perm filename PBG.XGP[DIS,DBL] blob sn#229980 filedate 1976-08-07 generic text, type T, neo UTF8
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␈↓"␈↓ ↓⊗␈↓λSTRUCTURES



␈↓"␈↓ ↓⊗␈↓λ     3               8     10     12            22
␈↓"␈↓ ↓⊗␈↓λ  SETS            BAGS  OSETS  LISTS  EMPTY-STRUCS
␈↓"␈↓ ↓⊗␈↓λ     7              25     11     13                           Generalize
␈↓"␈↓ ↓⊗␈↓λ                                                                        (23)
␈↓"␈↓ ↓⊗␈↓λ  4                9         25   31        44                        (failure)
␈↓"␈↓ ↓⊗␈↓λ                                                        Canonicalize
␈↓"␈↓ ↓⊗␈↓λ      5                                                              44
␈↓"␈↓ ↓⊗␈↓λINT-SET BI-SET    INT-BAG BI-BAGS SINGL-BAG DOUBL-BAG TRIPL-BAG NUMBERS
␈↓"␈↓ ↓⊗␈↓λ      6
␈↓"␈↓ ↓⊗␈↓λ                                                                130 138 149

␈↓"␈↓ ↓⊗␈↓λ                                                                  130     147   150   151    152   154
␈↓"␈↓ ↓⊗␈↓λSINGLETONS DOUBLETONS                                           EVENS SQUARES 1-DIV 0-DIV PRIMES 3-DIV
␈↓"␈↓ ↓⊗␈↓λ                                                                                   ≡EMPTY    153   155




␈↓"␈↓ ↓⊗␈↓λACTIVES




␈↓"␈↓ ↓⊗␈↓λ          14            15     17    18    21    26    28         30    32         33          35      36
␈↓"␈↓ ↓⊗␈↓λALL-BUT-FIRST ALL-BUT-LAST LIST-∪ PROJ1 PROJ2 BAG-∪ SET-∪ BAG-INSERT BAG-∩ SET-INSERT BAG-DELETE BAG-DIFF OSET-∩
␈↓"␈↓ ↓⊗␈↓λ          19            20     24          27          29         31    37         34
␈↓"␈↓ ↓⊗␈↓λ                                                 45             50 Restrict 48            49          52
␈↓"␈↓ ↓⊗␈↓λ                      (16)                       Restrict                  Restrict       Restrict    Restrict
␈↓"␈↓ ↓⊗␈↓λ                                                                 51 50
␈↓"␈↓ ↓⊗␈↓λ                  (failure)                                      ADD-1                                 53
␈↓"␈↓ ↓⊗␈↓λ                                              47 46      226                                           53
␈↓"␈↓ ↓⊗␈↓λ                                               ADD2 SUPERSET BAG-DISJOINTNESS MINIMUM  SUB1      SUBTRACT
␈↓"␈↓ ↓⊗␈↓λ                                                 77      227

␈↓"␈↓ ↓⊗␈↓λ                                                                                                         54
␈↓"␈↓ ↓⊗␈↓λ                                                                                      LESS-THAN-OR-EQUAL-TO
␈↓"␈↓ ↓⊗␈↓λ                                                                                                         55
␈↓"␈↓ ↓⊗␈↓λ                                                                                           Coalesce

␈↓"␈↓ ↓⊗␈↓λ      70                                                                                               56
␈↓"␈↓ ↓⊗␈↓λCOALESCE                                                                                         LEQ-SELF
␈↓"␈↓ ↓⊗␈↓λ      76                                                                                      ≡ CONSTANT-T

␈↓"␈↓ ↓⊗␈↓λ 70

␈↓"␈↓ ↓⊗␈↓λ         71           73     75     78           79                                128         131            184
␈↓"␈↓ ↓⊗␈↓λSELF-DELETE SELF-MEMBER  DOUBLE SQUARE SELF-COMPOSE COA-REPLACE2 COA-JOIN2 COA-REPEAT2 SELF-INSERT SELF-SET-UNION
␈↓"␈↓ ↓⊗␈↓λ  ≡IDEN  72 ≡ALWAYS-F 74            82                                             129         132    ≡IDEN   185
␈↓"␈↓ ↓⊗␈↓λ                         130    159 162 135
␈↓"␈↓ ↓⊗␈↓λ                      Invert   Restrict  Invert                                                   133     139
␈↓"␈↓ ↓⊗␈↓λ                                                                          =FIRST-ELE =LAST-ELE CR2-A2 Exponen
␈↓"␈↓ ↓⊗␈↓λ                                                                                           ≡TIMES 134     140

␈↓"␈↓ ↓⊗␈↓λ                                                                                                          139

␈↓"␈↓ ↓⊗␈↓λ                                 161 160     164         136            80       81     86     87    228    230
␈↓"␈↓ ↓⊗␈↓λ                         HALVING SQUARE2 SQUARE3 SQUARE-ROOT  X↑4  (X+Y)+Z  X+(Y+Z)  (XY)Z  X(YZ)  (FG)H  F(GH)
␈↓"␈↓ ↓⊗␈↓λ                                                 137     138            84       83     89     88    229    231
␈↓"␈↓ ↓⊗␈↓λ                                                                          ≡X+Y+Z          ≡XYZ
␈↓"␈↓ ↓⊗␈↓λ                                         165        156  163             (see ADD)     (see TIMES)
␈↓"␈↓ ↓⊗␈↓λ                                     Compose      Restrict Restrict

␈↓"␈↓ ↓⊗␈↓λ                                             166   157      176
␈↓"␈↓ ↓⊗␈↓λ                                         DIV-SQ3 ROOT3    ROOT2     ADD                              (232-252)
␈↓"␈↓ ↓⊗␈↓λ                                             167   158   ≡ALWAYS-F
␈↓"␈↓ ↓⊗␈↓λ                                                                           214
␈↓"␈↓ ↓⊗␈↓λ                                                                            Restrict

␈↓"␈↓ ↓⊗␈↓λ                                                                            254 253 256 255             212
␈↓"␈↓ ↓⊗␈↓λ                                                                            +SQUARE +PRIME  +EVEN +0 +1 Ad2 +3
␈↓"␈↓ ↓⊗␈↓λ                                                                    85                                  213
␈↓"␈↓ ↓⊗␈↓λ                                                                Invert          254        256

␈↓"␈↓ ↓⊗␈↓λ                                                                        188
␈↓"␈↓ ↓⊗␈↓λ                                                                    INV-ADD X␈↓#
2␈↓#+Y␈↓#
2␈↓#=Z␈↓#
2␈↓# PRIME-PAIR
␈↓"␈↓ ↓⊗␈↓λ                                                                        189
␈↓"␈↓ ↓⊗␈↓λ                                                                195         190
␈↓"␈↓ ↓⊗␈↓λ                                                            Restrict       Restrict

␈↓"␈↓ ↓⊗␈↓λ                                                                199      193       191
␈↓"␈↓ ↓⊗␈↓λ                                                         SINGLE-ADD INV+EVEN INV+PRIME INV+SQUARE INV+0 INV+1 INV+2
␈↓"␈↓ ↓⊗␈↓λ                                                      ≡SINGL-x  200      194       192
␈↓"␈↓ ↓⊗␈↓λ                                                                     195
␈↓"␈↓ ↓⊗␈↓λ                                                                Restrict
␈↓"␈↓ ↓⊗␈↓λ                                                                          197
␈↓"␈↓ ↓⊗␈↓λ                                                                    PRIME-ADD
␈↓"␈↓ ↓⊗␈↓λ                                                                          198

␈↓"␈↓ ↓⊗␈↓λ                                                                Restrict  201
␈↓"␈↓ ↓⊗␈↓λ                                                                               202
␈↓"␈↓ ↓⊗␈↓λ                                                                    PRIME-ADD-SING
␈↓"␈↓ ↓⊗␈↓λ                                                                               203















␈↓"␈↓ ↓⊗␈↓λ   38     40              41                      57   (2)                91   (1),108
␈↓"␈↓ ↓⊗␈↓λSET-∩ LIST-∩        EQUALITY          PARALLEL-JOIN2 SET-∪ PARALLEL-REPLACE2 COMPOSE
␈↓"␈↓ ↓⊗␈↓λ    39
␈↓"␈↓ ↓⊗␈↓λ                        42
␈↓"␈↓ ↓⊗␈↓λ                        Generalize                                                          (108)

␈↓"␈↓ ↓⊗␈↓λ   224                     43           61      66               97                 109
␈↓"␈↓ ↓⊗␈↓λSUBSET DISJOINTED   SAME-SIZE EQ-CAR TIMES G-UNION         MR2-BBP2         INT-COMPOSE
␈↓"␈↓ ↓⊗␈↓λ   225                                  62      68              102
␈↓"␈↓ ↓⊗␈↓λ                 44   44
␈↓"␈↓ ↓⊗␈↓λ                 Canonicalize
␈↓"␈↓ ↓⊗␈↓λ                                                                                 112           114          121
␈↓"␈↓ ↓⊗␈↓λ               SIZE                90   148                             G-∪oMR2-BBP2 INSERToDELETE TIMESoSQUARE
␈↓"␈↓ ↓⊗␈↓λ                                 Invert                                  ≡TIMES  115           125          127

␈↓"␈↓ ↓⊗␈↓λ                                 141  205 204 206 209  210    216       218         219
␈↓"␈↓ ↓⊗␈↓λ                           INV-TIMES  xSQUARE x1  x0   x2   xEVEN x-TO-EVEN x-TO-SQUARE
␈↓"␈↓ ↓⊗␈↓λ                          142 143,177     208 207 215  211    217       221         220
␈↓"␈↓ ↓⊗␈↓λ                                             ≡IDEN    ≡DOUBLE               ≡xSQUARE
␈↓"␈↓ ↓⊗␈↓λ                              178 179 144
␈↓"␈↓ ↓⊗␈↓λ                              Restrict  Compose          Analogy

␈↓"␈↓ ↓⊗␈↓λ           186        222     180     182         145
␈↓"␈↓ ↓⊗␈↓λSELF-BAG-UNION SELF-UNION PRIME-x SINGL-x DIVISORS-OF (see AD2)
␈↓"␈↓ ↓⊗␈↓λ           187        223     181     183 146     149
␈↓"␈↓ ↓⊗␈↓λ                                  ≡BAG-INS