// file:    a10.rex
// author:  R. Keller
// purpose: Solution to rex part of a10

/*
CS 60,  Fall 2003, Assignment 9, rex part            

The allowed rex functions are (n is arbitrary in each case):

    or(x1, x2, ..., xn), alternatively x1 || x2 || ... || xn

    and(x1, x2, ..., xn), alternatively x1 && x2 && ... && xn    

    not(x1), alternatively !x1

*/

/* Problem 1: define DecimalDigitToBCD */

DecimalDigitToBCD(0) => [0, 0, 0, 0];
DecimalDigitToBCD(1) => [0, 0, 0, 1];
DecimalDigitToBCD(2) => [0, 0, 1, 0];
DecimalDigitToBCD(3) => [0, 0, 1, 1];
DecimalDigitToBCD(4) => [0, 1, 0, 0];
DecimalDigitToBCD(5) => [0, 1, 0, 1];
DecimalDigitToBCD(6) => [0, 1, 1, 0];
DecimalDigitToBCD(7) => [0, 1, 1, 1];
DecimalDigitToBCD(8) => [1, 0, 0, 0];
DecimalDigitToBCD(9) => [1, 0, 0, 1];


/* Problem 2: define BCDtoSevenSegment */

BCDtoSevenSegment([b3, b2, b1, b0]) =>

 [or(  b3,          b2 &&  b0,   !b2 && !b0,  b1                          ),
  or(  b3,          b2 && !b1,    b2 && !b0, !b1 && !b0                   ),
  or( !b2,          b1 &&  b0,   !b1 && !b0                               ),
  or(  b3,          b2 && !b1,   !b2 && b1,   b1 && !b0                   ),
  or( !b2 && !b0,   b1 && !b0                                             ),
  or(  b2,         !b1,           b0                                      ),
  or(  b3,         !b2 && !b0,   !b2 && b1,   b2 && !b1 && b0,  b1 && !b0 )
 ];


/* Functions for testing */

decimalToSevenSegment(0) => [1, 1, 1, 0, 1, 1, 1];
decimalToSevenSegment(1) => [0, 0, 1, 0, 0, 1, 0];
decimalToSevenSegment(2) => [1, 0, 1, 1, 1, 0, 1];
decimalToSevenSegment(3) => [1, 0, 1, 1, 0, 1, 1];
decimalToSevenSegment(4) => [0, 1, 1, 1, 0, 1, 0];
decimalToSevenSegment(5) => [1, 1, 0, 1, 0, 1, 1];
decimalToSevenSegment(6) => [1, 1, 0, 1, 1, 1, 1];
decimalToSevenSegment(7) => [1, 0, 1, 0, 0, 1, 0];
decimalToSevenSegment(8) => [1, 1, 1, 1, 1, 1, 1];
decimalToSevenSegment(9) => [1, 1, 1, 1, 0, 1, 1];

sevenSegmentToDecimal([1, 1, 1, 0, 1, 1, 1]) => 0;
sevenSegmentToDecimal([0, 0, 1, 0, 0, 1, 0]) => 1;
sevenSegmentToDecimal([1, 0, 1, 1, 1, 0, 1]) => 2;
sevenSegmentToDecimal([1, 0, 1, 1, 0, 1, 1]) => 3;
sevenSegmentToDecimal([0, 1, 1, 1, 0, 1, 0]) => 4;
sevenSegmentToDecimal([1, 1, 0, 1, 0, 1, 1]) => 5;
sevenSegmentToDecimal([1, 1, 0, 1, 1, 1, 1]) => 6;
sevenSegmentToDecimal([1, 0, 1, 0, 0, 1, 0]) => 7;
sevenSegmentToDecimal([1, 1, 1, 1, 1, 1, 1]) => 8;
sevenSegmentToDecimal([1, 1, 1, 1, 0, 1, 1]) => 9;

/* define BCDtoDecimalDigit */

BCDtoDecimalDigit([0, 0, 0, 0]) => 0;
BCDtoDecimalDigit([0, 0, 0, 1]) => 1;
BCDtoDecimalDigit([0, 0, 1, 0]) => 2;
BCDtoDecimalDigit([0, 0, 1, 1]) => 3;
BCDtoDecimalDigit([0, 1, 0, 0]) => 4;
BCDtoDecimalDigit([0, 1, 0, 1]) => 5;
BCDtoDecimalDigit([0, 1, 1, 0]) => 6;
BCDtoDecimalDigit([0, 1, 1, 1]) => 7;
BCDtoDecimalDigit([1, 0, 0, 0]) => 8;
BCDtoDecimalDigit([1, 0, 0, 1]) => 9;


/*

A function 'display' that will print out a seven-segment
encoding in a manner simulating an LED display, e.g.

rex > display(decimalToSevenSegment(9));

******
*    *
*    *
*    *
******
     *
     *
     *

*/

// format seven-segment code as a mock LED display

display([s0, s1, s2, s3, s4, s5, s6]) =>

   concat("\n",
       s0 ? "******" : "     ",                        "\n",
       s1 ? "*    "  : "     ",        s2 ? "*" : " ", "\n",
       s1 ? "*    "  : "     ",        s2 ? "*" : " ", "\n",
       s1 ? "*    "  : "     ",        s2 ? "*" : " ", "\n",
       s3 ? "******" : s1 ? (s2 ? "*    *" : "*") : (s2 ? "     *" : ""), "\n",
       s4 ? "*    "  : "     ",        s5 ? "*" : " ", "\n",
       s4 ? "*    "  : "     ",        s5 ? "*" : " ", "\n",
       s4 ? "*    "  : "     ",        s5 ? "*" : " ", "\n",
       s6 ? "******" : "     ",                        "\n",
       "\n");

/* The following is an illustration of the 7-segment code. */

showAll() = map((N) => display(decimalToSevenSegment(N)), range(0, 9));


test() =
  map((N) => sevenSegmentToDecimal(BCDtoSevenSegment(DecimalDigitToBCD(N))),
      range(0, 9));

test(test(), range(0, 9));


testec() = 

test(
map((X) => BCDtoDecimalDigit(SevenSegmentToBCD(decimalToSevenSegment(X))) == X, 
    range(0, 9)),
    [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
    );