Download Lectures on constructive functional programming by Richard Bird PDF
By Richard Bird
The topic of those lectures is a calculus of services for deriving courses from their requirements. This calculus contains more than a few options and notations for outlining capabilities over numerous info forms
(including lists, timber and arrays), including their algebraic and different homes. every one lecture starts off with a selected challenge, and the idea essential to remedy it really is theu constructed. during this means we are hoping to teach sensible method of the matter of systematically calculating courses from their standards can take its position along different methodologies.
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Second, there is the question of how many directions one might wish to identify as being useful. We shall adopt the following solutions to these questions. Each directed reduction will involve a single operator, and we focus on two legitimate directions: top-down (top reductions), and left-right (left reductions). We shall use the notation EElt for a top-reduction, and for a left reduction. ) The effect of a top reduction is illustrated by e+ EIlt Thus e tx ( 123) = 4 5 6 7 8 9 ((1E1l4)EIl7 (2 Ell 5) Ell 8 (3 Ell 6) Ell 9 ) produces a single row as its result.
Y reductions, in the way that list accumulations were related to list reductions in the first lecture, we need to consider the array analogues'of inits and tails. This we do next. 9 Tops and bottoms There are four reasonable ways of dissecting an array: we shall call them tops, bottoms, lefts and rights. Two of them are illustrated by the following examples: lefts 0~ n = (( non 0~ n) 1 2 3 123 PS(456)= tO 789 ( 123 456 (123 456 789 The essential points here are that lefts and rights each return a single row, while tops and bottoms each return a single column.
0fe where e =~ and a0b=a$fb We omit the simple proof. I . f!. efficiently. n write minimax where 00 is the identity element of a0x Since! x Using the specialisation lemma. c) Now, a is a left-zero of EBa (and so, by the way, is 00), and -00 is a. left-zero of 0. 6 The alpha-beta algorithm \Ve now generalise the minimax problem to trees. Consider the data-type tree ::~ Tip numlFork [tree] The syntax of this declaration is that of the functional language Miranda, and it is also employed in the notation of Bird and \Vadler (reference [2] of Lecture 1).