75.31. Teoría de lenguaje - Ejercicios Resueltos

Estos ejercicios pertenecen al libro Concepts, Techniques, and Models of Computer Programming, escrito por Peter Van Roy y Seif Haridi.

Section 1.1 uses the system as a calculator. Let us explore the possibilities:

1. Calculate the exact value of without using any new functions. Try to think of shortcuts to do it without having to type with one hundred 2s. Hint: use variables to store intermediate results.
2. Calculate the exact value of without using any new functions. Are there any possible shortcuts in this case?

Se puede simplificar de varias maneras.

V1=2*2*2*2*2
V2=V1*V1*V1*V1*V1 
V3=V2*V2*V2*V2

{Browse V3}

Matemáticamente sería:

Th is exercise investigates another way of introducing state: a memory store. The memory store can be used to make an improved version of FastPascal that remembers previously calculated rows.

We have given the memory store as a library. It turns out that the memory store can be defined by using a memory cell. We outline how it can be done and you can write the definitions. The cell holds the store contents as a list of the form , where the cons means that cell number has content .This means that memory stores, while they are convenient, do not introduce any additional expressive power over memory cells.

declare NewStore Size Put Get

fun {NewStore}
   {NewCell nil}
end

fun {Size S}
   fun {SizeAuxiliar S}
      fun {Max X Y} if X>Y then X else Y end end
   in
      case S of [H1 T1]|T then
	 {Max H1 {SizeAuxiliar T}}
      else
	 0
      end
   end
in
   {SizeAuxiliar @S}
end

proc {Put S N E}
   fun {PutAuxiliar S N E}
      case S of [H1 T1]|T then
	 if H1==N then
	    [H1 E]|T
	 else
	    [H1 T1]|{PutAuxiliar T N E}
	 end
      else
	 [N E]|S
      end
   end
in	
   S:={PutAuxiliar @S N E}
end

fun {Get S N}
   fun{GetAuxiliar S N}
      case S of [H1 T1]|T then
	 if H1==N then
	    T1
	 else
	    {GetAuxiliar T N}
	 end
      else
	 nil
      end
   end
in
   {GetAuxiliar @S N}
end

S={NewStore}
{Put S 1 [1 3 5]}
{Put S 2 454}
{Put S 3 [777 888]}
{Put S 7 'vanRoy'}

{Browse {Size S}}

{Browse {Get S 1}}
{Browse {Get S 2}}
{Browse {Get S 3}}
{Browse {Get S 4}}