C.Bhm, A.Berarducci: Automatic synthesis of typed l-programs on term algebras, Theoretical Computer Science, 39, pp. 135-154, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....have an F 1 term, a , such that E # 1 a : A and E # : aa : A . The thesis then follows by the identity coercions lemma and (Eq appl) M 3. Expressiveness Since F : is an extension of F, one can already carry out all the standard encodings of algebraic data types that are possible in F [BB 85] However, it is not clear that anything of further interest can be obtained from the subtyping rules of F : which involve only an apparently useless type Top and the simple rules for and . In this section we begin to show that we can in fact construct rich subtyping relations on familiar ....

....two records are equivalent if they coincide on the components that are observable at a given type. This holds ultimately because any two values are equivalent at type Top. Page 28 3.6. Lists Following the pattern used in the encoding of Naturals, we can define the algebra of parametric lists [BB 85] List[A] stands for the homogeneous lists of type A. List[A] L) L(ALL)L We have: A : B List[A] List[B] nil: A) List[A] l(A) l(L) l(n:L) l(c:ALL) n cons: A) AList[A]List[A] l(A) l(hd:A) l(tl:List[A] l(L) l(n:L) l(c:ALL) c(hd) tl(L) n) c) length: A) List[A]Nat l(A) ....

C.Bhm, A.Berarducci: Automatic synthesis of typed l-programs on term algebras, Theoretical Computer Science, 39, pp. 135-154, 1985.

....a , such that E # 1 a : A and E # : aa : A . The thesis then follows by the identity coercions lemma and (Eq appl) M Page 25 3. Expressiveness Since F : is an extension of F, one can already carry out all the standard encodings of algebraic data types that are possible in F [BB 85] However, it is not clear that anything of further interest can be obtained from the subtyping rules of F : which involve only an apparently useless type Top and the simple rules for and . In this section we begin to show that we can in fact construct rich subtyping relations on familiar ....

....two records are equivalent if they coincide on the components that are Page 30 observable at a given type. This holds ultimately because any two values are equivalent at type Top. 3.6. Lists Following the pattern used in the encoding of Naturals, we can define the algebra of parametric lists [BB 85] List[A] stands for the homogeneous lists of type A. List[A] L) L(ALL)L We have: A : B List[A] List[B] nil: A) List[A] l(A) l(L) l(n:L) l(c:ALL) n cons: A) AList[A]List[A] l(A) l(hd:A) l(tl:List[A] l(L) l(n:L) l(c:ALL) c(hd) tl(L) n) c) length: A) List[A]Nat l(A) ....

C.Bhm, A.Berarducci: Automatic synthesis of typed l-programs on term algebras, Theoretical Computer Science, 39, pp. 135-154, 1985.

....them to first order (types to types) Higher order operators embody a surprising expressive power; they define one of the largest known classes of total functions [Girard 71] and every free algebra with total operations (booleans, integers, lists, trees, etc. is uniformly representable in them [Bhm Berarducci 85] see the example below for booleans) Because of this, we believe they will turn out to be very useful for parametrization and for carrying out compile time computations. An operator has the form: Fun(S)A where S is a signature introducing only type variables, and A is a type. The kind of an ....

C.Bhm, A.Berarducci: Automatic synthesis of typed l-programs on term algebras, Theoretical Computer Science, 39, pp. 135-154, 1985.

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C.Bhm, A.Berarducci: Automatic synthesis of typed l-programs on term algebras, Theoretical Computer Science, 39, pp. 135-154, 1985.

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