8.1 Action specification for a simple calculator

Consider the following action specification for a simple calculator.

Informal Requirements or Intentions...

1. The application should be graphical, and should have an appearance similar to the following...
 


Fig. 8.1
Fig. 8.1


 


2. Buttons should be "active" and button pushes actually activate calculator functions.

3. An internal accumulator maintains a running total value reflecting the operations that have been made so far during use of the calculator.

4. An operator flag indicates what is the pending operation that will be performed once another operand is entered.

5. The display area shows the latest numeral that has been entered, the memory value that is recalled using MR, or the total value computed so far when the = or M+ keys are pushed.

6. The memory for the calculator contains a value, initially zero. It is changed by the M+ and MR keys.
 

Domains ...

Button --> Digit | Arithmetic_Operator | Memory_Operator | Clear | Equal
Digit --> 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
Numeral --> Digit | Numeral Digit
Arithmetic_Operator --> plus | minus | times | plus_minus
Memory_Operator --> mem_plus | mem_rec
Clear --> clear
Equal --> equal
Mode --> init | cont
Changeable Properties 
accumulator(N)   where N is Numeral  
op(F)            where F is Arithmetic_Operator  
displayed(D)     where D is Numeral  
memory(M)        where M is Numeral  
mode(C)          where C is Mode
Action 
push(B)          where B is Button
Action Animator
Animator --> Show_Action | Show_Action Animator
Show_Action --> Action Show
Show --> ...
Action Specifications

The calculator registers are modelled as a 4-tuple
 

[a,op,d,m]


where

accumulator(a)
op(op)
displayed(d)
memory(m)
declare (or express) the current "true" values of these changeable properties.

An action changes the values of these four registers, that is, an action changes the truth or falsity of the changeable properties... 

[a,op,d,m] -- Action --> [a',op', d', m'] 

or 

Action < - {preconditions},
             deny({old properties}), 
             {local calculations}, 
             affirm({new properties}).
The specifications are each given in two forms. The first is a more intuitive summary expression, the second is the formal action specification ... 
action_module(calculator) .


%[-,-,d1,-] --push(D)-->          [-,-,D,-]  if mode(init)  
push(D) < - 
  mode(init), 
  deny([displayed(D1),mode(init)]), 
  affirm([displayed(D),mode(cont)]).
  
%[-,-,D1,-] --push(D)-->          [-,-,10*D1+D,-]  if mode(cont) 
push(D) < - 
  mode(cont), 
  deny(displayed(D1)), 
  New = 10*D1 + D, 
  affirm(displayed(New)). 

%[a,op,d,m] --push(clear)-->      [0,nop,0,0] 
push(clear) < -
  deny([accumulator(A),op(O),displayed(D),memory(M),mode(X)]), 
  affirm([accumulator(0),op(nop),displayed(0),memory(0),mode(init)]). 

%[a,op,d,m] --push(mem_rec)-->    [a,op,m,m] 
push(mem_rec) < -
  memory(M), 
  deny([displayed(D),mode(X)]), 
  affirm([displayed(M),mode(init)]). 

%[a,op,d,m] --push(plus)-->       [op(a,d),plus,d,m] 
push(plus) < -
  displayed(D), 
  deny([accumulator(A),op(O),mode(X)]),  
  eval(O,A,D,V),   ; use normal arithmetic, i.e., V=O(A,D)  
  affirm([accumulator(V),op(plus),mode(init)]).  
 
%[a,op,d,m] --push(minus)-->      [op(a,d,minus,d,m] 
push(minus) lt -
  displayed(D), 
  deny([accumulator(A),op(O),mode(X)]), 
  eval(O,A,D,V),   ; use normal arithmetic, i.e., V=O(A,D) 
  affirm([accumulator(V),op(minus),mode(init)]). 

%[a,op,d,m] --push(times)-->      [op(a,d),times,d,m] 
push(times) < -
  displayed(D), 
  deny([accumulator(A),op(O),mode(X)]), 
  eval(O,A,D,V),   ; use normal arithmetic, i.e., V=O(A,D) 
  affirm([accumulator(V),op(times),mode(init)]). 

%[a,op,d,m] --push(equal)-->      [a,nop,op(a,d),m] 
push(equal) < -
  accumulator(A), 
  deny([op(O),displayed(D),mode(X)]), 
  eval(O,A,D,V), 
  affirm([op(nop),displayed(V),mode(init)]). 

%[a,op,d,m] --push(mem_plus)-->   [a,nop,v,plus(m,v)] where v=op(a,d) 
push(mem_plus) < -
  accumulator(A), 
  deny([op(O),displayed(D),memory(M),mode(X)]), 
  eval(O,A,D,V), 
  eval(plus,M,V,V1), 
  affirm([op(nop),displayed(V),memory(V1),mode(init)]).

%[a,op,d,m] --push(plus_minus)--> [a,op,-d,m] 
push(clear) < -
  deny([displayed(D),mode(X)]), 
  eval(minus,0,D,V), 
  affirm([displayed(V),mode(init)]). 
A fairly straightforward translation of the action clauses gives a Prolog prototype.

Exercise 8.1 Extend the calculator specification for real arithmetic, implement the specification, and test the implementation.

Prolog Tutorial Contents