Skip to content
Switch branches/tags

Name already in use

A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?
Go to file
Cannot retrieve contributors at this time
module LICK.ProgramType
%default total
||| The primitive types within the language are given explicitly with
||| this data type. User-defined types will be built from these.
public export
data ProgramType : Type where
||| A function between two types.
: (input : ProgramType)
-> (output : ProgramType)
-> ProgramType
||| The integer type.
PInt : ProgramType
||| If the domains don't match, the functions definitely don't.
: Not ( i = i' )
-> Not (PFunction i o = PFunction i' o')
domainsDoNotMatch f Refl
= f Refl
||| If the codomains don't match, the functions definitely don't.
: Not ( o = o')
-> Not (PFunction i o = PFunction i' o')
codomainsDoNotMatch f Refl
= f Refl
||| A function is not an integer.
: Not (PFunction i o = PInt)
functionIsNotInt Refl impossible
||| Decidable equality on program types.
public export
implementation DecEq ProgramType where
decEq PInt PInt
= Yes Refl
decEq PInt (PFunction i o)
= No (functionIsNotInt . sym)
decEq (PFunction i o) PInt
= No functionIsNotInt
decEq (PFunction i o) (PFunction i' o')
with (decEq i i', decEq o o')
decEq (PFunction i o) (PFunction i o)
| (Yes Refl, Yes Refl) = Yes Refl
decEq (PFunction i _) (PFunction i' _)
| (No contra, _) = No (domainsDoNotMatch contra)
decEq (PFunction _ o) (PFunction _ o')
| (_, No contra) = No (codomainsDoNotMatch contra)