Contents:

1. Adding Run-time environment to interpreter
   1. Pascal
      1. Built-In:
      2. Enumeration types.
      3. Subranges
      4. Arrays
      5. Variant records
      6. Pointers
      7. Sets
      8. Sequential files
      1. Problems with Types in Pascal
         1. Name EquivalenceA
         2. Name Equivalence (called declaration equivalence in text)
         3. Structural Equivalence
   2. Ada
      1. Built-In:
      2. Enumeration types.
      3. Subranges
      4. Arrays
      5. Ada Subtypes and derived types:
      1. Compare Ada's solutions w/ Pascal's problems:
   3. Type completeness principle:
   4. Summary of types so far:
2. STORAGE
   1. Program Units:
      1. To call:
      2. To return:
   2. Memory allocation
      1. Static using FORTRAN as example

Adding a run-time environment to interpreter

We normally expect that if we change the names of formal parameters that it should not make any difference, but ...

Suppose we evaluate:

   let  fun g x y = x + y  in g y end;

   (fn g => g y) (fn x => fn y => x+y))

   fn y => y + y

We should get: fn w => y + w, which has a very different meaning!!

(Note that we did not run into this problem earlier since during our evaluations we never worked with terms with free variables - when going inside functions we replaced all formal parameters by the actual parameters, which didn't involve free variables).

A different order of evaluation would have brought forth the same problem, however.

We would like to have fn x => B to represent the same function as
fn y => B[x:=y] as long as y doesn't occur freely in B. (Called alpha-conversion)

If you always alpha-convert to a new bound variable before substituting in, will never have problems.

Evaluate terms via environments:

Env = string -> values

An environment, rho, tells value of identifiers in term.

Write [[e]] rho for meaning of e with respect to environment rho.

E.g. if rho(x) = 12 and rho(y) = 2, then [[x+y]] rho = 14.

How does function application result in change of environment?

[[(fn x => body) actual]]rho = [[body]] rho [ [[actual]]rho / x]

where rho[v / x] is environment like rho except x has value "v".

This and rec are the only rules in which the environment changes!

Rest of rules look like the old interpreter (except identifiers looked up in environment)!

Replaces all uses of subst!

This means that computation no longer takes place by rewriting terms into new terms, interp is now a function from term to value.

Note that

	let val x = arg in e

	(fn x => e) arg

   val test = let 
                  val x = 3;
                  fun f y = x + y;
                  val x = 12
              in 
                  x + (f 7)
              end;

Change in scope is reflected by change in environment.

With functions must remember environment function was defined in!

When apply function, apply in defining environment.

test is equivalent to

   (fn x => (fn f => ((fn x => x + (f 7)) 12) (fn y => x + y))) 3

 
   [[(fn x => (fn f => ((fn x => x + (f 7)) 12) (fn y => x + y))) 3]] rho0
	= [[(fn f => ((fn x => x + (f 7)) 12) (fn y => x + y)) ]] rho1
	= [[(fn x => x + (f 7)) 12]] rho2
	= [[x + (f 7)]] rho3
	= 12 + ([[fn y => 3 + y]] rho1) 7
	= 12 + [[3 + y]] rho4
	= 12 + 3 + 7 
	= 22

   rho1 = rho0 [ [[3]] rho0 / x] = rho0[ 3 / x]
   rho2 = rho1 [ [[fn y => x + y]] rho1 / f] 	<-	Closure for f
   rho3 = rho2 [ [[12]] rho2 / x] = rho2[ 12 / x]
   rho4 = rho1 [ 7 / y]

Pascal

Built-In:

Enumeration types. Subranges

Arrays

Array [1..10, 'a'..'z'] of Real = Array [1..10] of Array ['a'..'z'] of Real

User fooled into thinking Array[A,B] of C is AxB->C, but really A->B->C.

Any discrete type as index.

No semi-dynamic arrays. Result of 2 principles:

1. All types must be determinable at compile time.

2. Array bounds are part of type.

Therefore, must have statically determinable array bounds.

3. Type of actual parameters must agree w/ type of formals

Therefore, no general sort routines, etc.

The major problem with Pascal

Variant records

Pointers

Sets

Sequential files

Problems with Types in Pascal

		Procedure x(...; procedure y;...)

			:

			y(a,2);

No checking if type of file read in matches what was originally written.

2. Problems w/ type compatibility

Assignment compatibility:

When is x := y legal? x : integer, y : 1..10? reverse?

What if type hex = 0..15; ounces = 0..15;

var x : hex; y : ounces;

Is x := y legal?

Original report said both sides must have identical types.

When are types identical?

Ex.:

    Type    T = Array [1..10] of Integer;
    Var  A, B : Array [1..10] of Integer;
             C : Array [1..10] of Integer;
             D : T;
             E : T;

Name EquivalenceA

Name Equivalence (called declaration equivalence in text)

--> A, B and D, E only.

Structural Equivalence

Structural not always easy. Let

  T1 = record a : integer; b : real  end; 
  T2 = record c : integer; d : real  end;
  T3 = record b : real; a : integer  end;

Worse:

  T = record info : integer; next : ^T  end; 
  U = record info : integer; next : ^V  end; 
  V = record info : integer; next : ^U  end; 

Ada uses Name EquivalenceA

Pascal & Modula-2 use Name Equivalence for most part. Check!

Modula-3 uses Structural Equivalence

Two types are assignment compatible iff

1. have equivalent types or

2. one subrange of other or

3. both subranges of same base type.

Ada

Built-In:

Enumeration types.

e.g., type Boolean is (False, True)

Can overload values:

    Color is (Red, Blue, Green)
    Mood is (Happy, Blue, Mellow)

    Color(Blue), Mood(Blue)

Subranges

i.e., Hex is range 0..15

Other attributes available to modify type definitions:

	Accurate is digits 20
	Money is delta 0.01 range 0.00 .. 1000.00     -- fixed pt!

	Hex'FIRST -> 1
	Hex'LAST  -> 15

	declare k : integer := 0

	type Two_D is array (1..10, 'a'..'z') of Real 

	type Real_Vec is array (INTEGER range <>) of REAL;

Of course, to use, must specify bounds,

	declare x : Real_Vec (1..10)

   Procedure sort (Y: in out Real_Vec; N: integer) is -- Y is open array parameter
      Temp1 : Real_Vec(1..N);             -- depends on N
      Temp2 : Real_Vec (Y'FIRST..Y'LAST); -- depends on parameter Y
      begin 
         for I in Y'FIRST ..Y'LAST loop
            ...
         end loop;
         ... 
      end sort;

All unconstrained types (w/ parameters) elaborated at block entry (semi-dynamic)

String type is predefined open array of chars:

	array (POSITIVE range <>) of character;

Can take slice of 1-dim'l array.

E.g., if

    Line : string(1..80)

    Line(10..20) := ('a','b',.'c','d','e','f','g','h','i','j')  
                                         -- gives assignment to slice

Ada Subtypes and derived types:

and dynamic properties - checked at run time

Example of dynamic are range, subscript, etc.

Specify dynamic properties by defining subtype. E.g.,

   subtype digit is integer range 0..9;

	subtype short_vec is Real_Vec(1..3);
	subtype square_type is geometric (square)

Therefore can mix different subtypes of same type w/ no problems

Derived types define new types:

	type Hex is new integer 0..15
	type Ounces is new integer 0..15

Can convert from one to other:

	Hex(I), Integer(H), Hex(Integer(G))

	E.g., Hex gets 0,1,2,... +,-,*,...

Compare Ada's solutions w/ Pascal's problems:

Helped by removing dynamic features from def of type subrange or index of array.

Can now have open array parameters (also introduced in ISO Pascal).

Variants fixed

Name equivalence in Ada to prevent mixing of different types. E.g., can't add Hex and Ounce.

Can define overloaded multiplication such that if

	l:Length;
	w:Width;

Type completeness principle:

Avoid second-class types.

Ex. in Pascal: Restrictions on return values of functions, lack of procedure variables, etc.

ML comes much closer to satisfying.

Summary of types so far:

Modern tendency to strengthen static typing and avoid implicit holes in types system.

- usually explicit (dangerous ) means for bypassing types system, if desired

Try to push as many errors to compile time as possible by:

• Requiring overspecification through typing

• Distinguishing btn diff. uses of same types (name equiv.)

• Mandating constructs designed to eliminate typing holes

• Minimizing or eliminating use of explicit pointers (esp. user-controlled deallocation of ptrs).

Important direction of current research in computer science:

Provide type safety, but increase flexibility.

Important progress over last 20 years:

Polymorphism, ADT's, Subtyping & other aspects of object-oriented languages.

STORAGE

What are storable values of language? Those that cannot be selectively updated.

Varies between languages.

Pascal: primitive (integer, real, char, boolean), sets, pointers

ML: primitive, records, tuples, lists, function abstractions, ref's to vbles.

Examine how variables allocated and lifetime.

Program Units:

E.g. Procedures, functions, and blocks (from ALGOL 60 & C, like parameterless procedures located in-line.)

Program unit represented during execution by unit instance, composed of code segment and activation record (gives info on parameters and local variables, and where to return after execution).

Activation Record Structure:

Return address

Access info on parameters

Space for local variables

Units often need access to non-local variables.

How is procedure call made?

To call:

2. Save state of caller (register, prog. counter).

3. Make sure callee knows how to find where to return to.

4. Enter callee at 1st instruction.

To return:

2. Caller restores state.

3. If fcn, make sure result value left in accessible location (register, on top of stack, etc.)

Memory allocation

Static: E.g. FORTRAN and COBOL.

Stack-Based: E.g. ALGOL-like languages (including Pascal and C).

Dynamic: LISP, PROLOG, APL, ML, Miranda, Eiffel, etc. as well as aspects of Pascal, Ada, etc.

Static using FORTRAN as example

All storage (local and global) known at translation time (hence static).

Activation records can be associated with each code segment.

Structure:

Return address

Access info on parameters

Space for local variables

At compile time, both instructions and vbles can be accessed by

(unit name, offset)

At link time can resolve to absolute addresses.

Global info shared via common statement:

COMMON/NAME1/A,B,S(25)

Statement must occur in all units wishing to share information. Name of the block must be identical, though can give different names to variables. (Gives rise to holes in typing) Identifiers are matched in order w/ no checking of types across unit boundaries.

Space for all common blocks allocated and available globally.

Procedure call and return straightforward