PCase42.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: Num split across two arms — guarded first, unguarded fallback later
-- (same constructor appearing in two separate groups is fine in pCase)
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 a b        -> sAdd a b .== sAdd a b =: e .== e =: qed
         Num i          -> sNum i .== sNum i =: e .== e =: qed
         Let nm a b     -> sLet nm a b .== sLet nm a b =: e .== e =: qed
       |]