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logicmoo

CALC

logicmoo
Aug 16th, 2017
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  1. /*
  2.  
  3.  CALCULATOR WORLD
  4.  
  5. [13:28] * dmiles attempts to write a program in FOL today! just a simple 14 key caclulator
  6. [13:29] <dmiles> just to discover the hellishness
  7. [13:29] <anniepoo_> the calculator believes that X is 7?
  8. [13:31] <dmiles> yes
  9. [13:31] <dmiles> well the other parts is believing the key buffer represents cerain values and so forth
  10. [13:32] <dmiles> and even believing there are keys to be pressed
  11.  
  12.   part of why i doing the calculator (outside of a test case for logicmoo/prologmud).. is it has been belived that programs might be hard to express physically
  13.  
  14. */
  15.  
  16. :_ include(test_header).
  17.  
  18. % =================================================================================
  19. % Set our engine up
  20. % =================================================================================
  21.  
  22. :_ set_lang(clif).
  23. :_ begin_pfc.
  24.  
  25. % deduce instances from usages in args having the effect of deducing human,dwelling,beverage_class are classes
  26. ==> feature_setting(make_wff,true).
  27. ==> feature_setting(add_admitted_arguments,true).
  28. % set truth maintainance system to remove previous assertions that new assertions disagree with
  29. ==> feature_setting(tms_mode,remove_conflicting).
  30. % i been resisting the urge to expand the 'dictoo' language (of one of my packs) into a scripting language for prolog.
  31.  
  32. :_ set_prolog_flag(runtime_debug,3). % mention it when we remove previous assertions
  33.  
  34. :_ set_prolog_flag_until_eof(do_renames,mpred_expansion).
  35.  
  36. :_ kif_compile.
  37.  
  38.  
  39. % =================================================================================
  40. % Begin program
  41. % =================================================================================
  42.  
  43. % Create out 14 keys
  44. exists(Key,labeled(Key,"1")). exists(Key,labeled(Key,"2")).
  45. exists(Key,labeled(Key,"3")). exists(Key,labeled(Key,"4")).
  46. exists(Key,labeled(Key,"5")). exists(Key,labeled(Key,"6")).
  47. exists(Key,labeled(Key,"7")). exists(Key,labeled(Key,"8")).
  48. exists(Key,labeled(Key,"9")). exists(Key,labeled(Key,"0")).
  49. exists(Key,labeled(Key,"+")). exists(Key,labeled(Key,"_")).
  50. exists(Key,labeled(Key,"=")). exists(Key,labeled(Key,"CLR")).
  51.  
  52. % Make each key unique depending on its label
  53. forall([Key1,Key2,Label1,Label2],
  54.   labeled(Key1,Label1) & labeled(Key2,Label2) & different(Label1,Label2) => different(Key1,Key2)).
  55.  
  56. % Let same/2 be our unification identify
  57. forall(X,same(X,X)).    
  58.  
  59. % same/2 implies not differnt
  60. forall([X,Y], same(X,Y) => ~ different(X,Y)).
  61.  
  62. % Note all unquantified vars will be universal from here on out
  63. subclass(S,C) & isa(I,S) => isa(I,C).
  64.  
  65. % an accumulator is a numeric buffer
  66. subclass(accumulator,numbuffer).
  67.  
  68. % a display is a numeric buffer
  69. subclass(display,numbuffer).
  70.  
  71. % numeric buffer and operation buffer are buffers
  72. subclass(numbuffer,buffer). subclass(opbuffer,buffer).
  73.  
  74. % Create some buffers
  75. exists(X,isa(X,accumulator)).
  76. exists(X,isa(X,display)).
  77. exists(X,isa(X,opbuffer)).
  78.  
  79. /*
  80. Extra TODO ?
  81.  
  82. define how a buffer is shown in screen locations
  83. exactly(10,X, isa(X,screenLocation)).
  84.  
  85. */
  86.  
  87. % All number buffers have a, inital value of 0
  88. forall(X,isa(X,numbuffer) => initalValue(X,0)).
  89.  
  90. % exists an initial world
  91. exists(C,initialWorld(C)).
  92.  
  93. % initial world is populated by inital values
  94. initalValue(N,V) & initialWorld(W) =>  currentValue(W,N,V).
  95.  
  96. % All numeric buffers have a value
  97. forall(W,forall(N,exists(V,isa(N,numbuffer) & world(W) => currentValue(W,N,V))).
  98.  
  99. % Op buffer is intialized to null
  100. forall(X,isa(X,opbuffer) => initalValue(X,null)).
  101.  
  102. % exists a current world (Fluent 1)
  103. exists(C,currentWorld(C)).
  104.  
  105.  
  106. nextWorld(C,N)=> isa(C,world) & isa(C,world).
  107.   => currentValue
  108.  
  109.  
  110. % CTL or LTL version of automation?
  111.  
  112. currentWorld(C) & onEvent(Evt,Props) =>
  113.    exists(W,
  114.       isa(W,world)
  115.     & nextWorld(C,W)) ....
  116.    
  117.  
  118.  
  119. % after "CLR" is pressed re_init the buffers
  120. onEvent(pressed("CLR"), forall([N,V], initalValue(N,V) => currentValue(N,V))).
  121.  
  122. % after "=" is pressed the "accumulator" buffer is shown.
  123.  
  124. % after "+" or "_" is pressed the  
  125.  
  126.  
  127.  
  128.  
  129.  
  130.  
  131.  
  132.  
  133.  
  134. my_minus_one(N,M) <=>  (N > 1)  &  (M = N-1).
  135.  
  136. % Lits in KBs are considered true
  137. consistent(W) <=> min_lits(1, W) .
  138.  
  139. exactly_N_lits(1,W) <=>
  140.  exists([W,Prop],  
  141.     (   true_in_world(Prop,W)
  142.       & ~exists(Other_Prop,
  143.            (  true_in_world(Other_Prop,W)
  144.              & ~equiv(W,Other_Prop,Prop))))) .
  145.  
  146. exactly_N_lits(2,W) <=>
  147.  exists([W,Prop1,Prop2],  
  148.   (  true_in_world(Prop1,W)
  149.    & true_in_world(Prop2,W)
  150.    & ~equiv(W,Prop1,Prop2)  
  151.    & ~ exists(Other_Prop,
  152.          (  true_in_world(Other_Prop,W)
  153.           & ~equiv(W,Other_Prop,Prop1)
  154.           & ~equiv(W,Other_Prop,Prop2)))))
  155.  
  156. exactly_N_lits(N,W) <=>
  157.    range_lits(N,N,W).  
  158.  
  159.  
  160. range_lits(N,M,W) <=>
  161.  exists(W,
  162.   ( min_lits(N,W)
  163.     & max_lits(M,W))) .
  164.  
  165. min_lits(1,W) <=>
  166.  exists([W,Prop],
  167.      (true_in_world(Prop,W))).
  168.  
  169. min_lits(2,W) <=>
  170.  exists([W,Prop1,Prop2],
  171.    (  true_in_world(Prop1,W)
  172.     & true_in_world(Prop2,W)
  173.     & ~equiv(W,Prop1,Prop2))).
  174.  
  175. max_lits(2,W) <=>  
  176. exists([W,Prop1,Prop2],
  177.    (  true_in_world(Prop1,W)
  178.     & true_in_world(Prop2,W)
  179.     &  ~exists(Other_Prop,
  180.           (  true_in_world(Other_Prop,W)
  181.             & ~equiv(W,Other_Prop,Prop1)
  182.             & ~equiv(W,Other_Prop,Prop2))))).
  183.  
  184. % exists a W with no lits?
  185. exactly_N_lits(0,W) <=>
  186.   exists(W,
  187.      ~exists(Prop1, true_in_world(Prop1,W))).
  188.  
  189. max_lits(1,W) <=>
  190.  exactly_N_lits(0,W) v exactly_N_lits(1,W).
  191.  
  192. difference_at_least_1_truths(W1,W2) <=>
  193.   exists(Prop, (true_in_world(Prop,W1) => ~true_in_world(Prop,W2))) .
  194.  
  195. disjoint_truths(W1,W2) <=>
  196.   ~exists(Prop, (true_in_world(Prop,W1) & true_in_world(Prop,W2))).
  197.  
  198. subset_truths(W1,W2) <=>
  199.     all(Prop,
  200.       true_in_world(Prop,W1) => true_in_world(Prop,W2) ).
  201.  
  202. union_s_v2(W1,W2,W) <=>
  203.  all(Prop,
  204.    (true_in_world(Prop,W) <=>
  205.        (true_in_world(Prop,W1) v true_in_world(Prop,W2)))).
  206.  
  207. union_truths(W1,W2,W) <=>
  208.   exists(KB,
  209.       union_truths(W1,W2,KB)
  210.      & ~difference_at_least_1_truths(W,KB)).
  211.  
  212.  
  213. union_disjoint_truths(W1,W2,W) <=>
  214.    (   union_truths(W1,W2,W)
  215.      & disjoint_truths(W1,W2)).
  216.  
  217.  
  218. min_lits(4,W) <=>
  219.   exists([W1,W2],
  220.      min_lits(2,W1)
  221.    & min_lits(2,W2)
  222.    & union_disjoint_truths(W1,W2)).
  223.  
  224. min_lits(N,W) <=>
  225.   exists([W1,W2],
  226.      min_lits(1,W1)
  227.    & min_lits(M,W2)
  228.    & consistent(W2)
  229.    & union_disjoint_truths(W1,W2)
  230.    & my_minus_one(N,M)).
  231.  
  232.  
  233. max_lits(N,W) <=>
  234.   exists([W1,W2],
  235.      max_lits(1,W1)
  236.    & max_lits(M,W2)
  237.    & consistent(W2)
  238.    & union_disjoint_truths(W1,W2)
  239.    & my_minus_one(N,M)).
  240.  
  241.  
  242. equal_v1_truths(W1,W2) <=>
  243.    ( ~difference_at_least_1_truths(W1,W2)
  244.      & ~difference_at_least_1_truths(W2,W1)
  245.      & consistent(W1)
  246.      & consistent(W2)).
  247.  
  248. equal_v2_truths(W1,W2) <=>
  249.  ( consistent(W1)
  250.    & all(Prop,
  251.       (true_in_world(Prop,W1) <=> true_in_world(Prop,W2)))).
  252.  
  253.  
  254. % v1: lameness
  255. equiv_v1(W,Prop1,Prop2) <=>
  256.   true_in_world(Prop1,W) <=>   true_in_world(Prop2,W).
  257.  
  258. % v2  Prop2 and Prop2 logically "imply" each other in the W.
  259. equiv_v2(W,Prop1,Prop2) <=>
  260.   true_in_world((Prop1 <=> Prop2),W).
  261.  
  262. % v3 the actual semantics implemented based that both logical sentences use the same proof
  263. equiv(W,Prop1,Prop2) <=>
  264.   equiv_v4(W,Prop1,Prop2) v equiv_v2(W,Prop1,Prop2).
  265.  
  266. % v4 sameness (current implementation in LogicMOO )
  267. equiv_v4(W,X,Y) <=>
  268.  same(X,Y) &
  269.  forall(X,
  270.   exists(W,
  271.    true_in_world(X,W))).
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