PCase16.hs

{-# LANGUAGE QuasiQuotes      #-}
{-# LANGUAGE DataKinds          #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeAbstractions    #-}
{-# LANGUAGE TypeApplications    #-}

{-# OPTIONS_GHC -Wall -Werror -ddump-splices #-}

module T where

import Expr
import Data.SBV
import Data.SBV.TP

-- Positive: nested pattern; use matched fields including nested ones
t :: TP (Proof (Forall "e" Expr -> SBool))
t = calc "t" (\(Forall @"e" (e :: SExpr)) -> e .== e) $ \e -> []
    |- [pCase| e of
         Zero            -> e .== e =: qed
         Num k           -> sNum k .== sNum k =: e .== e =: qed
         Var s           -> sVar s .== sVar s =: e .== e =: qed
         Add (Num i) _   -> sNum i .== sNum i =: e .== e =: qed
         Add a       b   -> sAdd a b .== sAdd a b =: e .== e =: qed
         Let nm a b      -> sLet nm a b .== sLet nm a b =: e .== e =: qed
       |]