Write You a Haskell Stephen Diehl

(+) : Int → Int → Int
(×) : Int → Int → Int
(−) : Int → Int → Int
(=) : Int → Int → Bool
Literals
e type of literal integer and boolean types is trivially their respective types.
Γ ⊢ n : Int
Γ ⊢ True : Bool
Γ ⊢ False : Bool
(T-Int)
(T-True)
(T-False)
Constraint Generation
e previous implementation of Hindley Milner is simple, but has this odd property of intermingling
two separate processes: constraint solving and traversal. Let’s discuss another implementation of the
inference algorithm that does not do this.
In the constraint generation approach, constraints are generated by bottom-up traversal, added to a ordered
container, canonicalized, solved, and then possibly back-substituted over a typed AST. is will be the
approach we will use from here out, and while there is an equivalence between the “on-line solver”, using
the separate constraint solver becomes easier to manage as our type system gets more complex and we
start building out the language.
Our inference monad now becomes a RWST ( Reader-Writer-State Transformer ) + Except for typing
errors. e inference state remains the same, just the fresh name supply.
-- | Inference monad
type Infer a = (RWST
Env
-- Typing environment
[Constraint] -- Generated constraints
InferState -- Inference state
(Except
-- Inference errors
TypeError)
a) -- Result
-- | Inference state
data InferState = InferState { count :: Int }
Instead of unifying type variables at each level of traversal, we will instead just collect the unifiers inside
the Writer and emit them with the uni function.
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