1 | PLL is a set of implementations of Prolog in Scheme. It is not |
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2 | supposed to be efficient, but rather as a simple way to teach the |
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3 | fundamentals of Logic Programming and the internal working of a |
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4 | Prolog interpreter (conceptually only -- a real implementation would |
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5 | be radically different). This interpreter is based on a simple |
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6 | implementation of the AMB operator. |
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7 | |
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8 | PLL is very small (less than 500 lines of code, including different |
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9 | versions of the interpreter). |
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10 | |
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11 | Each variant is built on top of the other. |
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12 | |
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13 | * Pure prolog: no variables, no assertions, only plain Prolog and SLD-resolution. |
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14 | * Prolog w/built-ins: with an extensible set of built-in predicates. Only the built-ins within a list are allowed. |
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15 | * Prolog w/Scheme functions: call any Scheme function from Prolog. |
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16 | * Prolog w/local vars: this version has support for "IS" and local Prolog variables. |
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17 | * Prolog w/meta-predicates: this version has support for "assert" and "retract". |
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18 | * Prolog w/cut: this version supports cuts. |
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19 | |
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20 | One last implementation is missing, that would allow for writing |
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21 | and reading the database (so it would be possible to store and |
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22 | retrieve programs). This is very simple to implement and planned |
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23 | for the near future. |
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24 | |
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25 | == Loading PLL |
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26 | |
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27 | |
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28 | Just |
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29 | (use (pll)) |
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30 | |
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31 | == VARIABLES |
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32 | |
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33 | |
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34 | Traditionally, Prolog systems treat symbols beginning |
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35 | with uppercase letters as variables: X, Y, Variable are |
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36 | variables, while x, y, constant are constants. |
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37 | |
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38 | Lisp-based Prologs usually do this differently: the variables |
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39 | are the symbols that begin with a question mark: {{?x}}, {{?y}}, |
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40 | {{?variable}}, etc. We do the same in this implementation. |
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41 | |
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42 | |
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43 | == CALLING THE INTERPRETER |
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44 | |
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45 | |
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46 | Our Prolog use the following syntax: |
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47 | |
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48 | |
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49 | (pure-prolog PROGRAM GOAL) |
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50 | |
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51 | |
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52 | The program is a list of assertions. The program |
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53 | |
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54 | p(x). |
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55 | p(Z) :- q, r(Z). |
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56 | |
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57 | |
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58 | is written as a list of assertions. Each assertion is a list |
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59 | where the head represents the left side (the consequent), and |
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60 | the tail is a list of the goals to be met in order to prove |
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61 | the consequent. For example, |
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62 | |
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63 | |
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64 | '(( (p x) )) |
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65 | ( (p ?z) q (r ?z))) |
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66 | |
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67 | |
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68 | The GOAL is a list of goals: |
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69 | |
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70 | |
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71 | p(1), q(X). |
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72 | |
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73 | |
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74 | is written as |
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75 | |
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76 | |
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77 | '((p 1) (q ?x)) |
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78 | |
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79 | EXAMPLE: Suppose we want to enter the following program: |
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80 | |
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81 | |
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82 | f(0). |
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83 | f(Z) :- g(Z). |
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84 | h(3). |
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85 | h(4). |
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86 | p(Z,Y,S) :- f(Z),g(Y),h(S) |
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87 | g(10). |
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88 | |
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89 | |
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90 | And ask the question |
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91 | |
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92 | |
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93 | p(10,D,A), q(A). |
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94 | |
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95 | |
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96 | We can do this: |
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97 | |
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98 | (define facts '(( (f 0) ) |
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99 | ( (f ?z) (g ?z) ) |
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100 | ( (h 3) ) |
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101 | ( (h 4) ) |
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102 | ( (q 4) ) |
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103 | ( (p ?z ?y ?s) (f ?z) (g ?y) (h ?s) ) |
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104 | ( (g 10) ))) |
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105 | (define goals '((p 10 ?d ?a) (q ?a))) |
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106 | |
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107 | |
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108 | And call |
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109 | |
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110 | (pure-prolog facts goals) |
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111 | |
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112 | Or, directly enter the facts and goal (as we do in the examples |
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113 | that are included in {{prolog-examples.scm}}): |
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114 | |
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115 | (pure-prolog '(( (f 0) ) |
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116 | ( (f ?z) (g ?z)) |
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117 | ( (h 3) ) |
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118 | ( (h 4) ) |
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119 | ( (q 4) ) |
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120 | ( (p ?z ?y ?s) (f ?z) (g ?y) (h ?s)) |
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121 | ( (g 10) )) |
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122 | '((p 10 ?d ?a) (q ?a))) |
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123 | |
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124 | |
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125 | The result will be a list of substitutions that satisfy |
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126 | the goal: |
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127 | |
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128 | ((?a . 4) (?d . 10)) |
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129 | |
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130 | === GETTING MULTIPLE ANSWERS |
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131 | |
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132 | |
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133 | This can be done with the {{amb+}} operator. |
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134 | |
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135 | (pure-prolog '(((f 1)) |
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136 | ((f 2))) |
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137 | '((f ?x))) |
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138 | |
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139 | ((?x 1)) |
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140 | |
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141 | If we call {{(amb+)}}, then we get another solution: |
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142 | |
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143 | |
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144 | ((?x 2)) |
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145 | |
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146 | == DIFFERENT INTERPRETERS |
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147 | |
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148 | The different interpreters included are: |
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149 | |
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150 | * {{pure prolog}} (prolog only) |
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151 | * {{prolog+built-ins}} (with built-in predicates with side-effect) |
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152 | * {{prolog+scheme}} (with an FFI to Scheme, but NO built-ins) |
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153 | * {{prolog+local}} (with "IS" and local vars; on top of prolog+scheme) |
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154 | * {{prolog+meta}} (with assert and retract; on top of prolog+local) |
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155 | * {{prolog+cut}} (with cut (!); on top of prolog+meta) |
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156 | |
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157 | So the features are added one on top of the other, except for the |
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158 | built-ins feature, which is not included in the later interpreters. |
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159 | |
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160 | In the source code, there is one initial implementation (pure-prolog) |
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161 | with short comments explaining how it works. Each interpreter after |
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162 | that one has comments only on the modified parts. |
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163 | |
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164 | === Pure Prolog |
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165 | |
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166 | This is the most basic of all. You can only statet facts as |
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167 | we described above, nothing else. Call it as |
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168 | |
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169 | (pure-prolog facts goals) |
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170 | |
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171 | |
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172 | For example, we define a graph by declaring its edges, then |
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173 | define a {{reach/2}} predicate. |
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174 | |
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175 | edge(a,b). |
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176 | edge(a,c). |
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177 | edge(c,b). |
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178 | edge(c,d). |
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179 | edge(d,e). |
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180 | reach(A,B) :- edge(A,B). |
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181 | reach(A,B) :- edge(A,X), reach(X,B). |
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182 | |
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183 | |
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184 | We could then as "{{reach(b,e)}}" and find that ''b'' doesn't reach |
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185 | ''e''. |
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186 | |
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187 | In PLL: |
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188 | |
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189 | (define graph '( ((edge a b)) |
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190 | ((edge a c)) |
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191 | ((edge c b)) |
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192 | ((edge c d)) |
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193 | ((edge d e)) |
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194 | ((reach ?a ?b) (edge ?a ?b)) |
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195 | ((reach ?a ?b) (edge ?a ?x) |
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196 | (reach ?x ?b)))) |
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197 | |
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198 | (pure-prolog graph '( (reach b e) )) |
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199 | #f |
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200 | |
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201 | |
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202 | === Prolog with built-in "procedures" |
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203 | |
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204 | This adds some predicates with side-effects. |
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205 | |
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206 | Define a list of Scheme functions that you want to be |
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207 | accessible from Prolog: |
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208 | |
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209 | |
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210 | (define write-it |
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211 | (lambda (args sub) |
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212 | (cond ((not (null? args)) |
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213 | (if (matching-symbol? (car args)) |
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214 | (display (assoc (car args) sub)) |
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215 | (display (car args))) |
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216 | (write-it (cdr args) sub)) |
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217 | (else #t)))) |
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218 | |
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219 | Here "{{sub}}" is the current substitution, where Prolog will find |
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220 | the values of variables. |
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221 | |
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222 | (define built-ins `((write . ,write-it))) |
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223 | |
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224 | |
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225 | So {{(write a b c ...)}} will be translated to |
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226 | |
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227 | (write-it (a b c ...) sub) |
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228 | |
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229 | Then, whenever one of these predicates show up in the |
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230 | goal, Prolog will execute them: |
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231 | |
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232 | |
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233 | father(john,johnny). |
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234 | father(old-john,john). |
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235 | grandpa(A,B) :- father(A,X), father(X,B). |
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236 | |
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237 | |
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238 | Our goal is |
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239 | |
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240 | grandpa(old-john,Who), write("grandson is: "), write(Who). |
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241 | |
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242 | In our Prolog, this is expressed as follows: |
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243 | |
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244 | |
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245 | (prolog+built-ins '( ((father john johnny)) |
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246 | ((father old-john john)) |
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247 | ((grandpa ?a ?b) (father ?a ?x) (father ?x ?b)) ) |
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248 | '( (grandpa old-john ?who) (write "Grandson is: " ?who) )) |
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249 | |
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250 | Grandson is: johnny |
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251 | (((?who . johnny)) ()) |
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252 | |
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253 | The first line was the effect of having a {{(write ...)}} in the goal. |
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254 | The second is the answer. |
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255 | |
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256 | === Prolog with any scheme function |
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257 | |
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258 | This interpreter has no sandbox -- it will recognize and execute |
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259 | any Scheme function when it sees one. |
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260 | |
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261 | Suppose we want to run this Prolog program, and use a Scheme |
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262 | function "{{print}}" in the goal: |
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263 | |
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264 | a(5). |
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265 | b(3). |
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266 | b(5). |
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267 | |
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268 | Goal: |
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269 | |
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270 | a(X), b(Y), X=Y, print(X, " " Y). |
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271 | |
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272 | |
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273 | In our Prolog, we have: |
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274 | |
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275 | (prolog+scheme '( ((a 5)) |
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276 | ((b 3)) |
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277 | ((b 5))) |
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278 | '( (a ?x) (b ?y) ((= ?x ?y)) ((print ?x " " ?y)))) |
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279 | |
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280 | 5 5 |
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281 | ((?y . 5) (?x . 5)) |
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282 | |
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283 | |
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284 | The first line is the effect of the print. The second line is |
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285 | Prolog's answer. |
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286 | |
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287 | === With local variables |
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288 | |
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289 | |
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290 | (prolog+local '( ((f ?x ?y) |
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291 | (is ?y (* 2 ?x)) |
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292 | ((print 'OK: ?y)))) |
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293 | '( (f 3 ?a) )) |
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294 | |
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295 | OK:6 |
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296 | ((?a . 6)) |
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297 | |
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298 | === With assert and retract |
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299 | |
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300 | This adds the meta-predicates {{assert}} and {{retract}}. |
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301 | |
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302 | |
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303 | (prolog+meta '(( (f ?x) (asserta (h 1))) |
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304 | ( (g ?x) (h ?x))) |
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305 | '((f ?w) (g ?z))) |
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306 | |
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307 | |
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308 | The result will be {{((?z . 1))}} |
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309 | |
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310 | |
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311 | {{retract}} has the opposite effect. The Prolog program we show now is |
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312 | |
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313 | f(2). |
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314 | f(3). |
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315 | g(1) :- retract(f(2)). |
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316 | |
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317 | And the goal is |
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318 | |
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319 | g(1), f(X). |
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320 | |
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321 | |
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322 | In PPL's Schemish-Prolog, this is |
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323 | |
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324 | |
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325 | (define prolog-retract '( ((f 2)) |
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326 | ((f 3)) |
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327 | ((g 1) (retract ((f 2)))) |
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328 | ((g 1) (f 3)))) |
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329 | (prolog+meta prolog-retract '((g 1) (f ?x))) |
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330 | |
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331 | |
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332 | {{(g 1)}} causes retract to be evaluated, so the goal succeeds |
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333 | with ''X=3'', and not ''X=2'': |
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334 | |
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335 | |
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336 | ((?x 3)) |
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337 | |
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338 | |
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339 | === With cut |
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340 | |
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341 | This adds the cut operator. For example, in Prolog we could write |
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342 | |
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343 | a(X) :- b(X), !, c(X). |
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344 | b(1). |
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345 | b(2). |
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346 | c(2). |
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347 | |
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348 | The goal {{a(X)}} fails, because after the interpreter chooses {{b(1)}}, |
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349 | it cannot backtrack, and {{c(1)}} is not true. |
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350 | |
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351 | In our Prolog, we write: |
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352 | |
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353 | (prolog+cut '(( (a ?x) (b ?x) ! (c ?x) ) |
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354 | ( (b 1) ) |
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355 | ( (b 2) ) |
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356 | ( (c 2) )) |
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357 | '((a ?x))) |
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358 | |
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359 | #f |
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360 | |
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361 | If we remove the cut, then this goal will succeed with ''X=2''. |
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362 | |
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363 | The cut can be used also in the goal. |
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364 | |
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365 | == BUGS AND MISSING FEATURES |
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366 | |
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367 | |
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368 | * There is no way to save and load the database |
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369 | |
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370 | * There is no simple way to get all possible answers (substitutions) for a |
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371 | query in a list. |
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372 | |
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373 | * This manual is too short. |
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374 | |
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375 | == A BIBLIOGRAPHY |
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376 | |
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377 | The following is a list of some books related to Prolog programming and |
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378 | implementations of Prolog. |
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379 | |
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380 | 1. '''William Clocksin, Chris Mellish'''. ''"Programming in Prolog"''. |
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381 | Springer, 2003. [ a very basic text ] |
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382 | |
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383 | 2. '''Michael Covington, Donald Nute, AndrÃ© Vellino''' ''"Prolog Programming |
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384 | in Depth"''. Scott, Foresman and Company, 1988. [ quick introduction |
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385 | to Prolog, followed by some advanced programming techniques and |
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386 | application ] |
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387 | |
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388 | 3. '''Leon Sterling, Ehud Shapiro'''. ''"The Art of Prolog"''. MIT Press, 1994. |
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389 | [ solid introduction to Prolog, including the execution model -- |
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390 | strongly recommended for those who want to understand the |
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391 | internals of the interpreter ] |
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392 | |
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393 | 4. '''Richard O'Keefe'''. ''"The Craft of Prolog"''. MIT Press, 1990. [ advanced |
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394 | programming techniques ] |
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395 | |
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396 | 5. '''Harold Abelson, Gerald Jay Sussman''' ''"Structure and Interpretation |
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397 | of Computer Programs"''. Addison-Wesley, 1996. [ explains and implements in |
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398 | Scheme the AMB operator and a small Prolog interpreter ] |
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399 | |
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400 | 6. '''Peter Norvig'''. ''"Paradigms of Artificial Intelligence |
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401 | Programming"''. Morgan Kaufmann, 1992. [ part of the book explains |
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402 | unification and contains another Prolog implementation, in Common |
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403 | Lisp ] |
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404 | |
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405 | 7. '''Jacques Chazarain''', ''"Programmer Avec Scheme"''. International Thomson |
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406 | Publishing France, 1996 (in French). [ a very good book on |
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407 | Scheme. chapters 15-19 focus on Prolog ] |
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408 | |
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409 | 8. '''J. A. Campbell'''. ''"Implementations of PROLOG"''. Ellis Horwood, 1984. |
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410 | [ a study of implementation techniques. quite advanced. ] |
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