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␈↓ ↓H␈↓␈↓ ↓x␈↓αvalmax␈↓↓[␈↓αu␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓] ←
␈↓ ↓H␈↓↓␈↓ α_␈↓βif␈↓↓ ␈↓βn ␈↓αu␈↓↓ ␈↓βthen␈↓↓ ␈↓αalpha
␈↓ ↓H␈↓α␈↓ α_␈↓βelse␈↓↓ {␈↓βif␈↓↓ ␈↓αter␈↓↓[␈↓αrectify␈↓↓ ␈↓βa ␈↓αu␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓] ␈↓βthen␈↓↓ ␈↓αimval␈↓↓ ␈↓βa ␈↓αu␈↓↓ ␈↓βelse␈↓↓ ␈↓αvalmin␈↓↓[␈↓αsuccessors␈↓↓ ␈↓βa ␈↓αu␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓]}
␈↓ ↓H␈↓↓␈↓ α8[λ␈↓αs␈↓↓. ␈↓βif␈↓↓ ¬[␈↓αs␈↓↓ > ␈↓αalpha␈↓↓] ␈↓βthen␈↓↓ ␈↓αvalmax␈↓↓[␈↓βd ␈↓αu␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓]
␈↓ ↓H␈↓↓␈↓ αp␈↓βelse if␈↓↓ ␈↓αs␈↓↓ < ␈↓αbeta␈↓↓ ␈↓βthen␈↓↓ ␈↓αvalmax␈↓↓[␈↓βd ␈↓αu␈↓↓, ␈↓αs␈↓↓, ␈↓αbeta␈↓↓]
␈↓ ↓H␈↓↓␈↓ αp␈↓βelse␈↓↓ ␈↓αbeta␈↓↓]



␈↓ ↓H␈↓↓␈↓ ↓x␈↓αvalmin␈↓↓[␈↓αu␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓] ←
␈↓ ↓H␈↓↓␈↓ α_␈↓βif␈↓↓ ␈↓βn ␈↓αu␈↓↓ ␈↓βthen␈↓↓ ␈↓αbeta
␈↓ ↓H␈↓α␈↓ α_␈↓βelse␈↓↓ {␈↓βif␈↓↓ ␈↓αter␈↓↓[␈↓αrectify␈↓↓ ␈↓βa ␈↓αu␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓] ␈↓βthen␈↓↓ ␈↓αimval␈↓↓ ␈↓βa ␈↓αu␈↓↓ ␈↓βelse␈↓↓ ␈↓αvalmax␈↓↓[␈↓αsuccessors␈↓↓ ␈↓βa ␈↓αu␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓]}
␈↓ ↓H␈↓↓␈↓ α8[λ␈↓αs␈↓↓. ␈↓βif␈↓↓ ¬[␈↓αs␈↓↓ > ␈↓αalpha␈↓↓] ␈↓βthen␈↓↓ ␈↓αalpha
␈↓ ↓H␈↓α␈↓ αp␈↓βelse if␈↓↓ ␈↓αs␈↓↓ < ␈↓αbeta␈↓↓ ␈↓βthen␈↓↓ ␈↓αvalmin␈↓↓[␈↓βd ␈↓αu␈↓↓, ␈↓αalpha␈↓↓, ␈↓αs␈↓↓]
␈↓ ↓H␈↓↓␈↓ αp␈↓βelse␈↓↓ ␈↓αvalmin␈↓↓[␈↓βd ␈↓αu␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓]]



␈↓ ↓H␈↓↓␈↓ ↓x␈↓αlinemax␈↓↓[␈↓αu␈↓↓, ␈↓αline␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓] ←
␈↓ ↓H␈↓↓␈↓ α_␈↓βif␈↓↓ ␈↓βn ␈↓αu␈↓↓ ␈↓βthen␈↓↓ ␈↓αalpha␈↓↓ . ␈↓αline
␈↓ ↓H␈↓α␈↓ α_␈↓βelse␈↓↓ {␈↓βif␈↓↓ ␈↓αter␈↓↓[␈↓αrectify␈↓↓ ␈↓βa ␈↓αu␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓] ␈↓βthen␈↓↓ <␈↓αimval␈↓↓ ␈↓βa ␈↓αu␈↓↓>
␈↓ ↓H␈↓↓␈↓ αo␈↓βelse␈↓↓ ␈↓αlinemin␈↓↓[␈↓αsuccessors␈↓↓ ␈↓βa ␈↓αu␈↓↓, ␈↓αbeta␈↓↓ .  `BETA-CUTOFF' , ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓]}
␈↓ ↓H␈↓↓␈↓ α8[λ␈↓αs␈↓↓. ␈↓βif␈↓↓ ¬[␈↓βa ␈↓αs␈↓↓ > ␈↓αalpha␈↓↓] ␈↓βthen␈↓↓ ␈↓αlinemax␈↓↓[␈↓βd ␈↓αu␈↓↓, ␈↓αline␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓]
␈↓ ↓H␈↓↓␈↓ αp␈↓βelse if␈↓↓ ␈↓βa ␈↓αs␈↓↓ < ␈↓αbeta␈↓↓ ␈↓βthen␈↓↓ ␈↓αlinemax␈↓↓[␈↓βd ␈↓αu␈↓↓, ␈↓αext␈↓↓ ␈↓βa ␈↓αu␈↓↓ . ␈↓βd ␈↓αs␈↓↓, ␈↓βa ␈↓αs␈↓↓, ␈↓αbeta␈↓↓]
␈↓ ↓H␈↓↓␈↓ αp␈↓βelse␈↓↓ ␈↓αbeta␈↓↓ . ␈↓αline␈↓↓]



␈↓ ↓H␈↓↓␈↓ ↓x␈↓αlinemin␈↓↓[␈↓αu␈↓↓, ␈↓αline␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓] ←
␈↓ ↓H␈↓↓␈↓ α_␈↓βif␈↓↓ ␈↓βn ␈↓αu␈↓↓ ␈↓βthen␈↓↓ ␈↓αbeta␈↓↓ . ␈↓αline
␈↓ ↓H␈↓α␈↓ α_␈↓βelse␈↓↓ {␈↓βif␈↓↓ ␈↓αter␈↓↓[␈↓αrectify␈↓↓ ␈↓βa ␈↓αu␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓] ␈↓βthen␈↓↓ <␈↓αimval␈↓↓ ␈↓βa ␈↓αu␈↓↓>
␈↓ ↓H␈↓↓␈↓ αo␈↓βelse␈↓↓ ␈↓αlinemax␈↓↓[␈↓αsuccessors␈↓↓ ␈↓βa ␈↓αu␈↓↓, ␈↓αalpha␈↓↓ .  `ALPHA-CUTOFF' , ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓]}
␈↓ ↓H␈↓↓␈↓ α8[λ␈↓αs␈↓↓. ␈↓βif␈↓↓ ¬[␈↓βa ␈↓αs␈↓↓ > ␈↓αalpha␈↓↓] ␈↓βthen␈↓↓ ␈↓αalpha␈↓↓ . ␈↓αline
␈↓ ↓H␈↓α␈↓ αp␈↓βelse if␈↓↓ ␈↓βa ␈↓αs␈↓↓ < ␈↓αbeta␈↓↓ ␈↓βthen␈↓↓ ␈↓αlinemin␈↓↓[␈↓βd ␈↓αu␈↓↓, ␈↓αext␈↓↓ ␈↓βa ␈↓αu␈↓↓ . ␈↓βd ␈↓αs␈↓↓, ␈↓αalpha␈↓↓, ␈↓βa ␈↓αs␈↓↓]
␈↓ ↓H␈↓↓␈↓ αp␈↓βelse␈↓↓ ␈↓αlinemin␈↓↓[␈↓βd ␈↓αu␈↓↓, ␈↓αline␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓]]



␈↓ ↓H␈↓↓␈↓ ↓x␈↓αtreemax␈↓↓[␈↓αu␈↓↓, ␈↓αtrmax␈↓↓, ␈↓αtrmin␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓] ←
␈↓ ↓H␈↓↓␈↓ α_␈↓βif␈↓↓ ␈↓βn ␈↓αu␈↓↓ ␈↓βthen␈↓↓ <␈↓αalpha␈↓↓, ␈↓αtrmax␈↓↓, ␈↓αtrmin␈↓↓>
␈↓ ↓H␈↓↓␈↓ α_␈↓βelse␈↓↓ {␈↓βif␈↓↓ ␈↓αter␈↓↓[␈↓αrectify␈↓↓ ␈↓βa ␈↓αu␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓] ␈↓βthen␈↓↓ {␈↓αimval␈↓↓ ␈↓βa ␈↓αu␈↓↓}[λ␈↓αv␈↓↓. <␈↓αv␈↓↓, <␈↓αv␈↓↓>, <␈↓αv␈↓↓>>]
␈↓ ↓H␈↓↓␈↓ αo␈↓βelse␈↓↓ ␈↓αtreemin␈↓↓[␈↓αsuccessors␈↓↓ ␈↓βa ␈↓αu␈↓↓, NIL, ␈↓αbeta␈↓↓ .  `BETA-CUTOFF' , ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓]}
␈↓ ↓H␈↓↓␈↓ α8[λ␈↓αs␈↓↓. ␈↓βif␈↓↓ ¬[␈↓βa ␈↓αs␈↓↓ > ␈↓αalpha␈↓↓] ␈↓βthen␈↓↓ ␈↓αtreemax␈↓↓[␈↓βd ␈↓αu␈↓↓, ␈↓αtrmax␈↓↓, [␈↓αext␈↓↓ ␈↓βa ␈↓αu␈↓↓ . ␈↓βadd ␈↓αs␈↓↓] . ␈↓αtrmin␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓]
␈↓ ↓H␈↓↓␈↓ αp␈↓βelse if␈↓↓ ␈↓βa ␈↓αs␈↓↓ < ␈↓αbeta␈↓↓ ␈↓βthen␈↓↓ ␈↓αtreemax␈↓↓[␈↓βd ␈↓αu␈↓↓, ␈↓αext␈↓↓ ␈↓βa ␈↓αu␈↓↓ . ␈↓βad ␈↓αs␈↓↓, [␈↓αext␈↓↓ ␈↓βa ␈↓αu␈↓↓ . ␈↓βadd ␈↓αs␈↓↓] . ␈↓αtrmin␈↓↓, ␈↓βa ␈↓αs␈↓↓, ␈↓αbeta␈↓↓]
␈↓ ↓H␈↓↓␈↓ αp␈↓βelse␈↓↓ <␈↓αbeta␈↓↓, ␈↓αext␈↓↓ ␈↓βa ␈↓αu␈↓↓ . ␈↓βad ␈↓αs␈↓↓, NIL>]
␈↓ ↓H␈↓␈↓ j1


␈↓ ↓H␈↓↓␈↓ ↓x␈↓αtreemin␈↓↓[␈↓αu␈↓↓, ␈↓αtrmax␈↓↓, ␈↓αtrmin␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓] ←
␈↓ ↓H␈↓↓␈↓ α_␈↓βif␈↓↓ ␈↓βn ␈↓αu␈↓↓ ␈↓βthen␈↓↓ <␈↓αbeta␈↓↓, ␈↓αtrmax␈↓↓, ␈↓αtrmin␈↓↓>
␈↓ ↓H␈↓↓␈↓ α_␈↓βelse␈↓↓ {␈↓βif␈↓↓ ␈↓αter␈↓↓[␈↓αrectify␈↓↓ ␈↓βa ␈↓αu␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓] ␈↓βthen␈↓↓ {␈↓αimval␈↓↓ ␈↓βa ␈↓αu␈↓↓}[λ␈↓αv␈↓↓. <␈↓αv␈↓↓, <␈↓αv␈↓↓>, <␈↓αv␈↓↓>>]
␈↓ ↓H␈↓↓␈↓ αo␈↓βelse␈↓↓ ␈↓αtreemax␈↓↓[␈↓αsuccessors␈↓↓ ␈↓βa ␈↓αu␈↓↓, ␈↓αalpha␈↓↓ .  `ALPHA-CUTOFF' , NIL, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓]}
␈↓ ↓H␈↓↓␈↓ α8[λ␈↓αs␈↓↓. ␈↓βif␈↓↓ ¬[␈↓βa ␈↓αs␈↓↓ > ␈↓αalpha␈↓↓] ␈↓βthen␈↓↓ <␈↓αalpha␈↓↓, NIL, ␈↓αext␈↓↓ ␈↓βa ␈↓αu␈↓↓ . ␈↓βadd ␈↓αs␈↓↓>
␈↓ ↓H␈↓↓␈↓ αp␈↓βelse if␈↓↓ ␈↓βa ␈↓αs␈↓↓ < ␈↓αbeta␈↓↓ ␈↓βthen␈↓↓ ␈↓αtreemin␈↓↓[␈↓βd ␈↓αu␈↓↓, [␈↓αext␈↓↓ ␈↓βa ␈↓αu␈↓↓ . ␈↓βad ␈↓αs␈↓↓] . ␈↓αtrmax␈↓↓, ␈↓αext␈↓↓ ␈↓βa ␈↓αu␈↓↓ . ␈↓βadd ␈↓αs␈↓↓, ␈↓αalpha␈↓↓, ␈↓βa ␈↓αs␈↓↓]
␈↓ ↓H␈↓↓␈↓ αp␈↓βelse␈↓↓ ␈↓αtreemin␈↓↓[␈↓βd ␈↓αu␈↓↓, [␈↓αext␈↓↓ ␈↓βa ␈↓αu␈↓↓ . ␈↓βad ␈↓αs␈↓↓] . ␈↓αtrmax␈↓↓, ␈↓αtrmin␈↓↓, ␈↓αalpha␈↓↓, ␈↓αbeta␈↓↓]]



␈↓ ↓H␈↓↓␈↓ ↓x␈↓αrectify␈↓↓ ␈↓αp␈↓↓ ←
␈↓ ↓H␈↓↓␈↓ α_␈↓βprog␈↓↓ [␈↓αz␈↓↓, ␈↓αq␈↓↓]
␈↓ ↓H␈↓↓␈↓ αa␈↓αq␈↓↓ ← ␈↓αcommontail␈↓↓[␈↓αp␈↓↓, ␈↓αp1␈↓↓]
␈↓ ↓H␈↓↓␈↓ αA␈↓αl1␈↓↓ ␈↓βif␈↓↓ ␈↓αequal␈↓↓[␈↓αq␈↓↓, ␈↓αp1␈↓↓] ␈↓βthen␈↓↓ ␈↓αgo␈↓↓ ␈↓αl2
␈↓ ↓H␈↓α␈↓ αarevert␈↓↓[]
␈↓ ↓H␈↓↓␈↓ αa␈↓αgo␈↓↓ ␈↓αl1
␈↓ ↓H␈↓α␈↓ α<l2␈↓↓ ␈↓αz␈↓↓ ← ␈↓αlistsubt␈↓↓[␈↓αp␈↓↓, ␈↓αp1␈↓↓]
␈↓ ↓H␈↓↓␈↓ α;␈↓αl3␈↓↓ ␈↓βif␈↓↓ ␈↓βn ␈↓αz␈↓↓ ␈↓βthen␈↓↓ ␈↓αreturn␈↓↓ ␈↓αp
␈↓ ↓H␈↓α␈↓ αaupdate␈↓↓ ␈↓βa ␈↓αz
␈↓ ↓H␈↓α␈↓ αaz␈↓↓ ← ␈↓βd ␈↓αz
␈↓ ↓H␈↓α␈↓ αago␈↓↓ ␈↓αl3



␈↓ ↓H␈↓α␈↓ ↓xcommontail␈↓↓[␈↓αu␈↓↓, ␈↓αv␈↓↓] ← ␈↓αreverse␈↓↓ ␈↓αcommonhead␈↓↓[␈↓αreverse␈↓↓ ␈↓αu␈↓↓, ␈↓αreverse␈↓↓ ␈↓αv␈↓↓]



␈↓ ↓H␈↓↓␈↓ ↓x␈↓αcommonhead␈↓↓[␈↓αu␈↓↓, ␈↓αv␈↓↓] ← ␈↓βif␈↓↓ ␈↓βn ␈↓αu␈↓↓ ∨ ␈↓βn ␈↓αv␈↓↓ ∨ ¬␈↓αequal␈↓↓[␈↓βa ␈↓αu␈↓↓, ␈↓βa ␈↓αv␈↓↓] ␈↓βthen␈↓↓ NIL ␈↓βelse␈↓↓ ␈↓βa ␈↓αu␈↓↓ . ␈↓αcommonhead␈↓↓[␈↓βd ␈↓αu␈↓↓, ␈↓βd ␈↓αv␈↓↓]