Understanding Computation (60 page)
Q
- quine,
Programs Can Refer to Themselves - quotation marks,
String Interpolation
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
- avoiding arbitrary recursion,
- 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
- about,
- 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
- about,
- 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
- about,
- 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
- blocks of code,
- 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
- cyclic tag system and,
- rules
- deterministic finite automata,
States, Rules, and Input - deterministic pushdown automaton,
Rules - deterministic Turing machines,
Rules - nondeterministic finite automata,
Nondeterminism - rulebooks and,
Simulation
- deterministic finite automata,
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
- about,
- sequence statements
- big-step semantics,
Statements - small-step semantics,
Statements
- big-step semantics,
- Set class
- #& method,
Nondeterminism - #+ method,
Nondeterminism - about,
Nondeterminism - #subset? method,
Nondeterminism
- #& method,
- 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
- about,
- 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
- deterministic finite automata,
- 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
- about,
- 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
- about,
- 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
- accept,
- static semantics
- about,
Correctness
,
Static Semantics - benefits and limitations,
Benefits and Limitations
–
Benefits and Limitations - implementing,
Implementation
–
Implementation
- about,
- 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
- deterministic finite automata,
- streams
- infinite,
Infinite streams
–
Infinite streams - native Ruby,
Infinite streams
- infinite,
- strings
- concatenating,
Expressions
,
Syntax - FizzBuzz example,
Strings - interpolating,
String Interpolation - nested,
Just Add Power - printing,
Printing Strings
- concatenating,
- Struct class
- about,
Struct - #inspect method,
Expressions - new method,
Struct - #to_s method,
Expressions
- about,
- 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
- about,
- syntactic analysis
- about,
Parsing with Pushdown Automata - parsing with PDA,
Syntactic Analysis
–
Syntactic Analysis
- about,
- syntax
T
- tag systems
- about,
Tag Systems
–
Tag Systems - cyclic,
Cyclic Tag Systems
–
Cyclic Tag Systems
- about,
- tail call optimisation,
Statements - tape storage
- multidimensional tape,
Multidimensional Tape - multiple tapes,
Multiple Tapes
- multidimensional tape,
- 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
- (see also UTM)
- 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
- about,
- 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
- about,
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