| Some example code for Pure2 in System F
| Copyright 2008, K.D.P.Ross <kyle@osl.iu.edu>
|
| This program is free software; you can redistribute it and/or
| modify it under the terms of the GNU General Public License as
| published by the Free Software Foundation; either version 2 of the
| License, or (at your option) any later version.
|
| This program is distributed in the hope that it will be useful, but
| WITHOUT ANY WARRANTY; without even the implied warranty of
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
| General Public License for more details.
|
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| along with this program; if not, write to the Free Software
| Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
| USA

CHECKS

| Define our PTS

-- System F (polymorphic lambda calculus)
sort  Set Type.
axiom Set : Type.
rule  Set  -> Set.
rule  Type -> Set.


| Some polymorphic functions

-- standard polymorphic identity function
id = \ (a : Set)(prfA : a) -> prfA.
id : (a : Set) a -> a.

-- function composition
compose = \ (a b c : Set)(f : b -> c)(g : a -> b)(x : a) -> f (g x).
compose : (a b c : Set)(b -> c) -> (a -> b) -> a -> c.


| Some base datatypes

-- standard Peano `Nat`s
assume Nat : Set.
assume Zro : Nat.
assume Suc : Nat -> Nat.

-- posit an addition function
assume Add : Nat -> Nat -> Nat.


| Put it all together

-- compose some functions
composeNatTest = compose Nat Nat Nat (id Nat) (Add (Suc Zro)).
composeNatTest : Nat -> Nat.