kseo / systemf

An implementation of System F in Haskell

simple

An implementation of System F in Haskell

Overview

systemf is an implementation of System F presented by Benjamin C. Pierce in his Types and Programming Languages. I transliterated the original source code written in OCaml into Haskell except for the parser which I rewrote in Parsec.

Syntax

• Variables: x
• Applications: x x
• Lambda abstractions: \x.x
• Type abstractions: /\X.X
• Conditional: if x then y else z
• Booleans: true, false
• Universal quantification: All X.X->X
• Existential quantification : {*All Y.Y, \x:(All Y.Y). x} as {Some X,X->X}

Implementation Details

• The representation of a variable is a number - its De Brujin index
• Evaluation performs substitution

REPL

systemfi is a REPL where you can input a lambda calculus term.

% \x:Bool.x
(\x:Bool.x)
$ {*All Y.Y, \x:(All Y.Y). x} as {Some X,X->X}
(\x:(All X.(X->X)).x)