This document discusses implementing a rock-paper-scissors game in C language. It first defines an enum type for the three options - rock, paper, scissors. It then shows functions to print the name of a selected option, and to determine the winning option and even option based on two input options. However, it notes that the implementation allows for potential run-time errors if the logic in the functions is incorrect.
So einfach geht modernes Roaming fuer Notes und Nomad.pdf
Static typing and proof in ATS language
1. Static typing and proof in ATS
language
Static typing and proof in ATS
language
Static typing and proof in ATS
language
Static typing and proof in ATS
language
Static typing and proof in ATS
language
Kiwamu OkabeKiwamu OkabeKiwamu OkabeKiwamu OkabeKiwamu Okabe
2. Let's make Rock-paper-scissors libraryLet's make Rock-paper-scissors libraryLet's make Rock-paper-scissors libraryLet's make Rock-paper-scissors libraryLet's make Rock-paper-scissors library
☆ �じゃんけん� in Japanese.☆ �じゃんけん� in Japanese.☆ �じゃんけん� in Japanese.☆ �じゃんけん� in Japanese.☆ �じゃんけん� in Japanese.
3. R-P-S in C language #1R-P-S in C language #1R-P-S in C language #1R-P-S in C language #1R-P-S in C language #1
#include�<stdio.h>
#include�<stdlib.h>
typedef�enum�{
R_RPS_T�=�0,�/*�Rock�*/
P_RPS_T,�����/*�Paper�*/
S_RPS_T������/*�Scissors�*/
}�rps_t;
void�print_rps(rps_t�x)�{
switch�(x)�{
case�R_RPS_T:
printf("Rock");�break;
case�P_RPS_T:
printf("Paper");�break;
case�S_RPS_T:
printf("Scissors");�break;
}
}
#include�<stdio.h>
#include�<stdlib.h>
typedef�enum�{
R_RPS_T�=�0,�/*�Rock�*/
P_RPS_T,�����/*�Paper�*/
S_RPS_T������/*�Scissors�*/
}�rps_t;
void�print_rps(rps_t�x)�{
switch�(x)�{
case�R_RPS_T:
printf("Rock");�break;
case�P_RPS_T:
printf("Paper");�break;
case�S_RPS_T:
printf("Scissors");�break;
}
}
#include�<stdio.h>
#include�<stdlib.h>
typedef�enum�{
R_RPS_T�=�0,�/*�Rock�*/
P_RPS_T,�����/*�Paper�*/
S_RPS_T������/*�Scissors�*/
}�rps_t;
void�print_rps(rps_t�x)�{
switch�(x)�{
case�R_RPS_T:
printf("Rock");�break;
case�P_RPS_T:
printf("Paper");�break;
case�S_RPS_T:
printf("Scissors");�break;
}
}
#include�<stdio.h>
#include�<stdlib.h>
typedef�enum�{
R_RPS_T�=�0,�/*�Rock�*/
P_RPS_T,�����/*�Paper�*/
S_RPS_T������/*�Scissors�*/
}�rps_t;
void�print_rps(rps_t�x)�{
switch�(x)�{
case�R_RPS_T:
printf("Rock");�break;
case�P_RPS_T:
printf("Paper");�break;
case�S_RPS_T:
printf("Scissors");�break;
}
}
#include�<stdio.h>
#include�<stdlib.h>
typedef enum�{
R_RPS_T�=�0,�/*�Rock�*/
P_RPS_T,�����/*�Paper�*/
S_RPS_T������/*�Scissors�*/
}�rps_t;
void�print_rps(rps_t�x)�{
switch�(x)�{
case�R_RPS_T:
printf("Rock");�break;
case�P_RPS_T:
printf("Paper");�break;
case�S_RPS_T:
printf("Scissors");�break;
}
}
4. R-P-S in C language #2R-P-S in C language #2R-P-S in C language #2R-P-S in C language #2R-P-S in C language #2
int�main()�{
rps_t�paper_d�=�P_RPS_T;
rps_t�win_d�=�rps_win_d�(paper_d);
print_rps(win_d);�printf("�win�");�print_rps(paper_d);�printf(".n");
/*�=>�Scissors�win�Paper.�*/
rps_t�even_d�=�rps_even_d(win_d,�paper_d);
print_rps(even_d);�printf("�is�even�between�");�print_rps(win_d);
printf("�and�");�print_rps(paper_d);�printf(".n");
/*�=>�Rock�is�even�between�Scissors�and�Paper.�*/
}
int�main()�{
rps_t�paper_d�=�P_RPS_T;
rps_t�win_d�=�rps_win_d�(paper_d);
print_rps(win_d);�printf("�win�");�print_rps(paper_d);�printf(".n");
/*�=>�Scissors�win�Paper.�*/
rps_t�even_d�=�rps_even_d(win_d,�paper_d);
print_rps(even_d);�printf("�is�even�between�");�print_rps(win_d);
printf("�and�");�print_rps(paper_d);�printf(".n");
/*�=>�Rock�is�even�between�Scissors�and�Paper.�*/
}
int�main()�{
rps_t�paper_d�=�P_RPS_T;
rps_t�win_d�=�rps_win_d�(paper_d);
print_rps(win_d);�printf("�win�");�print_rps(paper_d);�printf(".n");
/*�=>�Scissors�win�Paper.�*/
rps_t�even_d�=�rps_even_d(win_d,�paper_d);
print_rps(even_d);�printf("�is�even�between�");�print_rps(win_d);
printf("�and�");�print_rps(paper_d);�printf(".n");
/*�=>�Rock�is�even�between�Scissors�and�Paper.�*/
}
int�main()�{
rps_t�paper_d�=�P_RPS_T;
rps_t�win_d�=�rps_win_d�(paper_d);
print_rps(win_d);�printf("�win�");�print_rps(paper_d);�printf(".n");
/*�=>�Scissors�win�Paper.�*/
rps_t�even_d�=�rps_even_d(win_d,�paper_d);
print_rps(even_d);�printf("�is�even�between�");�print_rps(win_d);
printf("�and�");�print_rps(paper_d);�printf(".n");
/*�=>�Rock�is�even�between�Scissors�and�Paper.�*/
}
int�main()�{
rps_t�paper_d�=�P_RPS_T;
rps_t�win_d�=�rps_win_d�(paper_d);
print_rps(win_d);�printf("�win�");�print_rps(paper_d);�printf(".n");
/*�=>�Scissors�win�Paper.�*/
rps_t�even_d�=�rps_even_d(win_d,�paper_d);
print_rps(even_d);�printf("�is�even�between�");�print_rps(win_d);
printf("�and�");�print_rps(paper_d);�printf(".n");
/*�=>�Rock�is�even�between�Scissors�and�Paper.�*/
}
5. R-P-S in C language #3R-P-S in C language #3R-P-S in C language #3R-P-S in C language #3R-P-S in C language #3
rps_t�rps_win_d(rps_t�x)�{
switch�(x)�{
case�R_RPS_T:
return�P_RPS_T;
case�P_RPS_T:
return�S_RPS_T;
case�S_RPS_T:
return�R_RPS_T;
default:
abort();
}
}
#define�PACK(X,Y)�((X)<<4�│�(Y))
rps_t�rps_even_d(rps_t�x,�rps_t�y)�{
switch�(PACK(x,�y))�{
case�PACK(P_RPS_T,�R_RPS_T):
case�PACK(S_RPS_T,�P_RPS_T):
case�PACK(R_RPS_T,�S_RPS_T):
return�rps_win_d(x);
default:
abort();
}
}
rps_t�rps_win_d(rps_t�x)�{
switch�(x)�{
case�R_RPS_T:
return�P_RPS_T;
case�P_RPS_T:
return�S_RPS_T;
case�S_RPS_T:
return�R_RPS_T;
default:
abort();
}
}
#define�PACK(X,Y)�((X)<<4�│�(Y))
rps_t�rps_even_d(rps_t�x,�rps_t�y)�{
switch�(PACK(x,�y))�{
case�PACK(P_RPS_T,�R_RPS_T):
case�PACK(S_RPS_T,�P_RPS_T):
case�PACK(R_RPS_T,�S_RPS_T):
return�rps_win_d(x);
default:
abort();
}
}
rps_t�rps_win_d(rps_t�x)�{
switch�(x)�{
case�R_RPS_T:
return�P_RPS_T;
case�P_RPS_T:
return�S_RPS_T;
case�S_RPS_T:
return�R_RPS_T;
default:
abort();
}
}
#define�PACK(X,Y)�((X)<<4�│�(Y))
rps_t�rps_even_d(rps_t�x,�rps_t�y)�{
switch�(PACK(x,�y))�{
case�PACK(P_RPS_T,�R_RPS_T):
case�PACK(S_RPS_T,�P_RPS_T):
case�PACK(R_RPS_T,�S_RPS_T):
return�rps_win_d(x);
default:
abort();
}
}
rps_t�rps_win_d(rps_t�x)�{
switch�(x)�{
case�R_RPS_T:
return�P_RPS_T;
case�P_RPS_T:
return�S_RPS_T;
case�S_RPS_T:
return�R_RPS_T;
default:
abort();
}
}
#define�PACK(X,Y)�((X)<<4�│�(Y))
rps_t�rps_even_d(rps_t�x,�rps_t�y)�{
switch�(PACK(x,�y))�{
case�PACK(P_RPS_T,�R_RPS_T):
case�PACK(S_RPS_T,�P_RPS_T):
case�PACK(R_RPS_T,�S_RPS_T):
return�rps_win_d(x);
default:
abort();
}
}
rps_t�rps_win_d(rps_t�x)�{
switch�(x)�{
case�R_RPS_T:
return�P_RPS_T;
case�P_RPS_T:
return�S_RPS_T;
case�S_RPS_T:
return�R_RPS_T;
default:
abort();
}
}
#define�PACK(X,Y)�((X)<<4�│�(Y))
rps_t�rps_even_d(rps_t�x,�rps_t�y)�{
switch�(PACK(x,�y))�{
case�PACK(P_RPS_T,�R_RPS_T):
case�PACK(S_RPS_T,�P_RPS_T):
case�PACK(R_RPS_T,�S_RPS_T):
return�rps_win_d(x);
default:
abort();
}
}
6. However you can make run-time errorHowever you can make run-time errorHowever you can make run-time errorHowever you can make run-time errorHowever you can make run-time error
rps_t�rps_win_d(rps_t�x)�{
switch�(x)�{
case�R_RPS_T:
return�R_RPS_T;�/*�Run-time�error!�*/
case�P_RPS_T:
return�S_RPS_T;
/* case�S_RPS_T:
return�R_RPS_T;�*/�/*�Not�exhaustive!�*/
default:
abort();�/*�Abort�occurs!�*/
}
}
#define�PACK(X,Y)�((X)<<4�│�(Y))
rps_t�rps_even_d(rps_t�x,�rps_t�y)�{
switch�(PACK(x,�y))�{
case�PACK(P_RPS_T,�R_RPS_T):
case�PACK(S_RPS_T,�P_RPS_T):
case�PACK(R_RPS_T,�S_RPS_T):
return�rps_win_d(y);�/*�Run-time�error!�*/
default:
abort();�/*�Abort�occurs!�*/
}
}
rps_t�rps_win_d(rps_t�x)�{
switch�(x)�{
case�R_RPS_T:
return�R_RPS_T;�/*�Run-time�error!�*/
case�P_RPS_T:
return�S_RPS_T;
/* case�S_RPS_T:
return�R_RPS_T;�*/�/*�Not�exhaustive!�*/
default:
abort();�/*�Abort�occurs!�*/
}
}
#define�PACK(X,Y)�((X)<<4�│�(Y))
rps_t�rps_even_d(rps_t�x,�rps_t�y)�{
switch�(PACK(x,�y))�{
case�PACK(P_RPS_T,�R_RPS_T):
case�PACK(S_RPS_T,�P_RPS_T):
case�PACK(R_RPS_T,�S_RPS_T):
return�rps_win_d(y);�/*�Run-time�error!�*/
default:
abort();�/*�Abort�occurs!�*/
}
}
rps_t�rps_win_d(rps_t�x)�{
switch�(x)�{
case�R_RPS_T:
return�R_RPS_T;�/*�Run-time�error!�*/
case�P_RPS_T:
return�S_RPS_T;
/* case�S_RPS_T:
return�R_RPS_T;�*/�/*�Not�exhaustive!�*/
default:
abort();�/*�Abort�occurs!�*/
}
}
#define�PACK(X,Y)�((X)<<4�│�(Y))
rps_t�rps_even_d(rps_t�x,�rps_t�y)�{
switch�(PACK(x,�y))�{
case�PACK(P_RPS_T,�R_RPS_T):
case�PACK(S_RPS_T,�P_RPS_T):
case�PACK(R_RPS_T,�S_RPS_T):
return�rps_win_d(y);�/*�Run-time�error!�*/
default:
abort();�/*�Abort�occurs!�*/
}
}
rps_t�rps_win_d(rps_t�x)�{
switch�(x)�{
case�R_RPS_T:
return�R_RPS_T;�/*�Run-time�error!�*/
case�P_RPS_T:
return�S_RPS_T;
/* case�S_RPS_T:
return�R_RPS_T;�*/�/*�Not�exhaustive!�*/
default:
abort();�/*�Abort�occurs!�*/
}
}
#define�PACK(X,Y)�((X)<<4�│�(Y))
rps_t�rps_even_d(rps_t�x,�rps_t�y)�{
switch�(PACK(x,�y))�{
case�PACK(P_RPS_T,�R_RPS_T):
case�PACK(S_RPS_T,�P_RPS_T):
case�PACK(R_RPS_T,�S_RPS_T):
return�rps_win_d(y);�/*�Run-time�error!�*/
default:
abort();�/*�Abort�occurs!�*/
}
}
rps_t�rps_win_d(rps_t�x)�{
switch�(x)�{
case�R_RPS_T:
return�R_RPS_T;�/*�Run-time�error!�*/
case�P_RPS_T:
return�S_RPS_T;
/* case�S_RPS_T:
return�R_RPS_T;�*/ /*�Not�exhaustive!�*/
default:
abort();�/*�Abort�occurs!�*/
}
}
#define�PACK(X,Y)�((X)<<4�│�(Y))
rps_t�rps_even_d(rps_t�x,�rps_t�y)�{
switch�(PACK(x,�y))�{
case�PACK(P_RPS_T,�R_RPS_T):
case�PACK(S_RPS_T,�P_RPS_T):
case�PACK(R_RPS_T,�S_RPS_T):
return�rps_win_d(y);�/*�Run-time�error!�*/
default:
abort();�/*�Abort�occurs!�*/
}
}
7. Please imagine specification on codePlease imagine specification on codePlease imagine specification on codePlease imagine specification on codePlease imagine specification on code
☆ Introduce specification using static typing.☆ Introduce specification using static typing.☆ Introduce specification using static typing.☆ Introduce specification using static typing.☆ Introduce specification using static typing.
☆ You will get more compile-time errors.☆ You will get more compile-time errors.☆ You will get more compile-time errors.☆ You will get more compile-time errors.☆ You will get more compile-time errors.
☆ You will get less run-time errors.☆ You will get less run-time errors.☆ You will get less run-time errors.☆ You will get less run-time errors.☆ You will get less run-time errors.
☆ You can do that in ATS language.☆ You can do that in ATS language.☆ You can do that in ATS language.☆ You can do that in ATS language.☆ You can do that in ATS language.
8. ATS languageATS languageATS languageATS languageATS language
☆ http://www.ats-lang.org/☆ http://www.ats-lang.org/☆ http://www.ats-lang.org/☆ http://www.ats-lang.org/☆ http://www.ats-lang.org/
☆ DML-style dependent types☆ DML-style dependent types☆ DML-style dependent types☆ DML-style dependent types☆ DML-style dependent types
☆ Linear types☆ Linear types☆ Linear types☆ Linear types☆ Linear types
☆ Optional GC☆ Optional GC☆ Optional GC☆ Optional GC☆ Optional GC
☆ Optional malloc/free☆ Optional malloc/free☆ Optional malloc/free☆ Optional malloc/free☆ Optional malloc/free
☆ Optional run-time☆ Optional run-time☆ Optional run-time☆ Optional run-time☆ Optional run-time
More strong type can be used on the ATS.More strong type can be used on the ATS.More strong type can be used on the ATS.More strong type can be used on the ATS.More strong type can be used on the ATS.
9. DML-style dependent types in ATSDML-style dependent types in ATSDML-style dependent types in ATSDML-style dependent types in ATSDML-style dependent types in ATS
10. Type of R-P-S in ATSType of R-P-S in ATSType of R-P-S in ATSType of R-P-S in ATSType of R-P-S in ATS
datasort�rps_s�=
��│�r_rps_s�(*�Rock�*)
��│�p_rps_s�(*�Paper�*)
��│�s_rps_s�(*�Scissors�*)
datatype�rps_t�(rps_s)�=
��│�r_rps_t�(r_rps_s)�(*�Rock�*)
��│�p_rps_t�(p_rps_s)�(*�Paper�*)
��│�s_rps_t�(s_rps_s)�(*�Scissors�*)
typedef�rps_t_any�=�[x:rps_s]�rps_t�(x)
datasort�rps_s�=
��│�r_rps_s�(*�Rock�*)
��│�p_rps_s�(*�Paper�*)
��│�s_rps_s�(*�Scissors�*)
datatype�rps_t�(rps_s)�=
��│�r_rps_t�(r_rps_s)�(*�Rock�*)
��│�p_rps_t�(p_rps_s)�(*�Paper�*)
��│�s_rps_t�(s_rps_s)�(*�Scissors�*)
typedef�rps_t_any�=�[x:rps_s]�rps_t�(x)
datasort�rps_s�=
��│�r_rps_s�(*�Rock�*)
��│�p_rps_s�(*�Paper�*)
��│�s_rps_s�(*�Scissors�*)
datatype�rps_t�(rps_s)�=
��│�r_rps_t�(r_rps_s)�(*�Rock�*)
��│�p_rps_t�(p_rps_s)�(*�Paper�*)
��│�s_rps_t�(s_rps_s)�(*�Scissors�*)
typedef�rps_t_any�=�[x:rps_s]�rps_t�(x)
datasort�rps_s�=
��│�r_rps_s�(*�Rock�*)
��│�p_rps_s�(*�Paper�*)
��│�s_rps_s�(*�Scissors�*)
datatype�rps_t�(rps_s)�=
��│�r_rps_t�(r_rps_s)�(*�Rock�*)
��│�p_rps_t�(p_rps_s)�(*�Paper�*)
��│�s_rps_t�(s_rps_s)�(*�Scissors�*)
typedef�rps_t_any�=�[x:rps_s]�rps_t�(x)
datasort�rps_s�=
��│�r_rps_s�(*�Rock�*)
��│�p_rps_s�(*�Paper�*)
��│�s_rps_s�(*�Scissors�*)
datatype�rps_t�(rps_s)�=
��│�r_rps_t�(r_rps_s)�(*�Rock�*)
��│�p_rps_t�(p_rps_s)�(*�Paper�*)
��│�s_rps_t�(s_rps_s)�(*�Scissors�*)
typedef�rps_t_any�=�[x:rps_s]�rps_t�(x)
11. Only use Dynamics of ATSOnly use Dynamics of ATSOnly use Dynamics of ATSOnly use Dynamics of ATSOnly use Dynamics of ATS
fun{}�rps_win_d�(x:�rps_t_any):�rps_t_any
fun{}�rps_even_d�(x:�rps_t_any,�y:�rps_t_any):�rps_t_any�(*�The�x�should�win�
the�y.�*)
implement{}�rps_win_d�(x)�=
��case+�x�of
��│�r_rps_t()�=>�p_rps_t()
��│�p_rps_t()�=>�s_rps_t()
��│�s_rps_t()�=>�r_rps_t()
implement{}�rps_even_d�(x,�y)�=
��case+�(x,�y)�of
��│�(p_rps_t(),�r_rps_t())�=>�rps_win_d�(x)
��│�(s_rps_t(),�p_rps_t())�=>�rps_win_d�(x)
��│�(r_rps_t(),�s_rps_t())�=>�rps_win_d�(x)
��│�(_,�_)�=>�$raise�GenerallyExn("The�x�should�win�the�y.")
fun{}�rps_win_d�(x:�rps_t_any):�rps_t_any
fun{}�rps_even_d�(x:�rps_t_any,�y:�rps_t_any):�rps_t_any�(*�The�x�should�win�
the�y.�*)
implement{}�rps_win_d�(x)�=
��case+�x�of
��│�r_rps_t()�=>�p_rps_t()
��│�p_rps_t()�=>�s_rps_t()
��│�s_rps_t()�=>�r_rps_t()
implement{}�rps_even_d�(x,�y)�=
��case+�(x,�y)�of
��│�(p_rps_t(),�r_rps_t())�=>�rps_win_d�(x)
��│�(s_rps_t(),�p_rps_t())�=>�rps_win_d�(x)
��│�(r_rps_t(),�s_rps_t())�=>�rps_win_d�(x)
��│�(_,�_)�=>�$raise�GenerallyExn("The�x�should�win�the�y.")
fun{}�rps_win_d�(x:�rps_t_any):�rps_t_any
fun{}�rps_even_d�(x:�rps_t_any,�y:�rps_t_any):�rps_t_any�(*�The�x�should�win�
the�y.�*)
implement{}�rps_win_d�(x)�=
��case+�x�of
��│�r_rps_t()�=>�p_rps_t()
��│�p_rps_t()�=>�s_rps_t()
��│�s_rps_t()�=>�r_rps_t()
implement{}�rps_even_d�(x,�y)�=
��case+�(x,�y)�of
��│�(p_rps_t(),�r_rps_t())�=>�rps_win_d�(x)
��│�(s_rps_t(),�p_rps_t())�=>�rps_win_d�(x)
��│�(r_rps_t(),�s_rps_t())�=>�rps_win_d�(x)
��│�(_,�_)�=>�$raise�GenerallyExn("The�x�should�win�the�y.")
fun{}�rps_win_d�(x:�rps_t_any):�rps_t_any
fun{}�rps_even_d�(x:�rps_t_any,�y:�rps_t_any):�rps_t_any�(*�The�x�should�win�
the�y.�*)
implement{}�rps_win_d�(x)�=
��case+�x�of
��│�r_rps_t()�=>�p_rps_t()
��│�p_rps_t()�=>�s_rps_t()
��│�s_rps_t()�=>�r_rps_t()
implement{}�rps_even_d�(x,�y)�=
��case+�(x,�y)�of
��│�(p_rps_t(),�r_rps_t())�=>�rps_win_d�(x)
��│�(s_rps_t(),�p_rps_t())�=>�rps_win_d�(x)
��│�(r_rps_t(),�s_rps_t())�=>�rps_win_d�(x)
��│�(_,�_)�=>�$raise�GenerallyExn("The�x�should�win�the�y.")
fun{}�rps_win_d�(x:�rps_t_any):�rps_t_any
fun{}�rps_even_d�(x:�rps_t_any,�y:�rps_t_any):�rps_t_any�(*�The�x�should�win�
the�y.�*)
implement{}�rps_win_d�(x)�=
��case+�x�of
��│�r_rps_t()�=>�p_rps_t()
��│�p_rps_t()�=>�s_rps_t()
��│�s_rps_t()�=>�r_rps_t()
implement{}�rps_even_d�(x,�y)�=
��case+�(x,�y)�of
��│�(p_rps_t(),�r_rps_t())�=>�rps_win_d�(x)
��│�(s_rps_t(),�p_rps_t())�=>�rps_win_d�(x)
��│�(r_rps_t(),�s_rps_t())�=>�rps_win_d�(x)
��│�(_,�_)�=>�$raise�GenerallyExn("The�x�should�win�the�y.")
12. Also you can make run-time errorAlso you can make run-time errorAlso you can make run-time errorAlso you can make run-time errorAlso you can make run-time error
implement{}�rps_win_d�(x)�=
��case+�x�of
��│�r_rps_t()�=>�r_rps_t()�(*�Run-time�error!�*)
��│�p_rps_t()�=>�s_rps_t()
(*│�s_rps_t()�=>�r_rps_t()�*)�(*�Compile-time�error!�*)
implement{}�rps_even_d�(x,�y)�=
��case+�(x,�y)�of
��│�(p_rps_t(),�r_rps_t())�=>�rps_win_d�(x)
��│�(s_rps_t(),�p_rps_t())�=>�rps_win_d�(y)�(*�Run-time�error!�*)
��│�(r_rps_t(),�s_rps_t())�=>�rps_win_d�(x)
��│�(_,�_)�=>�$raise�GenerallyExn("The�x�should�win�the�y.")�(*�Exception�
occurs!�*)
implement{}�rps_win_d�(x)�=
��case+�x�of
��│�r_rps_t()�=>�r_rps_t()�(*�Run-time�error!�*)
��│�p_rps_t()�=>�s_rps_t()
(*│�s_rps_t()�=>�r_rps_t()�*)�(*�Compile-time�error!�*)
implement{}�rps_even_d�(x,�y)�=
��case+�(x,�y)�of
��│�(p_rps_t(),�r_rps_t())�=>�rps_win_d�(x)
��│�(s_rps_t(),�p_rps_t())�=>�rps_win_d�(y)�(*�Run-time�error!�*)
��│�(r_rps_t(),�s_rps_t())�=>�rps_win_d�(x)
��│�(_,�_)�=>�$raise�GenerallyExn("The�x�should�win�the�y.")�(*�Exception�
occurs!�*)
implement{}�rps_win_d�(x)�=
��case+�x�of
��│�r_rps_t()�=>�r_rps_t()�(*�Run-time�error!�*)
��│�p_rps_t()�=>�s_rps_t()
(*│�s_rps_t()�=>�r_rps_t()�*)�(*�Compile-time�error!�*)
implement{}�rps_even_d�(x,�y)�=
��case+�(x,�y)�of
��│�(p_rps_t(),�r_rps_t())�=>�rps_win_d�(x)
��│�(s_rps_t(),�p_rps_t())�=>�rps_win_d�(y)�(*�Run-time�error!�*)
��│�(r_rps_t(),�s_rps_t())�=>�rps_win_d�(x)
��│�(_,�_)�=>�$raise�GenerallyExn("The�x�should�win�the�y.")�(*�Exception�
occurs!�*)
implement{}�rps_win_d�(x)�=
��case+�x�of
��│�r_rps_t()�=>�r_rps_t()�(*�Run-time�error!�*)
��│�p_rps_t()�=>�s_rps_t()
(*│�s_rps_t()�=>�r_rps_t()�*)�(*�Compile-time�error!�*)
implement{}�rps_even_d�(x,�y)�=
��case+�(x,�y)�of
��│�(p_rps_t(),�r_rps_t())�=>�rps_win_d�(x)
��│�(s_rps_t(),�p_rps_t())�=>�rps_win_d�(y)�(*�Run-time�error!�*)
��│�(r_rps_t(),�s_rps_t())�=>�rps_win_d�(x)
��│�(_,�_)�=>�$raise�GenerallyExn("The�x�should�win�the�y.")�(*�Exception�
occurs!�*)
implement{}�rps_win_d�(x)�=
��case+�x�of
��│�r_rps_t()�=>�r_rps_t()�(*�Run-time�error!�*)
��│�p_rps_t()�=>�s_rps_t()
(*│�s_rps_t()�=>�r_rps_t()�*) (*�Compile-time�error!�*)
implement{}�rps_even_d�(x,�y)�=
��case+�(x,�y)�of
��│�(p_rps_t(),�r_rps_t())�=>�rps_win_d�(x)
��│�(s_rps_t(),�p_rps_t())�=>�rps_win_d�(y)�(*�Run-time�error!�*)
��│�(r_rps_t(),�s_rps_t())�=>�rps_win_d�(x)
��│�(_,�_)�=>�$raise�GenerallyExn("The�x�should�win�the�y.")�(*�Exception�
occurs!�*)
It's caused by having no specification in the
implementation. ATS language can have
specification as Statics or Proofs.
It's caused by having no specification in the
implementation. ATS language can have
specification as Statics or Proofs.
It's caused by having no specification in the
implementation. ATS language can have
specification as Statics or Proofs.
It's caused by having no specification in the
implementation. ATS language can have
specification as Statics or Proofs.
It's caused by having no specification in the
implementation. ATS language can have
specification as Statics or Proofs.
13. Specification using Statics of ATSSpecification using Statics of ATSSpecification using Statics of ATSSpecification using Statics of ATSSpecification using Statics of ATS
stacst�rps_win_sta:�(rps_s,�rps_s)�->�bool
fun{}�rps_win_s
��{r1:rps_s}�(x:�rps_t�(r1)):
��[r2:rps_s�│�rps_win_sta�(r2,�r1)]�(rps_t�(r2))
stacst�rps_win_sta:�(rps_s,�rps_s)�->�bool
fun{}�rps_win_s
��{r1:rps_s}�(x:�rps_t�(r1)):
��[r2:rps_s�│�rps_win_sta�(r2,�r1)]�(rps_t�(r2))
stacst�rps_win_sta:�(rps_s,�rps_s)�->�bool
fun{}�rps_win_s
��{r1:rps_s}�(x:�rps_t�(r1)):
��[r2:rps_s�│�rps_win_sta�(r2,�r1)]�(rps_t�(r2))
stacst�rps_win_sta:�(rps_s,�rps_s)�->�bool
fun{}�rps_win_s
��{r1:rps_s}�(x:�rps_t�(r1)):
��[r2:rps_s�│�rps_win_sta�(r2,�r1)]�(rps_t�(r2))
stacst�rps_win_sta:�(rps_s,�rps_s)�->�bool
fun{}�rps_win_s
��{r1:rps_s}�(x:�rps_t�(r1)):
��[r2:rps_s�│�rps_win_sta�(r2,�r1)]�(rps_t�(r2))
14. Implementation using Statics of ATSImplementation using Statics of ATSImplementation using Statics of ATSImplementation using Statics of ATSImplementation using Statics of ATS
extern�praxi�rps_win_r_s_pf�():�[rps_win_sta(r_rps_s,�s_rps_s)]�void�(*�
Spec:�Paper�wins�Rock�*)
extern�praxi�rps_win_p_r_pf�():�[rps_win_sta(p_rps_s,�r_rps_s)]�void�(*�
Spec:�Scissors�win�Paper�*)
extern�praxi�rps_win_s_p_pf�():�[rps_win_sta(s_rps_s,�p_rps_s)]�void�(*�
Spec:�Rock�wins�Scissors�*)
implement{}�rps_win_s�(x)�=�let
��prval�()�=�rps_win_r_s_pf()�(*�Introduce�specification�*)
��prval�()�=�rps_win_p_r_pf()
��prval�()�=�rps_win_s_p_pf()
in
��case+�x�of
��│�r_rps_t()�=>�p_rps_t()
��│�p_rps_t()�=>�s_rps_t()
��│�s_rps_t()�=>�r_rps_t()
end
extern�praxi�rps_win_r_s_pf�():�[rps_win_sta(r_rps_s,�s_rps_s)]�void�(*�
Spec:�Paper�wins�Rock�*)
extern�praxi�rps_win_p_r_pf�():�[rps_win_sta(p_rps_s,�r_rps_s)]�void�(*�
Spec:�Scissors�win�Paper�*)
extern�praxi�rps_win_s_p_pf�():�[rps_win_sta(s_rps_s,�p_rps_s)]�void�(*�
Spec:�Rock�wins�Scissors�*)
implement{}�rps_win_s�(x)�=�let
��prval�()�=�rps_win_r_s_pf()�(*�Introduce�specification�*)
��prval�()�=�rps_win_p_r_pf()
��prval�()�=�rps_win_s_p_pf()
in
��case+�x�of
��│�r_rps_t()�=>�p_rps_t()
��│�p_rps_t()�=>�s_rps_t()
��│�s_rps_t()�=>�r_rps_t()
end
extern�praxi�rps_win_r_s_pf�():�[rps_win_sta(r_rps_s,�s_rps_s)]�void�(*�
Spec:�Paper�wins�Rock�*)
extern�praxi�rps_win_p_r_pf�():�[rps_win_sta(p_rps_s,�r_rps_s)]�void�(*�
Spec:�Scissors�win�Paper�*)
extern�praxi�rps_win_s_p_pf�():�[rps_win_sta(s_rps_s,�p_rps_s)]�void�(*�
Spec:�Rock�wins�Scissors�*)
implement{}�rps_win_s�(x)�=�let
��prval�()�=�rps_win_r_s_pf()�(*�Introduce�specification�*)
��prval�()�=�rps_win_p_r_pf()
��prval�()�=�rps_win_s_p_pf()
in
��case+�x�of
��│�r_rps_t()�=>�p_rps_t()
��│�p_rps_t()�=>�s_rps_t()
��│�s_rps_t()�=>�r_rps_t()
end
extern�praxi�rps_win_r_s_pf�():�[rps_win_sta(r_rps_s,�s_rps_s)]�void�(*�
Spec:�Paper�wins�Rock�*)
extern�praxi�rps_win_p_r_pf�():�[rps_win_sta(p_rps_s,�r_rps_s)]�void�(*�
Spec:�Scissors�win�Paper�*)
extern�praxi�rps_win_s_p_pf�():�[rps_win_sta(s_rps_s,�p_rps_s)]�void�(*�
Spec:�Rock�wins�Scissors�*)
implement{}�rps_win_s�(x)�=�let
��prval�()�=�rps_win_r_s_pf()�(*�Introduce�specification�*)
��prval�()�=�rps_win_p_r_pf()
��prval�()�=�rps_win_s_p_pf()
in
��case+�x�of
��│�r_rps_t()�=>�p_rps_t()
��│�p_rps_t()�=>�s_rps_t()
��│�s_rps_t()�=>�r_rps_t()
end
extern praxi�rps_win_r_s_pf�():�[rps_win_sta(r_rps_s,�s_rps_s)]�void�(*�
Spec:�Paper�wins�Rock�*)
extern praxi�rps_win_p_r_pf�():�[rps_win_sta(p_rps_s,�r_rps_s)]�void�(*�
Spec:�Scissors�win�Paper�*)
extern praxi�rps_win_s_p_pf�():�[rps_win_sta(s_rps_s,�p_rps_s)]�void�(*�
Spec:�Rock�wins�Scissors�*)
implement{}�rps_win_s�(x)�=�let
prval�()�=�rps_win_r_s_pf()�(*�Introduce�specification�*)
prval�()�=�rps_win_p_r_pf()
prval�()�=�rps_win_s_p_pf()
in
��case+�x�of
��│�r_rps_t()�=>�p_rps_t()
��│�p_rps_t()�=>�s_rps_t()
��│�s_rps_t()�=>�r_rps_t()
end
15. Statics can catch error at compile-timeStatics can catch error at compile-timeStatics can catch error at compile-timeStatics can catch error at compile-timeStatics can catch error at compile-time
implement{}�rps_win_s�(x)�=�let
��prval�()�=�rps_win_r_s_pf()�(*�Introduce�specification�*)
��prval�()�=�rps_win_p_r_pf()
��prval�()�=�rps_win_s_p_pf()
in
��case+�x�of
��│�r_rps_t()�=>�r_rps_t()�(*�Compile-time�error!�*)
��│�p_rps_t()�=>�s_rps_t()
��│�s_rps_t()�=>�r_rps_t()
end
implement{}�rps_win_s�(x)�=�let
��prval�()�=�rps_win_r_s_pf()�(*�Introduce�specification�*)
��prval�()�=�rps_win_p_r_pf()
��prval�()�=�rps_win_s_p_pf()
in
��case+�x�of
��│�r_rps_t()�=>�r_rps_t()�(*�Compile-time�error!�*)
��│�p_rps_t()�=>�s_rps_t()
��│�s_rps_t()�=>�r_rps_t()
end
implement{}�rps_win_s�(x)�=�let
��prval�()�=�rps_win_r_s_pf()�(*�Introduce�specification�*)
��prval�()�=�rps_win_p_r_pf()
��prval�()�=�rps_win_s_p_pf()
in
��case+�x�of
��│�r_rps_t()�=>�r_rps_t()�(*�Compile-time�error!�*)
��│�p_rps_t()�=>�s_rps_t()
��│�s_rps_t()�=>�r_rps_t()
end
implement{}�rps_win_s�(x)�=�let
��prval�()�=�rps_win_r_s_pf()�(*�Introduce�specification�*)
��prval�()�=�rps_win_p_r_pf()
��prval�()�=�rps_win_s_p_pf()
in
��case+�x�of
��│�r_rps_t()�=>�r_rps_t()�(*�Compile-time�error!�*)
��│�p_rps_t()�=>�s_rps_t()
��│�s_rps_t()�=>�r_rps_t()
end
implement{}�rps_win_s�(x)�=�let
prval�()�=�rps_win_r_s_pf()�(*�Introduce�specification�*)
prval�()�=�rps_win_p_r_pf()
prval�()�=�rps_win_s_p_pf()
in
��case+�x�of
��│�r_rps_t()�=>�r_rps_t()�(*�Compile-time�error!�*)
��│�p_rps_t()�=>�s_rps_t()
��│�s_rps_t()�=>�r_rps_t()
end
$�patscc�main.dats�-DATS_MEMALLOC_LIBC
/home/kiwamu/src/practice-ats/static_rps/rps.dats:�933(line=36,�offs=18)�--�
942(line=36,�offs=27):�error(3):�unsolved�constraint:�C3NSTRprop(C3TKmain();�
S2Eapp(S2Ecst(rps_win_sta);�S2EVar(4434->S2Eapp(S2Ecst(r_rps_s);�)),�S2Evar
(r1$2870(7929))))
$�patscc�main.dats�-DATS_MEMALLOC_LIBC
/home/kiwamu/src/practice-ats/static_rps/rps.dats:�933(line=36,�offs=18)�--�
942(line=36,�offs=27):�error(3):�unsolved�constraint:�C3NSTRprop(C3TKmain();�
S2Eapp(S2Ecst(rps_win_sta);�S2EVar(4434->S2Eapp(S2Ecst(r_rps_s);�)),�S2Evar
(r1$2870(7929))))
$�patscc�main.dats�-DATS_MEMALLOC_LIBC
/home/kiwamu/src/practice-ats/static_rps/rps.dats:�933(line=36,�offs=18)�--�
942(line=36,�offs=27):�error(3):�unsolved�constraint:�C3NSTRprop(C3TKmain();�
S2Eapp(S2Ecst(rps_win_sta);�S2EVar(4434->S2Eapp(S2Ecst(r_rps_s);�)),�S2Evar
(r1$2870(7929))))
$�patscc�main.dats�-DATS_MEMALLOC_LIBC
/home/kiwamu/src/practice-ats/static_rps/rps.dats:�933(line=36,�offs=18)�--�
942(line=36,�offs=27):�error(3):�unsolved�constraint:�C3NSTRprop(C3TKmain();�
S2Eapp(S2Ecst(rps_win_sta);�S2EVar(4434->S2Eapp(S2Ecst(r_rps_s);�)),�S2Evar
(r1$2870(7929))))
$�patscc�main.dats�-DATS_MEMALLOC_LIBC
/home/kiwamu/src/practice-ats/static_rps/rps.dats:�933(line=36,�offs=18)�--�
942(line=36,�offs=27):�error(3):�unsolved�constraint:�C3NSTRprop(C3TKmain();�
S2Eapp(S2Ecst(rps_win_sta);�S2EVar(4434->S2Eapp(S2Ecst(r_rps_s);�)),�S2Evar
(r1$2870(7929))))
16. Specification using Proofs of ATSSpecification using Proofs of ATSSpecification using Proofs of ATSSpecification using Proofs of ATSSpecification using Proofs of ATS
dataprop�RPS_WIN�(rps_s,�rps_s)�=
��│�RPS_P_WIN_R�(p_rps_s,�r_rps_s)�(*�Spec:�Paper�wins�Rock�*)
��│�RPS_S_WIN_P�(s_rps_s,�p_rps_s)�(*�Spec:�Scissors�win�Paper�*)
��│�RPS_R_WIN_S�(r_rps_s,�s_rps_s)�(*�Spec:�Rock�wins�Scissors�*)
fun{}�rps_win_p
��{r1:rps_s}�(x:�rps_t�(r1)):
��[r2:rps_s]�(RPS_WIN�(r2,�r1)�│�rps_t�(r2))
dataprop�RPS_WIN�(rps_s,�rps_s)�=
��│�RPS_P_WIN_R�(p_rps_s,�r_rps_s)�(*�Spec:�Paper�wins�Rock�*)
��│�RPS_S_WIN_P�(s_rps_s,�p_rps_s)�(*�Spec:�Scissors�win�Paper�*)
��│�RPS_R_WIN_S�(r_rps_s,�s_rps_s)�(*�Spec:�Rock�wins�Scissors�*)
fun{}�rps_win_p
��{r1:rps_s}�(x:�rps_t�(r1)):
��[r2:rps_s]�(RPS_WIN�(r2,�r1)�│�rps_t�(r2))
dataprop�RPS_WIN�(rps_s,�rps_s)�=
��│�RPS_P_WIN_R�(p_rps_s,�r_rps_s)�(*�Spec:�Paper�wins�Rock�*)
��│�RPS_S_WIN_P�(s_rps_s,�p_rps_s)�(*�Spec:�Scissors�win�Paper�*)
��│�RPS_R_WIN_S�(r_rps_s,�s_rps_s)�(*�Spec:�Rock�wins�Scissors�*)
fun{}�rps_win_p
��{r1:rps_s}�(x:�rps_t�(r1)):
��[r2:rps_s]�(RPS_WIN�(r2,�r1)�│�rps_t�(r2))
dataprop�RPS_WIN�(rps_s,�rps_s)�=
��│�RPS_P_WIN_R�(p_rps_s,�r_rps_s)�(*�Spec:�Paper�wins�Rock�*)
��│�RPS_S_WIN_P�(s_rps_s,�p_rps_s)�(*�Spec:�Scissors�win�Paper�*)
��│�RPS_R_WIN_S�(r_rps_s,�s_rps_s)�(*�Spec:�Rock�wins�Scissors�*)
fun{}�rps_win_p
��{r1:rps_s}�(x:�rps_t�(r1)):
��[r2:rps_s]�(RPS_WIN�(r2,�r1)�│�rps_t�(r2))
dataprop�RPS_WIN�(rps_s,�rps_s)�=
��│�RPS_P_WIN_R�(p_rps_s,�r_rps_s)�(*�Spec:�Paper�wins�Rock�*)
��│�RPS_S_WIN_P�(s_rps_s,�p_rps_s)�(*�Spec:�Scissors�win�Paper�*)
��│�RPS_R_WIN_S�(r_rps_s,�s_rps_s)�(*�Spec:�Rock�wins�Scissors�*)
fun{}�rps_win_p
��{r1:rps_s}�(x:�rps_t�(r1)):
��[r2:rps_s]�(RPS_WIN�(r2,�r1)�│�rps_t�(r2))
17. Implementation using Proofs of ATSImplementation using Proofs of ATSImplementation using Proofs of ATSImplementation using Proofs of ATSImplementation using Proofs of ATS
implement{}�rps_win_p�(x)�=�case+�x�of
��│�r_rps_t()�=>�(RPS_P_WIN_R()�│�p_rps_t())
��│�p_rps_t()�=>�(RPS_S_WIN_P()�│�s_rps_t())
��│�s_rps_t()�=>�(RPS_R_WIN_S()�│�r_rps_t())
implement{}�rps_win_p�(x)�=�case+�x�of
��│�r_rps_t()�=>�(RPS_P_WIN_R()�│�p_rps_t())
��│�p_rps_t()�=>�(RPS_S_WIN_P()�│�s_rps_t())
��│�s_rps_t()�=>�(RPS_R_WIN_S()�│�r_rps_t())
implement{}�rps_win_p�(x)�=�case+�x�of
��│�r_rps_t()�=>�(RPS_P_WIN_R()�│�p_rps_t())
��│�p_rps_t()�=>�(RPS_S_WIN_P()�│�s_rps_t())
��│�s_rps_t()�=>�(RPS_R_WIN_S()�│�r_rps_t())
implement{}�rps_win_p�(x)�=�case+�x�of
��│�r_rps_t()�=>�(RPS_P_WIN_R()�│�p_rps_t())
��│�p_rps_t()�=>�(RPS_S_WIN_P()�│�s_rps_t())
��│�s_rps_t()�=>�(RPS_R_WIN_S()�│�r_rps_t())
implement{}�rps_win_p�(x)�=�case+�x�of
��│�r_rps_t()�=>�(RPS_P_WIN_R()�│�p_rps_t())
��│�p_rps_t()�=>�(RPS_S_WIN_P()�│�s_rps_t())
��│�s_rps_t()�=>�(RPS_R_WIN_S()�│�r_rps_t())
18. Proofs can catch error at compile-timeProofs can catch error at compile-timeProofs can catch error at compile-timeProofs can catch error at compile-timeProofs can catch error at compile-time
implement{}�rps_win_p�(x)�=�case+�x�of
��│�r_rps_t()�=>�(RPS_R_WIN_S()�│�r_rps_t())�(*�Compile-time�error!�*)
��│�p_rps_t()�=>�(RPS_S_WIN_P()�│�s_rps_t())
��│�s_rps_t()�=>�(RPS_R_WIN_S()�│�r_rps_t())
implement{}�rps_win_p�(x)�=�case+�x�of
��│�r_rps_t()�=>�(RPS_R_WIN_S()�│�r_rps_t())�(*�Compile-time�error!�*)
��│�p_rps_t()�=>�(RPS_S_WIN_P()�│�s_rps_t())
��│�s_rps_t()�=>�(RPS_R_WIN_S()�│�r_rps_t())
implement{}�rps_win_p�(x)�=�case+�x�of
��│�r_rps_t()�=>�(RPS_R_WIN_S()�│�r_rps_t())�(*�Compile-time�error!�*)
��│�p_rps_t()�=>�(RPS_S_WIN_P()�│�s_rps_t())
��│�s_rps_t()�=>�(RPS_R_WIN_S()�│�r_rps_t())
implement{}�rps_win_p�(x)�=�case+�x�of
��│�r_rps_t()�=>�(RPS_R_WIN_S()�│�r_rps_t())�(*�Compile-time�error!�*)
��│�p_rps_t()�=>�(RPS_S_WIN_P()�│�s_rps_t())
��│�s_rps_t()�=>�(RPS_R_WIN_S()�│�r_rps_t())
implement{}�rps_win_p�(x)�=�case+�x�of
��│�r_rps_t()�=>�(RPS_R_WIN_S()�│�r_rps_t())�(*�Compile-time�error!�*)
��│�p_rps_t()�=>�(RPS_S_WIN_P()�│�s_rps_t())
��│�s_rps_t()�=>�(RPS_R_WIN_S()�│�r_rps_t())
$�patscc�main.dats�-DATS_MEMALLOC_LIBC
/home/kiwamu/src/practice-ats/static_rps/rps.dats:�1199(line=45,�offs=18)�--�
1226(line=45,�offs=45):�error(3):�the�dynamic�expression�cannot�be�assigned�
the�type�[S2Eexi(r2$2876(7935);�;�S2Etyrec(flt0;�npf=1;�0=S2Eapp(S2Ecst
(RPS_WIN);�S2Evar(r2$2876(7935)),�S2Evar(r1$2875(7934))),�1=S2Eapp(S2Ecst
(rps_t);�S2Evar(r2$2876(7935)))))].
$�patscc�main.dats�-DATS_MEMALLOC_LIBC
/home/kiwamu/src/practice-ats/static_rps/rps.dats:�1199(line=45,�offs=18)�--�
1226(line=45,�offs=45):�error(3):�the�dynamic�expression�cannot�be�assigned�
the�type�[S2Eexi(r2$2876(7935);�;�S2Etyrec(flt0;�npf=1;�0=S2Eapp(S2Ecst
(RPS_WIN);�S2Evar(r2$2876(7935)),�S2Evar(r1$2875(7934))),�1=S2Eapp(S2Ecst
(rps_t);�S2Evar(r2$2876(7935)))))].
$�patscc�main.dats�-DATS_MEMALLOC_LIBC
/home/kiwamu/src/practice-ats/static_rps/rps.dats:�1199(line=45,�offs=18)�--�
1226(line=45,�offs=45):�error(3):�the�dynamic�expression�cannot�be�assigned�
the�type�[S2Eexi(r2$2876(7935);�;�S2Etyrec(flt0;�npf=1;�0=S2Eapp(S2Ecst
(RPS_WIN);�S2Evar(r2$2876(7935)),�S2Evar(r1$2875(7934))),�1=S2Eapp(S2Ecst
(rps_t);�S2Evar(r2$2876(7935)))))].
$�patscc�main.dats�-DATS_MEMALLOC_LIBC
/home/kiwamu/src/practice-ats/static_rps/rps.dats:�1199(line=45,�offs=18)�--�
1226(line=45,�offs=45):�error(3):�the�dynamic�expression�cannot�be�assigned�
the�type�[S2Eexi(r2$2876(7935);�;�S2Etyrec(flt0;�npf=1;�0=S2Eapp(S2Ecst
(RPS_WIN);�S2Evar(r2$2876(7935)),�S2Evar(r1$2875(7934))),�1=S2Eapp(S2Ecst
(rps_t);�S2Evar(r2$2876(7935)))))].
$�patscc�main.dats�-DATS_MEMALLOC_LIBC
/home/kiwamu/src/practice-ats/static_rps/rps.dats:�1199(line=45,�offs=18)�--�
1226(line=45,�offs=45):�error(3):�the�dynamic�expression�cannot�be�assigned�
the�type�[S2Eexi(r2$2876(7935);�;�S2Etyrec(flt0;�npf=1;�0=S2Eapp(S2Ecst
(RPS_WIN);�S2Evar(r2$2876(7935)),�S2Evar(r1$2875(7934))),�1=S2Eapp(S2Ecst
(rps_t);�S2Evar(r2$2876(7935)))))].
19. The code is found at GitHubThe code is found at GitHubThe code is found at GitHubThe code is found at GitHubThe code is found at GitHub
https://github.com/jats-ug/practice-ats/tree/master/static_rpshttps://github.com/jats-ug/practice-ats/tree/master/static_rpshttps://github.com/jats-ug/practice-ats/tree/master/static_rpshttps://github.com/jats-ug/practice-ats/tree/master/static_rpshttps://github.com/jats-ug/practice-ats/tree/master/static_rps