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Could someone give me a clear distinction between latent and manifest type system?
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The main difference between latent and manifest functions is that latent functions are unintended, but manifest functions are intended and planned. In sociology, a function is any consequence of social practice or structure that positively affects society and impacts structural continuity.
For instance, if a rule is made, the manifest function will be the intended function for the fulfillment of which the rule is made. On the contrary, the unintended function is the latent function, e.g. if the rule is made in order to maintain peace, but it harms the public, that harm will be the latent function.
Manifest function refers to the intended function of social policies, processes, or actions that are consciously and deliberately designed to be beneficial in their effect on society. Meanwhile, a latent function is one that is not consciously intended, but that, nonetheless, has a beneficial effect on society.
A manifest social problem is the harmful myth of the American Creed. A latent social problem is the emerg- ing values which contend that discrimi- nation is inhuman or immoral. In order to remain neutral in study- ing social problems, the sociologist may not question the values of the group.
Sometimes, the same concept gets invented independently in different areas of computer science. This is one of those occasions. What the Scheme community calls latent and manifest typing, the rest of the world calls implicit and explicit typing. The meaning is exactly the same:
In explicit / manifest typing, the programmer has to explicitly write down the types, thus the types become manifest in the source code.
In implicit / latent typing, the programmer does not write down the types. The types are thus implicit or latent.
Please note that the question of implicit vs. explicit typing is completely orthogonal to e.g. dynamic vs. static typing, strong vs. weak typing, sound vs. unsound typing, safe vs. unsafe typing and nominal vs. structural vs. duck typing.
Haskell for example is implicitly, strongly, statically, sound, safe, structurally typed.
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See Anton van Straaten's post on Lambda the Ultimate. It describes latent typing in the context of Scheme.
Manifest typing would be used in a statically typed language where the type of a term is declared syntactically or can be inferred at compile time from other such terms.
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