Writes a Lambda type into a text representation.

import Lambda exposing (Type(..))
import Lambda.Write


-- Builtin types
Lambda.Write.type_ IntType --> "@Int"
Lambda.Write.type_ NumType --> "@Num"


-- Named types
Lambda.Write.type_ (Type "T") --> "T"


-- Abstraction types
Lambda.Write.type_ (AbsType (Type "A") (Type "B")) --> "A->B"
Lambda.Write.type_ (AbsType (Type "A") (AbsType (Type "B") (Type "C"))) --> "A->B->C"
Lambda.Write.type_ (AbsType (AbsType (Type "A") (Type "B")) (Type "C")) --> "(A->B)->C"

Writes a Lambda expression into a text representation.

import Lambda exposing (Expr(..))
import Lambda.Write


-- Values
Lambda.Write.expression (Int 42) --> "42"
Lambda.Write.expression (Num 3.14) --> "3.14"


-- Variables
Lambda.Write.expression (Var "x") --> "x"


-- Abstractions
Lambda.Write.expression (Abs "x" (Var "y")) --> "λx.y"
Lambda.Write.expression (Abs "x" (Abs "y" (Var "z"))) --> "λx.λy.z"


-- Applications
Lambda.Write.expression (App (Var "f") (Var "x")) --> "f x"
Lambda.Write.expression (App (App (Var "f") (Var "x")) (Var "y")) --> "f x y"
Lambda.Write.expression (App (Var "f") (App (Var "x") (Var "y"))) --> "f (x y)"
Lambda.Write.expression (Abs "x" (App (Var "y") (Var "z"))) --> "λx.y z"


-- Variable definitions (syntax sugar)
Lambda.Write.expression (App (Abs "x" (Var "z")) (Var "y")) --> "x=y; z"