LISP, Lore, and Logic: An Algebraic View of LISP by W. Richard Stark

By W. Richard Stark

Here is a presentation of LISP that is either functional and theoretical. For the sensible, the syntax of the language, the programming kinds, and the semantics of computation are rigorously constructed. For the theoretical, the algebra of interpreters, the lambda calculus as a origin for LISP, and the algebraic importance of LISP's method of man made intelligence are mentioned. because the identify indicates, the booklet reaches past the technical part of LISP to provide colourful purposes, historic reviews and quotations, computational philosophy, effects of LISP's extraordinary energy, and lots more and plenty extra. the fabric has been designed to entice various readers, from the brilliant freshman to the working towards specialist, and from laptop scientists and mathematicians to chemists, engineers, and philosophers.

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Sample text

Goldbach's conjecture is the simple and unsolved assertion made in the first sentence of this example. Example 18: Let L be a Boolean-valued function of Boolean variables Vl , V2 , V3, v 4. , as in the dictionary) Boolean ordering of values for Vl , V2 , V3 , V4, as follows: Vl=NIL =NIL =NIL V2=NIL =NIL =NIL V3=NIL =NIL =T V4=NIL =T =NIL ; first binding ; second binding ;third binding =T =T =T =T ;last binding. The function BOOLEAN-SE;ARCH will use B-NEXT (a "next" function analogous to 1 +, but for lists of Boolean values).

The last node is defined by LAST(node). We will use L-CHILD, R-CHILD, and TERMINAL to define our movement through the tree, and NODE-TEST and LAST to limit our search. For example, * (DEFUN DF-SEARCH (N) (PRINT N) iprint search position (COND ((NODE-TEST N) N) isolution found, end search ((TERMINAL N) iterminal node (NOT (LAST N» ibacktrack and continue if not last node ((EQ T (SETQ TEMP (DF-SEARCH (L-CHILD N»» i i f T after searching L subtree (DF-SEARCH (R-CHILD N» ) ithen search R subtree (TEMP TEMP) iif TEMP is nonNIL, then TEMP is the node (T NIL) ino node satisfies TEST-NODE,end search ) ) ==> DF-SEARCH .

DEFUN NUMBER-SEARCH (N) (IF ;If (NOT (P-SUM N)) ;if we have found the exception N ;then return it, (NUMBER-SEARCH (+ 2 N)) )) ;else keep looking. ==> NUMBER-SEARCH If NIL = P-SUM(n) has a solution in the even integers greater than 2, then the least solution is the value returned by (NUMBER-SEARCH 4), and we have proved the assertion to be false. If no solution exists, then (NUMBER-SEARCH 4) never returns a value. This example deals with a mathematical claim known as Goldbach's conjecture. Goldbach's conjecture is the simple and unsolved assertion made in the first sentence of this example.

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