Eric C.R. Hehner's A Practical Theory of Programming PDF
By Eric C.R. Hehner
Realizing programming and programming languages calls for wisdom of the underlying theoretical version. This booklet explores elements of programming which are amenable to mathematical evidence. the writer describes a programming concept that is a lot easier and extra finished than the present theories so far. within the theoretical version, a specification is simply a boolean expression and refinement is simply a typical implication. the writer develops a pragmatic and vast strategy for writing designated necessities and designing courses whose executions most likely fulfill the necessities. starting with preparatory fabric in good judgment, numbers, units, lists, features and kinfolk, the booklet advances extra into software concept, the center of the publication. next chapters can be chosen or passed over in keeping with direction emphasis. The textual content should be necessary 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 tested within the publication anywhere attainable. No complicated mathematical wisdom or programming language is thought. The publication includes a variety of workouts and worked-out strategies for particular workouts. Transparency masters and recommendations for the remainder routines can be found from the writer.
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Additional resources for A Practical Theory of Programming
0 Specification Notations For our specification language we will not be definitive or restrictive; we allow any well understood notations. Often this will include notations from the application area. When it helps to make a specification clearer and more understandable, a new notation may be invented and defined by new axioms. In addition to the notations already presented, we add two more. = σ′=σ ok = x′=x ∧ y′=y ∧ ... x:= e = = σ′ = σ address "x" e x′=e ∧ y′=y ∧ ... The notation ok specifies that the final values of all variables equal the corresponding initial values.
X:= x+y In part (g) we saw that x:= 1. y:= 2 = x′=1 ∧ y′=2 . If we use that, we are then faced with a dependent composition x′=1 ∧ y′=2. x:= x+y for which the Substitution Law does not apply. In a sequence of assignments, it is much better to use the Substitution Law from right to left. = x:= 1. x′ = x+2 ∧ y′=2 = x′=3 ∧ y′=2 (j) x:= 1. if y>x then x:= x+1 else x:= y This part is unremarkable. It just shows that the Substitution Law applies to ifs. = if y>1 then x:= 2 else x:=y (k) x:= 1. x′>x. x′ = x+1 We can use the Substitution Law on the first two pieces of this dependent composition to obtain = x′>1.
They talk about what a program “does”; of course it just sits there on the page or screen; it is the computer that does something. They ask whether a program “terminates”; of course it does; it is the behavior that may not terminate. A program is not behavior, but a specification of behavior. Furthermore, a computer may not behave as specified by a program for a variety of reasons: a disk head may crash, a compiler may have a bug, or a resource may become exhausted (stack overflow, number overflow), to mention a few.
A Practical Theory of Programming by Eric C.R. Hehner