RFC for initial implementation of types for untyped contracts

Author: btlachance

rfcs/text/0000-basic-typed-contracts.md

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+- Feature Name: basic-typed-contracts
+- Start Date: 2019-06-30
+- RFC PR: (leave this empty)
+- Feature Commit(s): (leave this empty)
+
+# Summary
+
+Give TR typed analogues of the `racket/contract` module. This needs a
+new type constructor, `Contract`, to support higher-order
+contracts. And adding a `FlatContract` type constructor helps e.g. to
+give a more precise type to combinators like `not/c`.
+
+(The MS thesis related to this work is on my personal page at Tufts
+<https://www.eecs.tufts.edu/~blachanc/ms-thesis.pdf>. I don't yet have
+an arXiv link because I need to get my Scribble build working enough
+to at least get the intermediate TeX out.
+
+Any mention of "the current implementation" refers to the pull request
+at <https://github.com/racket/typed-racket/pull/420>.)
+
+# Motivation
+
+Racket programmers use the contract forms provided by
+`racket/contract` but there currently isn't a clear path for Typed
+Racket programmers to do the same. Without those forms, enforcing
+invariants outside of the type system's sweet spot is harder, and
+migrating contract-using Racket programs to Typed Racket is harder.
+
+The current implementation supports most of the data structure
+contracts in the contract documentation, and it also supports most of
+`->i`, `->*`, and `contract-out`.
+
+# Guide-level explanation
+
+## Basics/contracts over first-order types
+
+(Assumes a passing knowledge of Racket's contract library and TR's
+propositions. In typed contracts, I write `->/c` for Racket's `->`
+contract combinator.)
+
+Racket's contract system monitors how values flow through
+contracts. Using those same contracts in Typed Racket means we'll need
+to give typed values to the contract system, and so the type system
+will have to ensure that those values are used appropriately.
+
+We can use typed functions as contracts. To properly use a typed
+function, the type system has to ensure that the contract is only ever
+used to monitor values that agree with the function's type. Being a
+predicate on `Integer`s, we can use `even?` to monitor integers:
+
+`(contract even? -6 'pos 'neg)`
+`(contract even? 6 'pos 'neg)`
+
+We can also combine typed functions using contract combinators like
+`and/c`:
+
+`(contract (and/c even? positive?) 10 'pos 'neg)`
+
+When we combine contracts, we need to be careful that the combination
+makes sense. But first we need to talk about the types of the
+contracts *being* combined. We've already seen that we need to make
+sure a function is only used as a contract to monitor values of the
+right type. But one idiom in Racket is to write contracts like `(and/c
+exact-integer?  even?)`: Here, a (Racket) contract programmer uses the
+`exact-integer?` test to guard that `even?` in their contract is only
+applied to integers. Without the guard, `even?` might raise a runtime
+error (its own contract violation) unrelated to the contract the
+programmer wrote. To give types to these contracts, then, we need to
+know that whatever comes out of the `exact-integer?` contract is safe
+to flow into the `even?` contract. So in addition to needing to know
+the types of values a contract can be used on, we also need to know
+that what comes out of a contract is safe for some subsequent
+contract, like in `and/c`. Typed Racket's propositions help us uncover
+this last part.
+
+The two parts of a contract's type explain what the contract can be
+used on and what comes out of the contract. For `exact-integer?`, its
+function type says it can be used on `Any` and that it has a positive
+proposition for `Integer`, thus it has contract type `(Contract Any
+Integer)`. The type of `even?` is `(-> Integer Boolean)`, with no
+propositions, and so it has contract type `(Contract Integer
+Integer)`. We say that the first part of a contract's type is its
+*input type* and that the second part of a contract's type is its
+*output type*. For example, the input type of `exact-integer?` is
+`Any` and its output type is `Integer`.
+
+Back to type checking the combined contract, `(and/c exact-integer?
+even?)`. From the types above, we know that what comes out of
+`exact-integer?` can safely go in to `even?`. And since everything
+lines up, we take the the input type of the first contract type
+(`Integer`) and the output type of the last contract (`Integer`) and
+give the whole contract type `(Contract Any Integer)`.
+
+## Contracts on higher-order types
+
+If a function only consumes and produces positive reals, a Racket
+programmer might express that information using the contract `(->/c
+positive? positive?)`. In Typed Racket, that same information could be
+expressed with the type `(-> Positive-Real Positive-Real)`. So
+although that exact contract might not make sense in a Typed Racket
+program, we still want to give it a type---the path from Racket to
+Typed Racket isn't always smooth so we might be able to help the
+Racket programmer if we give a meaningful type to that contract.
+
+Starting with the function `positive?`, its type is `(-> Real
+Boolean)` and it has a positive proposition for `Positive-Real`. So
+based on what we saw in the previous section, it has the contract type
+`(Contract Real Positive-Real)`.
+
+The function contract combinator `->/c` wraps whatever function it is
+applied to, ensuring that a caller provides arguments that satisfy the
+domain contract and that the function returns a result that satisfies
+the range contract; Values flow from the caller through the domain
+contract into the function, and out of the function and through the
+range contract.
+
+This value flow is reflected in the type of a function contract. For
+our `(->/c positive? positive?)` the type is
+
+    (Contract (-> {2} Positive-Real Real {3})
+              (-> {1} Real Positive-Real {4}))
+
+In the output type of the contract, here a function type, the domain
+type is `Real` (marked `{1}`). This is because after applying the
+contract to a function, calling the result with a value will apply the
+domain contract (with input type `Real`) to that value. If the value
+passes the domain contract, we know it is a `Positive-Real` by the
+domain contract's output type, which is reflected in the input type's
+domain contract (marked `{2}`). This means that a function we apply
+this contract to has to accept `Positive-Real` values.
+
+In the input type of the contract, the range of the type is `Real`
+(marked `{3}`) because applying the contract to a function is only
+allowed if that function returns a value that can flow through the
+range contract (whose input type is `Real`). Finally, in the output
+type of the contract the range type is `Positive-Real` (marked `{4}`)
+because that's the output type of the range contract. This means that
+if we apply this contract to a function, then the resuling function
+returns at least a `Positive-Real` if it returns at all.
+
+# Reference-level explanation
+
+## Interaction with other features
+
+As far as I can tell contracts are mostly self-contained. Some
+exceptions:
+
+  - Predicates are subtypes of the `FlatContract` type.
+
+  - Values of `FlatContract` type are not functions (`FlatContract`
+    currently corresponds to Racket's `flat-contract?` which is `#t`
+    for e.g. numbers)
+
+  - Applying a function contract (with the current type rule for
+    contract application) combines the range type of the function
+    contract's output type with the range type of the function that
+    will be monitored. In the code this is called "pairwise
+    intersection" and in the thesis this is the `comb` operator.
+
+As far as subtyping goes, `(Contract S T)` and `(FlatContract S T)` is
+contravariant in `S` and covariant in `T`.
+
+## How the feature would be implemented
+
+The MS thesis linked up top gives type rules formalizing what I walked
+through in the guide-level explanation. It also discuss some of the
+implementation techniques used.
+
+(The current implementation may have some support for this part of the
+RFC, too.)
+
+## Corner cases
+
+Because I haven't worked out how to compile a contract type to a
+contract for typed/untyped interaction, typed code can't let untyped
+code use a value of contract type. At the moment I believe the current
+implementation raises an error (maybe an internal one?) when providing
+a value of contract type because I haven't defined a way to compile
+those types to contracts.
+
+I haven't properly looked at how these contract types interact with
+polymorphic types. Currently the only way to get primitive contracts
+with such a type are a predicates on values of some polymorphic type,
+e.g. a function like `null?`.
+
+# Drawbacks and Alternatives
+
+[drawbacks]: #drawbacks
+
+I don't see drawbacks in adding typed contracts themselves to Typed
+Racket; I see a potential drawback to the type system I've proposed.
+
+The rule for contract application is complicated by the two-argument
+`Contract` type, and it may not be worth the cognitive overhead. One
+reason for the two type arguments is so that the type computed by the
+`and/c` rule is not far from what you get from a sequence of contract
+applications (i.e. the `and/c` rule is privileged, but with the two
+type arguments it's not as privileged). But this may not be worth the
+complexity.
+
+Using a unary type constructor would remove the whole notion of input
+and output types, which could make for an easier type rule for the
+`and/c` combinator and for the other combinators, too.
+
+# Prior art
+[prior-art]: #prior-art
+
+I haven't seen a language that combines typed, higher-order contracts
+and subtyping---the combination seems to be unique to bringing
+Racket's contracts to Typed Racket. The current design is written up
+in the MS thesis linked up top.
+
+The original higher-oder contract paper [ff-icfp2002] uses contract
+types in a simply typed language, and that type system was also used
+in some work around higher-oder assertions and Haskell
+[hjl-flp2006]. The Haskell work supports polymorphism but doesn't have
+subtyping.
+
+- [ff-icfp2002] Robert Bruce Findler and Matthias Felleisen. Contracts
+for Higher-Order Functions. ICFP 2002
+- [hjl-flp2006] Ralf Hinze, Johan Jeuring, and Andres Löh. Typed
+Contracts for Functional Programming. Functional and Logic
+Programming, 2006.
+
+# Unresolved questions
+[unresolved]: #unresolved-questions
+
+> What parts of the design do you expect to resolve through the RFC
+> process before this gets merged?
+
+Whether the two-argument `Contract` type constructor and the
+corresponding contract application rule is too complex
+
+> What parts of the design do you expect to resolve through the
+> implementation of this feature before stabilization?
+
+Giving better error messages, simplifying tricky parts of the
+implementation (assuming that's in scope for "parts of the design";
+e.g. recovering the dependency identifiers in a ->i contract from a
+fully expanded program)
+
+> What related issues do you consider out of scope for this RFC that
+> could be addressed in the future independently of the solution that
+> comes out of this RFC?
+
+- Types for object contracts, unit contracts, parametric contracts
+  (i.e. `racket/contract/parametric`)
+
+- Typed/untyped interaction at contract types