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coq-switch

coq-switch plugin for Coq

Introduction

Sometimes you need to dispatch on several constant values that have a decidable type. Unfortunately, Coq does not have a switch statement, so a common approach is to map these constants to an inductive type on which a match can be performed later. This leads to code like this (taken from real-life projects):

Definition BER_bits2radix (b : Z) : radix :=
  if (b =? 0)%Z
  then radix2
  else if (b =? 1)%Z
       then radix4
       else if (b =? 2)%Z
            then radix8
            else if (b =? 4)%Z
                 then radix16
                 else radix2.

or like this:

Definition parse_SHCOL_Op_Name (s:string): SHCOL_Op_Names :=
  if string_dec s "eUnion" then n_eUnion
  else if string_dec s "eT" then n_eT
    else if string_dec s "SHPointwise" then n_SHPointwise
       else if string_dec s "SHBinOp" then n_SHBinOp
          else if string_dec s "SHInductor" then n_SHInductor
            else if string_dec s "IUnion" then n_IUnion
              else if string_dec s "ISumUnion" then n_ISumUnion
                else if string_dec s "IReduction" then n_IReduction
                  else if string_dec s "SHCompose" then n_SHCompose
                    else if string_dec s "SafeCast" then n_SafeCast
                      else if string_dec s "UnSafeCast" then n_UnSafeCast
                        else if string_dec s "HTSUMUnion" then n_HTSUMUnion
                          else n_Unsupported s.

Writing manually such a biolerplate code is tiresome and error-prone. This plugin allows to automate such tasks.

Installation

The easiest way to install is via OPAM:

opam repo add coq-released https://coq.inria.fr/opam/released
opam install coq-switch

If you want to compile it from source, you need to install the following dependencies:

Usage

This plugin is written using TemplateCoq. After importing, you run the template program mkSwitch providing the following parameters:

  • a type (A)
  • a boolean equality predicate on this type (A -> A -> bool)
  • a list of choices ((A * string)) where each element is a tuple consisting of a constant of type A and the name of a constructor (as a string)
  • the name of the new inductive type
  • the name of the selection function

For example, running the following template program in Coq:

 MetaCoq Run
     (mkSwitch nat
               beq_nat
               [(0,"Love") ; (10,"Ten") ; (20, "twenty")]
               "Ex1_Choices" "ex1_select"
     ).

Will define a new type and a function:

Print Ex1_Choices.

  Inductive Ex1_Choices : Set :=
    | Love   : Ex1_Choices 
    | Ten    : Ex1_Choices 
    | twenty : Ex1_Choices

Print ex1_select.

  ex1_select = 
  fun x : nat =>
  if Nat.eqb x (fst (0, "Love"))
  then Some Love
  else
   if Nat.eqb x (fst (10, "Ten"))
   then Some Ten
    else if Nat.eqb x (fst (20, "twenty")) then Some twenty else None
      : nat -> option Ex1_Choices

Now, the generated definitions could be used for easy matching:

Definition Ex1 (n:nat) : T :=
  match ex1_select n with
  | Some Love => ...
  | Some Ten => ...
  | Some Twenty => ...
  | None => ...
  end.

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