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-(* *********************************************************************)
-(* *)
-(* The Compcert verified compiler *)
-(* *)
-(* Jacques-Henri Jourdan, INRIA Paris-Rocquencourt *)
-(* *)
-(* Copyright Institut National de Recherche en Informatique et en *)
-(* Automatique. All rights reserved. This file is distributed *)
-(* under the terms of the GNU General Public License as published by *)
-(* the Free Software Foundation, either version 2 of the License, or *)
-(* (at your option) any later version. This file is also distributed *)
-(* under the terms of the INRIA Non-Commercial License Agreement. *)
-(* *)
-(* *********************************************************************)
-
-Require Import List.
-Require Import Syntax.
-Require Import Alphabet.
-Require Import Orders.
-Require Tuples.
-
-(** The terminal non-terminal alphabets of the grammar. **)
-Module Type Alphs.
- Parameters terminal nonterminal : Type.
- Declare Instance TerminalAlph: Alphabet terminal.
- Declare Instance NonTerminalAlph: Alphabet nonterminal.
-End Alphs.
-
-(** Definition of the alphabet of symbols, given the alphabet of terminals
- and the alphabet of non terminals **)
-Module Symbol(Import A:Alphs).
-
- Inductive symbol :=
- | T: terminal -> symbol
- | NT: nonterminal -> symbol.
-
- Program Instance SymbolAlph : Alphabet symbol :=
- { AlphabetComparable := {| compare := fun x y =>
- match x, y return comparison with
- | T _, NT _ => Gt
- | NT _, T _ => Lt
- | T x, T y => compare x y
- | NT x, NT y => compare x y
- end |};
- AlphabetFinite := {| all_list :=
- map T all_list++map NT all_list |} }.
- Next Obligation.
- destruct x; destruct y; intuition; apply compare_antisym.
- Qed.
- Next Obligation.
- destruct x; destruct y; destruct z; intuition; try discriminate.
- apply (compare_trans _ t0); intuition.
- apply (compare_trans _ n0); intuition.
- Qed.
- Next Obligation.
- intros x y.
- destruct x; destruct y; try discriminate; intros.
- rewrite (compare_eq t t0); intuition.
- rewrite (compare_eq n n0); intuition.
- Qed.
- Next Obligation.
- rewrite in_app_iff.
- destruct x; [left | right]; apply in_map; apply all_list_forall.
- Qed.
-
-End Symbol.
-
-Module Type T.
- Export Tuples.
-
- Include Alphs <+ Symbol.
-
- (** [symbol_semantic_type] maps a symbols to the type of its semantic
- values. **)
- Parameter symbol_semantic_type: symbol -> Type.
-
- (** The type of productions identifiers **)
- Parameter production : Type.
- Declare Instance ProductionAlph : Alphabet production.
-
- (** Accessors for productions: left hand side, right hand side,
- and semantic action. The semantic actions are given in the form
- of curryfied functions, that take arguments in the reverse order. **)
- Parameter prod_lhs: production -> nonterminal.
- Parameter prod_rhs_rev: production -> list symbol.
- Parameter prod_action:
- forall p:production,
- arrows_left
- (map symbol_semantic_type (rev (prod_rhs_rev p)))
- (symbol_semantic_type (NT (prod_lhs p))).
-
-End T.
-
-Module Defs(Import G:T).
-
- (** A token is a terminal and a semantic value for this terminal. **)
- Definition token := {t:terminal & symbol_semantic_type (T t)}.
-
- (** A grammar creates a relation between word of tokens and semantic values.
- This relation is parametrized by the head symbol. It defines the
- "semantics" of the grammar. This relation is defined by a notion of
- parse tree. **)
- Inductive parse_tree:
- forall (head_symbol:symbol) (word:list token)
- (semantic_value:symbol_semantic_type head_symbol), Type :=
-
- (** A single token has its semantic value as semantic value, for the
- corresponding terminal as head symbol. **)
- | Terminal_pt:
- forall (t:terminal) (sem:symbol_semantic_type (T t)),
- parse_tree (T t)
- [existT (fun t => symbol_semantic_type (T t)) t sem] sem
-
- (** Given a production, if a word has a list of semantic values for the
- right hand side as head symbols, then this word has the semantic value
- given by the semantic action of the production for the left hand side
- as head symbol.**)
- | Non_terminal_pt:
- forall {p:production} {word:list token}
- {semantic_values:tuple (map symbol_semantic_type (rev (prod_rhs_rev p)))},
- parse_tree_list (rev (prod_rhs_rev p)) word semantic_values ->
- parse_tree (NT (prod_lhs p)) word (uncurry (prod_action p) semantic_values)
-
- (** Basically the same relation as before, but for list of head symbols (ie.
- We are building a forest of syntax trees. It is mutually recursive with the
- previous relation **)
- with parse_tree_list:
- forall (head_symbols:list symbol) (word:list token)
- (semantic_values:tuple (map symbol_semantic_type head_symbols)),
- Type :=
-
- (** The empty word has [()] as semantic for [[]] as head symbols list **)
- | Nil_ptl: parse_tree_list [] [] ()
-
- (** The cons of the semantic value for one head symbol and for a list of head
- symbols **)
- | Cons_ptl:
- (** The semantic for the head **)
- forall {head_symbolt:symbol} {wordt:list token}
- {semantic_valuet:symbol_semantic_type head_symbolt},
- parse_tree head_symbolt wordt semantic_valuet ->
-
- (** and the semantic for the tail **)
- forall {head_symbolsq:list symbol} {wordq:list token}
- {semantic_valuesq:tuple (map symbol_semantic_type head_symbolsq)},
- parse_tree_list head_symbolsq wordq semantic_valuesq ->
-
- (** give the semantic of the cons **)
- parse_tree_list
- (head_symbolt::head_symbolsq)
- (wordt++wordq)
- (semantic_valuet, semantic_valuesq).
-
-
- Fixpoint pt_size {head_symbol word sem} (tree:parse_tree head_symbol word sem) :=
- match tree with
- | Terminal_pt _ _ => 1
- | Non_terminal_pt l => S (ptl_size l)
- end
- with ptl_size {head_symbols word sems} (tree:parse_tree_list head_symbols word sems) :=
- match tree with
- | Nil_ptl => 0
- | Cons_ptl t q =>
- pt_size t + ptl_size q
- end.
-End Defs.