Write You a Haskell Stephen Diehl

Type Mismatch: Bool is not Nat
Arith> if 0 then true else false
Type Mismatch: Nat is not Bool
is is good, we’ve made a whole class of illegal programs unrepresentable. Lets do more of this!
Simply Typed Lambda Calculus
e simply typed lambda calculus ( STLC ) of Church and Curry is an extension of the lambda calculus
that annotates each lambda binder with a type term. e STLC is explictly typed, all types are present
directly on the binders and to determine the type of any variable in scope we only need to traverse to its
enclosing scope.
e := x
e 1 e 2
λx : τ.e
e simplest STLC language is these three terms, however we will add numeric and boolean literal terms
so that we can write meaningful examples.
e := x
e 1 e 2
λx : τ.e
n
true
false
if e then e else e
We can consider a very simple type system for our language that will consist of Int and Bool types and
function types.
τ := Int
Bool
τ → τ
Type Checker
e typing rules are quite simple, and again we get the nice property that there is a one-to-one mapping
between each syntax term and a typing rule.
62