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Breakdown proof reconstruction file. (#81)
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,140 @@ | ||
| /- | ||
| Copyright (c) 2021-2023 by the authors listed in the file AUTHORS and their | ||
| institutional affiliations. All rights reserved. | ||
| Released under Apache 2.0 license as described in the file LICENSE. | ||
| Authors: Abdalrhman Mohamed | ||
| -/ | ||
|
|
||
| import Smt.Reconstruct.Arith.ArithMulSign | ||
| import Smt.Reconstruct.Arith.MulPosNeg | ||
| import Smt.Reconstruct.Arith.Rewrites | ||
| import Smt.Reconstruct.Arith.SumBounds | ||
| import Smt.Reconstruct.Arith.Rewrites | ||
| import Smt.Reconstruct.Arith.TangentPlane | ||
| import Smt.Reconstruct.Arith.TightBounds | ||
| import Smt.Reconstruct.Arith.Trichotomy | ||
| import Smt.Reconstruct.Reconstruct | ||
|
|
||
| namespace Smt.Reconstruct.Arith | ||
|
|
||
| open Lean hiding Rat | ||
| open Qq | ||
|
|
||
| @[smt_sort_reconstruct] def reconstructArithSort : SortReconstructor := fun s => do match s.getKind with | ||
| | .INTEGER_SORT => return q(Int) | ||
| | .REAL_SORT => return q(Real) | ||
| | _ => return none | ||
|
|
||
| def getTypeAndInst (s : cvc5.Sort) : Σ α : Q(Type), Q(LinearOrderedRing $α) := match s.isInteger with | ||
| | false => ⟨q(Real), q(Real.instLinearOrderedRingReal)⟩ | ||
| | true => ⟨q(Int), q(Int.linearOrderedCommRing.toLinearOrderedRing)⟩ | ||
|
|
||
| @[smt_term_reconstruct] def reconstructUF : TermReconstructor := fun t => do match t.getKind with | ||
| | .SKOLEM_FUN => match t.getSkolemId with | ||
| | .DIV_BY_ZERO => return q(fun (x : Real) => x / 0) | ||
| | .INT_DIV_BY_ZERO => return q(fun (x : Int) => x / 0) | ||
| | .MOD_BY_ZERO => return q(fun (x : Int) => x % 0) | ||
| | _ => return none | ||
| | .CONST_INTEGER => | ||
| let x : Int := t.getIntegerValue | ||
| let x' : Q(Nat) := mkRawNatLit x.natAbs | ||
| if x ≥ 0 then | ||
| return q(OfNat.ofNat $x' : Int) | ||
| else | ||
| return q(-(OfNat.ofNat $x' : Int)) | ||
| | .CONST_RATIONAL => | ||
| let x : Rat := t.getRationalValue | ||
| let num : Q(Real) := mkRealLit x.num.natAbs | ||
| if x.den == 1 then | ||
| if x.num ≥ 0 then | ||
| return q($num) | ||
| else | ||
| return q(-$num) | ||
| else | ||
| let den : Q(Real) := mkRealLit x.den | ||
| if x.num ≥ 0 then | ||
| return q($num / $den) | ||
| else | ||
| return q(-$num / $den) | ||
| | .NEG => | ||
| let ⟨α, _⟩ := getTypeAndInst t.getSort | ||
| let x : Q($α) ← reconstructTerm t[0]! | ||
| return q(-$x) | ||
| | .SUB => | ||
| let ⟨α, _⟩ := getTypeAndInst t.getSort | ||
| let x : Q($α) ← reconstructTerm t[0]! | ||
| let y : Q($α) ← reconstructTerm t[1]! | ||
| return q($x - $y) | ||
| | .ADD => | ||
| let ⟨α, _⟩ := getTypeAndInst t.getSort | ||
| let x : Q($α) ← reconstructTerm t[0]! | ||
| let y : Q($α) ← reconstructTerm t[1]! | ||
| return q($x + $y) | ||
| | .MULT => | ||
| let ⟨α, _⟩ := getTypeAndInst t.getSort | ||
| let x : Q($α) ← reconstructTerm t[0]! | ||
| let y : Q($α) ← reconstructTerm t[1]! | ||
| return q($x * $y) | ||
| | .INTS_DIVISION => | ||
| let x : Q(Int) ← reconstructTerm t[0]! | ||
| let y : Q(Int) ← reconstructTerm t[1]! | ||
| return q($x / $y) | ||
| | .INTS_MODULUS => | ||
| let x : Q(Int) ← reconstructTerm t[0]! | ||
| let y : Q(Int) ← reconstructTerm t[1]! | ||
| return q($x % $y) | ||
| | .DIVISION => | ||
| let x : Q(Real) ← reconstructTerm t[0]! | ||
| let y : Q(Real) ← reconstructTerm t[1]! | ||
| return q($x / $y) | ||
| | .ABS => | ||
| let x : Q(Int) ← reconstructTerm t[0]! | ||
| return q(Int.natAbs $x : Int) | ||
| | .LEQ => | ||
| let ⟨α, _⟩ := getTypeAndInst t[0]!.getSort | ||
| let x : Q($α) ← reconstructTerm t[0]! | ||
| let y : Q($α) ← reconstructTerm t[1]! | ||
| return q($x ≤ $y) | ||
| | .LT => | ||
| let ⟨α, _⟩ := getTypeAndInst t[0]!.getSort | ||
| let x : Q($α) ← reconstructTerm t[0]! | ||
| let y : Q($α) ← reconstructTerm t[1]! | ||
| return q($x < $y) | ||
| | .GEQ => | ||
| let ⟨α, _⟩ := getTypeAndInst t[0]!.getSort | ||
| let x : Q($α) ← reconstructTerm t[0]! | ||
| let y : Q($α) ← reconstructTerm t[1]! | ||
| return q($x ≥ $y) | ||
| | .GT => | ||
| let ⟨α, _⟩ := getTypeAndInst t[0]!.getSort | ||
| let x : Q($α) ← reconstructTerm t[0]! | ||
| let y : Q($α) ← reconstructTerm t[1]! | ||
| return q($x > $y) | ||
| | .TO_REAL => | ||
| let x : Q(Int) ← reconstructTerm t[0]! | ||
| return q($x : Real) | ||
| | .TO_INTEGER => | ||
| let x : Q(Real) ← reconstructTerm t[0]! | ||
| return q(⌊$x⌋) | ||
| | .IS_INTEGER => | ||
| let x : Q(Real) ← reconstructTerm t[0]! | ||
| return q($x = ⌊$x⌋) | ||
| | _ => return none | ||
| where | ||
| mkRealLit (n : Nat) : Q(Real) := match h : n with | ||
| | 0 => q(0 : Real) | ||
| | 1 => q(1 : Real) | ||
| | _ + 2 => | ||
| let h : Q(Nat.AtLeastTwo $n) := h ▸ q(instNatAtLeastTwo) | ||
| let h := mkApp3 q(@instOfNat Real) (mkRawNatLit n) q(Real.natCast) h | ||
| mkApp2 q(@OfNat.ofNat Real) (mkRawNatLit n) h | ||
|
|
||
| def reconstructRewrite (pf : cvc5.Proof) : ReconstructM (Option Expr) := do | ||
| match cvc5.RewriteRule.fromNat! pf.getArguments[0]!.getIntegerValue.toNat with | ||
| | _ => return none | ||
|
|
||
| @[smt_proof_reconstruct] def reconstructArithProof : ProofReconstructor := fun pf => do match pf.getRule with | ||
| | .DSL_REWRITE => reconstructRewrite pf | ||
| | _ => return none | ||
|
|
||
| end Smt.Reconstruct.Arith |
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