Write You a Haskell Stephen Diehl

[s]τ = [s]τ ′
Two identical terms are trivially unifiable by the empty unifier.
c ∼ c : [ ]
e unification rules for our little HM language are as follows:
c ∼ c : []
α ∼ α : []
α /∈ ftv(τ)
α ∼ τ : [α/τ]
α /∈ ftv(τ)
τ ∼ α : [α/τ]
τ 1 ∼ τ ′ 1 : θ 1 [θ 1 ]τ 2 ∼ [θ 1 ]τ ′ 2 : θ 2
τ 1 τ 2 ∼ τ ′ 1 τ ′ 2 : θ 2 ◦ θ 1
τ 1 ∼ τ ′ 1 : θ 1 [θ 1 ]τ 2 ∼ [θ 1 ]τ ′ 2 : θ 2
τ 1 → τ 2 ∼ τ ′ 1 → τ ′ 2 : θ 2 ◦ θ 1
(Uni-Const)
(Uni-Var)
(Uni-VarLeft)
(Uni-VarRight)
(Uni-Con)
(Uni-Arrow)
ere is a precondition for unifying two variables known as the occurs check which asserts that if we are
applying a substitution of variable x to an expression e, the variable x cannot be free in e. Otherwise
the rewrite would diverge, constantly rewriting itself. For example the following substitution would not
pass the occurs check and would generate an infinitely long function type.
[x/x → x]
e occurs check will forbid the existence of many of the pathological livering terms we discussed when
covering the untyped lambda calculus, including the omega combinator.
occursCheck :: Substitutable a => TVar -> a -> Bool
occursCheck a t = a ‘Set.member‘ ftv t
e unify function lives in the Infer monad and yields a subsitution:
unify :: Type -> Type -> Infer Subst
unify (l ‘TArr‘ r) (l’ ‘TArr‘ r’) = do
s1