[YouAreGreat]

> "A type system is a syntactic method for enforcing levels of abstraction in programs. " [1]

> What syntactic methods are used in dynamically "typed" languages?

Interesting. You may have unwittingly provided one of the best justifications for the term "dynamically typed" I've seen so far.

That's because operations that violate a (safe) dynamically typed language's chosen set of abstractions (built using bits, church encoding, whatever) are syntactically inaccessible.

[naasking]

> That's because operations that violate a (safe) dynamically typed language's chosen set of abstractions (built using bits, church encoding, whatever) are syntactically inaccessible.

They are semantically inaccessible, not syntactically inaccessible. These languages enforce abstractions by attaching meaning to the tags implicit to all values, and these meanings combined with the operation are what drive the next evaluation step, ie. success or raise error value. This is not what happens in typed languages.

Lexical scoping is an example of a syntactic method commonly employed by dynamically typed languages. It's possibly the only one.

Edit: I have both of Pierce's "Types and Programming Languages", and "Advanced Topics in Types and Programming Languages". "Dynamic typing" is mentioned exactly once, on page 2 of the first text where Pierce says:

> The word "static" is sometimes added explicitly [...] to distinguish the sorts of compile-time analysis we are considering here from the dynamic or latent typing found in languages such as Scheme, where runtime type tags are used to distinguish different kinds of structures on the heap. Terms like "dynamically typed" are arguably misnomers and should probably be replaced by "dynamically checked".

[YouAreGreat]

> semantically inaccessible, not syntactically inaccessible.

You can give the semantics of everything that happens in a safe d-t language in terms of church encoded tag-value pairs and yet the programmer can't break the abstraction because abstraction-breaking operations are syntactically unavailable.

It should count as testament to the success of dynamic typing that the abstractions are so safely enforced that you can squint and suddenly the whole language is semantically founded on them.

[naasking]

> You can give the semantics of everything that happens in a safe d-t language in terms of church encoded tag-value pairs and yet the programmer can't break the abstraction because abstraction-breaking operations are syntactically unavailable.

This strikes me as just a Turing tarpit argument. Sure you can represent and enforce semantics syntactically, and you can probably also do this via automatic translations in many or most cases. Why is this compelling? And what does this have to do with types?

The definition of type system I gave is, "a syntactic method for enforcing levels of abstraction in programs". Ergo, not all syntactic methods qualify as a type system, but a specific kind of syntactic method classify type systems. Why do you think your translation qualifies?