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|
||| Abstract syntax for terms.
module Obs.Term
import Data.Fin
import Obs.Sort
import Text.Bounded
import Text.PrettyPrint.Prettyprinter
%default total
-- Definition ------------------------------------------------------------------
public export
data Term : Nat -> Type where
Var : WithBounds String -> Fin n -> Term n
-- Sorts
Sort : Bounds -> Sort -> Term n
-- Dependent Product
Pi : Bounds -> String -> Term n -> Term (S n) -> Term n
Lambda : Bounds -> String -> Term (S n) -> Term n
App : Term n -> Term n -> Term n
-- Dependent Sums
Sigma : Bounds -> String -> Term n -> Term (S n) -> Term n
Pair : Bounds -> Term n -> Term n -> Term n
Fst : Bounds -> Term n -> Term n
Snd : Bounds -> Term n -> Term n
-- True
Top : Bounds -> Term n
Point : Bounds -> Term n
-- False
Bottom : Bounds -> Term n
Absurd : Bounds -> Term n -> Term n -> Term n
-- Equality
Equal : Bounds -> Term n -> Term n -> Term n
Refl : Bounds -> Term n -> Term n
Transp : Bounds -> Term n -> Term n -> Term n -> Term n -> Term n -> Term n
Cast : Bounds -> Term n -> Term n -> Term n -> Term n
CastId : Bounds -> Term n -> Term n
public export
record Definition (n : Nat) where
constructor MkDefinition
bounds : Bounds -- of the name
name : String
ty : Term n
tm : Term n
public export
data Block : Nat -> Type where
Nil : Block 0
(:<) : Block n -> Definition n -> Block (S n)
-- Operations ------------------------------------------------------------------
export
fullBounds : Term n -> WithBounds (Term n)
fullBounds tm@(Var var i) = map (\_ => tm) var
fullBounds tm@(Sort x s) = MkBounded tm False x
fullBounds tm@(Pi x var a b) = mergeBounds (mergeBounds (fullBounds a) (fullBounds b)) (MkBounded tm False x)
fullBounds tm@(Lambda x var t) = mergeBounds (fullBounds t) (MkBounded tm False x)
fullBounds tm@(App t u) = map (\_ => tm) (mergeBounds (fullBounds t) (fullBounds u))
fullBounds tm@(Sigma x var a b) = mergeBounds (mergeBounds (fullBounds a) (fullBounds b)) (MkBounded tm False x)
fullBounds tm@(Pair x t u) = mergeBounds (mergeBounds (fullBounds t) (fullBounds u)) (MkBounded tm False x)
fullBounds tm@(Fst x t) = mergeBounds (fullBounds t) (MkBounded tm False x)
fullBounds tm@(Snd x t) = mergeBounds (fullBounds t) (MkBounded tm False x)
fullBounds tm@(Top x) = MkBounded tm False x
fullBounds tm@(Point x) = MkBounded tm False x
fullBounds tm@(Bottom x) = MkBounded tm False x
fullBounds tm@(Absurd x a t) = mergeBounds (mergeBounds (fullBounds a) (fullBounds t)) (MkBounded tm False x)
fullBounds tm@(Equal x t u) = mergeBounds (mergeBounds (fullBounds t) (fullBounds u)) (MkBounded tm False x)
fullBounds tm@(Refl x t) = mergeBounds (fullBounds t) (MkBounded tm False x)
fullBounds tm@(Transp x t b u t' e) = mergeBounds (mergeBounds (mergeBounds (fullBounds t) (fullBounds b)) (mergeBounds (fullBounds u) (fullBounds t'))) (mergeBounds (fullBounds e) (MkBounded tm False x))
fullBounds tm@(Cast x b e t) = mergeBounds (mergeBounds (fullBounds b) (fullBounds e)) (mergeBounds (fullBounds t) (MkBounded tm False x))
fullBounds tm@(CastId x t) = mergeBounds (fullBounds t) (MkBounded tm False x)
-- Pretty Print ----------------------------------------------------------------
export
Pretty (Term n) where
prettyPrec d (Var var _) = pretty var.val
prettyPrec d (Sort _ s) = prettyPrec d s
prettyPrec d (Pi _ var a b) =
parenthesise (d > Open) $
group $
parens (pretty var <++> colon <+> softline <+> prettyPrec Open a) <++>
pretty "->" <+> softline <+>
prettyPrec Open b
prettyPrec d (Lambda _ var t) =
parenthesise (d > Open) $
group $
backslash <+> pretty var <++>
pretty "=>" <+> softline <+>
prettyPrec Open t
prettyPrec d (App t u) =
parenthesise (d >= App) $
group $
fillSep [prettyPrec Open t, prettyPrec App u]
prettyPrec d (Sigma _ var a b) =
parenthesise (d >= App) $
group $
parens (pretty var <++> colon <+> softline <+> prettyPrec Open a) <++>
pretty "**" <+> softline <+>
prettyPrec Open b
prettyPrec d (Pair _ t u) =
angles $
group $
neutral <++> prettyPrec Open t <+> comma <+> softline <+> prettyPrec Open u <++> neutral
prettyPrec d (Fst _ t) =
parenthesise (d >= App) $
group $
fillSep [pretty "fst", prettyPrec App t]
prettyPrec d (Snd _ t) =
parenthesise (d >= App) $
group $
fillSep [pretty "snd", prettyPrec App t]
prettyPrec d (Top _) = pretty "()"
prettyPrec d (Point _) = pretty "tt"
prettyPrec d (Bottom _) = pretty "Void"
prettyPrec d (Absurd _ a t) =
parenthesise (d > Open) $
group $
fillSep [pretty "absurd", prettyPrec App a, prettyPrec App t]
prettyPrec d (Equal _ t u) =
parenthesise (d >= Equal) $
group $
prettyPrec Equal t <++> pretty "~" <+> softline <+> prettyPrec Equal u
prettyPrec d (Refl _ t) =
parenthesise (d >= App) $
group $
fillSep [pretty "refl", prettyPrec App t]
prettyPrec d (Transp _ t b u t' e) =
parenthesise (d >= App) $
group $
fillSep $
[ pretty "transp"
, prettyPrec App t
, prettyPrec App b
, prettyPrec App u
, prettyPrec App t'
, prettyPrec App e
]
prettyPrec d (Cast _ b e t) =
parenthesise (d >= App) $
group $
fillSep [pretty "cast", prettyPrec App b, prettyPrec App e, prettyPrec App t]
prettyPrec d (CastId _ t) =
parenthesise (d >= App) $
group $
fillSep [pretty "castRefl", prettyPrec App t]
export
Pretty (Definition n) where
pretty def = group $
pretty def.name <++> colon <+> softline <+> pretty def.ty <+> hardline <+>
pretty def.name <++> equals <+> softline <+> pretty def.tm
export
Pretty (Block n) where
pretty [] = neutral
pretty ([] :< def) = pretty def
pretty (blk :< def) = pretty blk <+> hardline <+> hardline <+> pretty def
|
