| Runciman, C. and Jagger, N. 1990. Relative specification and transformational re-use of functional programs. Lisp and Symbolic Computation, 3:21--37. |
....precisely when the range of g is at least the range of f . A sufficient condition for h to exist is that the function g : C2 A be surjective, which is often the case in practice. In other cases, one can try strengthening the specification by adding extra requirements on h, in the manner of (Runciman and Jagger, 1990). Substituting y = h x in (1) gives an equivalent functional equality: f = g ffi h: 3) We can also express (1) in the form of a relational inclusion (4) by observing that h x = y iff x h y and that f x = g y iff x (g Gamma1 ffi f) y. Here functions are implicitly viewed as relations by ....
Runciman, C. and Jagger, N. 1990. Relative specification and transformational re-use of functional programs. Lisp and Symbolic Computation, 3:21--37.
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C. Runciman and N. Jagger, "Relative specification and transformational re-use of functional programs", Journal of Lisp and Symbolic Computation 3(1), pp. 21-37 (January 1990).
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