Slide Number 1

1
A Case Study

• This case study is about specifying a video
  recorder

• This Unit defines
• underlying functionality
• plumbing together components
• dates (example of schema disjunction)

• Tutorial 3 is on extending this specification.

2
Video recorder basic functionality
Antenna
RF Radio Frequency all channels together
RF
RF
RF
YUV Sound

• YUV Sound Picture Sound for a single channel
• mod_ch? channel on which recorder output is
  added to RF signal.
• tune_ch? channel that recorder is tuned to.

YUV Sound
3
Terminology

• Two kinds of signals RF and YUVSound.
• RF (Radio Frequency) signal
• as picked up by antenna
• also needed by the TV
• contains all the channels.
• Physical Channel frequency band, numbered
  between 21 and 69.
• YUVSound signal information for a single
  channel
• as used for tape deck
• 4 information components 3 for colour picture, 1
  for sound
• Tuner converts RF to YUVSound
• selects signal for a given channel tune_ch? and
  extracts YUVSound information

4
Hardware specification

• Can describe inputs and outputs for components.
• Sorts
• RFsig for RF signal
• YUVsig for YUVSound signal
• CHAN nN 21 ? n ? 69 for physical channels
• TAPE for tape signals
• Expressions
• empty YUVsig for absent signal
• sch YUVsig (s RFsig, chCHAN)
• for signal on s at channel ch
• sig(t) YUVsig (tTAPE)
• YUVSound signal stored on tape

5
Specifying components
tuner_in?
Tuner tune_ch?
tuner_out!
6
(No Transcript)
7
Plumbing

• Can specify how components are connected together

Exercise what are connections for playback?
8
Timer mode v. manual mode

• Need to avoid conflict between recording and
  playback.
• Assume machine has two modes
• Timer mode
• Will record automatically according to recording
  schedule. It needs specifications of
• time
• schedule of programs
• internal timer tick operation
• Manual mode
• Can record or play back under manual control.
• Ignores recording schedule.

9
Dates
month_lengths (1,31), (2,28), (3,31), (4,30),
(5,31), (6,30), (7,31), (8,31), (9,30), (10, 31),
(11, 30), (12, 31)
Feb29 d,m,y N d 29 m 2 (y mod 4 0 ? y
mod 100 ? 0) ? y mod 400 0

• NormalDate
• d,m,y N
• nN. ((m,n) ? month_lengths
• ? 1 ? d ? n)

Date NormalDate ? Feb29
10
Tomorrow
Note Axioms in Date and Date' ensure that both
days are valid.
11
TomorrowFeb29 DDate Feb29' d 28 ? m 2 y' y
TomorrowMar1Leap DDate Feb29 d' 1 ? m' 3 ?
y' y
Tomorrow TomorrowSameMonth ? TomorrowNewMonth ?
TomorrowFeb29 ? TomorrowMar1Non-leap ?
TomorrowMar1Leap ? TomorrowNewYear
12
Substitution

• Will might need to substitute variables in
  schema. Assume the schema Date given in slide 9.
  
• Consider the following schema

• Consider start. and stop. as decorations.
• Day1BeforeDay2 Date1/start.Date,
  Date2/stop.Date
• Axioms of Day1BeforeDay2 but with d1
  substituted with start.d d2 substituted with
  stop.d, m1 substituted with start.m, ect

13
The End