The Coq Proof Assistant

# Library Ltac2.Pattern

Require Import Ltac2.Init.
Require Ltac2.Control.
Ltac2 Type t := pattern.
Ltac2 Type context.
Ltac2 Type match_kind := [
| MatchPattern
| MatchContext
].
Ltac2 @ external empty_context : unit -> context :=
"ltac2" "pattern_empty_context".
A trivial context only made of the hole.
Ltac2 @ external matches : t -> constr -> (ident * constr) list :=
"ltac2" "pattern_matches".
If the term matches the pattern, returns the bound variables. If it doesn't, fail with Match_failure. Panics if not focused.
Ltac2 @ external matches_subterm : t -> constr -> context * ((ident * constr) list) :=
"ltac2" "pattern_matches_subterm".
Returns a stream of results corresponding to all of the subterms of the term that matches the pattern as in matches. The stream is encoded as a backtracking value whose last exception is Match_failure. The additional value compared to matches is the context of the match, to be filled with the instantiate function.
Ltac2 @ external matches_vect : t -> constr -> constr array :=
"ltac2" "pattern_matches_vect".
Internal version of matches that does not return the identifiers.
Ltac2 @ external matches_subterm_vect : t -> constr -> context * constr array :=
"ltac2" "pattern_matches_subterm_vect".
Internal version of matches_subterms that does not return the identifiers.
Ltac2 @ external matches_goal : bool -> (match_kind * t) list -> (match_kind * t) ->
ident array * context array * constr array * context :=
"ltac2" "pattern_matches_goal".
Given a list of patterns hpats for hypotheses and one pattern cpat for the conclusion, matches_goal rev hpats cpat produces (a stream of) tuples of:

- An array of idents, whose size is the length of hpats, corresponding to the name of matched hypotheses.
- An array of contexts, whose size is the length of hpats, corresponding to the contexts matched for every hypothesis pattern. In case the match kind of a hypothesis was MatchPattern, the corresponding context is ensured to be empty.
- An array of terms, whose size is the total number of pattern variables without duplicates. Terms are ordered by identifier order, e.g. ?a comes before ?b.
- A context corresponding to the conclusion, which is ensured to be empty if the kind of cpat was MatchPattern.

This produces a backtracking stream of results containing all the possible result combinations. The order of considered hypotheses is reversed if rev is true.
Ltac2 @ external instantiate : context -> constr -> constr :=
"ltac2" "pattern_instantiate".
Fill the hole of a context with the given term.
Implementation of Ltac matching over terms and goals
Ltac2 lazy_match0 t pats :=
let rec interp m := match m with
| [] => Control.zero Match_failure
| p :: m =>
let next _ := interp m in
let (knd, pat, f) := p in
let p := match knd with
| MatchPattern =>
(fun _ =>
let context := empty_context () in
let bind := matches_vect pat t in
fun _ => f context bind)
| MatchContext =>
(fun _ =>
let (context, bind) := matches_subterm_vect pat t in
fun _ => f context bind)
end in
Control.plus p next
end in
Control.once (fun () => interp pats) ().
Ltac2 multi_match0 t pats :=
let rec interp m := match m with
| [] => Control.zero Match_failure
| p :: m =>
let next _ := interp m in
let (knd, pat, f) := p in
let p := match knd with
| MatchPattern =>
(fun _ =>
let context := empty_context () in
let bind := matches_vect pat t in
f context bind)
| MatchContext =>
(fun _ =>
let (context, bind) := matches_subterm_vect pat t in
f context bind)
end in
Control.plus p next
end in
interp pats.
Ltac2 one_match0 t m := Control.once (fun _ => multi_match0 t m).
Ltac2 lazy_goal_match0 rev pats :=
let rec interp m := match m with
| [] => Control.zero Match_failure
| p :: m =>
let next _ := interp m in
let (pat, f) := p in
let (phyps, pconcl) := pat in
let cur _ :=
let (hids, hctx, subst, cctx) := matches_goal rev phyps pconcl in
fun _ => f hids hctx subst cctx
in
Control.plus cur next
end in
Control.once (fun () => interp pats) ().
Ltac2 multi_goal_match0 rev pats :=
let rec interp m := match m with
| [] => Control.zero Match_failure
| p :: m =>
let next _ := interp m in
let (pat, f) := p in
let (phyps, pconcl) := pat in
let cur _ :=
let (hids, hctx, subst, cctx) := matches_goal rev phyps pconcl in
f hids hctx subst cctx
in
Control.plus cur next
end in
interp pats.
Ltac2 one_goal_match0 rev pats := Control.once (fun _ => multi_goal_match0 rev pats).