-- needs ghc -fglasgow-exts -fallow-overlapping-instances -package data

{- HetCATS/Logic.hs

$Id$

Till Mossakowski, Christian Maeder

Provides data structures for logics (with symbols). Logics are

a type class with an "identitiy" type (usually interpreted

by a singleton set) which serves to treat logics as

data. All the functions in the type class take the

identity as first argument in order to determine the logic.

For logic representations see LogicRepr.hs

References:

J. A. Goguen and R. M. Burstall

Institutions: Abstract Model Theory for Specification and

Programming

JACM 39, p. 95--146, 1992

(general notion of logic - model theory only)

J. Meseguer

General Logics

Logic Colloquium 87, p. 275--329, North Holland, 1989

(general notion of logic - also proof theory;

notion of logic representation, called map there)

T. Mossakowski:

Specification in an arbitrary institution with symbols

14th WADT 1999, LNCS 1827, p. 252--270

(treatment of symbols and raw symbols, see also CASL semantics)

T. Mossakowski, B. Klin:

Institution Independent Static Analysis for CASL

15h WADT 2001, LNCS 2267, p. 221-237, 2002.

(what is needed for static anaylsis)

S. Autexier and T. Mossakowski

Integrating HOLCASL into the Development Graph Manager MAYA

FroCoS 2002, to appear

(interface to provers)

Todo:

ATerm, XML

Weak amalgamability

Metavars

-}

module Logic where

import Id

import GlobalAnnotations

import Set

import FiniteMap

import Graph

import Result

import Parsec

import Prover -- for one half of class Sentences

import PrettyPrint

-- for coercion used in LogicGraph.hs and Grothendieck.hs

import GlaExts(unsafeCoerce#)

-- maps

type EndoMap a = FiniteMap a a

-- diagrams are just graphs

data Diagram object morphism = Graph object morphism

-- languages, define like "data CASL = CASL deriving Show"

class Show id => Language id where

language_name :: id -> String

language_name i = show i

-- (a bit unsafe) coercion using the language name

coerce :: (Language id1, Language id2) => id1 -> id2 -> a -> Maybe b

coerce i1 i2 a = if language_name i1 == language_name i2 then

(Just $ unsafeCoerce# a) else Nothing

-- Categories are given by a quotient,

-- i.e. we need equality

-- Should we allow arbitrary composition graphs and build paths?

class (Language id, Eq sign, Show sign, Eq morphism) =>

Category id sign morphism | id -> sign, id -> morphism where

ide :: id -> sign -> morphism

o :: id -> morphism -> morphism -> Maybe morphism

dom, cod :: id -> morphism -> sign

legal_obj :: id -> sign -> Bool

legal_mor :: id -> morphism -> Bool

-- abstract syntax, parsing and printing

class (Language id, PrettyPrint basic_spec, Eq basic_spec,

PrettyPrint symb_items, Eq symb_items,

PrettyPrint symb_map_items, Eq symb_map_items) =>

Syntax id basic_spec symb_items symb_map_items

| id -> basic_spec, id -> symb_items,

id -> symb_map_items

where

-- parsing

parse_basic_spec :: id -> Maybe(GenParser Char st basic_spec)

parse_symb_items :: id -> GenParser Char st symb_items

parse_symb_map_items :: id -> GenParser Char st symb_map_items

-- sentences (plus prover stuff and "symbol" with "Ord" for efficient lookup)

class (Category id sign morphism, Show sentence,

Ord symbol, Show symbol)

=> Sentences id sentence sign morphism symbol

| id -> sentence, id -> sign, id -> morphism,

id -> symbol

where

-- sentence translation

map_sen :: id -> morphism -> sentence -> Result sentence

-- parsing of sentences

parse_sentence :: id -> sign -> String -> Result sentence

-- is a term parser needed as well?

provers :: id -> [Prover sentence symbol]

cons_checkers :: id -> [Cons_checker

(TheoryMorphism sign sentence morphism)]

-- static analysis

class ( Syntax id basic_spec symb_items symb_map_items

, Sentences id sentence sign morphism symbol

, Show raw_symbol, Eq raw_symbol)

=> StaticAnalysis id

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol

| id -> basic_spec, id -> sentence, id -> symb_items,

id -> symb_map_items,

id -> sign, id -> morphism, id -> symbol, id -> raw_symbol

where

-- static analysis of basic specifications and symbol maps

basic_analysis :: id ->

Maybe((basic_spec, -- abstract syntax tree

sign, -- efficient table for env signature

GlobalAnnos) -> -- global annotations

Result (sign,sign,[(String,sentence)]))

-- the first output sign is the accumulated sign

-- the second output sign united with the input sing

-- should yield the first output sign

stat_symb_map_items ::

id -> symb_map_items -> Result (EndoMap raw_symbol)

stat_symb_items :: id -> symb_items -> Result [raw_symbol]

-- architectural sharing analysis for one morphism

ensures_amalgamability :: id ->

(Diagram sign morphism, Node, sign, LEdge morphism, morphism) ->

Result (Diagram sign morphism)

-- do we need it also for sinks consisting of two morphisms?

-- symbols and symbol maps

symbol_to_raw :: id -> symbol -> raw_symbol

id_to_raw :: id -> Id -> raw_symbol

sym_of :: id -> sign -> Set symbol

symmap_of :: id -> morphism -> EndoMap symbol

matches :: id -> symbol -> raw_symbol -> Bool

sym_name :: id -> symbol -> Id

-- operations on signatures and morphisms

add_sign :: id -> sign -> sign -> sign

empty_signature :: id -> sign

signature_union :: id -> sign -> sign -> Result sign

final_union :: id -> sign -> sign -> Result sign

is_subsig :: id -> sign -> sign -> Bool

generated_sign, cogenerated_sign ::

id -> [raw_symbol] -> sign -> Result morphism

induced_from_morphism ::

id -> EndoMap raw_symbol -> sign -> Result morphism

induced_from_to_morphism ::

id -> EndoMap raw_symbol -> sign -> sign -> Result morphism

extend_morphism ::

id -> sign -> morphism -> sign -> sign -> Result morphism

-- sublogics

class Ord l => LatticeWithTop l where

meet, join :: l -> l -> l

top :: l

-- logics

class (StaticAnalysis id

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol,

LatticeWithTop sublogics) =>

Logic id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol

| id -> sublogics, id -> basic_spec, id -> sentence, id -> symb_items,

id -> symb_map_items,

id -> sign, id -> morphism, id ->symbol, id -> raw_symbol

where

sublogic_names :: id -> sublogics -> [String]

-- the first name is the principal name

all_sublogics :: id -> [sublogics]

is_in_basic_spec :: id -> sublogics -> basic_spec -> Bool

is_in_sentence :: id -> sublogics -> sentence -> Bool

is_in_symb_items :: id -> sublogics -> symb_items -> Bool

is_in_symb_map_items :: id -> sublogics -> symb_map_items -> Bool

is_in_sign :: id -> sublogics -> sign -> Bool

is_in_morphism :: id -> sublogics -> morphism -> Bool

is_in_symbol :: id -> sublogics -> symbol -> Bool

min_sublogic_basic_spec :: id -> basic_spec -> sublogics

min_sublogic_sentence :: id -> sentence -> sublogics

min_sublogic_symb_items :: id -> symb_items -> sublogics

min_sublogic_symb_map_items :: id -> symb_map_items -> sublogics

min_sublogic_sign :: id -> sign -> sublogics

min_sublogic_morphism :: id -> morphism -> sublogics

min_sublogic_symbol :: id -> symbol -> sublogics

proj_sublogic_basic_spec :: id -> sublogics -> basic_spec -> basic_spec

proj_sublogic_symb_items :: id -> sublogics -> symb_items -> Maybe symb_items

proj_sublogic_symb_map_items :: id -> sublogics -> symb_map_items -> Maybe symb_map_items

proj_sublogic_sign :: id -> sublogics -> sign -> sign

proj_sublogic_morphism :: id -> sublogics -> morphism -> morphism

proj_sublogic_epsilon :: id -> sublogics -> sign -> morphism

proj_sublogic_symbol :: id -> sublogics -> symbol -> Maybe symbol

{- class hierarchy:

Language

__________/

Category

| /

Sentences Syntax

\ /

StaticAnalysis (no sublogics)

\

\

Logic

-}