PX: A computational logic

189

Book Announcements and possible

improvements).

Related

work in automated

Method for Doxastic Reasoning. Doxastic Chapter 10. Advantages and disadvantages

theories.

theorem

of an abstract

Chapter 9: A Modal Proof

proving.

The pure proof

method.

The augmented

Benjamin Arazi, A Commonsense Approach to the Theory Codes (MIT Press, Cambridge, MA, 1988) 208 pages Chapter 1: Introduction. A communication detection.

The concept

Basic concepts. the code.

Minimum

Hamming

The generating

matrix

parity

matrix.

error

correction.

Properties

of maximum-length

equations

of several

Review

shifts

codes.

of a burst

and the amount

The encoder

Maximum-length

error.

Single burst

of cyclic shift between the burst pattern circuitry-the

decoder.

matrix.

error

capability

a general

Hamming

of

code.

introduced.

Chapter 3: Basic

Multiplying

a message

by the

Automatic

single

and their effect and decoder

vectors.

error

of a code satisfying

detection.

Connection

on the generating

The connection

between

the location

and the error syndrome. correction

of

matrix. the parity

Chapter 5: Single Burst Error

sequences.

Ways of recovering

Burst

Error

Chapter 4: Cyclic Codes. Some properties

of code words

to detect the exact burst pattern.

correction

of parity.

Chapter 2: Linear Codes.

of long and short

code.

and cyclic shifts of the error syndrome.

it is possible

of the concepts

Encoding/decoding

code words.

independent

Correction. The definition

error

code.

of the rows of the generating

Linear

The concept

introduced.

of a linear code. Constructing

single error correcting

by LFSR.

of Error Correcting

of a code and the error detection/correction

matrix

process.

A general

generated

distance

of a systematic generation

system and the effect of errors. Review of the concepts

The parity

The encoding

burst pattern

codes.

Hamming

codes.

Circuitry. Automatic

matrices

of block

method.

architecture.

between

Conditions

the location

circuitry-the

the

of a burst error under which

of a burst encoder.

error.

Using

Burst a cyclic

Hamming code for detecting burst errors. Using a cyclic Hamming code for correcting burst errors based on knowing the burst pattern. The fire code. Single character error correction (the RS code). Chapter

6: Convolutional Codes. Basic concepts. threshold

decoding

codes: Decoding

Diffuse

process.

threshold

decoding

division modulo 2. The connection between polynomial division polynomial of a code. Cyclic properties of polynomials. More polynomial

manipulations.

A formal

codes:

treatment

Susumu Hayashi and Hiroshi Nakano, Cambridge, MA, 1988) 200 pages

logic. PX as a foundation

process.

and LFSR circuitry. properties of cyclic

of a single character

correction

Diffuse

of type theory.

The generating codes based on

RS code.

PX: A Computational

Chapter 1: Introduction. What is PX?. PX as a logic of computation. as a classical

Encoding

Appendix: The Basic Principles Re-Examined. Polynomial

Logic (MIT Press,

PX as a program

The origin of PX. Overview.

extractor.

PX

Chapter 2: Formal

System. DEF system: recursive system:

the logic of partial

predicates.

functions over symbolic expressions. The language of PX. Basic axiom terms (,+expression and a-convertibility. Axioms for programs and primitive

Rules for the usual logical

Miscellaneous

axioms).

of Join and Product. axiom

system

Total

variables

Classes: Graph

Rules for V and +. (CIG: conditional

and value class: the minimal

(The logic of partial versus

symbols.

data types as objects

partial

graph

axiom).

terms versus the logic of partial

variables).

Choice

existence.

Chapter 3: Realizability.

realizability. Chapter 4: Writing Programs via Proofs. How Howard isomorphism in PX. CIG recursion (Definition of CIG (Quotient and remainder. Maximal element in an integer list. whose termination is unknown. Searching for a prime number.

Axioms for the modal operator. inductive generation. Axioms rule. Remarks

Transparency

px-realizability.

on the

of classes.

A refined

px-

to extract programs with PX. Curryrecursion. Examples of CIG recursion The Ackermann function. A function The Chinese remainder theorem)). PX

Book Announcements

190

is extensionally

complete.

Transfinite

induction.

of Type Theories. A view of “dependent morphism

and an impredicative

Tarskian semantics of the impredicative checker and

(Formulas.

declarations).

Translating EKL from

of formulas. Semantics extension). Satisfication Proofs. Extractor.

expressions PX).

extension

Simulating

sums of PX.

translator

and functions.

logic. Chapter 5: PX as a Foundation

of module

implementations”.

Chapter 6: Semantics. Semantics

Type

poly-

of computation.

of classes (The restricted model. The full model. The model of MGA. Chapter 7: Implementing PX. Hypotheses. Proof

Top level and commands. EKL

Hoare

as types

Inference

(Interpreting

Translating

formulas.

Chapter 8: Conclusion. What was done?.

rules. Inference

LPT

Translating What

macros.

of PX in typed is missed?

axiom What

PX evaluator

language system. should

of EKL.

How to call be done?.