Programming Languages (CS302 2006S)
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Back to Types (2). On to Declarative Langauges.
Held: Friday, April 7, 2006
Summary: Today we conclude our exploration of types by exploring notions of type equivalence.
Related Pages:
Notes:
return homework and distribute examday.
Overview:
appropriateplaces.
eqv?
in Scheme requires
some careful consideration of when functions or pairs are equivalent.
type xy = record x: integer; y: real; end; xy_alias = xy; ab = record a: integer; b: real; end; yx = record y: real; x: integer; end; abc = record a: integer; b: real; c: real; end; intrec = record x: integer; end; iarr = array[1..10] of integer; iare = array[2..11] of integer; var rec1: xy; rec2: xy_alias; rec3: ab; rec4: abc; rec5,rec6: record a: integer; b: real; end; rec7: record a: integer; b: real; end; rec8: yx; rec9: intrec; rec10: xy; arr1: iarr; arr2: iare; arr3,arr4: array[1..10] of integer; arr5: array[1..10] of integer;
rec1
and rec3
are structurally equivalent as
they are both pairs of (integer,real).
rec1
and rec8
are not structurally equivalent,
as they order their elements differently.
rec1
and rec3
are not structurally
equivalent under naming as they name their pairs differently.
rec3
and rec6
are structurally equivalent
under naming.
rec1
and rec2
are not name equivalent.
rec1
and rec10
are name equivalent.
realequivalence, it may be difficult to determine in the presence of pointers (explicit or implicit) and inclusion.
type alpha = record i1: integer; i2: integer; end; aardvark = record i1: integer; i2: integer; beta = record i: integer; a: alpha; end; bandicoot = record i: integer; a: aardvark; end;
alpha
and aardvark
are clearly equivalent.
Are beta
and bandicoot
? How do you tell?
type listp = pointer to list; list = record i: integer; next: listp; end; lstp = pointer to lst; lst = record i: integer; next: lstp; end;
type gammap = pointer to gamma; deltap = pointer to delta; gamma = record i: integer; next: deltap; end; delta = record i: integer; next: gammap; end;
More generaltypes to
less generaltypes? (E.g., real to int.)
Less generaltypes to
more generaltypes? (E.g., int to real.)
3 + "4"
in languages that can convert strings to integers.
ab
and abc
above.
what isin type systems, we might also reflect on
what might be.
base typesin our system.
Back to Types (2). On to Declarative Langauges.
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