PCase35.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: single guarded arm with no fallback for that constructor
-- (sCase rejects this as "guarded match might fail"; pCase is fine)
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 i | i .< 3 -> sNum i .== sNum i =: e .== e =: qed
         Var s          -> sVar s .== sVar s =: e .== e =: qed
         Add _ _        -> e .== e =: qed
         Let _ _ _      -> e .== e =: qed
       |]