Understanding Computation (60 page)

Read Understanding Computation Online

Authors: Tom Stuart

Tags: #COMPUTERS / Programming / General

R
Range class,
Enumerable
range of values,
Data Structures
recursive code
avoiding arbitrary recursion,
Avoiding arbitrary recursion
–
Avoiding arbitrary recursion
infinite loops,
Numeric Operations
partial recursive functions,
Partial Recursive Functions
–
Partial Recursive Functions
stack overflow,
Statements
reduction contexts,
Applications
reduction relation,
Small-Step Semantics
reduction semantics,
Applications
reductions, small-step
about,
Small-Step Semantics
applications,
Applications
expressions,
Expressions
–
Expressions
statements,
Statements
–
Statements
Regexp class,
Just Add Power
regular expressions
about,
Regular Expressions
concatenating,
Semantics
converting NFA to,
Just Add Power
nested strings and,
Just Add Power
parsing,
Parsing
–
Parsing
semantics,
Semantics
–
Semantics
syntax,
Syntax
–
Syntax
regular languages,
Nondeterminism
relational semantics (see big-step semantics)
remove_constant message,
Removing Constants
Rendell, Paul,
Conway’s Game of Life
Rice’s theorem
about,
Other Undecidable Problems
abstract interpretation and,
Safety and Approximation: Adding Signs
,
Applications
implications of,
Depressing Implications
predicting program behavior,
Programming in Toyland
Ruby programming language
blocks of code,
Blocks
classes and modules,
Classes and Modules
control flow,
Control Flow
defining constants,
Defining Constants
Enumerable module,
Enumerable
inspecting objects,
Inspecting Objects
Interactive Ruby Shell,
Interactive Ruby Shell
local variables and assignment,
Local Variables and Assignment
monkey patching,
Monkey Patching
objects and methods,
Objects and Methods
printing strings,
Printing Strings
specification by implementation,
The Meaning of “Meaning”
string interpolation,
String Interpolation
Struct class,
Struct
value types supported,
Values
–
Procs
variadic methods,
Variadic Methods
rule 110,
Rule 110
rulebooks
cyclic tag system and,
Cyclic Tag Systems
deterministic finite automata,
Simulation
deterministic pushdown automata,
Simulation
deterministic Turing machines,
Simulation
nondeterministic finite automata,
Nondeterminism
Turing machines,
Subroutines
,
General-Purpose Machines
rules
deterministic finite automata,
States, Rules, and Input
deterministic pushdown automaton,
Rules
deterministic Turing machines,
Rules
nondeterministic finite automata,
Nondeterminism
rulebooks and,
Simulation
S
s-expressions,
Code Is Data
Sagan, Carl,
Programming with Nothing
Scheme programming language,
Applications
self-referential programs,
Programs Can Refer to Themselves
–
Programs Can Refer to Themselves
,
Why Does This Happen?
semantics
about,
The Meaning of “Meaning”
axiomatic,
Alternatives
comparing styles,
Statements
denotational,
Denotational Semantics
–
Applications
dynamic,
Correctness
,
Static Semantics
formal,
The Meaning of “Meaning”
,
Formal Semantics in Practice
–
Alternatives
lambda calculus,
Semantics
–
Reducing expressions
operational,
Operational Semantics
–
Applications
,
Expressions
,
Statements
reduction,
Applications
regular expressions,
Semantics
–
Semantics
static,
Correctness
,
Static Semantics
–
Benefits and Limitations
sequence statements
big-step semantics,
Statements
small-step semantics,
Statements
Set class
#& method,
Nondeterminism
#+ method,
Nondeterminism
about,
Nondeterminism
#subset? method,
Nondeterminism
Simple programming language example
about,
Small-Step Semantics
,
Programming with Nothing
big-step semantics,
Big-Step Semantics
–
Applications
denotational semantics,
Denotational Semantics
–
Applications
implementing parsers,
Implementing Parsers
–
Implementing Parsers
small-step semantics,
Small-Step Semantics
–
Applications
simulation
deterministic finite automata,
Simulation
deterministic pushdown automaton,
Simulation
–
Simulation
general-purpose machines,
Simulation
nondeterministic finite automata,
Nondeterminism
nondeterministic pushdown automaton,
Simulation
–
Simulation
Turing machines,
Simulation
universal Turing machines,
Simulation
SKI combinator calculus,
SKI Combinator Calculus
–
Iota
small-step semantics
about,
Small-Step Semantics
applications,
Applications
comparing styles,
Statements
correctness,
Correctness
expressions,
Expressions
–
Expressions
statements,
Statements
–
Statements
Smalltalk programming language,
Objects and Methods
Smith, Alex,
Wolfram’s 2,3 Turing Machine
square brackets [ ],
Data Structures
,
Procs
stack overflow,
Statements
start state,
States, Rules, and Input
,
Nondeterminism
statements
about,
Statements
assignment,
Statements
big-step semantics,
Statements
–
Statements
conditional,
Statements
,
Booleans
–
Booleans
denotational semantics,
Statements
–
Statements
do-nothing,
Statements
sequence,
Statements
,
Statements
small-step semantics,
Statements
–
Statements
states
accept,
Output
,
Nondeterminism
,
Semantics
balanced brackets example,
Just Add Power
deterministic finite automata,
States, Rules, and Input
Game of Life and,
Conway’s Game of Life
implementing,
Semantics
nondeterministic finite automata,
Nondeterminism
,
Semantics
start,
States, Rules, and Input
,
Nondeterminism
Turing machines,
Internal Storage
static semantics
about,
Correctness
,
Static Semantics
benefits and limitations,
Benefits and Limitations
–
Benefits and Limitations
implementing,
Implementation
–
Implementation
storage
deterministic finite automata,
Output
deterministic pushdown automaton,
Storage
deterministic Turing machines,
Storage
–
Storage
multidimensional tape,
Multidimensional Tape
multiple tapes,
Multiple Tapes
nondeterministic finite automata,
Nondeterminism
Turing machines,
Internal Storage
–
Internal Storage
streams
infinite,
Infinite streams
–
Infinite streams
native Ruby,
Infinite streams
strings
concatenating,
Expressions
,
Syntax
FizzBuzz example,
Strings
interpolating,
String Interpolation
nested,
Just Add Power
printing,
Printing Strings
Struct class
about,
Struct
#inspect method,
Expressions
new method,
Struct
#to_s method,
Expressions
structural operational semantics (see small-step semantics)
subroutines,
Subroutines
super keyword,
Classes and Modules
superclasses,
Classes and Modules
symbols
about,
Basic Data
,
Free Moves
hashes and,
Data Structures
key-value pairs and,
Data Structures
SKI combinator calculus and,
SKI Combinator Calculus
–
Iota
syntactic analysis
about,
Parsing with Pushdown Automata
parsing with PDA,
Syntactic Analysis
–
Syntactic Analysis
syntax
about,
The Meaning of “Meaning”
,
Syntax
lambda calculus,
Syntax
–
Syntax
parsers and,
Syntax
procs,
Syntax
programs and,
Syntax
regular expressions,
Syntax
–
Syntax
T
tag systems
about,
Tag Systems
–
Tag Systems
cyclic,
Cyclic Tag Systems
–
Cyclic Tag Systems
tail call optimisation,
Statements
tape storage
multidimensional tape,
Multidimensional Tape
multiple tapes,
Multiple Tapes
TM (Turing machines),
Encoding
(see also UTM)
about,
Programming with Nothing
decidability,
Decidability
–
Decidability
deterministic,
Deterministic Turing Machines
–
Simulation
deterministic finite automata and,
General-Purpose Machines
encoding,
Encoding
external memory and,
Deterministic Turing Machines
Game of Life,
Conway’s Game of Life
–
Conway’s Game of Life
halting problem,
The Halting Problem
–
Fundamentally impossible
lambda calculus and,
Lambda Calculus
–
Lambda Calculus
maximum power,
Maximum Power
–
Multidimensional Tape
multidimensional tape,
Multidimensional Tape
multiple tapes,
Multiple Tapes
nondeterministic,
Nondeterministic Turing Machines
partial recursive functions and,
Partial Recursive Functions
–
Partial Recursive Functions
programs standing in for,
Programs Can Stand In for Turing Machines
rule 110,
Rule 110
simulation,
Simulation
SKI combinator calculus and,
SKI Combinator Calculus
–
Iota
storage,
Internal Storage
–
Internal Storage
subroutines,
Subroutines
tag systems and,
Tag Systems
–
Cyclic Tag Systems
Wolfram’s 2,3 Turing machine,
Wolfram’s 2,3 Turing Machine
total programming languages,
Universal Systems Can Loop Forever
,
Depressing Implications
transition functions,
Free Moves
transition semantics (see small-step semantics)
transitions,
Free Moves
Treetop language,
Implementing Parsers
,
Parsing
–
Parsing
Turing machines (see TM)
Turing, Alan,
The Ultimate Machine
,
Storage
,
Rules
Turner, David,
Depressing Implications
U
unary representation,
Encoding
undecidable problems
about,
Decidability
halting problem,
The Halting Problem
–
Fundamentally impossible
implications of,
Depressing Implications
–
Depressing Implications
toy example,
Other Undecidable Problems
–
Other Undecidable Problems
universal Turing machines (see UTM)
unreachable code,
Coping with Uncomputability
untyped lambda calculus (see lambda calculus)
UTM (universal Turing machines)
about,
General-Purpose Machines
,
Universality Is Everywhere
code is data,
Code Is Data
decidability,
Decidability
–
Decidability
encoding,
Encoding
infinite looping,
Universal Systems Can Loop Forever
–
Universal Systems Can Loop Forever
lambda calculus and,
Lambda Calculus
–
Lambda Calculus
performing algorithms,
Universal Systems Can Perform Algorithms
–
Universal Systems Can Perform Algorithms
programs standing in for,
Programs Can Stand In for Turing Machines
,
Programs Can Stand In for Turing Machines
simulation,
Simulation

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