Question about type unification
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Date:   (:) 
From:  Jeremy Yallop <jeremy.yallop@e...> 
Subject:  Re: [Camllist] Question about type unification 
Robert Fischer wrote: > How is the compiler magically getting from the float to a string value? Can someone break down > what's actually happening here for me? Type aliases are analogous to functions. If you have a variable "f" that denotes a pure function and some values u1 ... un and v1 ... vn then to determine whether f u1 ... un is equal to f v1 ... vn you call the function (twice) by substituting u1 ... un and v1 ... vn for the parameters. If you have a constant function f = fun _ ... _ = v then any application of the function will give the same result (v) regardless of the values of the arguments. Analogously, if you have a type constructor "t" that denotes a type alias and some types s1 ... sn and t1 ... tn then to determine whether (s1, ... sn) t is equal to (t1, ... tn) t you "call" the type alias by substituting s1 ... sn and t1 ... tn for the type parameters. If you have a "constant" type alias in which none of the type parameters appear on the right hand side of the definition type ('a1, ... 'an) t = e a1...an not in fv(e) then any application of the type constructor will give the same result (e) regardless of the values of the arguments. Nominal types are analogous to constructors. (By "nominal" I mean record and sum types, or types made abstract using a module signature.) If you have a data constructor "C" and some values u1 ... un and v1 ... vn then to determine whether C u1 ... un is equal to C v1 ... vn you check whether ui is equal to vi for each i. Analogously, if you have a type constructor "s" that denotes a nominal type and some types s1 ... sn and t1 ... tn then to determine whether (s1, ... sn) s is equal to (t1, ... tn) s you check whether si is equal to ti for each i. In Richard's example "t" denotes a type alias. Thus to determine whether unit t is equal to string t we look at the definition of t: type 'a t = float then replace each 'a that occurs on the right hand side first with "unit" and then with "string" and compare the results. In this case "'a" doesn't appear at all on the right hand side of the definition so we compare "float" with "float", and find that the two are equal, i.e. "unit t" and "string t" denote the same type (float). Jeremy.