Dklib

This is a small human-written Dedukti library. It contains some definitions of simple datatypes and logical constructs.

Dependencies

GNU Make
Dedukti: versions 2.4 and 2.5 have been tested, for version 2.3.1 use the v2.3.1 branch
(Optional) CSI^HO higher-order confluence checker: version 0.1.1 has been tested

Usage

To compile all the files, invoke make.

Installation

Dedukti has no default load path so it is not very useful to install the compiled .dko files system wide. To copy the compiled file to some place <dir>, invoke

cp -t <DIR> *.dko

Confluence Checking

To check for confluence, invoke

make CSIHO_PATH=<path> all

where <path> is the path to the csiho.sh script.

Please note that the experimental files dk_monads.dk and dk_monads_coc.dk are purposely not confluent

Content

The library contains the following files:

File	Description	Operations
`cc`	Encoding of polymorphism	Polymorphic product and arrow types
`dk_type`	Basic type constructions	Cartesian product, Sigma-types, Sum-types
`dk_bool`	Booleans	dependent pattern-matching, alternative, logical connectives
`dk_list`	Polymorphic lists	dependent pattern-matching, concatenation, map
`dk_nat`	Peano (unary) natural numbers	ordering, equality, addition, multiplication, min, max, division, exponentiation, conversion from lists of digits
`dk_int`	Unary integers from smart constructor	abs, ordering, equality, addition, multiplication, opposite, subtraction, min, max, division
`dk_machine_int`	N-bits machine integers	same as dk_int + signed and unsigned orderings, conversion from unary
`dk_binary_nat`	Same but not dependent	same as dk_int + conversion to machine_int
`dk_char`	Chars are 7-bits integers	equality, representations for digits and letters
`dk_string`	Strings are lists of chars
`dk_opt`	Polymorphic option type
`dk_fail`		`dk_fail.fail : A : cc.uT -> cc.eT A`
`dk_logic`	Impredicative Prop : type	intuitionistic logical connectives, reasoning on booleans and equality

Obsolete

File	Description
`dk_tuple`	Use dk_type instead
`dk_builtins`	Basic types for the translation of FoCaLiZe standard library into Dedukti

Experimental

File	Description
`slist`	Lists of natural numbers sorted by construction
`dk_monads`	Monadic laws enforced by rewriting (non-linear)
`dk_monads_coc`	Going further by not encoding polymorphism (non-linear and requires -coc)

rafoo / dklib