D. v. Oheimb. Datentypspezifikationen in Higher-Order LCF. Master's thesis, Computer Science Department, Technical University Munich, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....values (which will be introduced formally in x5.2.3) may serve to illustrate this test, as it cannot be discharged by the structural rules described above. See x10 for several further applications. Recursive Domains. HOLCF provides a package for the convenient definition of recursive domains [Ohe95] It can handle mutually recursive definitions of free datatypes commonly used in functional programming, even infinite ones with non strict constructors. It determines and proves the characteristic properties of each domain defined, including freeness, as well as induction and coinduction ....

....n = take 0 s = take (Suc n) nil = nil take (Suc n) a # s) a # take n s Furthermore, several proof principles are derived, which will be discussed in x6.4. For more details about the domain package, especially concerning its logical foundations, the reader is referred to [MNOS98, Ohe95] We are now capable to capture the three flavors of sequences formally. Definition 6.2.2 (Finite, Partial, Infinite) The set fin of finite total sequences is defined inductively as the least set of sequences satisfying the following two rules: nil 2 fin (Finite 0) s 2 fin a 6= a # s 2 ....

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D. v. Oheimb. Datentypspezifikationen in Higher-Order LCF. Master's thesis, Computer Science Department, Technical University Munich, 1995.

....and infinite sequences are defined by the simple recursive domain equation domain (ff)sequence = nil j (ff)#(lazy (ff)sequence) 1) where nil and the cons operator # are the constructors of the datatype. # is strict in its first argument and lazy in the second. The datatype package of HOLCF [Ohe95] automatically proves a number of user relevant theorems concerning the constructors, discriminators, and selectors of the datatype, as well as induction and co induction principles. For example, hd(nil) and tl( are generated automatically. Definition (1) means that elements of type ....

D. v. Oheimb. Datentypspezifikationen in Higher-Order LCF. Master's thesis, Computer Science Department, Technical University Munich, 1995.

....standard domains. tr, the truth values, which are HOLCF s counterpart to HOL s bool, is a flat domain with the elements TT, FF and . Operations on them include andalso, orelse and neg, which are strict extensions of the standard predicates , and : on bool. HOLCF also provides a datatype package [14] that allows to introduce pcpo datatypes as simple recursive domain equations. The package proves a number of theorems concerning the constructors, discriminators, and selectors of the datatype, as well as induction and co induction principles. For example, the following equation domain ....

D. v. Oheimb. Datentypspezifikationen in Higher-Order LCF. Master's thesis, Computer Science Department, Technical University Munich, 1995.

....finite and infinite sequences are defined by the simple recursive domain equation domain (ff)sequence = nil j (ff)#(lazy (ff)sequence) where nil and the cons operator # are the constructors of the datatype. # is strict in its first argument and lazy in the second. The datatype package of HOLCF [24] automatically proves a number of user relevant theorems concerning the constructors, discriminators, and selectors of the datatype, as well as induction and co induction principles. For example, hd(nil) and tl( are generated automatically. See the next section for a short account of the ....

D. v. Oheimb. Datentypspezifikationen in HigherOrder LCF. Master's thesis, Computer Science Department, Technical University Munich, 1995.

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