow.

The idea of a 'selection' in structured programming, where a data (the condition's value) is turned into control flow (the next statement to execute).

PL	NM
...	...
if condition	diamond-shaped node
condition outcome	label on an arrow coming out of a condition (e.g., true, false)

Collected by Matthias Hauswirth

Representation

imperative / Java Language:

Understand concept of a multi-way selection (a conditional statement where the condition is not just a Boolean value, e.g., a switch-statement).

The idea of a multi-way 'selection' in structured programming, where a data (the condition's value) is turned into control flow (the next statement to execute).

PL	NM
...	...
switch condition	diamond-shaped node with multiple arrows leaving
switch cases	label on arrows coming out of a switch (including 'default')

Collected by Matthias Hauswirth

Representation

imperative / Java Language:

Understand concept of short-circuit Boolean operators (|| and &&), and see how they only evaluate their right operand if needed.

The idea that for short-circuit Boolean operators, the second operand may never be evaluated (allowing common constructs like if (o!=null && o.length>0) ...

PL	NM
...	...
\|\| in condition	'false' arrow to extra diamond node
&& in condition	'true' arrow to extra diamond node

Collected by Matthias Hauswirth

Representation

imperative / Java Language:

Understand concept of repetition from structured programming (loops like while, do-while, or for), where a given statement can be executed multiple times, by simply following the arrows through the cycle.

The idea of a 'repetition' in structured programming, where control-flow leads to statements getting executed multiple times

PL	NM
...	...
back edge	arrow pointing to a node that came prior in the flow (introducing a cycle)
while-, do-while-, for-loop	cycle in the graph

Collected by Matthias Hauswirth

Representation

imperative / any Language:

The notional machine is not an entirely separate representation from the code but acts as a secondary notation to add invisible aspects of the code execution.

Static view of control flow (possible paths), identification of expressions.

PL	NM
control flow	arrows, superimposed on the code
expression	rectangular outline around expression, superimposed on the code

Collected by Peter Donaldson

Representation

imperative / any Language:

The notional machine is not an entirely separate representation from the code but acts as a secondary notation to add invisible aspects of the code execution.

Dynamic view of control flow (actual execution); evaluation of expressions; declaration, initialisation, access and assignment of variables.

PL	NM
...	(all aspects from 1-Static Structure)
instruction execution	add current step number to arrow leading in, then execute by adding to or looking up information in memory table, expression evaluator, or output areas
expression evaluation	copy expression, substitute values, and evaluate it in expression evaluation area
variable declaration	find first blank column in memory table and add name of variable in first row; value added underneath if initialised
variable assignment	find variable in the memory table, strike through existing entry, and add entry to row below.
conditionals and loops	evaluate control expression to 'True' or 'False', then follow relevant labelled control path to next instruction

Collected by Peter Donaldson

Representation

imperative, OO / Java Language:

A large fraction of code consists of expressions. Students already know about expressions from school arithmetic. This notional machine makes the structure of such simple expressions explicit, and provides a way to explain their bottom-up step-by-step evaluation.

The structure, typing, and evaluation of arithmetic expressions students still know from school.

PL	NM
expression	tree of nodes linked together
operator	green node
operand	hole in a node where a child node can be attached
subexpression inside expression	subtree connected to a node's hole
type of subexpression	blue tag above subexpressions's root node
numerical literal	tree node labeled with the number
variable	tree node labeled with name of variable of a numeric type
unary arithmetic operator (+, -)	tree node with operator in front of a hole
binary arithmetic operator (+, -, *, /, %)	tree node with operator between two holes

Collected by Matthias Hauswirth

Representation

imperative, OO / Java Language:

Makes explicit the fact that logic expressions have the same structural properties as the well known arithmetic expressions.

The structure, typing, and evaluation of expressions involving logic operators and Boolean literals.

PL	NM
...	(all aspects from 1-Arithmetic)
Boolean literal	leaf tree node labeled with true or with false
variable	leaf tree node labeled with name of variable of type boolean
unary negation operator (!)	tree node with operator in front of a hole
binary logical operator (\|, &, \|\|, &&)	tree node with operator between two holes

Collected by Matthias Hauswirth

Representation

imperative, OO / Java Language:

Makes explicit the fact that object allocation, method invocation, and field access are just expressions and can be composed like any other expression.

The structure, typing, and evaluation of expressions involving instances and classes.

PL	NM
...	(all aspects from 2-Logic)
null	tree node containing 'null'
this	tree node containing 'this'
instantiation	tree node with 'new', class name, and a parentheses containing comma-separated holes for constructor parameters
variable	tree node containing name of variable of an Object type
instance field access	tree node containing a hole, a dot, and a field name
instance method invocation	tree node with a hole, a dot, and parentheses containing comma-separated holes for method parameters
class field access	tree node containing class name, a dot, and a field name
class method invocation	tree node with class name, a dot, and parentheses containing comma-separated holes for method parameters

Collected by Matthias Hauswirth

Representation

imperative, OO / Java Language:

Makes explicit the fact that array allocation and access are also just expressions and can be composed like any other expression.

The structure, typing, and evaluation of expressions involving arrays.

PL	NM
...	(all aspects from 3-Objects)
array allocation	tree node with 'new', element type, and [hole] for each dimension
array length	tree node with a hole and '.length'
array element access	tree node with a hole, and [hole]

Collected by Matthias Hauswirth

Representation

imperative, OO / Java Language:

Makes explicit the fact that comparisons are just expressions (they produce a boolean value), and that one can construct expressions with the ternary conditional operator (providing a boolean value as the first operand).

The structure, typing, and evaluation of expressions involving comparisons and conditionals.

PL	NM
...	(all aspects from 4-Arrays)
binary comparison operator (==, !=, <, <=, >=, >)	tree node with operator between two holes
ternary conditional operator (?:)	tree node with a hole for the condition, '?', a hole for the then-value, ':', and a hole for the else-value

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

Representation

any / any Language:

The spreadsheet shows how input is transferred to output in several steps. It shows the core of the functionality that students need to implement. It allows students to experiment with changing input and functionality, and it provides students test cases.

It shows the students how output depends on input and calculation. It shows the different steps in the calculation.

PL	NM
function	cell transforming input to output

Collected by Johan Jeuring

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

Representation

imperative / Java Language:

Helps students plan and debug code

The fact that each reference can only point to a single thing

PL	NM
Object	Type written and underlined in a rectangle
variable	variable name followed by a small box
int	number written in a small box
reference	arrow originating from a small box
null	X written in a small box
local variable	free floating
instance variable	shown inside an object

Collected by Colleen Lewis

Representation

imperative / Java Language:

Shows the need for references and shows int arrays as sequences of ints.

Two references can refer to the same array. And arrays are just sequences of variables.

PL	NM
int	number written on paper in a small blue pocket
int array	sequence of int variables
variable	variable name followed by a small box
stack frame	rectangle with the method name written on the side containing all local variables
reference	pocket containing a remote control with a ribbon to the referent
null	empty pocket with an X shown in the back

Collected by Colleen Lewis

Representation

imperative / Java Language:

Ignores instance variables when first introducing objects.

Creation of objects and aliasing.

PL	NM
...	(all aspects of Physical Java 1)
object	a small stuffed animal with a resemblance to the name of the object
instance variables	(not represented)

Collected by Colleen Lewis

Representation

imperative / Java Language:

Helps students plan code; avoids confusion of crossed out arrows.

The effect of resetting references.

PL	NM
...	(all aspects of Physical Java 1)
object	object type written/underlined in a rectangle
int	number written in a small box
instance variables	shown in an object

Collected by Colleen Lewis

Representation

imperative / Java Language:

Introduces references as arrows (i.e., something more standard)

Standard ways of drawing Java memory (X for null, arrows for references).

PL	NM
...	(all aspects of Physical Java 3)
reference	arrow originating from a small box
null	X written in a small box

Collected by Colleen Lewis

Representation

imperative / Java Language:

Helps students plan code; avoids confusion of crossed out arrows.

The effect of resetting references.

PL	NM
...	(all aspects of Physical Java 4)
local variable	free floating variable
stack frame	(not represented)

Collected by Colleen Lewis

Representation

imperative / Java Language:

Distinguish between the type of the reference and the type of the object.

Reference type constrains what methods can be called and object type determines what method is called.

PL	NM
...	(all aspects of Physical Java 2)
variable type	sticky note with the name of the type next to the pocket that holds the reference
parent reference	a remote control that only has buttons corresponding to the things that the parent object knows how to do.
child object	a stuffed animal that - as a child - 'does what it wants' and not necessarily what the parent would do.

Collected by Colleen Lewis

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

Representation

object-oriented / Java Language:

Graphs make the relevant parts of program state explicit and support detailed explanations by instructor.

Program state, and especially variables and references.

PL	NM
stack frame	red rectangle, with method name and line number in left compartment, boxes for paremeters and local variables in right compartment
object	purple rectangle, with class name in left compartment, boxes for instance variables in right compartment
array	blue rectangle consisting of boxes for elements
static fields	yellow rectangle, with class name in left compartment, boxes for class variables in right compartment
variable	box inside a rectangle
reference value	solid arrow pointing to a rectangle
primitive value	value written inside a box
callee-caller relationship	dashed red arrow from callee stack frame to caller stack frame

Collected by Craig S. Miller

Representation

imperative / Python Language:

Expandable 'offline' model of program execution. In its beginning stage, it only covers control flow and variables (without references) of Python scripts.

Semantics of control flow in Python. Visible effects of each line on the 'state' of the Python computer.

PL	NM
memory	table of identifer and value
instruction	update of state according to defined rules
variable	entry in the table
conditional	conditional evaluator (flag) that affects the 'program counter'
control flow	program counter that identifies next line to get executed and is updated according to a set of rules

Collected by Andreas Mühling

Representation

imperative / Python Language:

Expandable 'offline' model of program execution. In its intermediate stage (V2) it covers everything of V1 plus definition and execution of sub-routines (functions) of Python scripts.

Scoping (global vs. local variables) and sub-routines with parameters and return values.

PL	NM
...	...
method table	table of identifier and starting line
scope	'sub-table' area in the memory
parameter	entry in the memory sub-table of a function call

Collected by Andreas Mühling

Representation

imperative / Python Language:

Expandable 'offline' model of program execution. In its advanced stage (V3) it covers everything of V1 and V2 plus lists and references.

Object types and references.

PL	NM
...	...
heap	object table of address and value
reference	addresss used as a value (denoted in <...>)
object	entry in object table with address and value

Collected by Andreas Mühling

Representation

imperative / Python Language:

Expandable 'offline' model of program execution. In its ultimate stage (V4) it covers everything of V1, V2 and V3 plus classes, objects and methods.

Methods and classes.

PL	NM
...	...
method	entry in the table of sub-routines
object	entry in object table with address and value(s)

Collected by Andreas Mühling

Representation

imperative / Python Language:

Demonstrates what happens to variable values when they are passed to a function. Distinguishes frame elements among each recursive call. Shows separate stack frames, each with own parameters and variables, for each recursive call.

Addition of each stack frame as each recursive call is made. Collapse of stack frame as function completes and returns value.

PL	NM
frame	group of elements with function name
parameter	labeled box inside frame
local variable	labeled box inside frame

Collected by Craig S. Miller

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

Representation

imperative, OO / Java Language:

Makes explicit the notion of an object, that groups together all the variables that correspond to the object's state.

An object's state.

PL	NM
object	red rounded rectangle, with class name containing instance variables
instance variable	box inside object, with name, type, value

Collected by Matthias Hauswirth

Representation

imperative, OO / Java Language:

Makes explicit the notion of a stack frame (activation record), that groups together all the temporary variables needed during a method execution.

A method's state (variables that have a lifetime as long as the execution of the method).

PL	NM
stack	one side of the drawing (labeled stack), containing zero or more stacked 'stack frame' rectangles
stack frame	grey rectangle, with method name, containing local variables and parameters of the method
local variable	box inside stack frame, with name, type, value
parameter	box inside stack frame, with name, type, value

Collected by Matthias Hauswirth

Representation

imperative, OO / Java Language:

Makes explicit the notion of a reference, which refers to a specific object, and the notion of a null value as a reference that does not point anywhere.

References.

PL	NM
...	(all aspects of 1 - Objects and 2 - Stack Frames)
reference value	arrow from a variable rectangle (anywhere, i.e., in the stack or the heap) to an object rounded rectangle
null value	a ground symbol (i.e., the absence of an arrow)

Collected by Matthias Hauswirth

Representation

imperative, OO / Java Language:

Makes explicit that arrays are heap objects where elements are accessed by index, and where the length is stored in a special read-only field. Particularly useful when explaining arrays of arrays.

Arrays.

PL	NM
...	(all aspects of 1 - Objects, 2 - Stack Frames, 3 - References)
array	red rounded rectangle on the heap, labeled with array type
array element	a field in the array, with index, type, and value
array length	a field in the array, with name 'length' and type int, and a value corresponding to the number of elements

Collected by Matthias Hauswirth

Representation

imperative & OO / Java, C#, ... Language:

Students need to understand that program variables (or collections of variables in an object) refer to memory locations, which might contain different kinds of values, and that statements (methods) change memory locations for variables (objects).

Different kinds of variables (objects) take up different space in memory. Statements and methods change the memory, which is visualized by changing the contents of the boxes when executing a statement or method.

PL	NM
variable	typed box/memory location
statement	changes a memory location
object	collection of boxes in memory
method	changes an object

Collected by Johan Jeuring

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

Representation

imperative / any Language:

Makes variable tangible, helps prevent multiple values misconception

Variables contain *one* value

PL	NM
variable	clothespin
variable name	label on the pin
value	paper sheet in the pin

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

Representation

imperative / any Language:

Shows how variables are updated with assignments.

Variable values and their assignment.

PL	NM
variable	table heading
value	last element listed in the column

Collected by Craig S. Miller

Representation

imperative / any Language:

Distinguishes between (string) literals and variables that represent them. Makes white-space characters and punctuation explicit.

Individual characters in a string.

PL	NM
literal string	pronounce each character in string
variable	pronounce 'the variable' and give its whole name

Collected by Craig S. Miller

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