About the Church Numbering Program at Frege

Question

This program compiles and runs correctly under the GHC:

type Church a = (a -> a) -> a -> a

ch :: Int -> Church a
ch 0 _ = id
ch n f = f . ch (n-1) f

unch :: Church Int -> Int
unch n = n (+1) 0

suc :: Church a -> Church a
suc n f = f . n f

pre :: Church ((a -> a) -> a) -> Church a
pre n f a = n s z id
    where s g h = h (g f)
          z     = const a

main :: IO ()
main = do let seven = ch 7
              eight = suc seven
              six   = pre seven
          print (unch eight)
          print (unch six)

But when compiling with Frege, I got the following error:

E /home/xgp/work/flab/src/main/frege/flab/fold.fr:23: type error in expression seven
    type is : Int
    expected: (t1→t1)→t1
E /home/xgp/work/flab/src/main/frege/flab/fold.fr:23: type error in expression seven
    type is : (t1→t1)→t1
    expected: Int
E /home/xgp/work/flab/src/main/frege/flab/fold.fr:23: type error in expression seven
    type is : (t1→t1)→t1
    expected: Int
E /home/xgp/work/flab/src/main/frege/flab/fold.fr:23: type error in
    expression seven
    type is apparently Int
    used as function

Why? Is it possible to change the program to pass the compilation under Frege?

Answer 1

This is one of those rare cases where a generalization of the types of admissible related variables really matters.

, GHC -XMonoLocalBinds , . : https://github.com/Frege/frege/wiki/GHC-Language-Options-vs.-Frege#Let-Generalization : https://downloads.haskell.org/~ghc/latest/docs/html/users_guide/other-type-extensions.html#typing-binds ( SPJ, )

, , , , unannotated let bound veriabes . .

, seven

seven :: Church a

print/println: . , REPL:

frege> print 'a'
IO ()
frege> print 'b'
IO ()
frege> println "dammit!"
abdammit!
IO ()