By Eric C.R. Hehner
Realizing programming and programming languages calls for wisdom of the underlying theoretical version. This booklet explores facets of programming which are amenable to mathematical facts. the writer describes a programming concept that's a lot less complicated and extra entire than the present theories thus far. within the theoretical version, a specification is simply a boolean expression and refinement is simply a standard implication. the writer develops a pragmatic and large process for writing targeted requisites and designing courses whose executions most likely fulfill the standards. starting with preparatory fabric in common sense, numbers, units, lists, features and kin, the publication advances extra into software idea, the guts of the booklet. next chapters could be chosen or passed over in response to path emphasis. The textual content may be helpful to scholars in classes on programming technique or verification on the complicated undergraduate or starting graduate point, in addition to for software program engineers within the box. All technical phrases are defined after which verified within the booklet at any place attainable. No complex mathematical wisdom or programming language is thought. The booklet includes a variety of routines and worked-out strategies for particular routines. Transparency masters and suggestions for the rest workouts can be found from the writer.
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Extra resources for A Practical Theory of Programming
We could have said s′ = ΣL ⇐ s:= 0. n:= 0. #L] For those who were uncomfortable about the use of implicit information in the preceding paragraph, the first part of the antecedent (0≤n≤#L) makes the needed bound on n explicit. n]) is not used anywhere. 45 4 Program Theory When a compiler translates a program into machine language, it treats each refined specification as just an identifier. For example, the summation program looks like A ⇐ s:= 0. n:= 0. B B ⇐ if n=#L then C else D C ⇐ ok D ⇐ s:= s+Ln.
As in this example, the shortcut usually works, but beware: it can sometimes lead to inconsistencies. ) 3 Function Theory 32 Like application, composition distributes over bunch union. f (g, h) = f g, f h (f, g) h = f h, g h Operators and functions are similar; each applies to its operands to produce a result. Just as we compose functions, we can compose operators, and we can compose an operator with a function. For example, we can compose – with any function f that produces a number to obtain a new function.
L] ⇐ ok In the other problem, not all items have been summed (n #L) . That means there is at least one more item to be added to the sum, so let us add one more item to the sum. To complete the refinement, we must also add any remaining items. #L] ⇐ s:= s+Ln. n:= n+1. #L] This refinement is proven by two applications of the Substitution Law. The final specification has already been refined, so we have finished programming. One point that deserves further attention is our use of n #L to mean that not all items have been summed.
A Practical Theory of Programming by Eric C.R. Hehner