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| support-v1/basic.lisp | support-v2.1/basic.lisp | ||||
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507 lines 16148 bytes Last modified : Wed Jun 29 13:31:22 2005 |
515 lines 16236 bytes Last modified : Wed Jun 29 13:32:19 2005 |
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| 1 | ;;; Mode: Lisp; Package: ocml | 1 | ;;; Mode: Lisp; Package: ocml | ||
| 2 | 2 | ||||
| 3 | ;;; The Open University | 3 | ;;; The Open University | ||
| 4 | 4 | ||||
| 5 | (in-package "OCML") | 5 | (in-package "OCML") | ||
| 6 | 6 | ||||
| 7 | (in-ontology akt-support-ontology) | 7 | (in-ontology akt-support-ontology) | ||
| 8 | 8 | ||||
| 9 | ;;;Here we introduce a number of definitions, which provide | 9 | ;;;Here we introduce a number of definitions, which provide | ||
| 10 | ;;;the basic representational layer to define entities in the ontology. | 10 | ;;;the basic representational layer to define entities in the ontology. | ||
| 11 | ;;;Here we include basic data types, such | 11 | ;;;Here we include basic data types, such | ||
| 12 | ;;;as strings, lists, sets and numbers, as well as basic logical concepts, such | 12 | ;;;as strings, lists, sets and numbers, as well as basic logical concepts, such | ||
| 13 | ;;;as FUNCTION and RELATION. It also provides equality constructs and a meta-level | 13 | ;;;as FUNCTION and RELATION. It also provides equality constructs and a meta-level | ||
| 14 | ;;;relation HOLDS, which takes a rel, say ?rel, and a number of args, say ?args | 14 | ;;;relation HOLDS, which takes a rel, say ?rel, and a number of args, say ?args | ||
| 15 | ;;;and it is satisfied iff ?rel is satisfied by ?args. | 15 | ;;;and it is satisfied iff ?rel is satisfied by ?args. | ||
| 16 | ;;;The advantage of expliciting including here the representational layer | 16 | ;;;The advantage of expliciting including here the representational layer | ||
| 17 | ;;;for the set of AKT ontologies is that these become completely self-contained: | 17 | ;;;for the set of AKT ontologies is that these become completely self-contained: | ||
| 18 | ;;;all the notions required to specify any concept in the ontology are themselves | 18 | ;;;all the notions required to specify any concept in the ontology are themselves | ||
| 19 | ;;;to be found in the ontologies | 19 | ;;;to be found in the ontologies | ||
| 20 | 20 | ||||
| 21 | ;;;BASIC UNIFICATION MECHANISMS | 21 | ;;;BASIC UNIFICATION MECHANISMS | ||
| 22 | 22 | ||||
| 23 | 23 | ||||
| 24 | ;;;RELATION = | 24 | ;;;RELATION = | ||
| 25 | (def-relation = (?x ?y) | 25 | (def-relation = (?x ?y) | ||
| 26 | "True if ?x and ?y do unify" | 26 | "True if ?x and ?y do unify" | ||
| 27 | :lisp-fun #'(lambda ( x y env) | 27 | :lisp-fun #'(lambda ( x y env) | ||
| 28 | (Let ((result (unify x y env))) | 28 | (Let ((result (unify x y env))) | ||
| 29 | (if (eq result :fail) | 29 | (if (eq result :fail) | ||
| 30 | :fail | 30 | :fail | ||
| 31 | (List result))))) | 31 | (List result))))) | ||
| 32 | 32 | ||||
| 33 | ;;;RELATION == | 33 | ;;;RELATION == | ||
| 34 | (def-relation == (?x ?y) | 34 | (def-relation == (?x ?y) | ||
| 35 | "True if ?x and ?y do unify and they also have the same structure. | 35 | "True if ?x and ?y do unify and they also have the same structure. | ||
| 36 | This means that either they are both atoms, or they are lists with | 36 | This means that either they are both atoms, or they are lists with | ||
| 37 | the same structure" | 37 | the same structure" | ||
| 38 | :lisp-fun #'(lambda ( x y env) | 38 | :lisp-fun #'(lambda ( x y env) | ||
| 39 | (Let ((result (unify-strong x y env))) | 39 | (Let ((result (unify-strong x y env))) | ||
| 40 | (if (eq result :fail) | 40 | (if (eq result :fail) | ||
| 41 | :fail | 41 | :fail | ||
| 42 | (List result))))) | 42 | (List result))))) | ||
| 43 | 43 | ||||
| 44 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; | 44 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; | ||
| 45 | 45 | ||||
| 46 | (def-class LIST (Intangible-Thing) ?x | 46 | (def-class LIST (Intangible-Thing) ?x | ||
| 47 | "A class representing lists." | 47 | "A class representing lists." | ||
| 48 | :iff-def (or (= ?x nil) | 48 | :iff-def (or (= ?x nil) | ||
| 49 | (= ?x (?a . ?b))) | 49 | (= ?x (?a . ?b))) | ||
| 50 | :prove-by (or (= ?x nil) | 50 | :prove-by (or (= ?x nil) | ||
| 51 | (and (variable-bound ?x) | 51 | (and (variable-bound ?x) | ||
| 52 | (= ?x (?a . ?b)))) | 52 | (= ?x (?a . ?b)))) | ||
| 53 | :no-proofs-by (:iff-def)) | 53 | :no-proofs-by (:iff-def)) | ||
| 54 | 54 | ||||
| 55 | 55 | ||||
| 56 | (def-instance NIL list | 56 | (def-instance NIL list | ||
| 57 | "The empty list") | 57 | "The empty list") | ||
| 58 | 58 | ||||
| 59 | (def-relation NULL (?l) | 59 | (def-relation NULL (?l) | ||
| 60 | "True if ?l is the empty list" | 60 | "True if ?l is the empty list" | ||
| 61 | :iff-def (= ?l nil)) | 61 | :iff-def (= ?l nil)) | ||
| 62 | 62 | ||||
| 63 | (def-function FIRST (?l) | 63 | (def-function FIRST (?l) | ||
| 64 | "Takes the first element of a list. If the list is empty | 64 | "Takes the first element of a list. If the list is empty | ||
| 65 | the function returns :nothing" | 65 | the function returns :nothing" | ||
| 66 | :constraint (list ?l) | 66 | :constraint (list ?l) | ||
| 67 | :body (if (== ?l (?a . ?b)) | 67 | :body (if (== ?l (?a . ?b)) | ||
| 68 | ?a | 68 | ?a | ||
| 69 | :nothing)) | 69 | :nothing)) | ||
| 70 | 70 | ||||
| 71 | (def-function REST (?l) | 71 | (def-function REST (?l) | ||
| 72 | "Takes a list as argument, say ?l, removes the first element of ?s | 72 | "Takes a list as argument, say ?l, removes the first element of ?s | ||
| 73 | and returns the resulting list. If ?l = nil, then :nothing is returned" | 73 | and returns the resulting list. If ?l = nil, then :nothing is returned" | ||
| 74 | :constraint (list ?l) | 74 | :constraint (list ?l) | ||
| 75 | :body (if (== ?l (?a . ?b)) | 75 | :body (if (== ?l (?a . ?b)) | ||
| 76 | ?b | 76 | ?b | ||
| 77 | :nothing)) | 77 | :nothing)) | ||
| 78 | 78 | ||||
| 79 | (def-function LIST-OF (&rest ?els) | 79 | (def-function LIST-OF (&rest ?els) | ||
| 80 | "This is the primitive list constructor. It is implemented in terms of | 80 | "This is the primitive list constructor. It is implemented in terms of | ||
| 81 | the underlying LISP list construction primitive, LIST" | 81 | the underlying LISP list construction primitive, LIST" | ||
| 82 | :lisp-fun #'(lambda (&rest els) | 82 | :lisp-fun #'(lambda (&rest els) | ||
| 83 | (apply #'list els))) | 83 | (apply #'list els))) | ||
| 84 | 84 | ||||
| 85 | (def-function APPEND (?l1 &rest ?ls) | 85 | (def-function APPEND (?l1 &rest ?ls) | ||
| 86 | "Appends together a number of lists. I cannot be bothered giving its operational | 86 | "Appends together a number of lists. I cannot be bothered giving its operational | ||
| 87 | spec...so you only get a lisp attachment" | 87 | spec...so you only get a lisp attachment" | ||
| 88 | :constraint (and (list ?l1)(every ?ls list)) | 88 | :constraint (and (list ?l1)(every ?ls list)) | ||
| 89 | :lisp-fun #'append) | 89 | :lisp-fun #'append) | ||
| 90 | 90 | ||||
| 91 | 91 | ||||
| 92 | (def-function CONS (?el ?l) | 92 | (def-function CONS (?el ?l) | ||
| 93 | "Adds ?el to the beginning of list ?l. | 93 | "Adds ?el to the beginning of list ?l. | ||
| 94 | Note that this cons is less generic than the lisp function with the same name. | 94 | Note that this cons is less generic than the lisp function with the same name. | ||
| 95 | Here the 2nd argument must be a list (in lisp, it can also be an atom)." | 95 | Here the 2nd argument must be a list (in lisp, it can also be an atom)." | ||
| 96 | :constraint (list ?l) | 96 | :constraint (list ?l) | ||
| 97 | :body (append (list-of ?el) | 97 | :body (append (list-of ?el) | ||
| 98 | ?l)) | 98 | ?l)) | ||
| 99 | 99 | ||||
| 100 | 100 | ||||
| 101 | (def-function LENGTH (?l) | 101 | (def-function LENGTH (?l) | ||
| 102 | "Computes the number of elements in a list" | 102 | "Computes the number of elements in a list" | ||
| 103 | :constraint (list ?l) | 103 | :constraint (list ?l) | ||
| 104 | :body (if (= ?l nil) | 104 | :body (if (= ?l nil) | ||
| 105 | 0 | 105 | 0 | ||
| 106 | (if (== ?l (?first . ?rest)) | 106 | (if (== ?l (?first . ?rest)) | ||
| 107 | (+ 1 | 107 | (+ 1 | ||
| 108 | (length ?rest))))) | 108 | (length ?rest))))) | ||
| 109 | 109 | ||||
| 110 | (def-function REMOVE1 (?el ?l) | 110 | (def-function REMOVE1 (?el ?l) | ||
| 111 | "Removes the first occurrence of ?el in ?l and returns the resulting list. | 111 | "Removes the first occurrence of ?el in ?l and returns the resulting list. | ||
| 112 | If ?el is not a member of ?l then the result is ?l" | 112 | If ?el is not a member of ?l then the result is ?l" | ||
| 113 | :constraint (list ?l) | 113 | :constraint (list ?l) | ||
| 114 | :body (if (= ?l nil) | 114 | :body (if (= ?l nil) | ||
| 115 | ?l | 115 | ?l | ||
| 116 | (if (== ?l (?el . ?rest)) | 116 | (if (== ?l (?el . ?rest)) | ||
| 117 | ?rest | 117 | ?rest | ||
| 118 | (if (== ?l (?first . ?rest)) | 118 | (if (== ?l (?first . ?rest)) | ||
| 119 | (cons ?first | 119 | (cons ?first | ||
| 120 | (remove1 ?el ?rest)))))) | 120 | (remove1 ?el ?rest)))))) | ||
| 121 | 121 | ||||
| 122 | (def-function REMOVE (?el ?l) | 122 | (def-function REMOVE (?el ?l) | ||
| 123 | "Removes all occurrences of ?el in ?l and returns the resulting list. | 123 | "Removes all occurrences of ?el in ?l and returns the resulting list. | ||
| 124 | If ?el is not a member of ?l then the result is ?l" | 124 | If ?el is not a member of ?l then the result is ?l" | ||
| 125 | :constraint (list ?l) | 125 | :constraint (list ?l) | ||
| 126 | :body (if (= ?l nil) | 126 | :body (if (= ?l nil) | ||
| 127 | ?l | 127 | ?l | ||
| 128 | (if (== ?l (?el . ?rest)) | 128 | (if (== ?l (?el . ?rest)) | ||
| 129 | (remove ?el ?rest) | 129 | (remove ?el ?rest) | ||
| 130 | (if (== ?l (?first . ?rest)) | 130 | (if (== ?l (?first . ?rest)) | ||
| 131 | (cons ?first | 131 | (cons ?first | ||
| 132 | (remove ?el ?rest)))))) | 132 | (remove ?el ?rest)))))) | ||
| 133 | 133 | ||||
| 134 | 134 | ||||
| 135 | 135 | ||||
| 136 | 136 | ||||
| 137 | (def-relation MEMBER (?el ?list) | 137 | (def-relation MEMBER (?el ?list) | ||
| 138 | "A relation to check whether something is a member of a list" | 138 | "A relation to check whether something is a member of a list" | ||
| 139 | :constraint (list ?list) | 139 | :constraint (list ?list) | ||
| 140 | :iff-def (or (== ?list (?el . ?rest)) | 140 | :iff-def (or (== ?list (?el . ?rest)) | ||
| 141 | (and (== ?list (?first . ?rest)) | 141 | (and (== ?list (?first . ?rest)) | ||
| 142 | (member ?el ?rest)))) | 142 | (member ?el ?rest)))) | ||
| 143 | 143 | ||||
| 144 | (def-relation EVERY (?l ?rel) | 144 | (def-relation EVERY (?l ?rel) | ||
| 145 | "True if for each term in ?l, say ?term, (holds ?rel ?term) is true. | 145 | "True if for each term in ?l, say ?term, (holds ?rel ?term) is true. | ||
| 146 | For instance, (every '(1 2 3) 'number) is satisfied, while | 146 | For instance, (every '(1 2 3) 'number) is satisfied, while | ||
| 147 | (every '(1 2 pippo) 'number) is not" | 147 | (every '(1 2 pippo) 'number) is not" | ||
| 148 | :constraint (unary-relation ?rel) | 148 | :constraint (unary-relation ?rel) | ||
| 149 | :iff-def (or (= ?l nil) | 149 | :iff-def (or (= ?l nil) | ||
| 150 | (and (== ?l (?first . ?rest)) | 150 | (and (== ?l (?first . ?rest)) | ||
| 151 | (holds ?rel ?first) | 151 | (holds ?rel ?first) | ||
| 152 | (every ?rest ?rel)))) | 152 | (every ?rest ?rel)))) | ||
| 153 | 153 | ||||
| 154 | ;;;FUNCTION BUTLAST | 154 | ;;;FUNCTION BUTLAST | ||
| 155 | (def-function BUTLAST (?list) | 155 | (def-function BUTLAST (?list) | ||
| 156 | "Returns all the element of ?list, except the last one. | 156 | "Returns all the element of ?list, except the last one. | ||
| 157 | If ?list = NIL, then :nothing is returned. If ?list has | 157 | If ?list = NIL, then :nothing is returned. If ?list has | ||
| 158 | length 1, then nil is returned" | 158 | length 1, then nil is returned" | ||
| 159 | :constraint (list ?l) | 159 | :constraint (list ?l) | ||
| 160 | :body (cond ((null ?list) :nothing) | 160 | :body (cond ((null ?list) :nothing) | ||
| 161 | ((null (rest ?list)) nil) | 161 | ((null (rest ?list)) nil) | ||
| 162 | ((true) | 162 | ((true) | ||
| 163 | (cons (first ?list) (butlast (rest ?list)))))) | 163 | (cons (first ?list) (butlast (rest ?list)))))) | ||
| 164 | 164 | ||||
| 165 | 165 | ||||
| 166 | ;;;FUNCTION LAST | 166 | ;;;FUNCTION LAST | ||
| 167 | (def-function LAST (?list) | 167 | (def-function LAST (?list) | ||
| 168 | "Returns the last element of a list. If ?list is empty | 168 | "Returns the last element of a list. If ?list is empty | ||
| 169 | then :nothing is returned" | 169 | then :nothing is returned" | ||
| 170 | :constraint (list ?list) | 170 | :constraint (list ?list) | ||
| 171 | :body (cond ((null ?list) :nothing) | 171 | :body (cond ((null ?list) :nothing) | ||
| 172 | ((null (rest ?list)) (first ?list)) | 172 | ((null (rest ?list)) (first ?list)) | ||
| 173 | ((true) (last (rest ?list))))) | 173 | ((true) (last (rest ?list))))) | ||
| 174 | 174 | ||||
| 175 | 175 | ||||
| 176 | ;;;;;;;;;;;;;;;;;;;;;;;; | 176 | ;;;;;;;;;;;;;;;;;;;;;;;; | ||
| 177 | 177 | ||||
| 178 | 178 | ||||
| 179 | ;;;SET | 179 | ;;;SET | ||
| 180 | (def-class SET (Intangible-Thing) | 180 | (def-class SET (Intangible-Thing) | ||
| 181 | "A set is something which is not an individual. In cyc sets are distinguished | 181 | "A set is something which is not an individual. In cyc sets are distinguished | ||
| 182 | from collections. Here we just use the term generically to refer to | 182 | from collections. Here we just use the term generically to refer to | ||
| 183 | something which denotes a collection of elements, whether abstract or | 183 | something which denotes a collection of elements, whether abstract or | ||
| 184 | concrete. | 184 | concrete. | ||
| 185 | Functions and relations represent sets. ") | 185 | Functions and relations represent sets. ") | ||
| 186 | 186 | ||||
| 187 | (def-axiom BASIC-SET-TYPES-ARE-DISJOINT | 187 | (def-axiom BASIC-SET-TYPES-ARE-DISJOINT | ||
| 188 | "There are three basic types of sets in our ontology, functions | 188 | "There are three basic types of sets in our ontology, functions | ||
| 189 | relations and enumerated sets and these do not intersect" | 189 | relations and enumerated sets and these do not intersect" | ||
| 190 | (subclass-partition set (set-of function relation enumerated-set))) | 190 | (subclass-partition set (set-of function relation enumerated-set))) | ||
| 191 | 191 | ||||
| 192 | 192 | ||||
| 193 | (def-function SET-OF (&rest ?args) | 193 | (def-function SET-OF (&rest ?args) | ||
| 194 | "This is the basic set constructor to create a set by enumerating its elements. | 194 | "This is the basic set constructor to create a set by enumerating its elements. | ||
| 195 | For instance, (setof 1 2) denotes the set {1 2}. | 195 | For instance, (setof 1 2) denotes the set {1 2}. | ||
| 196 | We represent such a set as a list whose first item is :set" | 196 | We represent such a set as a list whose first item is :set" | ||
| 197 | :body (cons :set ?args)) | 197 | :body (cons :set ?args)) | ||
| 198 | 198 | ||||
| 199 | 199 | ||||
| 200 | (def-class ENUMERATED-SET (set) ?x | 200 | (def-class ENUMERATED-SET (set) ?x | ||
| 201 | "A set represented as (:set-of el1 el_2...el_n), where no el_i is repeated" | 201 | "A set represented as (:set-of el1 el_2...el_n), where no el_i is repeated" | ||
| 202 | :constraint (list ?x) | 202 | :constraint (list ?x) | ||
| 203 | :iff-def (and (= ?x (:set . ?elements)) | 203 | :iff-def (and (= ?x (:set . ?elements)) | ||
| 204 | (not (exists ?el | 204 | (not (exists ?el | ||
| 205 | (and (member ?el ?elements) | 205 | (and (member ?el ?elements) | ||
| 206 | (member ?el (remove1 ?el ?elements)))))) | 206 | (member ?el (remove1 ?el ?elements)))))) | ||
| 207 | :prove-by (and (variable-bound ?x) | 207 | :prove-by (and (variable-bound ?x) | ||
| 208 | (= ?x (:set . ?elements)) | 208 | (= ?x (:set . ?elements)) | ||
| 209 | (not (exists ?el | 209 | (not (exists ?el | ||
| 210 | (and (member ?el ?elements) | 210 | (and (member ?el ?elements) | ||
| 211 | (member ?el (remove1 ?el ?elements)))))) | 211 | (member ?el (remove1 ?el ?elements)))))) | ||
| 212 | :no-proofs-by (:iff-def)) | 212 | :no-proofs-by (:iff-def)) | ||
| 213 | 213 | ||||
| 214 | |||||
| 215 | |||||
| 216 | (def-class INDIVIDUAL (Thing) ?x | 3e) | |||
| 217 | "Something which is not a set. For instance an instance of a class." | ||||
| 218 | :iff-def (not (set ?x)) | ||||
| 219 | |||||
| 220 | ;;;the definitions below are effective ways to prove whether | ||||
| 221 | ;;;somebody is an individual in OCML | ||||
| 222 | :prove-by (or | ||||
| 223 | (and (variable-bound ?x) | ||||
| 224 | (not (set ?x))) | ||||
| 225 | (= ?x nil)) | ||||
| 226 | :no-proofs-by (:iff-def)) ;;;:iff-def above is not a good way to prove things! | ||||
| 227 | |||||
| 228 | |||||
| 229 | |||||
| 230 | (def-relation ELEMENT-OF (?el ?set) | 214 | (def-relation ELEMENT-OF (?el ?set) | ||
| 231 | "A relation to check whether something is an element of a set. | 215 | "A relation to check whether something is an element of a set. | ||
| 232 | Note that because functions and relations are sets, we can prove | 216 | Note that because functions and relations are sets, we can prove | ||
| 233 | whether a tuple satisfies a relation or a function using ELEMENT-OF. | 217 | whether a tuple satisfies a relation or a function using ELEMENT-OF. | ||
| 234 | For instance, (element-of '(1 2 3) '+) is satisfied because | 218 | For instance, (element-of '(1 2 3) '+) is satisfied because | ||
| 235 | 1+2=3 - see definitions below for an operationalization of this approach") | 219 | 1+2=3 - see definitions below for an operationalization of this approach") | ||
| 236 | 220 | ||||
| 237 | (def-rule ELEMENT-OF-ENUMERATED-SET | 221 | (def-rule ELEMENT-OF-ENUMERATED-SET | ||
| 238 | "An operationalization of element-of, which works with sets represented as lists." | 222 | "An operationalization of element-of, which works with sets represented as lists." | ||
| 239 | ((element-of ?el ?l) if | 223 | ((element-of ?el ?l) if | ||
| 240 | (enumerated-set ?l) | 224 | (enumerated-set ?l) | ||
| 241 | (member ?el (rest ?l)))) | 225 | (member ?el (rest ?l)))) | ||
| 242 | 226 | ||||
| 243 | (def-rule ELEMENT-OF-SET-AS-RELATION | 227 | (def-rule ELEMENT-OF-SET-AS-RELATION | ||
| 244 | "A tuple, say <t1 t2 t3> is an element of relation r iff | 228 | "A tuple, say <t1 t2 t3> is an element of relation r iff | ||
| 245 | (holds r ti t2 t3) is satisfied" | 229 | (holds r ti t2 t3) is satisfied" | ||
| 246 | ((element-of ?tuple ?rel) if | 230 | ((element-of ?tuple ?rel) if | ||
| 247 | (relation ?rel) | 231 | (relation ?rel) | ||
| 248 | (List ?tuple) | 232 | (List ?tuple) | ||
| 249 | (sentence-holds (cons ?rel ?tuple)))) | 233 | (sentence-holds (cons ?rel ?tuple)))) | ||
| 250 | 234 | ||||
| 251 | (def-rule ELEMENT-OF-SET-AS-FUNCTION | 235 | (def-rule ELEMENT-OF-SET-AS-FUNCTION | ||
| 252 | "A tuple, say <t1 t2 t3> is an element of function f iff | 236 | "A tuple, say <t1 t2 t3> is an element of function f iff | ||
| 253 | (= (apply f ti t2) t3) is satisfied" | 237 | (= (apply f ti t2) t3) is satisfied" | ||
| 254 | ((element-of ?el ?fun) if | 238 | ((element-of ?el ?fun) if | ||
| 255 | (function ?fun) | 239 | (function ?fun) | ||
| 256 | (list ?el) | 240 | (list ?el) | ||
| 257 | (= (last ?el) (apply ?fun (butlast ?el))))) | 241 | (= (last ?el) (apply ?fun (butlast ?el))))) | ||
| 258 | 242 | ||||
| 259 | 243 | ||||
| 260 | 244 | ||||
| 3c) | 245 | ;;;UNION - The union of a number of sets | |||
| 246 | ;;;For instance | ||||
| 247 | ;;; (ocml-eval (union (set-of 1 2)(set-of 1 2 3))) | ||||
| 248 | ;;; (:SET 3 2 1) | ||||
| 2 | 249 | (def-function UNION (&rest ?sets) | |||
| 250 | :constraint (every ?sets set) | ||||
| 251 | :body (apply set-of (setofall ?x | ||||
| 252 | (exists ?set (and (member ?set ?sets) | ||||
| 253 | (element-of ?x ?set)))))) | ||||
| 254 | |||||
| 255 | |||||
| 2 | 256 | (def-function INTERSECTION (&rest ?sets) | |||
| 257 | :constraint (every ?sets set) | ||||
| 258 | :body (in-environment ((?all . (apply union ?sets))) | ||||
| 259 | (apply set-of (setofall ?x | ||||
| 260 | (and (element-of ?x ?all) | ||||
| 261 | (not (exists ?set | ||||
| 262 | (and (member ?set ?sets) | ||||
| 263 | (not (element-of ?x ?set)))))))))) | ||||
| 264 | |||||
| 265 | |||||
| 266 | |||||
| 261 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; | 267 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; | ||
| 262 | 268 | ||||
| 263 | ;;;NUMBER | 269 | ;;;NUMBER | ||
| 264 | (def-class NUMBER (individual Intangible-thing) | 3d) | 270 | (def-class NUMBER (Quantity) | |
| 265 | "The class of all numbers" | 271 | "The class of all numbers" | ||
| 266 | :lisp-fun #'(lambda (x env) | 272 | :lisp-fun #'(lambda (x env) | ||
| 267 | (let ((y (unbound-variable? x env))) | 273 | (let ((y (unbound-variable? x env))) | ||
| 268 | (if y ;;if y is unbound we return a 'sample' number | 274 | (if y ;;if y is unbound we return a 'sample' number | ||
| 269 | (list (cons (cons y 0) env)) | 275 | (list (cons (cons y 0) env)) | ||
| 270 | (if (numberp (instantiate x env)) ;;;make sure to instantiate x | 276 | (if (numberp (instantiate x env)) ;;;make sure to instantiate x | ||
| 271 | (list env) | 277 | (list env) | ||
| 272 | :fail))))) | 278 | :fail))))) | ||
| 279 | |||||
| 1 | 280 | (def-class REAL-NUMBER (number)) | |||
| 281 | |||||
| 1 | 282 | (def-class INTEGER (real-number)) | |||
| 273 | 283 | ||||
| 274 | 284 | ||||
| 275 | ;;; RELATION < | 285 | ;;; RELATION < | ||
| 276 | (def-relation < (?x ?y) | 286 | (def-relation < (?x ?y) | ||
| 277 | "A predicate to test whether a number is less than another" | 287 | "A predicate to test whether a number is less than another" | ||
| 278 | :constraint (and (number ?x)(number ?y)) | 288 | :constraint (and (number ?x)(number ?y)) | ||
| 279 | :lisp-fun #'(lambda (x y env) | 289 | :lisp-fun #'(lambda (x y env) | ||
| 280 | (if (< (instantiate x env) | 290 | (if (< (instantiate x env) | ||
| 281 | (instantiate y env)) | 291 | (instantiate y env)) | ||
| 282 | (List env) | 292 | (List env) | ||
| 283 | :fail))) | 293 | :fail))) | ||
| 284 | ;;;RELATION > | 294 | ;;;RELATION > | ||
| 285 | (def-relation > (?x ?y) | 295 | (def-relation > (?x ?y) | ||
| 286 | "A predicate to test whether a number is greater than another" | 296 | "A predicate to test whether a number is greater than another" | ||
| 287 | :constraint (and (number ?x)(number ?y)) | 297 | :constraint (and (number ?x)(number ?y)) | ||
| 288 | :lisp-fun #'(lambda (x y env) | 298 | :lisp-fun #'(lambda (x y env) | ||
| 289 | (if (> (instantiate x env) | 299 | (if (> (instantiate x env) | ||
| 290 | (instantiate y env)) | 300 | (instantiate y env)) | ||
| 291 | (List env) | 301 | (List env) | ||
| 292 | :fail))) | 302 | :fail))) | ||
| 293 | 303 | ||||
| 294 | 304 | ||||
| 295 | (def-class POSITIVE-NUMBER (number) ?x | 305 | (def-class POSITIVE-NUMBER (number) ?x | ||
| 296 | :iff-def (and (number ?x) | 306 | :iff-def (and (number ?x) | ||
| 297 | (> ?x 0))) | 307 | (> ?x 0))) | ||
| 298 | 308 | ||||
| 299 | (def-class NEGATIVE-NUMBER (number) ?x | 309 | (def-class NEGATIVE-NUMBER (number) ?x | ||
| 300 | :iff-def (and (number ?x) | 310 | :iff-def (and (number ?x) | ||
| 301 | (< ?x 0))) | 311 | (< ?x 0))) | ||
| 302 | 312 | ||||
| 303 | (def-class NON-NEGATIVE-NUMBER (number) ?x | 313 | (def-class NON-NEGATIVE-NUMBER (number) ?x | ||
| 304 | :iff-def (and (number ?x) | 314 | :iff-def (and (number ?x) | ||
| 305 | (not (negative-number ?x)))) | 315 | (not (negative-number ?x)))) | ||
| 306 | 316 | ||||
| 307 | 317 | ||||
| 308 | (def-axiom POS-NEG-NUMBERS-EXHAUSTIVE-PARTITION | 318 | (def-axiom POS-NEG-NUMBERS-EXHAUSTIVE-PARTITION | ||
| 309 | (exhaustive-subclass-partition number (set-of positive-number negative-number))) | 319 | (exhaustive-subclass-partition number (set-of positive-number negative-number))) | ||
| 310 | 320 | ||||
| 311 | 321 | ||||
| 312 | |||||
| 313 | |||||
| 314 | (def-class INTEGER (number) | 2 | |||
| 315 | "The class of all integers" | ||||
| 316 | :lisp-fun #'(lambda (x env) | ||||
| 317 | (let ((y (unbound-variable? x env))) | ||||
| 318 | (if y ;;if y is unbound we return a 'sample' integer | ||||
| 319 | (list (cons (cons y 0) env)) | ||||
| 320 | (if (integerp (instantiate x env)) ;;;make sure to instantiate x | ||||
| 321 | (list env) | ||||
| 322 | :fail))))) | ||||
| 323 | |||||
| 324 | |||||
| 325 | (def-class POSITIVE-INTEGER (integer) ?x | 322 | (def-class POSITIVE-INTEGER (integer) ?x | ||
| 326 | :iff-def (and (integer ?x) | 323 | :iff-def (and (integer ?x) | ||
| 327 | (> ?x 0))) | 324 | (> ?x 0))) | ||
| 328 | 325 | ||||
| 329 | (def-class NEGATIVE-INTEGER (integer) ?x | 326 | (def-class NEGATIVE-INTEGER (integer) ?x | ||
| 330 | :iff-def (and (integer ?x) | 327 | :iff-def (and (integer ?x) | ||
| 331 | (< ?x 0))) | 328 | (< ?x 0))) | ||
| 332 | 329 | ||||
| 333 | (def-class NON-NEGATIVE-INTEGER (integer) ?x | 330 | (def-class NON-NEGATIVE-INTEGER (integer) ?x | ||
| 334 | :iff-def (and (integer ?x) | 331 | :iff-def (and (integer ?x) | ||
| 335 | (not (negative-integer ?x)))) | 332 | (not (negative-integer ?x)))) | ||
| 336 | 333 | ||||
| 337 | 334 | ||||
| 338 | (def-function + (?X &rest ?y) | 335 | (def-function + (?X &rest ?y) | ||
| 339 | "Adds numbers" | 336 | "Adds numbers" | ||
| 340 | :constraint (and (number ?x) (number ?y)) | 337 | :constraint (and (number ?x) (number ?y)) | ||
| 341 | :lisp-fun #'+) | 338 | :lisp-fun #'+) | ||
| 342 | 339 | ||||
| 343 | (def-function * (?X ?y) | 340 | (def-function * (?X ?y) | ||
| 344 | "Multiplies numbers" | 341 | "Multiplies numbers" | ||
| 345 | :constraint (and (number ?x) (number ?y)) | 342 | :constraint (and (number ?x) (number ?y)) | ||
| 346 | :lisp-fun #'*) | 343 | :lisp-fun #'*) | ||
| 347 | 344 | ||||
| 348 | (def-function SQUARE (?X) | 345 | (def-function SQUARE (?X) | ||
| 349 | :constraint (number ?x) | 346 | :constraint (number ?x) | ||
| 350 | :body (* ?X ?X)) | 347 | :body (* ?X ?X)) | ||
| 351 | 348 | ||||
| 352 | (def-function - (?X &rest ?y) | 349 | (def-function - (?X &rest ?y) | ||
| 353 | "Subtracts numbers" | 350 | "Subtracts numbers" | ||
| 354 | :constraint (and (number ?x) (number ?y)) | 351 | :constraint (and (number ?x) (number ?y)) | ||
| 355 | :lisp-fun #'(lambda (x &rest y) | 352 | :lisp-fun #'(lambda (x &rest y) | ||
| 356 | (apply #'- x y))) | 353 | (apply #'- x y))) | ||
| 357 | 354 | ||||
| 358 | (def-function / (?X ?y) | 355 | (def-function / (?X ?y) | ||
| 359 | "Divides numbers" | 356 | "Divides numbers" | ||
| 360 | :constraint (and (number ?x) (number ?y)) | 357 | :constraint (and (number ?x) (number ?y)) | ||
| 361 | :lisp-fun #'/) | 358 | :lisp-fun #'/) | ||
| 362 | 359 | ||||
| 360 | |||||
| 361 | (def-function log (?number ?base) | ||||
| 362 | :lisp-fun #'log) | ||||
| 363 | |||||
| 364 | (def-function round (?number) -> ?int | ||||
| 365 | :def (integer ?int) | ||||
| 366 | :lisp-fun #'round) | ||||
| 367 | |||||
| 368 | |||||
| 369 | |||||
| 370 | |||||
| 363 | ;;;;;;;;;;;;;;;;;;;;; | 371 | ;;;;;;;;;;;;;;;;;;;;; | ||
| 364 | 372 | ||||
| 365 | (def-class STRING (individual intangible-thing) | 373 | (def-class STRING (individual intangible-thing) | ||
| 366 | "A primitive class representing strings" | 374 | "A primitive class representing strings" | ||
| 367 | :lisp-fun #'(lambda (x env) | 375 | :lisp-fun #'(lambda (x env) | ||
| 368 | (let ((y (unbound-variable? x env))) | 376 | (let ((y (unbound-variable? x env))) | ||
| 369 | (if y | 377 | (if y | ||
| 370 | (list (cons (cons y "SAMPLE-STRING") env)) | 378 | (list (cons (cons y "SAMPLE-STRING") env)) | ||
| 371 | (if (stringp (instantiate x env)) | 379 | (if (stringp (instantiate x env)) | ||
| 372 | (list env) | 380 | (list env) | ||
| 373 | :fail))))) | 381 | :fail))))) | ||
| 374 | 382 | ||||
| 375 | ;;;;;;;;;;;;;;;;;;;;; | 383 | ;;;;;;;;;;;;;;;;;;;;; | ||
| 376 | 384 | ||||
| 377 | (def-class RELATION (set) | 385 | (def-class RELATION (set) | ||
| 378 | "The class of defined relations. We assume fixed arity" | 386 | "The class of defined relations. We assume fixed arity" | ||
| 379 | :lisp-fun #'(lambda (x env) | 387 | :lisp-fun #'(lambda (x env) | ||
| 380 | (let ((y (unbound-variable? x env))) | 388 | (let ((y (unbound-variable? x env))) | ||
| 381 | (if y | 389 | (if y | ||
| 382 | (mapcar #'(lambda (rel) | 390 | (mapcar #'(lambda (rel) | ||
| 383 | (cons (cons y rel) env)) | 391 | (cons (cons y rel) env)) | ||
| 384 | (all-relations)) | 392 | (all-relations)) | ||
| 385 | (if (get-relation (instantiate x env)) ;;;make sure to instantiate x | 393 | (if (get-relation (instantiate x env)) ;;;make sure to instantiate x | ||
| 386 | (list env) | 394 | (list env) | ||
| 387 | :fail))))) | 395 | :fail))))) | ||
| 388 | 396 | ||||
| 389 | 397 | ||||
| 390 | (def-class UNARY-RELATION (relation) ?r | 398 | (def-class UNARY-RELATION (relation) ?r | ||
| 391 | :iff-def (and (relation ?r) | 399 | :iff-def (and (relation ?r) | ||
| 392 | (= (arity ?r) 1))) | 400 | (= (arity ?r) 1))) | ||
| 393 | 401 | ||||
| 394 | 402 | ||||
| 395 | (def-class BINARY-RELATION (relation) ?r | 403 | (def-class BINARY-RELATION (relation) ?r | ||
| 396 | :iff-def (and (relation ?r) | 404 | :iff-def (and (relation ?r) | ||
| 397 | (= (arity ?r) 2))) | 405 | (= (arity ?r) 2))) | ||
| 398 | 406 | ||||
| 399 | (def-relation TRUE () | 407 | (def-relation TRUE () | ||
| 400 | "This is always satisfied" | 408 | "This is always satisfied" | ||
| 401 | :lisp-fun #'(lambda (env) (list env))) | 409 | :lisp-fun #'(lambda (env) (list env))) | ||
| 402 | 410 | ||||
| 403 | (def-relation FALSE () | 411 | (def-relation FALSE () | ||
| 404 | "This is never satisfied" | 412 | "This is never satisfied" | ||
| 405 | :lisp-fun #'(lambda (env) :fail)) | 413 | :lisp-fun #'(lambda (env) :fail)) | ||
| 406 | 414 | ||||
| 407 | 415 | ||||
| 408 | (def-function ARITY (?x) | 416 | (def-function ARITY (?x) | ||
| 409 | "The arity of a function or relation. If a function or relation | 417 | "The arity of a function or relation. If a function or relation | ||
| 410 | has variable arity, then we treat the last argument as if it were | 418 | has variable arity, then we treat the last argument as if it were | ||
| 411 | a sequence variable. For instance the argument list for + is | 419 | a sequence variable. For instance the argument list for + is | ||
| 412 | (?x &rest ?y). In this case we say that + has arity 2. | 420 | (?x &rest ?y). In this case we say that + has arity 2. | ||
| 413 | It is important to note that OCML does not support relations with variable | 421 | It is important to note that OCML does not support relations with variable | ||
| 414 | arity. The only exception is HOLDS, which has variable arity and is built in | 422 | arity. The only exception is HOLDS, which has variable arity and is built in | ||
| 415 | the OCML proof system" | 423 | the OCML proof system" | ||
| 416 | 424 | ||||
| 417 | :constraint (or (function ?X)(relation ?X)) | 425 | :constraint (or (function ?X)(relation ?X)) | ||
| 418 | :body (in-environment | 426 | :body (in-environment | ||
| 419 | ((?l . (the-schema ?x)) | 427 | ((?l . (the-schema ?x)) | ||
| 420 | (?n . (length ?l))) | 428 | (?n . (length ?l))) | ||
| 421 | (if (every ?l variable) | 429 | (if (every ?l variable) | ||
| 422 | ?n | 430 | ?n | ||
| 423 | ;we assume that the only non-var can be &rest | 431 | ;we assume that the only non-var can be &rest | ||
| 424 | (- ?n 1)))) | 432 | (- ?n 1)))) | ||
| 425 | 433 | ||||
| 426 | (def-relation VARIABLE (?x) | 434 | (def-relation VARIABLE (?x) | ||
| 427 | "True of an OCML variable" | 435 | "True of an OCML variable" | ||
| 428 | :lisp-fun #'(lambda (x env) | 436 | :lisp-fun #'(lambda (x env) | ||
| 429 | (if | 437 | (if | ||
| 430 | (variable? (instantiate x env)) | 438 | (variable? (instantiate x env)) | ||
| 431 | (list env) | 439 | (list env) | ||
| 432 | :fail))) | 440 | :fail))) | ||
| 433 | 441 | ||||
| 434 | (def-relation VARIABLE-BOUND (?var) | 442 | (def-relation VARIABLE-BOUND (?var) | ||
| 435 | "True if ?var is bound in teh current environment" | 443 | "True if ?var is bound in teh current environment" | ||
| 436 | :lisp-fun #'(lambda (x env) | 444 | :lisp-fun #'(lambda (x env) | ||
| 437 | (if | 445 | (if | ||
| 438 | (unbound-variable? x env) | 446 | (unbound-variable? x env) | ||
| 439 | :fail | 447 | :fail | ||
| 440 | (list env)))) | 448 | (list env)))) | ||
| 441 | 449 | ||||
| 442 | (def-function THE-SCHEMA (?x) | 450 | (def-function THE-SCHEMA (?x) | ||
| 443 | "The schema of a function or relation" | 451 | "The schema of a function or relation" | ||
| 444 | :constraint (or (function ?X)(relation ?X)) | 452 | :constraint (or (function ?X)(relation ?X)) | ||
| 445 | :body (if (relation ?x) | 453 | :body (if (relation ?x) | ||
| 446 | (relation-schema ?x) | 454 | (relation-schema ?x) | ||
| 447 | (if (function ?x) | 455 | (if (function ?x) | ||
| 448 | (function-schema ?x) | 456 | (function-schema ?x) | ||
| 449 | :nothing))) | 457 | :nothing))) | ||
| 450 | 458 | ||||
| 451 | (def-function FUNCTION-SCHEMA (?f) | 459 | (def-function FUNCTION-SCHEMA (?f) | ||
| 452 | :constraint (function ?f) | 460 | :constraint (function ?f) | ||
| 453 | :lisp-fun #'(lambda (x) | 461 | :lisp-fun #'(lambda (x) | ||
| 454 | (rename-variables (schema (get-function x))))) | 462 | (rename-variables (schema (get-function x))))) | ||
| 455 | 463 | ||||
| 456 | (def-function RELATION-SCHEMA (?rel) | 464 | (def-function RELATION-SCHEMA (?rel) | ||
| 457 | :constraint (relation ?rel) | 465 | :constraint (relation ?rel) | ||
| 458 | :lisp-fun #'(lambda (x) | 466 | :lisp-fun #'(lambda (x) | ||
| 459 | (rename-variables (schema (get-relation x))))) | 467 | (rename-variables (schema (get-relation x))))) | ||
| 460 | 468 | ||||
| 461 | 469 | ||||
| 462 | 470 | ||||
| 463 | (def-relation HOLDS (?rel &rest ?args) | 471 | (def-relation HOLDS (?rel &rest ?args) | ||
| 464 | "A meta-level relation which is true iff the sentence (?rel . ?args) is true. | 472 | "A meta-level relation which is true iff the sentence (?rel . ?args) is true. | ||
| 465 | The length of ?args must be consistent with the arity of the relation" | 473 | The length of ?args must be consistent with the arity of the relation" | ||
| 466 | :constraint (and (relation ?r) | 474 | :constraint (and (relation ?r) | ||
| 467 | (= (arity ?rel) | 475 | (= (arity ?rel) | ||
| 468 | (length ?args)))) | 476 | (length ?args)))) | ||
| 469 | 477 | ||||
| 470 | (def-relation SENTENCE-HOLDS (?sentence) | 478 | (def-relation SENTENCE-HOLDS (?sentence) | ||
| 471 | "The same as HOLDS, but takes only one argument, a sentence whose truth | 479 | "The same as HOLDS, but takes only one argument, a sentence whose truth | ||
| 472 | value is to be checked" | 480 | value is to be checked" | ||
| 473 | :constraint (and (== ?sentence (?rel . ?args )) | 481 | :constraint (and (== ?sentence (?rel . ?args )) | ||
| 474 | (relation ?rel) | 482 | (relation ?rel) | ||
| 475 | (= (arity ?rel) | 483 | (= (arity ?rel) | ||
| 476 | (length ?args))) | 484 | (length ?args))) | ||
| 477 | :lisp-fun #'(lambda (sent env) | 485 | :lisp-fun #'(lambda (sent env) | ||
| 478 | (ask-top-level | 486 | (ask-top-level | ||
| 479 | (cons 'holds (instantiate sent env)) | 487 | (cons 'holds (instantiate sent env)) | ||
| 480 | :env env | 488 | :env env | ||
| 481 | :all t))) | 489 | :all t))) | ||
| 482 | 490 | ||||
| 483 | 491 | ||||
| 484 | 492 | ||||
| 485 | (def-class FUNCTION (set) | 493 | (def-class FUNCTION (set) | ||
| 486 | "The class of all defined functions" | 494 | "The class of all defined functions" | ||
| 487 | :lisp-fun #'(lambda (x env) | 495 | :lisp-fun #'(lambda (x env) | ||
| 488 | (let ((y (unbound-variable? x env))) | 496 | (let ((y (unbound-variable? x env))) | ||
| 489 | (if y | 497 | (if y | ||
| 490 | (mapcar #'(lambda (rel) | 498 | (mapcar #'(lambda (rel) | ||
| 491 | (cons (cons y rel) env)) | 499 | (cons (cons y rel) env)) | ||
| 492 | (all-functions)) | 500 | (all-functions)) | ||
| 493 | (if (ocml-function? | 501 | (if (ocml-function? | ||
| 494 | (instantiate x env)) | 502 | (instantiate x env)) | ||
| 495 | (list env) | 503 | (list env) | ||
| 496 | :fail))))) | 504 | :fail))))) | ||
| 497 | 505 | ||||
| 498 | 506 | ||||
| 499 | 507 | ||||
| 500 | 508 | ||||
| 501 | (def-function APPLY (?f ?args) | 509 | (def-function APPLY (?f ?args) | ||
| 502 | "(apply f (arg1 .....argn)) is the same as | 510 | "(apply f (arg1 .....argn)) is the same as | ||
| 503 | (f arg1 ....argn)" | 511 | (f arg1 ....argn)" | ||
| 504 | :constraint (and (function ?f) | 512 | :constraint (and (function ?f) | ||
| 505 | (list ?args))) | 513 | (list ?args))) | ||
| 506 | 514 | ||||
| 507 | 515 |