package lambdapi

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package lambdapi

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This module provides a function to translate a signature to the HRS format used in the confluence competition.

see http://project-coco.uibk.ac.at/problems/hrs.php
.
- Lambdapi terms are translated to the following HRS term algebra with a unique type t:
A : t -> t -> t // for application
L : t -> (t -> t) -> t // for λ
B : t -> t -> (t -> t) -> t // for let
P : t -> (t -> t) -> t // for Π
Function symbols and variables are translated as symbols of type t.
Pattern variables of arity n are translated as variables of type t -> ... -> t with n times ->.
- In the hrs format, variable names must be distinct from function symbol names. So bound variables are translated into positive integers and pattern variables are prefixed by "$".
- There is no clash between function symbol names and A, B, L, P because function symbol names are fully qualified.
- Function symbol names are fully qualified but "." is replaced by "_" because "." cannot be used in identifiers ("." is used in lambda abstractions).
- Two occurrences of the same pattern variable name may have two different arities (in two different rules). So pattern variable names are prefixed by the rule number.
TO DO:
- HRS does not accept unicode characters.
- Optim: output only the symbols used in the rules.

val syms : string Core.Term.SymMap.t ref

syms maps every symbol to a name.

val bvars : Lplib.Extra.IntSet.t ref

bvars is the set of abstracted variables.

val nb_rules : int ref

nb_rules is the number of rewrite rules.

module V : sig ... end

pvars map every pattern variable name to its arity.

module VMap : sig ... end

val pvars : int VMap.t ref

val sym_name : Core.Term.sym Lplib.Base.pp

sym_name s translates the symbol name of s.

val add_sym : Core.Term.sym -> unit

add_sym declares a Lambdapi symbol.

val sym : Core.Term.sym Lplib.Base.pp

sym ppf s translates the Lambdapi symbol s.

val add_bvar : Core.Term.tvar -> unit

add_bvar v declares an abstracted Lambdapi variable.

val bvar : Core.Term.tvar Lplib.Base.pp

bvar v translates the Lambdapi variable v.

val pvar : int Lplib.Base.pp

pvar i translates the pattern variable index i.

val add_pvar : int -> int -> unit

add_pvar i k declares a pvar of index i and arity k.

val term : Core.Term.term Lplib.Base.pp

term ppf t translates the term t.

val rule : (Core.Term.term * Core.Term.term) Lplib.Base.pp

rule ppf r translates the pair of terms r as a rule.

val sym_rule : Core.Term.sym -> Core.Term.rule Lplib.Base.pp

sym_rule ppf s r increases the number of rules and translates the sym_rule r.

val rules_of_sym : Core.Term.sym Lplib.Base.pp

Translate the rules of symbol s.

val rules_of_sign : Core.Sign.t Lplib.Base.pp

Translate the rules of a dependency except if it is a ghost signature.

val sign : Core.Sign.t Lplib.Base.pp

sign ppf s translates the Lambdapi signature s.